POLE, Nelson, 1941- THE MEANING OF TERMS EMPLOYED IN SCIENTIFIC LANGUAGES AND THE PROBLEM OF INDUCTION.

The Ohio State University, Ph.D., 1971 Philosophy

University Microfilms. A XEROX Company, Ann Arbor, Michigan

THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED THE MEANING OF TERMS EMPLOYED IN SCIENTIFIC LANGUAGES

AND THE PROBLEM OF INDUCTION

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

By

Nelson Pole, B. Phil.

*****

The Ohio State University 1971

Approved by

Adviser Department of Philosophy PLEASE NOTE:

Some pages have light and indistinct print. Film as received.

UNIVERSITY MICROFILMS. ACKNOWLEDGMENTS

A great debt is owed to my Professors at The Ohio State

University but especially to my adviser Professor Charles F.

Kielkopf. Their constant encouragement and good advice made my days as a graduate student both enjoyable and profitable.

My gratitude is also owed to my colleagues in the

Department of Philosophy at The Cleveland State University for reading parts of this work and especially for giving me the free time to complete it.

Many thanks are due to the capable young ladies who typed the manuscript, Miss Linda Taus, Miss Cathy Stanley and

Miss Naomi Cope.

Finally, X can never fully express all that I owe to my wife for more things than I am able to mention here.

Nelson Pole Cleveland, Ohio

ii VITA

October 13, 1941. Born— Detroit, Michigan

1963 B. Phil, Monteith College, Wayne State University, Detroit, Michigan

1964-1968 Teaching Assistant, Department of Philosophy, The Ohio State University

1968-1971 Instructor, Department of Philosophy The Cleveland State University

PUBLICATIONS

"'Self-Supporting* Inductive Arguments," Boston Studies in The Philosophy of Science, Volume VIII, (Boston: Boston University, 1971).

FIELDS OF STUDY

Major Field: Philosophy

Studies in the History of Philosophy. Professors Marvin Fox and Robert Turnbull

Studies in Metaphysics, Epistemology and Philosophy of Science. Professors Alan Hausman and Virgil Hinshaw

Studies in Logic. Professors Charles Kielkopf and John Steltzer

ill TABLE OF CONTENTS

Page ACKNOWLEDGMENTS...... ii

VITA ...... iii

LIST OF TABLES ...... vi

INTRODUCTION ...... 1

Chapter

I. SCIENTIFIC LAWS AND M O D E L S ...... 8

1.1 Scientific Laws and T h e o r i e s ...... 9 1.2 Self-Evidence and Conventions ...... 15 1.3 Models and Theories ...... 21 1.4 The Extensions of the Terms of Scientific Discourse ...... 35 1.5 Ontological Status of M o d e l s ...... 39 1.6 Peter Achinstein's Theory ...... 46 1.7 Opera ti o n a l i s m ...... 55 1.8 Logical Positivism ...... 83 The Verifiability Criterion ...... 64 Reductionism ...... 65 Ultra Empiricism ...... 66 Fictionallsm ...... 67 1.9 Symbolic Language ...... 69 1.10 S u m m a r y ...... 72

II. COUNTERFACTUAL CONDITIONALS AND REFERENCE 74

2.1 The Problem of Counterfactuals .... 75 2.2 Truth Functionality ...... 78 2.3 Reference and Counterfactuals ...... 83 2.4 Nothing Wrong V i e w ...... 91 2.5 The Classical T h e o r y ...... 98 2.6 Extensional Logic ...... 104

III. THE PARADOX OF CONFIRMATION ...... 117

3.1 Paradox of Confirmation...... 117 3.2 The Paradox Dissolved ...... 121 3.3 Existential Import ...... 130 3.4 Other Approaches ...... 142 3.5 Choosing A Language...... 155

iv Chapter Page

IV. THE PROBLEM OF INDUCTION AND ITS SOLUTION . 164

4.1 The Characterization of Induction . . . 165 4.2 Counter Examples to Induction .... 185 4.3 Inductive Support...... 202 4.4 Some Misconceptions Clarified.. 222

BIBLIOGRAPHY ...... 229

v LIST OF TABLES

Table

1. The Incompatibility T a b l e ...... Page 126

vi In Memorial

William Pole 1904-1970

vii INTRODUCTION

This is a work in the Philosophy of Science. It is about the central semantic problem in the Philosophy of Science:

What is the extension of the terms employed in scientific discourse? The answer to this question is used to solve other important problems in the Philosophy of Science. Ultimately, the answer is used to attack the problem of induction.

There are at least two main ways of doing the Philosophy of Science. The prescriptive approach to the subject matter lays out the ideal conditions under which science operates.

The historical workings of the sciences are of no particular import to such an approach. If the actual workings of scientists do not reflect the findings of such a study, then so much the worse for the science. If procedure X is required for true science and actual science lacks procedure X, then actual science is not true science. For example, if the verifiability criterion was intended as a means of exorcising metaphysical entities from scientific theories, then it was an attempt, on the part of philosophers, to tell scientists how to do science.^-

If actual science employed metaphysical entities and true science does not, then actual science is not true science. Prescriptive

^See A. J. Ayer, Language. Truth and Logic, 2nd ed., (New York: Dover, 1952), Introduction.

1 philosophy of science shall only be found in this work as the

butt of criticism. Descriptive philosophy of science is an

attempt to describe the actual working processes of the 2 scientist. Thomas Kuhn and others have pioneered this approach.

It is not important to accept the judgements of scientists

about what they are doing but it is important to refrain from

telling them what to do. Scientists may be in the dark as to

what they are doing; that is, they may make mistaken judgements

about the importance of their activities or the nature of their

activities. For example, in Chapter One some scientists will

appear who claim to observe atomic particles. Philosophy of

Science in the descriptive mode notes their claim but need

only account for their making such judgements not for those

judgements being true. The descriptivist may well disagree with

the scientists who claim to observe atomic particles for the

scientist in making such a judgement is being a philosopher of science. As a philosopher, the scientist has no special competency; his pronouncements are as challengeable as any other philosopher. The measure of descriptive philosophy of science is that the philosopher is always examining his findings to insure that the scientist can actually do science if the scientist follows the philosopher's findings. Since the only measure of what can be done is what is actually done, the

^See The Structure of Scientific Revelations.(Chicago: University of Chicago, 1962). 3

descriptivist always checks to see that his findings describe

actual practice in the sciences. For him there is no difference

between true science and actual science.

The flavor of this work is descriptive. It will be

an operating principle of analysis that any philosopher's view

which has the consequence that science as practiced should not

be done is to be rejected for that very reason. Further, any

. scientific activity which seems to be necessary for the

functioning of science shall be regarded with utmost seriousness

for that very reason. Activities which have been important in

science since the rise of contemporary science shall be considered

central to the scientific enterprise. Philosophies of Science

which discount historically important phenomena shall be

themselves discounted here.

For example, positivists, especially logical positivists,

have always depreciated the role of models in the sciences. For

them, the model is merely a heuristic device. But models have

played a central role in the development of science by providing

a stimulus to new research. Further, models seem to be needed

for explanation to occur. Whatever logical problems there may

be with models, they will have to be lived with since models have

been so important for science and scientists show no sign of

giving them up.

The focus on models is the central innovation of this

study. It is a study in what Kuhn has termed "normal" science, science during the period following a significant innovation,

science principally concerned with getting the details straight

after an intellectual revolution. Scientists attempt to

discover laws which relate some properties of a system to

other properties. In Newtonian Mechanics the properties related

are acceleration, mass, distance, and force. Laws ignore most

properties of the system. Hence there is a distinction, funda­

mental to science, between primary qualities and secondary

qualities, between qualities necessary for the statement of

laws and those which are analysed in terms of the properties

mentioned in the laws. A model is a depiction of the world

using only the primary qualities. Nevertheless, the model

is no more a depiction of the real world than the world as

phenomenally presented is real. Since the world can be under­

stood either through the model or through the phenomenal

presentation of it, either way of understanding it is as good

as the other. There is but one world, it may be described

either scientifically or phenomenally, but it is the same

world.

The difficulty with constructing either description of

the world is to establish truth conditions for the descriptions.

The difficulty is somewhat simplified here because the only

interest is with the scientific description of the world. The

first chapter centers on the thesis that twentieth century philosophy of science has had a major problem with the truth conditions for laws of science but has not realized it. The

development of a thoroughly well founded deductive logic is

one of the prime achievements of the twentieth century. But

the truth functional logic which was developed was a continuation

of the ideas of George Boole whose logic permitted a generalization

to be true just in case its subject had an empty extension. If

science uses such a logic, then there too generalizations should be true just in case their subjects have empty extensions, but no scientist would accept a generalization as true on these grounds alone. Indeed, science has progressed on many occasions because of the development of laws for ideal, nonactual, situations which no one expected to have ever occur. Boyle's

Law relating the temperature, pressure, and volume of an ideal gas can only have an empty extension for its terms since an ideal gas is only a mathematical approximation to a real, phenomenal gas. A problem about the truth conditions for generalizations like Boyle’s Law arises in the twentieth century for in the universally accepted logic of this century such generalizations are true simply because they are about nonreal entities; to prove them a scientist would merely have to point out that the laws are about ideal and hence nonreal gases, no further argumentation would be necessary. Since this cannot be done in actual scientific practice, there is a crisis about truth conditions and one which has largely gone unnoticed. The first

3 See B. Russell and A. N. Whitehead, Principia Mathematics, 2nd. ed., (Cambridge; Cambridge University, 1925-27). chapter of this essay deals with the problem of truth conditions.

There it is argued that scientific laws are about models and

the development of a logic adequate to the needs of science is attempted.

Chapter Two focuses on a related and well known difficulty.

Contrary to the fact conditionals are extremely important in science.

They state what would be the case if circumstances had arisen other than those which in fact arose. In the semantics of the usually employed twentieth century logic, all such conditionals are true since they have false antecedants. In this chapter

the same techniques which seem so useful for analysing laws which cannot be true just because they have false antecedents are used to analyse conditionals which cannot be true just because they have false antecedents.

The ultimate goal of the essay is to shed much needed light on the foundations of inductive logic. Before this can be done some clarification has to be brought to the subject of confirmation. In the third chapter this is done by means of the logic developed in the first chapter. Further, in that chapter some clarification is also brought to bear on the issue of what constitutes a proper inductive argument. In the final chapter induction itself is tackled. There the notion of the evidence employed in an inductive argument is central. The only way to provide assurance that relevant evidence has not been overlooked is to demonstrate that the relationships covered' by the new generalization are capable of being depicted in the model. Thus

it is seen that models are indeed a central feature of scientific practice and that key philosophic problems seem to have a solution which depends upon them. CHAPTER I

SCIENTIFIC LAWS AND MODELS

This chapter deals with the general question of the reference of terms employed in scientific theories. It will be argued that the nonlogical terms of science have entities in models exclusively in their extension, that models are indispensabl parts of scientific theories, and that models are interpreted as representing features which are observably present in the world as perceived by our unaided senses. (The previous sentence employs many philosophically technical terms which will have to be defined as the essay is developed.) It will also be argued that the main twentieth century philosophic views of the subject contain valuable insights but ultimately are to be rejected.

Empiricist views such as positivism and operationalism are to be rejected because they fail to distinguish between observables and models. The other main twentieth century tradition, Oxford

Philosophy, here represented by Peter Achinstein, is to be rejected because of a confusion between nonphilosophic discourse and scientific discourse. For example, that the word 'theory' has the

(partial) meaning of 'unproven' in nonphilosophic, non-scientific discourse does not imply that this sense of the word is relevant to the use of 'theory' in scientific discourse; but more of this below Keeping with the two basic ways of approaching the philosophy of science elaborated in the Introduction to this work, considerable attention will be paid in these pages to the actual working of scientists. If I have adequately characterized science, a reader who decides that the enterprise described herein is not worth doing will have rejected the scientific enterprise as it is found. It is the great virtue of the Oxford movement that they too have tried to describe what scientists actually do. If the reader attempts to construct the ways a scientist should operate, he may well reject the conclusions found herein. The Empiricists dealt with here tried to describe how the scientist should operate and in doing so clarified many issues, that is their virtue. Their clarity will be emulated below, but the focus will be on how scientists actually opera te.

1.1 Scientific Laws and Theories

'Form', 1entelechy', 'phlogiston', and 'aether' are some of the terms which no longer appear in scientific theories. These words have been discarded from the vocabulary of science but not because they are no longer linguistically useful. In contrast,

'wicked' is no longer useful to make moral judgments since its use today would merely be quaint. Rather than being quaint, the theories which employed these scientific terms and their respective concepts are no longer accepted. Better, more accurate theories have replaced the old theories and (some of) their vocabulary. The passing into disuse of such terms cannot be properly understood nor 10

can the retention of other terms in the theories which employed

the discarded words be understood unless the concepts of a scientific

law and of a scientific theory be first understood.

Scientists, on the pre-theoretic level, often employ two

different kinds of universal propositions, laws and generalizations.

Both laws and generalizations may be categorical or statistical.

An example of what is accepted today as a categorical law is "sodium

compounds burn with a characteristically yellow flame". An example

of a statistical law accepted today is "50% of the offspring of a

man with AB type blood and a woman with 0 type blood have A type

blood". An example of a categorical generalization accepted today

is, the by now trite, "all ravens are black". An example of a

statistical generalization accepted today is "for every 106 boys

born in the U.S.A., 100 girls are born". That both laws and

generalizations, as they are accepted today, may be either

statistical or nonstatistical, shows that it is not a statistical

character which distinguishes generalizations from laws. What

then is the difference between them?

How generalizations are distinguished from laws is, to some

extent, dependent upon the purposes for the classification. As will become increasingly evident below, generalizations but not laws are

merely summaries of past experience. A generalization is fully

explained by the instances falling under it, but a law goes further

for it fits together with other laws to form theories and ultimately

theories go together to form a "picture" of the world. Put in

another way: generalizations are explained by their instances, laws 11

explain their instances. As an example of a generalization,

consider the (U.S.) Presidential Succession Law. If F(t) is a

positive integer where F(t) = C^j) ” 91 and _t is the number of the

year in which the President is elected, then the President elected

in that year will die in office. t_ has had the value of a positive

integer for seven U.S. Presidents each of whom has died in office,

and hence the "Law” is true. But nothing seems to unite their

deaths. Some of the Presidents died of natural causes while

others were assassinated. Some died following their election in a year which satisfies the F-function. Others died in later terms.

The deaths of these Presidents have nothing in common except

that they occurred about twenty years apart. There seems to be

nothing about American society which requires that this occur

since the deaths have nothing in common except their timing. If

this generalization were a genuine law, then scientists could

find something underlying the deaths which would account for the

spacing of them, which would give them something in common besides

the spacing. For this reason the generalization is seen to be true

once it is seen that each of its instances is true. On the other hand a law requires more since the assertion of a law is a commitment to the existence of an underlying structure and hence a commitment to the possibility of giving an explanation of why the events related by the law are so related. If the above generalization were a law, then the claim that it is a law would be the claim that the Presidents elected in the years satisfying F have something in common besides the timing of their deaths and that 12

this common thing was the cause of their deaths. In actual

scientific practice, laws are explained by other laws, by the construction of a theory. This is necessary in order to assure

that the same underlying structure for the phenomena in question also underlies other phenomena, that the new law "pictures" the same world that the other laws have already pictured; but more of this later.

But not any theory will do, it has to be one generally accepted. To illustrate, it might be held that the reason why more boys than girls are born is that more boys than girls die in the first year after birth. However, such a teleological theory would not be accepted in modern science. There is no known reason, no known explanation as to why such a thing occurs, and hence the statistical report is merely a generalization and not a law. The theory functions by providing a connection between the events or entities described by the law. For example, a person with AB blood has a blood gene composed of an A gene and a B gene. The 0 blood type is due to a gene which is 0 in each half. This leaves four possible combinations in an offspring of an AB father and an

0 mother (illustrating the two different 0 genes in the mother by subscripts), AO^, A02» BO^, and BC>2* A child with AO or BO genes will have A or B blood, respectively. Since the transference of genes from parent to child is essentially at random, 50% of the offspring of such a union will have A-type blood. Since an explanation can be given to explain why such parents have such children 50% of the time, the statistical report is a law and not a 13

generalization. There is, in this case, a "mechanism" by which it has to be so. If a genetic connection would be found to connect

the genes for a raven with the genes for a raven's color, that is,

if it would be the case that only black genes can occur in chromosomes for ravens, then "all ravens are black" would be a law and not a (presumably) true generalization.

What of the categorical and statistical statements which occur in the theory to explain the law? Is "all people with AO genes are people with A blood type" a law or a generalization? If it were a generalization, it would be extremely puzzling for it to be able to explain laws. Laws are somehow "better" than generalizations since the former but not the latter are such that

their occurrence is intelligible. However, if the statements are laws, according to this analysis, there would have to be further laws to explain the ones employed in the explanation. This appears to lead to an infinite regress, but it, in fact, does not.

Israel Scheffler,^ I believe, has something like this in mind when he says that laws are confirmed by further instances while generalizations are not. Laws could only be confirmed by evidence if there is a connection among the phenomena described by the law, otherwise there is just another instance of the generalization. Without a connection between the described phenomena there would be no reason to expect further instances of the generalization so that the new instance would merely widen

*Tne Anatomy of Inquiry, (New York: Alfred A. Knopf, 1963), Part III, Section I. I

14

the extension of the generalization. But if there is a connection,

if there is an underlying structure between the phenomena, then

there is reason to expect further instances since the structure

can recur and hence new instances would provide confirmation. The

philosophical problem to be faced is the justification of the

transition from being accepted as a generalization to being accepted

as a law. Under what conditions may "law-likeness" be conferred

on a generalization? The next section of this paper will be

concerned with this issue.

In spite of this general agreement with Scheffler’s

position, his way of putting the point is erroneous. Suppose

that a student remarks that all students who are taking

logic this term are atheists, if he is not believed, his

generalization could be tested by looking at instances in

addition to those which prompted the student's remark, for the

issue is the size of the extension of the generalization. But at

no time would it be believed that there is a connection between

taking logic this term and being an atheist, or at least it would

be surprising that there were one. Even if, only atheists are

enrolled, nonatheists could have taken the course, presumably, but

just did not. Similarly, it might not be believed that (to use

Scheffler's example) everyone in the house is between 5'7" in

height and 5'10" in height, but it might come to be believed

through the examination of the people in the house, even though

it would not presumably be believed that there is a fact which

requires that only people of these heights be in the house; there 15 is no single fact which makes it intelligible that only people of these heights be there, it is merely a quirk, a lucky accident.

It is the connection which provides the intelligibility by which it is sought to distinguish laws from generalizations.

1.2 Self-Evidence and Conventions

Before the regress is avoided, however, another point has to be made. It could be argued that the regress is avoided by introducing self-evident statements which because of their self­ evidence are seen to be the case and require no further explanation as to why the events or objects described in them are so related.

Such statements would be self-evident laws. Such a position is somewhat like the positivist account of highly general laws such as the law of conservation of mass-energy. A. J. Ayer^ holds that such laws are really imperatives which direct scientists to construe experimental results in such a manner that input mass-energy always equals output mass-energy in an experiment. To see that Ayer's position virtually amounts to the position under discussion, note that there is, on Ayer's account, no non-pragmatic reason to pick this experimental imperative over any others. If it were assumed that some mass-energy is always lost in an experiment or a physical process, it would agree well with experimental results

2 Language, Truth, and Logic, 2nd ed., (New York: Dover, 1952). 16

and there would need be no search for new atomic particles.3 But

this imperative was chosen and the scientists who depended on it

did not seem to feel that it was a convention. The principle seems

rather a carry-over from the classical philosophic view that there

was no creation or annihilation of matter, just re-arrangement of

existing pieces. However, Ayer would have to say that it was the most parsimonious possible convention and therefore scientists

were led to adopt it. Of course, there is no defense for parsimony.

At last the self-evident principle is uncovered. For positivism

then the question has to be raised whether all laws are explained by the occurrence of conventions and their empirical results.

Conventionalism has played its leading roles in positivistic accounts of spatial geometry and temporal chronometry. Hans

A •• e Reichenbach, using the verifiability principle, and Adolph Grunbaum,-' using the claim that space-time lacks an intrinsic metric, have argued that once a convention has been adopted as to what constitutes a congruent measuring device, what constitutes a measuring device

It was the seeming loss of energy in certain collisions between atomic particles which led to the discovery of the meson. For further information consult R. F. Marshek, "Pions," Scientific American, Vol. CXCVI, (January, 1957).

^Philosophy of Space and Time, (New York: Dover, 1957). The verifiability principle has been widely criticized. See S. Passmore, A Hundred Years of Philosophy. (Baltimore: Penguin, 1968), Chapter 16.

^Philosophic Problems of Space and Time. (New York: Alfred A. Knopf, 1964). 17

which gives the same reading at different "places" in space

and at different "moments" in time, the geometry of space is

determined as it follows from the empirical results of measurement.

For example, it can then be determined what spatial loci are

straight lines. This, as they point out, will profoundly

influence what statements come to be accepted as laws of physics.

But change the conventions and the resulting measurements and

the resulting geometry chronometry will (presumably) change as

well. These arguments depend upon the principle that there is

no measuring device "built into" nature; a measuring device must

be arbitrarily stipulated. Hilary Putnam** has argued against

them not on the grounds that there are geometric or chronometric

devices "built into" nature but rather that there are no measuring

devices of any kind built into nature. Nature does not present

science with categories by which it must be understood. All

devices by which man measures nature are arbitrary, so that the

quibbles among positivists do not obviate the point that at

least some of the laws which are discovered go back to arbitrary

conventions which direct scientists on how to construe the data

they obtain.

Suppose that two different rods, one wood and the other

metal, are found to both be congruent to a third, another metal

**See A. Grunbaum, Geometry and Chronometry in Philosophic Perspective, (Minneapolis, Minnesota: University of Minnesota, 1968) for an historical account of the controversy and a bibliography of the literature on the argument. 18

rod: This by itself is not sufficient for the conclusion that

the first two rods are of the same length. If the metal rod

is at 100% C and the wood rod is at 0% C and the measuring rod

is moved from the wooden rod to the metal one, then since it

is also metal, the metal measuring rod will expand in the heat and if then the wooden rod were brought next to the metal one,

the former would be observed to be shorter than the latter. In order to interpret the data it is required to have an account of whether the measuring rod remains congruent to itself at previous positions in space. This cannot be done by measuring

since the same problems would arise with the rod used to measure

the first measuring rod. Since there is no measuring rod "built into" space, a stipulation has to be set down. The question posed here is whether all laws which are explained are ultimately explained by laws which do not require further scientific explanation since they are conventions.

Consider a judgment like "this is a chair", on the conventionalist view it would depend upon adopting a convention about what will count as measuring rod. These conventions are needed to determine, for example, whether the chair is rigid enough to support a human being. But then the judgment presupposes a theory about space (and time) and is consequently theory laden. Put in other words, on this account the judgment is about a theoretical entity, since it is a theoretical judgment. To judge that the thing before me is a chair is 19

to first have a theory about what constitutes a chair, for

example, about how much force an object must be able to withstand

in order to be a chair. On this view the chair is no longer

simply observed, it is an object whose existence is theorized

to. The statements of the convention are philosophical. Hence,

on the conventionalist account every judgment is either about a theoretical entity or in the philosophy of science; ultimately everything is conventional. It turns even the most prosaic ordinary statement--the chair example above, for instance--into either a convention or the empirical result of adopting a convention. Certainly that the sound 'chair' is used to describe this object underneath me and that the sound 'table' is not, is purely conventional; the meaning of the word 'chair' could have been given to the sound 'table'. But it seems painfully obvious that I am not making a theoretic judgment when I judge that this is a chair. The view does not preserve the common sense truism that I came into a world which was full of tables, chairs, and so on, and that science is an attempt to move beyond what is presented to the unaided eye. It simply does not require reference to scientific theories to judge that this is a chair and not a table. To make a point about how we judge that this is a chair requires philosophy and science, but to make the judgment itself does not. Put in another way, the philosophical point is that not all men are either philosophers or scientists and therefore not all pronouncements of men are 20 either philosophic or scientific. On the extreme conventionalist thesis they are and hence extreme conventionalism is wrong.

Perhaps, however, conventionalism has been treated too severely; it may be the case that all the conventionalists are maintaining is that scientific judgments reduce to conventions but nonscientific ones do not. Granting this to the convention­ alists does not help the quest on these pages since other kinds of enterprises besides science may stem from conventions.

Lexicography probably does, for example. So does the assignment of license plates to a population. Hence the goal of discovering what distinguishes generalizations from laws is not yet fully realized.

The other possibility which has to be examined is that the ultimate laws are self-evident but not conventions. The possibility here being suggested is that the laws are innate.

The arguments against innate principles are too well known to have to be repeated here, so that this possibility may also be rejected. For example, even if an idea is inborn, there is still required a proof that the world external to our mind is like the inborn idea of it. The result which remains is that conventions play a role in the ultimate explanation of laws but that there is something else which is also present in an adequate account of laws. 1.3 Models and Theories

On the pain of an infinite regress, low-level laws cannot be distinguished from generalizations on the ground that they, but not generalizations, follow from other laws. This spectre simply invites the question of what distinguishes the justifying laws from generalizations. If further laws are appealed to, the question of what distinguishes them arises again and the regress is in the making. Ultimately something other than laws, which require other laws for "certification" as being laws, are needed to make the distinction. The regress cannot be avoided by appealing to special sorts of laws which are self-evident because they are conventions since this does not help to distinguish science from other enterprises. Nor can the self- evident laws be innate since there are no innate principles.

The only choice left is to turn to something which can supply the requisite connection between the events-things described by the law but which is not itself a law, and which is more fundamental than either laws or generalizations. Whatever this may be it will also have to help distinguish between a series of laws and a theory; not any collection of accepted laws form a theory. For example, Boyle's law relating the pressure, temperature and volume of a gas and Mendel's law relating characteristics of a parent and offspring together do not make a theory but they are a series of laws. Newton's laws together do make a theory and this difference between a 22

mere series of laws and a theory has to be explained just as

the difference between a series of related events, a law,

and a mere sequence of correlated events, a generalization,

has to be explained.

Before proceeding it will be useful to distinguish

between a law and a lawful statement. Strictly speaking a

law is a true sentence which asserts a (counterfactual warranting)

connection between a sequence of correlated phenomena (what

is observed by the unaided senses). A law states a correlation between phenomena which is such that it is intelligible as

to why the phenomena should be related. A generalization is

then a true sentence which simply asserts a correlation between phenomena which is not understood or which is accidental. For

the phenomena described by a generalization, there is no explanation as to why the phenomena appear to be so related or there is an explanation as to why the phenomena's exhibiting a pattern of occurrence, a constant conjunction, is not due to a connection between the phenomena, it is purely accidental.

For example, it is presumably purely accidental that since

1840 every American president elected in a year divisible by

20 has died in office, since it is widely agreed that time cannot be a causal factor in explanation. Science is not static; what was thought to be a good theory or a good law changes: Newtonian mechanics is replaced by Relativity; "causal chains are propagated instantaneously" is replaced by "causal chains are 23 propagated at a finite speed equal to the speed of light.

What is accepted as a theory or law may turn out to be false

(since, by definition, theories and laws are true). Hence the concepts of "theory-like" and "law-like" are introduced. These apply to what is today accepted as being adequate theories and laws. If they are in fact true, they are not just like theories and laws but are theories and laws. To be prudent, they are said to be theory-like or law-like. Above, when 'accepted theories' or 'accepted laws' was used it was the theory-like or law-like counterparts to which reference was being made.

Below the '-like' shall similarly be dropped. Where confusion may ensue from this phrase, 'accepted' will be employed to make it clear as to whether laws or law-like statements are being discussed. Similarly for theories.

What then could it be, by which laws and generalizations may be distinguished? What provides the intelligibility of a law but is absent in a generalization? By means of what is the occurrence of a connection between constantly conjoined phenomena understood? Hume and other classical philosophers would have answered that there is a causal connection between lawfully connected phenomena but not between merely correlated phenomena.

The point puzzled Hume since he could not discover any difference

^Thomas Kuhn, The Structure of Scientific Revolutions. (Chicago: University of Chicago, 1962). 24

between causally connected phenomena and correlated phenomena

except in the mental habits of the observer. Yet, a connection

in the mind is hardly sufficient as Hume laments,**

And how we must be disappointed, when we learn, that this connection, tie, or energy lies merely in ourselves, and is nothing but that determination of the mind. . .?

Hume’s lament has echoed throughout philosophy in the last two centuries but it is unwarranted. For two reasons a causal connection will not be discussed on these pages. First,

scientists have developed a whole host of laws in the twentieth century which do not employ causality. Among these are the laws of Quantum Mechanics. Quantum phenomena are not causal.

So that even if a causal connection will do the job in other areas, it will not help explain the difference between laws about quantum phenomena and generalizations about them. The second reason is perhaps more basic. Hume is consciously

trying to follow Newton in his method, but he develops an analysis of causality which is incompatible with Newton's laws'

For example, according to Hume, the effect occurs after its cause and he is deliberate about it. He argues that if this were not true, causal chains would be instantaneous and not "spread out" in time.9 Commonsensically, causal chains take time, chains of events, in which one event follows another are often

**A Treatise On Human Nature, ed. L. A. Selby-Bigge, (Oxford: Clarendon Press, 1964), Book I, Part IV, Section VII. 9 Treatise,.., Book I, Part III, Section II. 25 ordinarily used to explain a current occurrence. The chain which led to the evolution o£ man, to take a contemporary biological example, goes back through millions of years.

However, Newton has none of this. For him, a cause and its effect are simultaneous. The gravitational attraction between the Sun and the Earth keeps the Earth in its orbit around the sun. If the Sun's mass were suddenly removed from the solar system, the Earth would instantaneously leave its orbit.

Since it is science which is the subject here, it would be improper to stick to a sense of 'cause' which plays a role only in ordinary discourse. Hume's point has to be inapplicable to science, for it ignores the science of his day. Since

Einstein, scientists accept that there is a finite propagation speed for causal chains which is what Hume claimed, but this holds only for macro phenomena. On the micro level, on the level of masses which are small with respect to Planck's constant, causality does not apply. Hence, to stick to a

Humean account here would be to fall back into the first difficulty. Either error is by itself sufficient to doom the Humean program. Hence, the key to the difficulty of answering the question as to what provides the intelligibility of the correlation between phenomena described by laws does not lie with causality. Something else will have to be examined.

Scientists employ models in their discussions and presentations of laws. A model is, usually, a picturable representation of the process about which the law in question

is concerned. On one level, these are laws which relate

phenomena to phenomena. But usually, laws relate events

which cannot be observed with the unaided senses, if at all.

A simple law which relates observable phenomena would be

Boyle's law: PlV]^= p2^2» P an<^ V are the pressure and

volume of a gas and the subscripts indicate these properties

at different times. The pressure and volume of a gas are

observable without aid by most people, but, of course, their

quantitative measurement requires instruments. The law

maintains that if the temperature of a gas is held constant,

then the product of the pressure and volume of the gas is

a constant through time. Boyle’s law was held on experimental

evidence, even though Newton had previously derived a similar

result from an atomic model for gases.But, Boyle went on

to try to understand why it held. He postulated two different atomic models for gases, each of which had its difficulties but each of which could explain the observed relationship.

The details of his models are of no concern here, what is

important is that he sought to understand an observed phenomenal

relationship by means of something picturable, something which "got behind" the phenomena, and something which he

thought was far more intelligible than the phenomena by

Holton and D. Roller, Foundations of Modern Physical Science. (New York: John Wiley and Sons, 1958), Chapter 21. Hereafter this work will be cited as H and R. 27 themselves. Heuristically, a phenomenal relationship can become intelligible by assimilation to something which is already thought to be intelligible, this is one of the functions of the model. The development of quantum mechanics is a most helpful illustration of this use of models.

In the late nineteenth century one of the more perplexing phenomena for physicists was that of the absorption and radiation of radiant energy.^ .It had been earlier theoretically proved that a body which completely absorbed all radiant energy falling upon it, a perfect absorber, would also most efficiently radiate energy, would be a perfect radiator.

Wilhelm Wein and others proposed that a physical object with a small hole in it would, at the hole, be a perfect absorber of radiant energy and consequently it would also be a perfect radiator at the hole. Experiments were conducted to determine the relationship of the frequency of incident radiant energy and the frequency of emission at which the greatest quantity of energy was radiated, called J >v . The resulting functional relationship expressed as a curve or graph was a function of the temperature of the radiating body, so that for each distinct temperature a different curve resulted. From

Maxwell's equations and classical physical assumptions two important laws were derived. The Stephen-Boltzmann law held that the total emissive power of the radiated radiant energy,

^See H and R . Chapter 31. 28

J , was directly proportional to the fourth power of the

absolute temperature of the radiating surface, T^. This law,

J=k \ was derived from the laws of heat and Maxwell's field

theory; its empirical verification was a triumph for classical

mechanics. Wein also developed from similar sources a law

which held that the frequency at which J was greatest,

^ peak, was inversely proportional to the absolute temperature

of the radiating body. With Wein's law, peak = K/T, and

the Stephen-Boltzmann law, a new development was possible,

given the curve for any one temperature, the curves for

all other temperatures could be plotted.' However, there

was no law which enabled a physicist to plot such curves

without already possessing the curve for one temperature.

Two main attempts were made to develop such a law. Wein

postulated that Maxwell's law for the distribution of molecular

velocities in a gas also held for the distribution of radiant

energy with respect to the frequency of radiation.Wein's

equation, J = Ci "5 / 1 \ , agrees with Wein's law, ^ C2/ > . T J the displacement law, and with the Stephen-Boltzmann law

but only agrees with the empirical results of the relationship

between J and for values of below 3/c , it has fair

agreement with values 3J4. and 6/< , and no agreement for

120. H. Blackwood, T. H. Osgood, and A. E. Ruark, An Outline of Atomic Physics. (New York: Wiley, 1955), Chapter IV.

4 29

values of above 6J 4 . . Lord Rayleigh argued from different

assumptions. He drew an analogy between radiant emission

and sound emission. When, say, violin strings vibrate, they

produce not only a characteristic note but also harmonies

of that note. Rayleigh postulated that the radiator did

the same and that the energy of emission from one main

frequency and each of its harmonies were the same. His

equation, J •>*. = C3 T) , agrees with the displacement

law but not with Stephen-Boltzmann's four power law. Although

it has excellent agreement with the empirical results for

wavelength beyond 6/<. , for values below bj j u , it too is

erroneous. Thus, when Planck came upon the scene, there were

two different equations, each of which fit part of the data

and each of which diverged from the data where the other was

accurate. Planck, like many many others, attempted to find a

single equation which would agree with all the data. He worked with Wein's equation and noticed that if it could be

forced to give higher values for over 3j j L , it would agree with the experimental results. He tried subtracting

_1 from the numerator of Wein's equation and got good agreement.'

Planck's equation, J = c3 did not satisfy > 5 (e" C47 > T_l) him even though it agreed well with experiment, since in general, 13 an equation can be found to fit any family of related curves. J

13 - Noble Lectures: Physics. 1901-1921, (New York: Nobel Foundation, 1964), 407-420. 30

Planck's equation found almost immediate success when, shortly

after it was proposed, a method was discovered for measuring

J at values of never before tried and agreement was

gotten with Planck's result.

The important point for the purposes of this essay

is that Planck was not satisfied with just having an equation,

he wanted to understand it. He tried to do two, not entirely

distinct, things, find a model for radiant energy emission

which made his equation intelligible (and not merely a calculating

device) and to replace his constants, C3 and C4 , with expressions

tied to other physical constants. The impulse for the latter

job was the fact that the constants were independent of the

substance of which the radiating body was composed. This also

gave him the key to the first job. He postulated a model in which radiation was emitted in quanta and at certain frequencies which are whole multiples of the lowest frequency of vibration of the radiator. With this assumption, contrary to classical mechanics, he found that C3 is 2TT an(* that C4 is hc/k, where 'h' is Planck's constant, 'c' is the speed of light, and 'k' is Boltzmann's constant. It was by means of the model that he was led to the correct solution. That it was the correct solution was further verified by the fact that the new expressions for C3 and C4 enabled Planck to deduce both the four power law and the displacement law from his new law. Still Planck was troubled, he had a law for the 31 relation between and but did not seem to have a connection with any other physical process. Einstein provided the connection. He took Planck's model for emission and used it to explain the photoelectric effect.

The surfaces of solids have the characteristic of emitting electrons when a suitable frequency of radiant energy falls upon them. This was first noted for surfaces which did this for radiant energy in the visible range. The difficulty in understanding the effect is that according to classical mechanics emission should occur from the surface as long as energy was falling upon it, but it did not. Only when energy of a minimal intensity fell on the surface was there emission.

Further, classical theory supported the view that it would take a finite time for radiators to absorb energy before they would begin to emit electrons, but once the minimal intensity was reached, emission began without any sensible delay. Hence the photoelectric effect was a puzzle for classical theorists.

Einstein argued, using Planck's model, that energy came in minimal bundles or quanta, now called photons, and that an electron would be emitted only if the photon falling on the radiator was large enough to do the work; if it was, the event would happen without delay; if it was not, the event would not happen at all. Hence if the incident energy was below a certain intensity, no photoelectric effect is observed but if it is above that intensity, the effect occurs without 32

sensible delay. Einstein also used Planck’s model to explain

other puzzling aspects of the effect,

Einstein's use of the effect pointed up certain new

difficulties. When energy is emitted from an intense source

such as the sun, the photons spread out across "the wave

front". The further the front is from the source, the less

the density of photons across the wave front of energy. But

there are so many photons, nevertheless, on the wave front

that they statistically average out and the wave front appears

to be a continuous energy front when it in fact is not. On

the other hand, discontinuity appears when the effect of the

wave front on a single absorber is under consideration. There

the individual photons have to be considered and there the

effects of quanta play a role; it is only here that the

discontinuity of physical processes becomes evident. The

difficulty in forming models is that originally models were

drawn from continuous phenomena, the only sort sensed unaided.

But now models need to be drawn from discontinuous phenomena,

ones which are never perceived as discontinuous by the unaided

senses. That scientists have continued to this day to employ

models, even when they employ processes which do not occur

on the macro level, shows the force with which they serve

science.^ Today we can give analogues of discontinuous

^ F o r a striking illustration of this see V. F. Weisskopf and E, P. Rosenbaum, "A Model of the Nucleus," Scientific American, Volume CXCXXI, Number 20, (December, 1955). 33

phenomena but: there is still no known physical process which

is observed by the unaided senses as discontinuous. The

importance of models is too great for them to be dispensed

with. They serve both to aid in understanding how the phenomena

related by equations are so related, as the quantum model does

for radiation and emission phenomena, and as a guide to further

investigation, as in the photoelectric effect.

The second point deserves elaboration. Following

Mary B. Hesse, two aspects of the model can be distinguished.15

The positive analogy between model and physical process is what is used to make the phenomena under consideration, the equations in question, intelligible. There are still other aspects of the model which are known not to be relevant. For example, Rutherford thought of atoms as being little billiard balls, though, of course, without color. The color of the billiard balls played no role in the model even though Rutherford could not help thinking of them as being red.' There is a difficulty in visualizing atomic processes: atoms and subatomic particles have no color but any visualization will employ a color. So that any visualization is, that far, wrong. But since the color is not employed in the model, there is no difficulty. Color does not emerge as a phenomenon until the molecular stage. Here, the phenomena under consideration ....

^^Models and Analogies in Science, (South Bend, Indiana: University of Notre Dame, 1966). force Che ignoring of Che color. Nevertheless, there are aspects of the model which are not used but for which there is no special reason not to use them. These aspects can be used to investigate

the model, to make it applicable to other phenomena. Planck's model was for the emission of radiant energy, and Einstein's extented it to cover the emission of electrons from a surface.

The role of models in providing clues to further investigation is also extremely important. Models guide a scientist in thinking about nonunderstood phenomena by interpreting them as extensions of understood phenomena.

This is the cash value of the philosophical point that there is but one nature which all sciences study. The laws which govern physical processes are few and connected.

There is not one law for each physical process but rather one law, or a few laws, for all physical processes. Scientists search for one model for all phenomena--the model which connects all scientific laws into a single theory. That models are used to extend what is understood to what is not understood, underlies this conviction. Philosophers often speak of the reduction of one science to another; the most famous example is the reduction of heat phenomena to statistical mechanics but another equally important example is the development of field theory and the resultant assimilation of mechanics to wave propagation. This process is nothing less than the extension of the model of one phenomenon to cover another. For example, the atomic model for mechanics was used to

interpret heat processes. Since heat is a characteristic of mechanical bodies, the model of mechanical bodies may also

cover the then previously not well-understood characteristics of heat. Since it.does, there is a reduction of the science of heat phenomena to the science of statistical mechanics.

This well illustrates the employment of models for investigative fruitfulness.

1.4 The Extensions of the Terms of Scientific Discourse

The nonlogical terms employed in scientific discourse, in the statements of laws, all have features of models as the sole constituents of their extensions. If there is talk of atomic and subatomic particles and their properties, then there is something in the model identified as a particle and something identified as its properties. Particles are spoken of as having mass and occupying a volume of space. These properties are features of the model. From them a third property is defined, namely, density. The property of density is admissible in scientific discourse not because it is defined in terms of properties which are directly in the model and not merely defined, but because the defined property plays a role in laws. If a new property was introduced into a scientific language by means of a definition which solely employed terms which do occur in laws but the new term had no scientific employment, there would be no laws which united 36 it with additional concepts and the term would be illegitimate.

Consider the hypothetical term 'cwork' which is defined as the work it takes to set in motion a unit mass of a substance with a particular color. The cwork-function would relate the work needed to overcome the rest mass of a body to the body's color. Both 'work' and 'color' are well-defined terms in physics so that on this account there is nothing wrong with the definition. There could even appear to be laws involving

'cwork'. For example, "as the work needed to move a body increases, so does its cwork" and "every body of a standard mass requires the same cwork to move it." The difficulty with such a term is that it could not be related to any other concepts except those by means of which it has been defined. But, 'density* can be related to other concepts, for example bouyancy. Thus, a term is permitted in a scientific language only if it has occurrence in a law and, if it is a defined term, if it can be related to terms other than those in terms of which it is defined, provided that other terms have employment outside of a closed circle of interdefined terms. This last requirement is to rule out the case where a term like 'cwork* is defended on the grounds that it is related by law to some other term which, like 'cwork*, is related only to its defining terms and 'cwork'-like terms. It is not sufficient to try to rule out such cases on the grounds that laws must be nonanalytic. This is for two reasons. There

I 37

has been much fuss in philosophic literature over whether the

concept of analytic is defensible and the discussion here

should not beg that question.16 Secondly, even with such a

circle of interdefined words, it is possible that some of the

alleged lawful relations among the entities in the extensions

of the terms will be relations which involved numerical

quantities and hence will be (classically) contingent judgments.

This, indeed, seems to be the case in the cwork-example above.

The present concern is only with the point that every scientifically

admissible term has a non-empty extension in the model but not

every term which has such an extension need be employed in a

scientific language. Which terms are employed in the language

is solely a function of the laws which scientists discover.

Terms which could be defined which have no scientific value

need not be defined although they would have a non-empty

extension in the model. The key to scientific meaning is two­

fold, use in laws and non-empty extensions in the model.

Some law-like statements are no longer accepted. For

example, scientists have given up the concept of the aether

and hence statements which related it to other phenomena are

now known to be not true, to be scientifically meaningless,

since ’aether* has no extension in current models. But, some

^This literature begins with Willard van Orman Quine, "Two Dogmas of Empiricism."Philosophical Review. LX, (January, 1951). It is reprinted in From a Logical Point of View. (New York: Harper Torchbooks, 1963). of the laws of aether theory are still accepted, some are

restated without employing the term, and some of the features

of the aether model of wave propagation are still retained.

These constitute a continuity between classical physics and

relativistic physics by enabling scientists to dispense with

the incorrect features of old theories and to employ the correct

parts in new theories. In the reduction of heat phenomena to

mechanics, an old model was extended into a new area. In the

overthrow of classical mechanics by relativistic mechanics, a new model replaced an old one. In both cases, the use of a new model to make old laws intelligible provided a continuity between old theories and new ones. If theories made the constituent terms intelligible, then a change in the theory would change the meaning of the terms. In such a case, 'heat1 could not be the same term in phlogiston theory and thermo­ dynamics, but it is. Hence, something besides theories must

give terms meaning. That something is the model. Each scientific nonlogical term in the law-like statements has something in the model for its extension. If some of the law-like statements are rejected, the new model must still make the remaining law-like statements intelligible; this is

the continuity of theories. The meaning of a term can change by changing the law-like statements in which it occurs or by changing the model which makes the statements intelligible, but since the new model still makes some of the old law-like 39

statements intelligible, there is continuity of meaning and

the newly understood terms retain enough of their old meaning

to remain the same term.

So far three important points have been established:

(1) each descriptive or nonlogical term of scientific discourse

has a non-empty extension in the model; (2) not every term

which has a non-empty extension in the model has employment

in scientific discourse; and (3) models are important in

defending the claim that a new theory has the same subject

matter as the theory which it replaces in spite of a change

in the extensions of the terms of the theory from one model to

another.

1.5 Ontological Status of Models

If there were a scientific term which had an empty

extension, the law-like statements which employed that term

in their logical subject would be vacuously true. Since there

is no aether and consequently no bodies which move through

the aether, "all bodies which move through the aether are

bodies which have an absolute motion with respect to the

aether" would be true in any standard semantics which permitted

terms with empty extensions such as those of Boolean and

Principia-Mathematics logics. Or consider Newton's law that bodies moving with constant velocity in a perfect vacuum causally isolated from all other bodies would not change their velocity: since there are no such bodies, on these kinds of logics, the law would be true independent of any verification.

Once it is known that the term has an empty extension, the laws in which it is the logical subject are known to be true, no other evidence is needed. Scientists, however, do not accept such arguments, so they do not employ such logics. The logic which they employ requires that all introduced predicates have non-empty extensions. However, since the above example from

Newton is a legitimate law, the extension cannot be in the sensed world because no one has sensed bodies moving in perfect vacuums causally isolated from all other bodies nor is such experience expected. Indeed, it is usually maintained that such a thing could not occur. To what then do the nonlogical terms in Newton’s law refer? Each term has its extension in the model. From this, however, it does not follow that something has all of the predicates or properties. For example, from the law "A body maintains constant velocity unless acted upon by an outside force" it does not follow that there are bodies which maintain constant velocity. It only follows that there are bodies, that there are constant velocities, and so on. The existence of bodies with constant velocity has to be proven either by observation or construction. (This is further discussed below in Section 3 . 3 .) But note also that from the presence of an outside force acting upon a body it does not follow that the body will change its velocity since classical mechanics holds that opposing forces neutralize each other. In part then, it is 41 only the series of laws which is modeled. As the point was put above, the model is for a theory, it unifies the series of laws into a theory. In the model there can be perfect vacuums, causally isolated processes, and so on, but not in the sensed world. However, the conditions of the model are close enough

to phenomena that, within a determinate error, phenomena behave like the model. Because of this, the laws which govern behavior in the model are also applicable to the sensed world.

Notice the picture drawn here. Generalizations about the sensed world, about phenomena, are made intelligible, are seen to be laws by means of models, which models have or may have features not expected to be in the physical sensed world.

The laws based upon experience exactly describe the model and are close approximations to descriptions of the physical world.

Science began with the program that the phenomena observed by the unaided senses can be related to each other by means of processes not directly experienced. What are these processes which are not directly experienced is understood by means of the model. The model is thus seen to contain features which could not be in the directly experienced world.

Are the processes ''behind" the phenomena identical to the processes in the model? The question admits of the answer "yes" JUE the question is to be answered by a reapplication of scientific method since within an experimental error they 42

are the same. If other considerations are relevant, then the

answer may, perhaps, be "no". This controversy as to what

constitutes the correct criteria for the ontological status

of the real shall not be entered. No one expects to observe

a physical process at absolute zero. No one expects to

observe a particle moving in a vacuum. There are many physical

processes which are discussed in models which have not and

are not expected to occur. Whatever the role of phenomena

in the discovery of the laws, the terms in laws do not and

cannot have phenomena as their extensions. The terms in laws

can only have features of models as their extensions. But

the laws are correlated to phenomena since the model admits

of phenomenal or physical interpretation. 1

The semantics opted for here has it that models have

physical interpretations in the world as observed and that

the language of science has its referents in models. It is

only because models have physical interpretations that scientific

language may be spoken of as having a physical interpretation

or being about the observed world. A model is acceptable if

it can be consistently given a physical interpretation. Some

of the process of giving such an interpretation shall be

discussed in succeeding chapters. If such a sharp distinction

is not drawn between the physical interpretation and the

extension of scientific languages, then fundamental points become obliterated. Most crucial is that without the distinction it seems as if the sentences in scientific languages are about

the observed world and hence are true of the observed world.

Since they are "true" statements about the observed world, it would seem that the objects which they are about are real.

But the objects which they are about lack the qualities which are perceived. Take a simple example, the qualities employed in Newton's equations are mass, acceleration, velocity, force, and distance (hence these terms must have non-empty extensions in the model). The qualities perceived may possibly include the latter two but certainly not the whole group. The perceived qualities are color, taste, and so on. That there is such a difference in qualities is evident in the classical distinction between primary and secondary qualities. The primary qualities are the parameters of the basic laws of science while the secondary qualities are all the ones which are perceived but not required for a scientific description of the world. With the collapse of the distinction it turns out then that the world as perceived is almost totally unlike the real world, the world which is described by the (true) laws of science. .

Once the distinction is made, however, it turns out that science is only indirectly about the observed world.

Maintaining the distinction leads to the view that scientific language may be interpreted to be about perceived objects only because language is about models which may receive physical interpretation. There is no competition between observed entities and scientific entities for the status of being real since each may be interpreted as the other. Prom

the usual point of view the theory advocated here has the unfor­

tunate consequence that scientific languages get their meaning in a place different from the one where they get their truth conditions. Classically, a sentence is true if what it is about is related in the same way that the words in the sentence are related. This is the picture theory of meaning.^ This theory, as shown above, led to the intellectual disaster of having the real world be unlike the observed world because it led to the view that the truths of science were about the observed world. Since the observed world had more qualities in it than were needed for a scientific description of it, these qualities were relegated to a secondary place; but also since there were more unneeded qualities than needed ones, it turned out that perception was almost never of reality.

Contrary to this view: that the model may receive a physical interpretation shows that there is a way of translating any statement about the model into a statement about the observed world and translating any statement about the observed world into a statement about the model. Model language and observed world language are two ways of describing the same thing.

^Ludvig Wittgenstein, Tractates logicus-philosophicus. trans. D. F. Pears and B. F. McGuinness, (New York: Harcourt, Brace, 1922) has a concise account of this view. Neither is more real than the other, they are the same.

Scientific laws and language are about models. They are true

if they describe the model. This holds because the ultimate

model will have a physical interpretation. (Here an ultimate

model is spoken of because science progresses by discovering

limitations in current models. This process was discussed

and illustrated above.) The mistake to avoid is thinking that

scientific statements are true in the same sense that sentences

about observable objects are true because then the two kinds

of judgments seem to he competing for the status of being about

the real as if they were about the same thing in the same sense.

Without the distinction not only is this mistake made but it

also turns out that models are dispensable for they are not

needed as a referent for scientific language. But as argued

above, it then becomes a puzzle as to what distinguishes

generalizations from laws and as to how science progresses.

The distinction between the meaning or referent for scientific

languages and the conditions under which such judgments are

true is thus crucial for a correct understanding of science.

Indeed it will be seen below that other philosophic controversies

hinge on this distinction.

This is thus the correct theory of scientific reference.

Each scientific term occurring in a law has something in a

model as its extension. (In an ideal language of the Principia-

Mathematica type, a scientific term would be a nonlogical term.) )

46

Hence logics which allow for terms with empty extensions cannot

be employed in scientific discourse. A correct logic will be

formalized below in Section 1.8. Before then, however, alternative

contemporary theories of reference will be considered and objections

raised against them.

1.6 Peter Achinsteinrs Theory

Peter Achinstein is taken here to be a good example of what

may loosely be called the ordinary language approach to philosophy 18 of science. It is not the issue here to attack a whole program

of doing philosophy. Some of the metaphilosophical views expressed

in these pages are stated explicitly, others are merely displayed

as done philosophy. What is important in this and the next two

sections of the paper is to evaluate the results of alternative

philosophic programs and not the programs themselves except where

the criticized results are the only thing sought through the

program. It is not important here whether all philosophers or

Achinstein would agree that he is an ordinary language philosopher;

what is important is the evaluation of the results he gets when he

does philosophy.

The central issue faced in this and the two succeeding

sections is the ontological status of theoretical entities. The

distinction between theoretical and observational entity may

not be entirely sharply delineated but, above, it has been made

18 Most of the material from Achinstein is drawn from a summary and continuation of his published articles, Concepts of Science. (Baltimore: John Hopkins, 1968). 47

on the grounds that observational but not theoretical entities may

be observed by means of the unaided senses. Theoretical entities

are the ones in models. Atomic and sub-atomic particles may be

taken as paradigm cases of theoretical entities. Above it has

been argued that since science employs laws which already do not

have instances in the universe presented to the unaided senses

(e.g. Newton's law that "outside" force is required to change the

velocity of a body moving in a vacuum not within a gravitational

field), the laws refer to models and not to the observed

universe. Not every feature of a model is given an observed

correlate which it approximates. Hence science, by itself, does

not give ontological status to models. Philosophers interpret

science so as to fulfill the quest of the correct ontological

status of models. It has been argued above that this quest is

ended once it is seen that models are useful but uneliminable

devices for making laws intelligible; they are somewhat like

metaphors since they are alternative descriptions of the perceived

world. This solves the problem of the extension of terms

employed in scientific discourse. The alternative views explored

here present other attempts to solve this problem. The focus will

be on the extension of terms like 'atom' and 'electron' which, as

indicated previously, are paradigms of theoretical terms.

Achinstein has two main arguments each of which is designed

to break down the view that there is a single hard line of demarcation between the applications of the categories "theoretical entity" and "observable entity". His first argument is that what 48 19 a scientist describes as observable depends upon the context.

In some contexts a scientist may report that he observed a line in a Wilson cloud chamber, in others he may say that he observed

the path of an electron. Norwood Hanson makes a similar point 20 in an argument with a different purpose. He asks us to imagine

Tycho Brahe and Kepler watching the sunrise, Tycho Brahe sees the sun move so that it becomes visible while Kepler sees the

Earth rotate so that the sun becomes visible. The force of either example is that what a scientist observes and reports depends upon his scientific sophistication, his purpose in reporting, and his audience. Achinstein's second argument takes a different . 21 direction on 'observable'. For Achinstein, the wrong view has it that what is observable is seen directly while what is theorectical may only be observed through its effects. An electron may only be studied by means of counts on a screen or condensation fires in a cloud chamber and hence it is theoretical. Table and chairs may be studied through their effects but they may also be studied directly; hence they are not theoretical. From

Achinstein's point of view, the difficulty with this characteriza­ tion of 'theoretical' is that new discoveries may enable scientists to study directly what previously could only be studied through its

19 Concepts..., 164ff. 20 Patterns of Discovery. (Cambridge: Cambridge University Press, 1958), Chapter I. 21 Concepts.... Chapter Five, Part 4. 49

effects. Thirty years ago the fish, Coelacanth, was postulated

to explain certain fossil remains. It could not be studied

directly since the only knowledge that we had of it was from its

effects, fossils. However, in the past few decades live examples

of the coelacanth were discovered. Now it can be studied directly.

Given the previous criterion for distinguishing theoretical and

nontheoretical entities, the coelacanth has changed from

theoretical to nontheoretical, . Hence, Achinstein concludes, the

boundary between theoretical and observable entities is constantly

changing; the distinction is not hard and fast. It is thus a

mistake to worry about what is and what is not a theoretical entity.

Part of the difficulty in attacking Achinstein's first

argument is that scientists themselves often engage in philosophy

of science and it may therefore be hard to separate their scientific

competency from their philosophic. If some philosophic theory

leads to their usage of the term 'electron1 or 'observable', then

that usage should only be evaluated by evaluating the philosophic view which prompts the usage.

Other philosophic disciplines besides philosophy of science have profited from ignoring the views of laymen which are founded

on "philosophic" views. For example, people working in ethics

sometimes remark that if a moral theory leads to a normative view

that most (thoughtful) people would reject, then that is some evidence against the theory and, at least, the theory must defend

See Life. Volume 61, (July 22, 1966). 50

itself against such an attack. But, even though most people

believe that it is good to worship God and that there is even an

obligation to do so, most philosophers of ethics do not even

consider whether or not the normative theories they defend are

compatible with this widely held belief. It is proposed here that

the reason is that most philosophers recognize that attitudes

towards churchgoing are an intimate part of commonly held

philosophic views about the relationship between God and morality

and that these views were shown to be wrong as far back as Plato's

Euthyphro. Since philosophy of science has played a notoriously

important role in the development of science, the pronouncements

of scientists which are taken as philosophic data have to be

weighed carefully, especially in an area like the "theoretical/

nontheoretical distinction", since philosophy of science was

turned to by scientists to help them with the problem (hence all

the scientist's interest in the verifiability criterion).

What of the scientists changing usage of 'observable'?

Before the fact that he does change his usage can be counted

heavily it is necessary to ascertain whether the word changes its

meaning from context to context and whether the usage is due to a

preconceived philosophic theory. For example, when it is said

that an electron is observed on a cloud chamber, it this a "loose"

way of speaking--is it a shorthand way of saying that what he has

observed is evidence that there is an electron in this area, or what? Achinstein has made no attempt to answer such questions and

thus his first argument cannot be accepted. How anyone speaks is 5i

only important if it is known why he speaks that way. Achinstein

proposes an answer to the latter question in terms of the former

one: Scientists speak the way that they do because there is no

precise division between application of "observable" and

"theoretical". But then that they do speak in the way that they do cannot be evidence that there is no precise division between

the two areas. One way to defend a theory independent of the

phenomena it is introduced to explain is to refute all competing

theories and then show it does explain the data. How a term is used only helps if it is known why it is used that way. Of course his view that there is no precise distinction explains that on some occasions 'observable1 is used and on other occasions

'theoretical' is used but it does not explain how to predict which one will be used when. Until that can be done, it is not known that whether or not the data contain misuses of the categories.

Overlooking these points, however, attention will now be turned to Achinstein's other argument since, as has been pointed out above, the real support for his views has to come from it. The argument just considered can only be successful if his other arguments are. The second argument is more interesting than the first because it attempts to provide counter examples to a plausible sharp distinction between 'theoretical' and 'observable1.

The first question to be considered in connection with the second argument is whether it is a defect in an account of the distinction that what entities fall into each category will shift as knowledge increases. What has to be noticed is that the 52

extension of the term will change but the intension will not. This will present a problem only for a philosopher who maintains that

the only proper kind of definition is an ostensive one. But such a position is, presumably, indefensible. (Of course, what counts as a theoretical entity will be a function of what theory is under consideration. If an entity is introduced via a theory and later becomes accepted as a piece of raw data, then it may well change from being theoretical to observable. An illustration from mechanics may help. When Newton introduced the equation

"F = ma", he took mass as a defined concept and force and acceleration as data. Contemporary physics takes mass and acceleration as data and defines force.) That only ostensive definitions are important is not a position which should be pinned on Achinstein, since he does not seem to explicitly endorse it.

Perhaps a diversion into aesthetics may prove useful. A pointillist painting is composed of a multitude of dots of color which when observed from a distance take on a coherent arrangement as a picture of people or plants, or what have you. The points of color compose the picture much as the points of ink in a newspaper compose a photograph. Now when a pointillist painting is observed, what is seen, dabs of color or, say, a woman? If from a distance a woman can be seen, the observer can always move closer to see just the colors. Here the answer is that both the dabs of paint and the woman may be seen. Scientists claim that tables are composed of atoms. When a table is seen are the atoms also observed? If so, the distinction between theoretical and observable entities clearly 53

breaks down. If paths of electrons are seen in a cloud chamber,

then why are electrons not seen when the table is observed?

Surely, when a bacterial culture is being observed, the bacteria

are not seen unless the culture is being observed by means of

a microscope. As Achinstein points out, the question of

whether bacteria or staining dyes are observed under the microscope is identical to the question of whether electrons or

loci of condensation are observed in a cloud chamber, and it

is also identical to whether tables or electrons are observed.

Even from an ordinary language point of view it would be queer to say that atoms were being observed when tables were being looked at. There is no difference between this case and the cloud chamber case so that the best which can be o *» maintained is that ordinary discourse is inconsistent. J

If the purpose of the observer was to make the point that the physical object was a model for the atomic object or better

to use the physical object to interpret a model, then the manner of speaking which employed locutions like "electrons are being observed" would make sense.

This raises a second kind of difficulty with Achinstein's views. Are molecules directly observed by means of an electron microscope just as bacteria may be correctly said to be directly observed through an optical microscope? If the answer is "yes",

^Spelling out the context of the observation will not help avoid the problem for then electrons are seen in laboratories and similar places but no where else. 54 then there may come a day of such technological sophistication that there are no theoretical entities. (Of course, if electrons are observed when tables are seen, then there are also no theoretical entities, but this played no role in the discussion of that view.) While it is true that contemporary physicists maintain the impossibility in principle of ever observing an atomic or subatomic particle due to the Heisenberg Uncertainty

Principle, this consideration should not be brought to bear here; more important objections can be raised. The direct means by which something is studied. whether by aid of instruments or with the unaided senses, is not what distinguishes theoretical from non-theoretical entities. Achinstein has created a straw man. Both operationalists and positivists wanted to "reduce" all entities to their observational consequences, and this program may have influenced Achinstein. The correctness of their views will be discussed in subsequent sections. What they wanted to do was to eliminate all reference to entities which cannot be observed in principle. But what was at stake was perceptual principles and not technological sophistication in the case of positivists. For positivists, any entity, any thing as opposed to quality, is not observed.^ In the case

24 For a discussion of the issue see J. Passmore, A Hundred Years of Philosophy, (Baltimore: Penguin, 1968), or G. Bergmann, The Metaphysics of Logical Positivism, (New York: Longmans, Green, 1954). The point particularly goes against a positivist like Rudolph Carnap, The Logical Structure of the World, trans. Rolf A. Grouse, (Berkeley: University of California, 1963). 55 of operationalists, they wanted to eliminate any entity which could not be observed either by the unaided senses or by instru­ ments. Neither group saw the instrument versus unaided senses methods of observation as what distinguished between theoretical and non-theoretical entities. In short, Achinstein has to be dismissed because he does not consider the arguments of his opponents. What then accounts for the distinction? What counts is the role the entity plays in the model. Atomic and subatomic particles are the entities in the model, but tables and chairs are not in the model; they are rather physical objects used to interpret the model; for example, certain configurations of atoms are chairs. The geometric patterns gotten from electron microscopes are interpretations of the model. To be a theoretical entity is to be in the model.

The correctness of this view will come out in the following sections where the major attempts to interpret theoretical entities as being reducible solely to observable entities will be considered. For now, it is only important to see that Achinstein's view collapses because he takes verbal behavior as the key to the distinction when it is not. The reference of theories is the key. Discussion of positivists and operationalists will bring this out further.

1.7 Operationalism

Operationalists, like logical positivists, are concerned to eliminate from science any concept which lacks empirical 56

meaning. The method which operationalists use is to identify

the meaning of every noun employed in scientific discourse

with the procedures employed by scientists to verify the

existence of the referent of the noun, and to also identify

the meaning with the operations used in science to discover the

properties of the referent of the noun. This identification

leads to a curious feature of operationalist theories which

is reminiscent of some of the critical remarks directed

towards Achinstein in the previous section of the paper.

If the meaning of every name of an entity employed by science

is identified with the sceintific operations requisite for

investigating the entity, then unless the distinction between

theoretical and non-theoretical entities lies in the procedures

for investigating the kinds of entities, there is no such distinction. Every entity studies by science, at least in

recent times, is, on occasion, studied by means of instruments.

Hence, unless there is a difference in kind among instruments,

there is no distinction between theoretical and non-theoretical entities. (This, of course, presumes that the operationalist program is complete, and that every entity not amenable to an operational definition has been eliminated from science.)

It is not clear that operationalists sought this consequence; however, it is clear that they wished to remove from science entities which could not be measured. 57

Contemporary philosophers usually gleefully note that

metaphysics has no empirical consequences. Whether an absolute

idealism is employed or a neutral monism, for example, the

description of how the world appears to the senses is unchanged.

For this reason there is no empirical test which can decide

which of two competing metaphysics is the correct one. From

the operationalists point of view, all metaphysics are the

same since they lack observational consequences. The operation­ alist goal of specifying the meaning of a concept in terms of the physical operations required to measure the entities which are denoted by the concept would indicate that metaphysical concepts lack significance since they lack empirical content, and therefore an operational specification. The difficulty, is whether theoretical entities such as electrons are like metaphysical entities.

Certain experiments which have required an atomic hypothesis for explanation can be specified, and operational procedures for measuring theoretical entities can also be specified. But, is the meaning of "electron" fully elucidated once pointers on meters, diffraction patterns, cathode-anode, and so on are mentioned? One difficulty is technological sophistication. Planck's theory required that the value of

Boltzmann's constant, k, be equal to 4.69 x 10 electrostatic units, whereas experimental measurement gave the value 58

4.65 x if the operationalists were correct, scientists would accept the experimental value, but they do not; they accept the theoretical value. It would be strange to have experiments give concepts meaning but not give concepts numerical values. For any physical measurement there is always an experimental discrepancy between predicted values and empirical values. The discrepancy, under ideal conditions, is due to the technological inadequacy of the tools for measurement. If an alternative theory, a series of laws with a different model, were proposed which gave different predicted values, but ones still within the range of experimental error, operationalists would have to accept both theories; there would be no operationalist criterion to distinguish among them. Of course, if the operationalist were not too strict, non-operationalist criteria for the job could be introduced.

One of the main difficulties with the operationalist position is that it turns all routine properties into dispositional properties. Suppose that measurement of the velocity of a moving particle were made at different points in its path, then the operationalist, at best, could only speak of the particle’s velocity between those points as values that would be obtained

^Noble Lectures. Planck remarks that more recent experimental values agree better with the theoretical value. The values are within the range of experimental error from the theore­ tical value. From an operationalist point of view this should indicate that the theoretical value is close to the true value but not quite accurate. 59

if measurements were made. Thus, the quantitative value and

even the existence of a property between measurements is a

dispositional property of the entity. There can be no operation­

alist analysis of dispositional properties since to measure a

property is to give an actual value and not to measure what a

value would be Lf a measurement were made. Science talks

(mostly) of actual values of qualities and not possible values.

For the operationalist most values are possible, hence they

do not describe science as it is carried out. The correct

analysis of a problem related to that of the nature of

dispositional properties--the problem of counterfactual

conditionals— will be presented in the next chapter. The

problems are related because they both depend upon "what would

be the case." The key to the analysis will be the reference

theory outlined above.

Developments in twentieth century science have shown

that the behavior of atomic and subatomic particles between

measurements is not properly understood to be analogous to

the behavior of macroscopic entities between measurement.

This is the point of the Heisenberg uncertainty principle.

Here the operationalists seem to have won a point. However,

this may not be to their credit. If the uncertainty principle

is understood operationally, then it may be greatly distorted.

Operationally, the principle amounts to the claim that each measurement on the atomic level interfers with the measured 60

entity in such a way that the entity has some other property

which can no longer be measured. But this is wrong. Rather,

the atomic particle does not have determinate conjugate

properties. A complementary pair such as velocity/mass are

unlike specific properties which have determinate values and

which can be measured. They are, rather, properties which are

had with probabilities. Fhillip Frank maintains, for example, t that the solution to the complementarity problem is that since

the complementary properties cannot be precisely measured

together, that the properties are not precisely had together.26

Frank notwithstanding, operationally there is no difference between the measurement of one property interfering with the measurement of another, and two properties being held as a

function of each other since either view has the same measurable consequences. But one view is right— the latter, and one is wrong—

the former. Hence, operationalism has to be rejected since it cannot explain scientific practice.

How did the operationalists go wrong? Percy Bridgman remarks that it was the method explored by Einstein to defend relativity that he was trying to incorporate into all of science,27

^ The Philosophy of Science, (Englewood Cliffs, New Jersey: Prentice-Hall, 1957), Chapter 9, Section 2.

27ii^he Logic of Modern Physics," Readings in the Philosophy of Science, ed. H. Feigl and M. Broadbeck, (New York: Apleton- Century-Crofts, 1953). He comments that since position in space can only be measured

relative to a measuring device, there can be no absolute space;

Einstein was right and "Newton" was wrong. Since there is

no way of measuring an absolute position in space, there is

no absolute space. Can it really be that such a simple point

overthrows Newtonian Mechanics? It would be suspected that

classical scientists certainly thought that they were measuring

absolute motions. Indeed, the classical Newtonian measurements

are excellent since they are the limiting case for relativity

theory. Relativistic considerations in measurement are now

commonplace in physics, but that Einstein brought about

fundamental changes in mensuration theory does not imply that his results can be expanded into new areas. Bridgman further

remarks that if the meaning of concepts is limited to their

operational meaning, then new results will not surprise us

the way everyone was stunned by the new results in physics after Einstein and Planck. This is reminiscent of Descartes'

point that error only comes in when the appearances are judged

to be like reality; if judgments were restricted to appearances

only and not extended to that of which the appearances are

appearance, there would never be error. Similarly, for Bridgman,

if scientists dealt with only what they could measure, and would

not extrapolate to where measurements have not been taken, no

error would arise, physics would not be threatened by every new measurement. But also, as indicated above, physics could not 62 be carried on. If nothing at all would be permissible about the values of properties between measurements, there could be no laws, for laws cover all cases and not just the measured ones. In the model, an electron has a specific, determinate mass and velocity, even if they are probability values. Only occasionally are some of these given a physical test by means of experimental verification in a laboratory. But, if the tests are satisfactory, if a means is- given to physically interpret the model, then the particle has those physical properties at other times and not just when measured. In short, operationalism fails because it failed to distinguish between the occasional process which has to be done to give a physical interpretation to a model and how each concept in the model gets its interpretation, operations which give physical interpretation to the entire model and not only to some parts of it. Operational definitions can be given to some parts of the model, but once done successfully it gives empirical meaning to the whole model and not just to some parts. Thermodynamics is a good example of this: there configurations of atoms are given operational or observable interpretation but no individual atom has one. The average kinetic energy of the molecules in a gas is interpreted as the temperature of the gas but the average kinetic energy of an individual molecule lacks an interpretation since atoms lack temperature. By requiring that each part get a separate operational meaning Bridgman and his followers asked for too I

63

much and consequently failed. A solid empiricism requires

less than they required, and, therefore, rests on a surer footing.

Now attention can be turned to the most influential of the modern

commentary on science--the logical positivists.

1.8 Logical Positivism

Logical positivists, like their contemporaries, the

operationalists, wished to eliminate from science all that was not

empirical. The difficulty is that atomic particles such as

electrons were thought to be non-observable, since they are

introduced by theory and not observation. If atomic particles

are not observable, then they are not empirical, since, for most

positivists, to be empirical is to be observable or to be

constructed by means of definitions from the observable. Positivists

and neo-positivists have taken several different positions on this 28 problem. Some, such as Reichenbach, simply maintained that since

science requires electrons, they have to be empirical. Others, 29 30 31 such as Carnap, Ramsey, and Craig attempted to construct

languages for science which did not require any predicates which

refer to theoretical entities. Each of these views will be

28 "Are There Atoms?," The Structure of Scientific Thought, ed. E. Madden, (Boston: Houghton Mifflin, 1960) . 29 Logical Structure.... 30 The Foundation of Mathematics, ed. Braithwaitle, (London: Routledge and Kegan Paul, 1950), Chapter IX. 31 See I. Scheffler, The Anatomy..., Sections 20 and 21, for a thorough discussion of Ramsey and of Craig. 64 discussed in turn below. First, however, a discussion of some of

the ties between positivism and operationalism and their influence on the issue of discussion. l.ftl The Verifiability Criterion

For a positivist, a sentence is only properly included in science if it is meaningful, by which they mean verifiable. Here, unlike most critiques of positivism, a distinction between the demarcation line between science and nonscience on one hand, and the demarcation line between verifiable and non-verifiable will be drawn. Positivists held to two important theses on these subjects which even they did not always discriminate. They held to the

(true) thesis that science can be separated from nonscience on the basis that there are proper empirical procedures, relying only on experience and logic, for verifying scientific claims. Non- scientific claims lack empirical or observable consequences and hence cannot be so verified. There are hybrid claims which present only a partial problem. Consider 0^ 3 (M*02), where the 0- statements are observation statements and hence properly empirical, and the M-statement is not empirical, it, together with 0^, by the usual "logical" operations of "Modus Ponens and "simplification" yield O2, a properly empirical statement. The scare quotes indicate that the operations are nonformal since they lack a truth functional analysis on the assumption, which the positivists make, that non-empirical statements are neither true nor false.

(For similar reasons, the word 'proposition' has been avoided.) However, such statements can be eliminated on the grounds that a

well-formed part is non-empirical. The difficulty, which is

readily apparent, is the need for a test to distinguish empirical

from non-empirical statements. The verifiability criterion is used to provide a procedure by which this may be done. The second positivist thesis is the analysis of what it is to be verifiable in terms of a specific procedure which, if followed, will indicate whether or not the statement in.question is verifiable. Positivists presented "recipies" which if followed would verify (or falsify) any meaningful assertion since the recipe of procedure would trace any assertion to the observations upon which it depends.

Since the procedure is usually given in such a way that what posseses it is not only verifiable but true, the procedure amounts to a proposed solution to Hume's problem of induction. Of course, the proposed procedures were all failures. A detailed discussion of Hume’s problem will occur in Chapter Four, below.

1.82 Reductionism

Humean problems about induction plague positivists, such as

Carnap, who attempt to eliminate theoretical entities from scientific discourse by replacing reference to theoretical entities by a description of the phenomena which led to the introduction of the entity. The difficulty with any such phenomenalistlc program is that phenomenal acquaintance is considered incorrigible and hence a source of immediate knowledge, while things, even theoretical entities, can only be learned about, on the usual acquaintance 66 view, by inductive reasoning. Since Hume showed that there is no deductive relationship between the premises and conclusion of an inductive argument, any attempt to provide a philosophic analysis of a theoretical entity in terms of phenomena must lead to contingent claims and, consequently, to a systematically challengeable analysis. The relationship between definiens and definiendum cannot *be inductive. It is no wonder that positivistic attempts to eliminate theoretical entities by means of reduction sentences, protocol sentences, and the like have failed; logically 32 impossible goals cannot be achieved.

1.83 Ultra Empiricism

Hans Reichenbach takes a different positivistic position.

He argues that, since contemporary science requires entities such as electrons in order to explain various phenomena, they are real. However, this is not of philosophic importance for him. The philosophic issue is whether particles or waves are the fundamental characteristic of reality. He holds that since physics requires both interpretations in order to avoid the well-known causal anomolies in interference experiments, reality must be both. This seems contradictory, he maintains, only in a two-value logic.

Hence, the world must function according to a three-value logic in which this is not contradictory.

The question of philosophical interest is whether whatever

^ F o r a discussion of such sentences see I. Scheffler, The Anatomy.... 169-178. 67 science requires is ontologically real. It has been argued above

that this is not so. Science employs a descriptive language which has reference to models which, in turn, are given physical interpretation; they are useful for predicting and understanding physical events. Philosophers of science often confuse metaphysics simpliciter with the commitments of science, with what is required in the model. What is scientifically real need not be metaphysically real. It may be, but that requires a further argument. What has been maintained above is that models are useful tools, they are not metaphysical. A metaphysical analysis of the world may yield something like the model. Whether or not it will do so has not yet been argued and will not be argued in this paper.

Reichenbach takes sides with what he calls scientific philosophy against speculative philosophy. Why? The answer seems to be that it has worked, that science has risen and conquered.

Though this is undoubtedly true, there may still be areas of knowledge not covered by science. That there are is not the topic here; it would lead too far afield. Let it just be said that Reichenbach has not eliminated the possibility.

1.84 Fictionalism

The core of fictionalism is to translate theories which contain reference to theoretical entities into new theories which do not and at the same time have the new theories yield the same observable consequences as the old ones. Once this is done, there no longer need be philosophic worry about theoretical terms, for science can be carried on without them. Among those who have constructed such transformations are W. Craig and F. P.

Ramsey. Craig's suggestions amount to constructing a new

scientific language in which all the observational consequences of the old language are. axioms of the new language. Ramsey's suggestion is to replace all theoretical predicates, such as

"is an electron" by variables and then existentially quantify over all such variables. Either logical maneuver will give the desired results, but at considerable cost. The issue at stake is the role of models; scientists employ them. On the fictionalist thesis, models are eliminable since no reference to theoretical entities occurs in a reconstructed scientific language. That no one ever has been able to conduct science without models counts heavily against the program. Without the model, the intelligibility of the laws collapses. There is nothing by which it can be understood that regularities arise. There is no distinction between laws and any accidental generalizations.

Further, the process by which scientists are led into new investigations is independent of past discoveries; it becomes a psychological mystery. Models, as pointed out previously, handle these problems. By eliminating theoretical entities and then eliminating models from centrality in science, the old problems are re-introduced. 69

1.9 Symbolic Language

What is to be proved in this section is that the

Aristotelian-type logic discussed on these pages is consistent.

This is just to say that if we start with true premises, only

true conclusions will be obtained by the inference rules.

The procedure used here to prove the desired result is parasitic;

it will be proved that the valid arguments of the Aristotelian-

type logic all have analogues in a logic already proven to be 33 consistent, Irving Copi's RSI. Since RSI is consistent, so

is the Aristotelian-type logic, for all of the letter's

theorems are a proper subset of all of the theorems of RSI.

The key to the proof is the analogue.

The Aristotelian-type logic is just like RSI except that the first of these two logics contains an extra inference rule and a restriction on the rule of addition. The extra inference rule is

(R) Qx ... Px ... i- (3x)Px where 'P/ is an Aristotelian-type predicate (emphasis is only a notational way of distinguishing it from a PM type predicate),

'Qx' is any quantifier on the variable 'x', 'Px' is any atomic property bound by Qx, and ’...Px...' is any function which contains an occurrence of 'Px'. An illustration should prove useful; (R) will be used to prove AAI-1, an Aristotelian valid syllogism but one which is invalid in a PM type logic such as RSI.

^Symbolic Logic, 3rd ed. (New York: Macmillan, 1967). RSI is a system based upon one developed by Rosser. 70

(A) 1. (x) ( M joPx ) 2 . (x) ( Sx d Mx ) /.*. (3x)(Sx*Px) 3. (3x)Sx ~ 2,R since 'fix'is a (presumably) atomic predicate with a bound occurrence in 2/ h. Sx 3, El Sx d Mx 2, UI 6 . Hx d Fx 1, UI 7. Sx d Px 5,6, H.S. e. Px 7,h, M.P. 9. Sx*Px U,£, conj, 1 0 . (3x) (Sx'Px) f, eg

A defined predicate is nonatomic or molecular. For the purposes of this paper, the laws of physics employ parameters which are atomic for they are the properties of individual atoms in the model. All other scientifically employed predicates are molecular for they are defined in terms of the properties of individual atoms.

(R) necessitates a change in the rule of addition; namely that in

(x)Px W (x)Px v Qx where ' (x)Px' is any formula and where 'Qx1 is any formula containing predicates, there must be a prior occurrence of the atomic properties in 'Qx' or there must be guarantees that each such property has a non-empty extension. This amendment also leads to similar sorts of changes in other rules including

Reductio Ad Absurdum.

The analogue is constructed in the following way: (R) amounts to the possibility of adding as a premise to a given argument a proposition of the form '(3 x)Fx' for each atomic predicate 'F/ which has an occurrence in the premises of the 71 argument or occurs in the conclusion where there are (scientific) guarantees that the latter predicates have non-empty extensions, and these additional premises may be added without affecting the validity of the original argument. If all of these possibilities are taken advantage of, it would amount to the introduction of the conjunction.

(F) (3x) Fx*(3x) Fx* ... *(3x) fic where the 'I?*-1 exhaust all of the distinct atomic predicates of the argument. Now consider two sets of premises, one in RSI, a PM type of logic, and the other in the Aristotelian-type logic, but otherwise identical; then the latter but not the former logic allows for the introduction of a conjunction like

(F). The analogue of the Aristotelian argument in PM logic would be the PM argument with (F) added as a premise. Let us use AAI-1 as an example again. The PM type argument would be

(B) 1 . (x)Ctorx) 2. (x) ( Sx d Mx ) /.*.( 3x ) ( S x *Px) which is, of course, invalid.

The PM analogue of argument (A) is constructed by adding to (B) the (F) for (A), (F-A), which in PM notation is

(F-A) (3x)Mx*(3x) Px*(3x)Sx or

(C) 1. (x) (Mx d Px ) 2. (x) (Sx d Mx ) 3. (3x)Mx• (3x)Fx • (3x) Sx /*. (3x)(Sx*Px) 72

This argument, like the argument for which it is an analogue,

is valid. Any conclusion which may be drawn from the premises

of (A) which cannot be drawn from the premises of (B) is

done so because of (R), since it is the only rule in the logic

of (A) which is not in the logic of (B). Since (R) cannot add

more to the argument than (F-A), the premises of (C) will

yield a PM version on any conclusion which the premises of

(A) yield.

Since for every valid argument in Aristotelian-type

logic there is an analogous valid argument in PM type logic and

since PM type logic is consistent, the Aristotelian-type logic

developed on these pages is too. This completes the formal

development.

1.10 Summary

If scientific terms had empty extensions, Boolean

logic would apply. In such a logic, a generalization whose antecedent lacked reference would be true. Since there are no bodies moving in a vacuum outside of a gravitational field, it

/ would be true that "all bodies moving with a uniform velocity

in a vacuum outside a gravitational field are bodies which have

to be acted upon by an outside force in order for a change in velocity to occur." A scientist need only point out the lack of denotation of the antecedent of this universal statement

to prove its truth. The same holds in any language like that of Principia Mathematica. Since no scientist would accept such an argument, science must use a logic which presupposes that all non-logical terms have non-empty extensions, or at least that the undefined terms have non-empty extensions.

The terms of scientific discourse must then refer, but not to the perceived world for, as has just been illustrated, there are counter-examples to this claim. The terms have their extensions in models part of whose characteristics are coordinated with the perceived world from which arises a physical interpretation for the entire model. The distinction between laws and generali­ zations also involves models. It is the model which explains why the phenomena referred to by laws are so related. There is no such explanation for generalizations. Models, because they contain non-coordinated features and because they are metaphors, lead to further research because of attempts to extend the coordination or because of attempts to make analogies to phenomena previously understood in different ways or not understood at all. In short, models and the theoretical entities in them are one of the central features of science.

In what follows, models will be put to new philosophic uses in attempts to solve some old philosophic problems. CHAPTER TWO

COUNTERFACTUAL CONDITIONALS AND REFERENCE

The thesis of this chapter is that contrary to traditional views, counterfactual conditionals do not pose a counter­ example to the position that each term employed in scientific discourse has a non-empty extension. Further, the failure to recognize the correct view together with failure to grasp the use of counterfactuals has led to incorrect analysis of counterfactual conditionals. The use of counterfactuals is just to assert scientific laws with a special emphasis. The special emphasis is brought out by the employment of the subjunctive in the counterfactual conditional. The point that counterfactuals are just an alternative way of stating scientific laws is defended in part by appealing to Berkeley's view that things may be concepts or place holders for (other) things as a basketball may be used to represent the sun and a pea to represent the earth. The subject terms of counter­ factuals do not refer to the object which is nominally being discussed; it rather is a place holder for (other) things which do exhibit the property in discussion. Hence, the counterfactual is not counterfactual in reality but only seems so. The objects of actual reference have the property under discussion lawfully; hence counterfactuals are disguised statements

74 75

of lawful connection. Several alternative views are considered and rejected. Before the thesis is developed an account is

given of the interest in the problem.

2.1 The Problem of Counterfactuals

Counterfactuals are statements in the conditional form where apparently the antecedent is false but where if the antecedent were true so would be the consequent. There are

four main uses for them in science. Predictions can occur either in future tense or subjunctive mood. "If this copper is heated hot enough, it will glow." "If this copper were heated hot enough, it would glow." What are here called alternatives are sentences to illustrate an alternative to what has happened or to what is about to happen. "If this copper had been heated hot enough, it would now be glowing."

Alternatives state what would happen if some other course of action had been taken. Evaluations are related to post- dictions--"predictions" about the past— but are like the considerations a detective would make in order to reconstruct what happened from available evidence. "If the copper had been heated, it would now be glowing." Not all evaluations are counter to,the facts since the detection process eventually, hopefully, arrives at the true cause. In this case what appears

to be the final counterfactual is not at all even though it is stated in the subjunctive mood. "If New York were the largest * city in the U. S., it would say so in the almanac and so it does." 76

Nevertheless, since an evaluation is often speculative instead

of predictive, evaluations are not usually construable as

postdictions. The final main use of counterfactuals is in

thought experiments. These can be of three kinds. Ideal

experiments which could never be carried out. "If the sun

were suddenly removed from the solar system, the earth would

not feel the effects for more than five minutes." The second

kind of thought experiment concerns the treatment of the

influence of one property in isolation from others. "If the

mass of the earth were doubled, it would move out of its orbit

around the sun." The purpose of such experiments is to trace

out the influence of one property on a system of relationships.

The third sort of experiment speculates about the behavior of

an entity or system with unrealizeable, at least at present,

properties. "If a human and an ape mated, their offspring would be sterile." "If there were a metal with the hardness

of steel and the conductivity of copper, it would have an

extremely high melting point."

What all of these have in common is that the antecedent

of the conditional is patently false, or at least it is this kind of subjunctive conditional which prompts the philosophical

problem of interest on these pages. All of these conditionals can be put in a categorical form. "All metals which would have

the hardness of steel and the conductivity of copper are metals which would have an extremely high melting point." One of the main I

77

philosophic difficulties with such conditionals is the problem

of what they can be about since the point of asserting them is

that they are counterfactual; their antecedents are false.

The copper was not heated; there are no (known) metals with

the hardness of steel and the conductivity of copper.

Twentieth century logic since the publication of

Principia Mathematics has embraced the truth functional analysis

of logical connectives. Under this analysis, so it seems, any

conditional proposition is true just in case its antecedent is

false.^ So it would appear that any counterfactual would be

true.' Since the copper was not heated, "if the copper were

heated sufficiently, it would glow" is true but so is "if the

copper were heated sufficiently, it would not glow." Both of

these propositions are true independent of the truth values

of their consequents solely because their antecedents are false.

But, it is a well-established law that copper heated hot enough

glows so that the second of these two sentences expresses a

false proposition. Truth-functional analysis has proved to

be an extremely powerful and fruitful tool and it is not

surprising that logicians have been loath to give it up. Its

total lack of ability to correctly treat counterfactuals has

*See for example N. Goodman, "The Problem of Counterfactual Conditionals," Journal of Philosophy, XLIV (February, 1947). This essay is reprinted in Fact. Fiction and Forecast. 2nd ed., (Indianapolis: Bobbs-Merrill, 1965). 78

proved an embarrassment.2 To the first philosophic problem

with counterfactuals, their lack of amenability to truth-

functional analysis must also be added. This is a radical way

of characterizing the problem. Usually the difficulty is

presented as being with truth-functional analysis, here it

is presented as being with counterfactuals. The defense of

this proposal will occur in the next section.

There are two main philosophic puzzles about counter-

factual conditionals. (1) There seems to be nothing about

which they are. (2) Under the usual truth-functional analysis,

all counterfactuals are true, even those which are intuitively

false.

2.2 Truth-Functionalitv

Most logicians would distinguish between propositions

which contain logical connectives and those that do not. The

latter are atomic propositions and the former are molecular

propositions. A logical connective is, by illustration, that part of a proposition which is symbolized in notation by 'v',

's', '=', and so on. The truth functionality thesis is that the

truth value of a molecular proposition is solely a function of

the truth values of its constituent atomic propositions. This thesis can be broken down into several parts. Consider a typical

2 Difficulties with truth-functional analysis have usually focused on the (material) conditional. See for example C. I. Lewis and C. H. Langford, Symbolic Logic. (New York: Appleton-Century Crofts, 1932). 79 3 example of the classical argument form Modus Ponens.

(A) If this copper is heated, then this copper will expand,

(B) This copper is heated. (Therefore)

(C) This copper will expand.

Premise (B) seems identical to the antecedent of premise

(A). and the conclusion, (C), seems identical to the consequent of premise (A). The word 'seems' is important here because, for example, (B), is clearly a proposition while the antecedent of

(A) may not be. The antecedent of (A) is a constituent of the molecular proposition (A) but it is a philosophic view about logic that it, like (A), is also a proposition.^ One of the aspects of the truth functionality thesis is that it is. On this thesis the antecedent of (A) and (B) are one and the same atomic proposition.

(Of course, molecular propositions may have constituents which are also molecular propositions. In "if magnetized soft iron is heated

3 In what follows it is always assumed that modus ponens is a valid argument form. What is examined is the reason contemporary logicians use to explain this fact. A basic statement of the truth functionality thesis is given in L. Wittgenstein, Tractatus.... 4 The fact that a conditional is even symbolized as 'psq', suggests that the antecedent and consequent of the conditional are propositions in their own right since they are symbolized in the same way as propositions are symbolized. This is nothing to marvel at because the wide-spread use of the symbolism is due to one of the chief proponents of the truth functionality thesis, Bertrand Russell. Actually, the symbolism predates Russell. It was explicitly adopted by Peano at least ten years before the publication of Principia Mathematics. See the article on Peano in G. T. Kneebone, Mathematical Logic and the Foundations of Mathematics, (Princeton: Van Nostrand, 1963). 80 or rapped sharply, then the strength of its magnetic field will decrease" the antecedent, "magnetized soft iron is heated or rapped sharply," is also a molecular proposition.) The second aspect of the thesis is that the truth value of (A), a molecular proposition, solely depends upon the truth value of its atomic propositional parts, (B) and (C) . Even if it is granted that molecular propositions contain parts which are atomic propositions it may still be the case that other parts or the relations among the parts are also parameters of the truth value of the molecular propositions. For example, the logical words may have a meaning of their own independent of any of the propositions that they relate. Below it will be pointed out that for truth functionalists, the logical connectives get their meanings from the type of occurrences that they have in sentences; they summarize the truth relations of propositions. One possible alternative to this is that the connectives, or a least some of them, have a separate meaning so that once the truth values of the propositions in a molecular proposition are known, the truth value of the molecular proposition itself is not known. For the truth-functionalist, to determine the truth value of a molecular proposition, only the truth values of its constituent atomic propositions need to be known. The third aspect of the thesis is that every two atomic propositions are logically independent of each other and that some atomic propositions are true and some are false. This means that given the form of an atomic proposition, symbolized by a small letter, a substitution instance may be found which is true I

81

and one may be found which Is false. Further, for any finite

number of distinct atomic propositional forms, substitution

instances may be found to yield any possible combination of true

and false propositions. This point, which is often overlooked, is

curcial for guaranteeing any desired logically possible substitution

instances for the atomic proposition in an argument form, which

guarantee is required to "establish" truth tables for connectives.

One of the main problems with counterfactuals is that if

the results of the truth-functional analysis for the conditional

are applied to a counterfactual conditional, the counterfactual

gets the value "true" no matter what its consequent may be. "If

this piece of sugar were copper, it would be an elephant" is

true according to the truth table for the conditional since its

antecedent is "false". However, the application of truth-functional

analysis to counterfactual conditionals is inappropriate since

truth-functional analysis depends upon the assumption that a

molecular proposition, one with a logical connective, has, among

its constituents, atomic propositions. No counterfactual in the

subjunctive mood meets this condition. In the last illustrated

instance, "this piece of sugar were copper" does not seem to

express any proposition, much less a false one. Unless it is

first argued that counterfactuals have propositional parts, truth-

functional analysis is just not appropriate. In short, at least on

the surface of the matter, counterfactual conditionals are not the

sort of conditionals which fit a truth-functional analysis since

it is not obvious how a counterfactual conditional is analyzed into atomic propositions. The problem to be faced is the translation of counterfactual conditionals into indicative sentences where the asserted propositon becomes apparent.

If a subjunctive sentence is used to assert a proposition, to make an assertion, then there ought to be an indicative sentence which is usually used to make the same assertion since that is the usual employement of indicative sentences. The existence of such an indicative is also indicated by the fact that no atomic sentence is in the subjunctive mood or at least no part of a counterfactual (subjunctive) conditional which appears to be connected by the 'if..., then...' can be used as a sentence by itself, but an atomic part of a conditional in the indicative mood may be so used. There is at least this much difference between subjunctive conditionals and indicative conditionals, the ones normally analysed by means of truth- functional logic. As pointed out above "this piece of copper were heated" cannot be used as a sentence and hence it does not seem to be an assertion or proposition. If it were being related to another proposition by the "if..., then..." it would be a proposition. In short, it needs a translation into a form where it does appear to be a proposition before it can be accepted with assurance that counterfactuals are molecular "if..., then..." propositions. The translation will be presented in the next section. 83

2.3 Reference and Counterfactuals

The problem of the correct symbolization for counterfactuals

is Just the problem of finding a sentence in the indicative mood

which expresses the same proposition as the counterfactual of issue.

One possibility, which is to be rejected, is that the correct

sentence is the indicative sentence obtained by substituting

for the verbs in the subjunctive, the corresponding verbs in the

, indicative; namely, from "if this copper were heated sufficiently

it would glow," to the indicative sentence "if this copper i£

heated sufficiently it will glow." The latter sentence can, in

some contexts, express the subjunctive mood. That this possibility

exists has confused some philosophers and has led them to declare

that counterfactuals exist in the indicative mood, but they are

mistaken.^ The example here Is in the indicative mood. The

sentence seems to be an instance of the generalization "for any­

thing at all, if it is copper and heated sufficiently, it will

glow" where the universal quantifier is instantiated to 'this.'

Such an example suggests a puzzle closely related to those about

counterfactuals; namely, what is the meaning of the proposition

obtained from a true generalization by instantiating to an

individual for which the antecedent is false? Suppose that the

above example is symbolized by

(D) (x) [(Cx • Hx) D Gx ].

"*See the survey in E. F. Schneider, "Recent Discussions of Subjunctive Conditionals," The Review of Metaphysics, VI, (June, 1953), 623-647. If 't' refers to a piece of copper which is not heated and which

is not glowing, then

(E) (Ct • Ht) o Gt

is a true proposition since it has a false antecedent. It is not

a counterfactual since (E) is not asserted with the intention of

speculating on what the situation might be instead of what it is.

But like counterfactuals (E) is a true proposition about which it

is uncomfortable to say that it is true because its antecedent is

false. This second kind of perplexity indicates that scientific

laws, just like counterfactuals, fail to have a truth-functional

analysis. This suggests fruitfulness in an examination of the

relationship between counterfactuals and laws.

It has been traditionally maintained that only laws justify

counterfactuals, accidental generalizations do not.^ At first

blush this claim seems false. A typical accidental generalization

is ’'All the coins in my pocket are made of silver." Presumably,

though an explanation can be given of this phenomenon, there is

nothing about m£ pocket which requires that only silver coins be

in it. There is something about how those coins got in my pocket

which requires that only silver coins be in my pocket, but there

is nothing about the pocket itself which forces the requirement.

Such an explanation might be that when a purchase was made,

I lacked change, and I was given only quarters back. But such a

state of affairs would justify a counterfactual like "If this pen

^See I. Scheffler, The Anatomy.... Part III. 85

were a coin in my pocket it would be silver" if what is meant is

"if this pen had all of the properties of a coin in my pocket,

it would be silver". Presumably, being silver is not a necessary

property of "this", nevertheless that this is silver justifies

the counterfactual (counteridentical) "If that were this, it would

be silver." Hence a property need not be held necessarily, either

by logical or physical necessity, for there to be justifiable

, counterfactuals about it; identities justify counterfactuals. This

point will also serve for counterfactuals warranted by scientific

laws, "If this were an object governed by scientific law L, it

would exhibit behavior B." The object in question "standing in"

for an object governed by a particular law is the interest in a

counterfactual. The context indicates which law is in use.

"If £ had the properties of b^ _it would be governed by the

laws which govern V* or "If £ had the properties of t>, it

would be governed by the laws La which govern £" are the two kinds

of counterfactuals. In.both cases the pronoun "it" is a placemarker

for "a". That £ lacks the properties of Jb is not the issue for £

too is a placemarker. Geometers do geometry by using diagrams as

placemarkers for geometrical forms, logicians do logic by using

forms as placemarkers for propositions (statements), and scientists

do science by using some objects to stand for others. Geometric

truths are not about the diagrams, theorems of the logician are not

about the marks on the paper, and the truths of science are not

about "a, if it had t>'s properties but does not", they are rather

about b itself where a is a placemarker for 1>. Counterfactual 86

conditionals are then just an alternative way of stating a

generalization, usually a law thougi it may be accidental. "If

this piece of copper were heated, it would expand" is not simply

true of the piece of copper to which I am pointing, it is

true of all pieces of copper--if any of them were heated, they

would expand. It is this fact which suggests that the counter*

factual conditional is just another way of asserting the law,

but with a special, emphatic, emphasis. However, it has to

be remembered that only the context in which the counterfactual

occurs will determine which scientific law is being asserted.

Hence, in different contexts, two different, true counterfactuals will seem to contradict each other. "If this piece of copper were water, it would be liquid at room temperatures," where it

is intended that copper be governed by the laws which usually

govern water, and "if this piece of copper were water, it would be solid at room temperature," where it is intended

that water be governed by the laws which usually govern copper.

Since different laws are intended, the propositions do not

contradict each other, they are in fact logically independent.

The scientific law which has a substitution instance which gives the antecedent the truth-value 'false1 still has to be dealt with. If the thesis laid out in Chapter One is

followed, it is readily handled. Laws have their extension primarily in models. There the context does not occur. Put

in another way, scientific laws like counterfactuals are not 87

truth-functional. Just because its antecedent is false does

not make a law true; no scientist would accept it for that

reason. Hence truth-functional analysis does not handle

scientific statements.

How is it that one object can "stand in" for another?

There are a few cues to this in the history of philosophy but

the problem is closely related to the problem of concepts.

, Berkeley has a view which is very similar to the one defended on

these pages.^ He says, discussing Locke's notion of general

ideas, that one idea can stand for many things. Locke had

maintained that a general idea is had of a "thing" like

triangle. The general idea Is triangular and nothing else.

Hence it is neither right-angled, obtuse-angled, nor acute-

angled, its sides are of no determinate length, and so on.

Berkeley objected that such an idea is impossible; a thing

which was triangular and lacked all other properties could

not be imagined. Instead an idea of a particular triangle is

employed where no attention is placed on the properties peculiar

to that triangle; attention is only placed on its triangularity.

For Berkeley there is no distinction, usually, between a

physical object and an idea since the former is merely a

collection of the latter. Hence a physical object may be a

concept or may be used to prove the possession of a concept

Treatise Concerning the Principles of Human Knowledge which is reprinted in Berkeley Selections, ed. M. W. Calkins, (New York: Charles Scribner's Sons, 1929), pp. 99-217. !

88

if it is used to stsnd for a group of similar objects indifferently,

representing what they have in common and nothing else. So

triangularity can be discussed by means of wooden blocks. The

blocks, however, to make an original point, need not themselves

exhibit the property for which they stand.1 A familiar example

of such an employment is when, at a dinner table, the sugar

bowl is used to represent a building, the salt shaker a light

, pole, glasses parked cars, and the pepper shaker a car trying

to park. Such situations are quite familiar and operate on

the basis of an isomorphism between the relations of interest

among the items of the table setting and the relations among

the items for which the table setting stands. It is the

isomorphism between the relations which grounds the claim that,

say, the sugar bowl stands for a building or that the person has

control of the concept of parking. In the case of counterfactuals

the situation is more complicated due to the fact that scientific

laws have models for their extensions. Hence the physical

object, the copper not heated, stands for an object, heated

copper, in the model. The counterfactual is used to make

a point about a set of relations which hold in a model which has

a physical interpretation in a possible universe which is

distinct from the actual universe but which is governed by the

same scientific laws. That the same scientific laws hold in

this possible world indicates that the only thing emphasized

in the assertion of a counterfactual is the difference in initial conditions. A counterfactual enables the assertion of a law while emphasizing that the situation to which the law applies has different initial conditions from those found in the actual world. The subjunctive mood simply flags the law as having something special about its application. In this example it is the nonactual initial conditions--the

Initial conditions simply being the state of the world before the process described by the law in question was begun. The point of the subjunctive mood is just to warn the audience that the law is being applied to a situation which did not occur, or one which is not yet known to have occurred.

The problem of counterfactuals arises in modern philosophy because it seemed that a counterfactual always had a false antecedent and therefore no matter what its consequent might be, the counterfactual was true. It is now seen that the problem is due to a misapprehension of the fact described by the antecedent. In "if this copper were heated..." the copper

"of the antecedent," is nominally the unheated object before the observer, but the actual subject is copper in the model where the law "all heated copper..." is operative.^ Verbally the counterfactual mentions an object for which the antecedent is counterfactual but this is only verbally.. As has been

®Since models are the atomic structure of things, the model for a process would simply involve the atomic processes requisite for its occurrence. For this reason, the model for the law "all heated copper..." can be used to interpret the activity of any piece of copper. Hence the phrase "the actual subject is copper..." is used above. 90

argued above, the true referent is an entity in the model which

does obey the law required by the context in which the counter-

factual occurs and the sentence which is verbally a counter-

factual is thus in reality an assertion of a law. What in

English is usually claimed to be an expression of a counterfactual has been so claimed only because it seems to be one on its

English face, but analysis of such sentences as being counter

to the fact has led to grave problems. The solution is to

reject the grammatical structure of the sentence as providing

the key to its meaning. Logically the sentence is not a counterfactual but instead is an assertion of a scientific

law. It should not be surprising that some sentences have a logical use radically different from that which is suggested by their grammatical structure; examples such as rhetorical questions come to mind.^

^Other philosophers have held similar views. G. Ryle, of course, rejected their hypothetical nature. See his Concept of Mind. (London: Hutchinson and Company, 1949). R. Chisholm in his fundamental article, "The Contrary to Fact Conditional,11 Qiind, LV, (October, 1946)J cites C. F. Bradley and M. Weber as having held that counterfactuals are supported by ideal experiments. See their respective Principles of Logic, Vol. I, 2nd ed., (Oxford: Clarendon Press, 1922) and The Methodology of the Social Sciences. (Glencoe, Illinois: The Free Press, 1949). Chisholm in "Law Statements and Counterfactual Inference" Analysis. XV, (April, 1955) criticizes Bradley's claim that counterfactuals are ways of asserting scientific laws. Chisholm opts for the view that they presuppose laws. His views are criticized in detail in Section 2.6 below. He says that Bradley's claim is misleading for he who employs the counterfactual is not explicitly asserting a law. Since the counterfactual is the idiom for emphasizing a law, Chisholm is just mistaken. 91

2.4 Nothing Wrong View

In order to better appreciate the strength of the position

developed above, it is useful to examine some of the main

alternative analyses of counterfactuals prevalent in modern

philosophy. The first view to be discussed is that there is

nothing wrong with counterfactuals: They are among the

fundamental kinds of statements employed in science, and their

, analysis does not reduce them to instances of the other funda­

mental kinds. In the above analysis, counterfactuals are

argued to be instances of the assertion of scientific laws

which employ the notion of a placeholder and not to be properly

analysed by means of truth-functional considerations. This

view has an economy which lies in the point that once the

notions of law and placeholding are properly understood,

counterfactuals are also properly understood. Those who

claim that there is nothing wrong with counterfactuals are

maintaining that when all the other problems in the philosophy

of science are solved, the problem of counterfactuals no longer

remains. To this extent their proposal is not simple. The

objection to it is stronger than this, however.

Consider one paper defending the nothing wrong view,

"Counterfactual Conditions" by R. Brown and J. Walton, they

agree with some of what was said in the previous section, for

they too maintain that the evidence for a counterfactual is

also evidence for the general law, but they also maintain that counterfactuals do not assert general laws since the former

but not the latter are undecidable.10 What they mean by calling

counterfactuals "undecidable" is that a counterfactual presumes

that Its antecedent Is false but does not Imply It, and hence

there are no facts relevant to the issue of whether the counterfactual is 'true' or 'false'. Suppose, to use their example, the subjunctive "If this bear were a Kodiak, it would be brown," were asserted, this could be done even if the bear were a Kodiak and the person who made the assertion did not know it. Hence, to use what is a counterfactual does not imply

that its antecedent is false, since the counterfactual can be asserted when this is in no way known; rather, Brown and

Walton say, it is presupposed. The counterfactual may be employed even where the antecedent is true. Such a use was illustrated in Section 2.1 in the example of the reasoning of a detective. He makes counterfactuals to discover what did happen.

He rejects them one by one until he discovers the truth, and in that case the counterfactual has a true antecedent. But is he, or the man who talks about Kodiak bears, asserting genuine counterfactuals? What they seem to be doing is asserting a scientific law which might be applicable jif certain conditions held. The subjunctive indicates, here, puzzlement about whether the conditions hold. The detective uses counterfactuals to eliminate one by one all the kinds of bear that could be in

^"Counterfactual Conditionals," Mind. LXI, (April, 1952), pp. 222-233. front of him. He takes the bear before him and sees if it can

be a physical interpretation for the model of a Kodiak bear.

He wishes to assert a scientific law but is not sure whether

it applies to the bear in front of him; so the law is asserted

in the subjunctive. If the law does apply, its application

constitutes evidence that the bear is a Kodiak, but not

conclusive evidence. If the law fails to apply, it is

. conclusive evidence that the bear is not a Kodiak. If the

bear can be a physical interpretation for a Kodiak, if it

has all or most of the attributes lawfully linked with being *

a Kodiak, then the detective can conclude that the bear is a

Kodiak. Suppose that he becomes convinced that it is a Kodiak

but nevertheless tries one more experiment. Suppose now he

says "if it is a Kodiak, then it would be brown" even though

he is convinced that it is a Kodiak, what is the point of the

subjunctive mood? The mood indicates that a law is at stake.

To emphasize that, the subjunctive is used. It is much like

saying "look, every Kodiak is brown." Puzzlement is not the

only attitude which can be conveyed by means of the subjunctive,

emphasis can also be expressed. One lesson in all this is to

not rely heavily upon the grammatical structure of a sentence

to determine what the user of the sentence is asserting. Many

other things are also relevant. Brown and Walton have been led

astray by grammar. A second of their points is somewhat more interesting.

They claim that counterfactuals are not translatable into

indicative sentences because indicatives do not state "what

would be the case."H However, they do so state when the

Indicative is about a model which cannot be given a physical

interpretation in the present state of affairs in the world.

Two examples should clarify this point: First, a model may be

used to talk about what would happen if say, all the molecules

in the container of gas were to be concentrated in one. part

of the container. Indicatives can be employed to state the

quantum number of that situation, to state the existence of a vacuum in the other part of the container, and so on. A

second case is, perhaps, more familiar by now. Boyle's law

is about the relative proportions of pressure, volume, and

temperature of an ideal gas--one which does not physically exist. It is an indicative statement about what would be t the case if ideal gases existed, but they do not. However,

the model for Boyle's law can be given a physical interpretation

•^Their main points are "that the analysis of counter- factual conditionals must be such that it is physically impossible, or believed impossible, to decide them; that the evidence for counterfactual conditionals is evidence for general laws and the applicability of these laws, but that a counterfactual conditional is not a statement of a law or of initial conditions. Neither is it a conditional obtained from a law by substitution, nor the conjunction of such a conditional with the denial of its antecedent, for both of these would be decidable at once. Rather it states the validity of an inference, usually derived from a law, that can for practical reasons never be made. Since there are no facts to decide these inferences no general laws need describe them (p. 232)." 95

such that actual gases behave very much as the law states. Here,

Brown and Walton, like many other philosophers of science, are

misled by not sticking close enough to the actual procedures

employed by scientists.

The final argument employed in their paper in defense of

the "no problem" view is that counterfactuals are statements which

are inherently undecidable and that is their virtue. Since laws

are decidable, counterfactuals are not just different ways of

asserting a law. No argument is given to defend the undecidable

thesis so that it is hard to understand what is meant by it.

However, some remarks are pertinent. The thesis may amount to

the claim that only facts can be used to defend or attack a

scientific claim. Since the world is just the way it is and not

some other way, there are only facts about the way the world is,

there are none about the way the world "would be." A proposed

scientific law is true (false) if it is (is not) a statement of

the relationships which do hold among things. A counterfactual,

since it is counter to the facts, does not correspond to or state

the relationships among things, for it is about a state of affairs which is not actual; it is about what would be if the world were some other way than it is, or so the claim goes. Such a view, nevertheless, is over restrictive. Every logically

possible state of affairs which is not physically actualized can be studied by means of the patterns of behavior which exist in

that system. When counterfactuals are at issue, the patterns of behavior are given by laws which are usually well established for the 96 actual, logically possible, physical world. In the alternative, logically possible state o£ affairs, the initial conditions are different from the ones which obtain in this world. By "plugging in" those initial conditions Into the laws, what would happen if the world were different from what it actually is can be deductively deduced from the laws. There are no facts which correspond to either the initial conditions or the desired result, but confidence in the technique of deduction and the truth of the laws employed in the deduction alleviate that necessity, for the deduction does show what would happen if the initial state were different from the actual state and the same laws held. What is present here is, then, a model which is different from the model which is given a physical interpretation by objects in the physical world but a model in which the same laws apply.

The above discussion requires one slight amendment. The intlal conditions employed in the model are statements describing the properties of individuals and not the relations among them given by laws. They are, as such, statements like: "A has density d_," "IJ has volume " or "A is heavier than ]J." However, the conclusion deductively derived from such facts by means of laws need not be of the form of statements of a kind similar to initial conditions. With suitable laws one could not only derive whether A or B had the greater density but one could also derive other kinds of statements. For example, it could be derived that

Boyle's law holds for A and B. even though they have these initial conditions. For example, Newton derived the inverse square law 97

for gravitational attraction from, among other facts, the 12 gravitational attraction of the Earth on the moon. This suggests

an astronomical model in which the forces acting on various bodies

are given and the scientist deduces the law governing attraction

in that system.

Brown and Walton have given a vigorous defense of the claim

that counterfactuals are sui generis, that they are one of the basic kinds of scientific statements which cannot be reduced

to the other kinds of scientific statements. Their arguments are not the only arguments which could be employed to defend

the thesis, but that their strong arguments can be refuted indicates that there is weak support for the view. So it may be rejected. It is, however, important to note that they have been misled by just those things which led astray the typical discussion of counterfactuals; namely, too close reliance on the grammatical structure of counterfactuals and too much emphasis on truth- functional logic or failure to appreciate what scientific words are about.

12 A. Wolf, A History of Science. Technology, and Philosophy in the 16th and 17th Centuries. Vol. I, 2nd. ed., (New York: Harper Torchbooks, 1959), 150. Wolf quotes Newton as follows. "And the same year [1666] I began to think of gravity extending to the Orb of the Moon, and having found out how to estimate the force with which [a] globe revolving within a sphere presses the surface of the sphere from Kepler's Rule of the periodical times of the Planets...I deduced that the forces which keep the PlanetB in their Orbs must [be] reciprocally as the squares of their distances...." 98

2.5 The Classical Theory

The classical theory of counterfactuals is that a

counterfactual is supported by the possibility of producing a

derivation which has as its premises an indicative version of the •

antecedent of the counterfactual, scientific laws, and other single

facts or initial conditions, and which has as its conclusion an

indicative version of the consequent of the counterfactual. The

. theory is held by such divergent philosophers as R. Chisholm,^ 14 F. P. Ramsey. The theory will be elaborated below and it will be

argued that much of the view defended above is not in essential

disagreement with the classical theory even though the latter 15 goes wrong in some minor ways.

In order to understand the classical theory of counter­

factuals it is necessary to first understand the covering law model

for explanation since the classical theory analyzes counterfactuals

13 "Law Statements...." 14 The Foundations....

^Mention should perhaps be made of other people in the logical positivist tradition. Carnap is famous for the notion of reduction sentences which has been discussed in Chapter One. Since these are, in part, attempts to analyse dispositional statements and their analysis presents problems similar to that of analysing counterfactuals, discussions of counterfactuals often include Carnap’s program. Since it has been criticized above and some of the criticisms of the classical theory which follow also apply to that procedure, reduction sentences will not be further discussed. The criticism which is mirrored below is that the reduction sentence does not entail the sentence it is supposed to analyse and hence the two sentences cannot be different ways of saying the same thing.

I by means of this model for explanation. This model for explanation is best introduced by means of an example. Suppose it is desired to explain why the temperature of gas has increased, from -14°C to -13°C. The explanation proceeds by taking the parameters for the state of the gas before its increase in temperature, its initial pressure, volume, and temperature, the parameters for the state of the gas after the increase in temperature but not including the changed temperature, that is, its final pressure and volume, and then by means of the laws governing the relationship among the parameters, deducing the temperature change.

Initial Conditions

pressure before change, F^, 1 atmosphere

volume before change, Vj_, 1 liter

temperature before change, Tj_, 249° Absolute (-14°C)

pressure after change, 72, 1 atmosphere

volume after change, V 2, 1.004 liters

Covering (Scientific) Laws:

*1 V 1 “ P2 ^2 Ti T2

With these initial conditions and this scientific law, the observed result may be deduced. The law shows how the result could have been predicted and hence, it is claimed explains the 16 result. It could have been predicted prior to the actual occurrence that a gas whose behavior is described by Boyle's

law and which is expanded in volume from 1.000 liters to 1.004

liters while keeping its pressure constant would undergo a

temperature rise of 1°C., if its initial temperature is -14°C.

In its simplest form, then, in a covering law model explanation of the state of a parameter of a physical system after a change is given by means of scientific laws instantiated to the values of the other parameters of the system both before and after the change. In fact such an explanation may quickly become extremely complicated. For example, laws have to be introduced which correlate instrument readings with properties of the measured system. In the case of our gas, there is need, as example, for a set of laws which correlate an observed mark on a themometer with the temperature of the gas. Again there is a need for a set of laws which correlate perceptions with physical reality, for example, a set of laws which correlate the perceptions of the thermometer with the condition of the thermometer. In practice, this seemingly infinite extension of the model is not carried out; actual explanations are seldom carried on beyond the first stage outlined above. This is the covering law model for explanation.

In a typical counterfactual conditional, inference from

16 For a full statement of the theory see C. Hempel and F. Oppenheim, "Studies in the Logic of Explanation," Philosophy of Science. XV, (April, 1948). This view has been criticized by Feyerabend and others. See J. Passmore, A Hundred.... Chapter 20. the indicative version of the antecedent to the indicative version

of the consequent is invalid. Consider "If this gas at -14°C were

to expand from 1.000 unit volume to 1.004 unit volumes while

its pressure remained constant, then its temperature would rise 1°C

This gas at -14°C expands from 1.000 unit volumes to 1.004 unit volumes under constant pressure .*. This gas undergoes a temperature rise of 1°C.

is invalid. If the difficulties encountered in the first 1

section of chapter concerning finding an indicative version of a

subjunctive grammatical construction are waived, the classical

theorist point is easily granted— the subjunctive conditional does

not express a valid inference. The classical theorist's

point is that the inference may be made valid by turning it into

a covering law model explanation. All that need be added is

the requisite scientific laws and the missing initial conditions.

How to tell which law(s) are required is not stated by them, but

they may be granted the fruits of the discussion of this point in

Section 2.2. For the classical theorist, the subjunctive conditional is a summary, or shorthand way of alluding to a deduction which could be constructed according to the covering law model.

The previous sentence states that a deduction which is a covering law model explanation could be given for each counter- factual conditional. A scientist who asserts a counterfactual does not thereby assert that he has written down such a derivation.

Nor does such a scientist thereby assert that someone or other 102

has written down such a derivation. The scientist is merely

asserting that he could perform such a derivation. But this is

a minor point.

Of more concern is -that it is not at all apparent that

every counterfactual conditional follows the pattern. Consider

the counterfactual "If this gas were to change its volume} then

the ratio of the product of its pressure and volume before the change to its absolute temperature before the change would be equal to the ratio of the product of its pressure and volume after the change to its absolute temperature after the change."

This counterfactual is simply a way of stating that gases obey

Boyle's law. If that could be proven (verified) deductively, then there would be no need ever to experiment. If a deductive derivation of its consequent from its antecedent could be carried out, the law would be analytic. No scientist would, then, need go into the laboratory to prove it. He could prove it with pencil and paper and a good book on deductive logic.

But, alas, the need to experiment remains. It might be objected that the law could be derived from the more general gas laws and ultimately from the laws governing atomic and subatomic behavior. This is probably true, and if it is, the example can easily be reconstructed in terms of the more basic scientific laws.

It might also be objected that the derivation could be given by having as one premise, Boyle's law, and the same formula as conclusion. Though the argument is valid, in the usual sense, a derivation of a formula from itself is not epistemologically 103 enlightening. The derivation would hardly be an explanation.

Since not every scientific "If..., then..." can be reconstrued according to the covering law model of explanation and since not every counterfactual conditional can be so reconstructed, the classical view is incorrect.

But it may still be asked if the classical view gives a correct analyses of some counterfactuals. Such a case would have to be one where the laws were actual scientific laws and where the initial conditions can be realized even though they were not. This would correspond to a model as described above which lacked a physical interpretation. The actual physical object which was the nominal subject of the counterfactual would be a surrogate for some object in the model. Since the counter- factual would be true for any object at all, it would have the generality of a scientific law. Point to anything, and of that object it is true that if it were copper being heated, it would glow. The derivation in this particular case simply obscures the generality. Even if the derivation is given, it hides the fact that the same derivation can be given for any object. In short, the classical theory does not account for the general character of a counterfactual. But the classical theory is correct in pointing out how the scientific law demanded by the context in which the counterfactual occurs does make the counter- factual intelligible by providing a connection between the behavior mentioned in the antecedent and the behavior mentioned in the consequent. Unfortunately, it fails to point out that the 104

counterfactual is not just true of its nominal subject. This is

only brought out by the point that the counterfactual is just

another way of asserting the law. The classical theorists

have been misled by the apparent reference to a particular

object in the verbal construction of the counterfactual. They have

not realized that this object stands in for any object which is

subject to the scientific law in question.

2.6 Extensional Logic

Chisholm has pointed out that part of the difficulty of

treating counterfactuals by means of truth-functional logic is

that the logic is extensional while the counterfactual is

intensional.^ In extensional logic to say "every F is a G" is

merely to say that "each F is a G" but in an intensional logic

it is also to say that there is a connection between being an F

and being a G. Suppose that there are three things in my

pocket, 'a', 'b', and'c1, and that each of them are silver, let

'P* be the predicate "being in my pocket" and 'S' be the

predicate "being silver", then 'Px' is the proposition "x is in

my pocket" and'Sx' is the proposition "x is silver". 'Everything

in my pocket is silver* is symbolized as '(x)(Px3 Sx)'. In an

extensional logic this means that "each thing in my pocket is

silver" or '(Pa*Sa)•(Pb*Sb)»(Pc»Sc) 1 or perhaps r(Pa 3 Sa) ■

(PbD Sb)*(Pc3 Sc)'. Now the question "if d were in my pocket would

^"Law Statements...." See also J. D. O'Connor, "The Analysis of Conditional Sentences," M i n d . XLI, (July, 1951) i 105 it be silver?" is asked. If there is a connection between being in my pocket and being silver, the answer is clearly

"yes". But in an extensional logic the answer is not so apparent. If the extension of (x)(FxoSx) is a conjunction of

' 3 ' statements, one for each thing in the universe, then since 'Pd D S d 1 is true because it has a false antecedent, because 'Pd1 is false, the counterfactual is true. But on such an analysis every counterfactual is true since its extension consists of a conjunction of 1 D 1 statements each of which is true because each 1 o 1 statement has a false antecedent. This is how the problem of counterfactuals arose. If the extension is a conjunction of conjunctions, each of which states the new things, e.g. 'd', have the property of being in my pocket and of being silver, then every counterfactual is false since 'd' is not in the pocket, which is the point of the counterfactual.

The problem arises out of asking whether an observed correlation holds for some object without the requisite initial conditions, "if d were a P, would it also be an S".

If the point is merely that d is to have all the properties of a, b, and c, then already the answer is yes. This is to suppose that d is Btanding in for a, b, or c; that is, (d » a)v

(d “ b) v (d “ c). But if the question is rather "what if d were a new thing, would it be an S if it were a P?" then there is no way to answer the question in extensional logic since d 106

Is not a P. The question amounts to asking about a three- member universe: if each individual has the property of being an S if its a P, would a fourth thing in the universe also have this property? To say that everything in a three-member universe has the property is to say (Fa o Sa) • (Pb 3 Sb) •

(Pc z> Sc); if we now ask about d, there is no information available to decide the issue. In an extensional logic, to say everything has a property is just to say that each thing has it and nothing more. Hence to know that all but one thing has a property in no way helps deductively to decide the issue of whether the additional thing has it as well. This goes beyond the ability of the extensional logic.

In an intensional logic, a statement like "If something is a P, then it is an S" is true because there is a connection between being a P and being an S. The connection is there not because the sentence holds for each thing; rather it is the other way around: the sentence holds for each thing because the connection is there. Hence for any new thing, it is always the case that it is an S, if it is a P since there is a connection between being a P and being an S. Causal claims are intensional. If having the property C causes a thing to also have the property E, then the sentence "if something is a C, then it is an E" is not true simply because it holds for each thing in the universe, even though that it does so hold is epistemologically relevant to the claim-that the causal 107

sentence Is true. The sentence "If something is in my pocket,

then it is silver" is true of each thing now in the universe

even though it is not a causal claim. For something new in

the universe if it is not already silver, the placing of it

in my pocket will not make it silver since there is no

connection between being in my pocket and being silver.

An accidental generalization is a generalization of

✓ the form "All A's are B's" where there is no connection between

being an A and being a B. The problem of counterfactuals is,

in part, the problem of deciding which generalizations support

counterfactuals and which do not. An accidental generalization

does not support a counterfactual, but a lawful generalization

does. This view has been criticized above, and it will also

be criticized below. Some philosophers have claimed that

the distinction between accidental generalizations and,say,

lawful claims can be drawn on the ground that accidental

generalizations but not lawful ones mention particular places.

For example, "if something is in my pocket,...." The accidental

generalization is only true of a particular region in the

universe or of a particular span of time while a law is true

of any region of space or of any span of time. The way the

particular place enters the generalization is important, it

must be specifically mentioned in the statement of the

*"®See E. Nagel, The Structure of Science, (New York: Harcourt, Brace and World, 1961), Chapter 4, Section I. 108

generalization. If, for example, there la a lawful connection

between being a member of the species of birds A and having

no red feathers, then the sentence which expresses this

generalization does not stop expressing a scientific law

just because species A becomes extinct. That the law refers

to things which occupied only a small span of time in no

way vitiates the claim that the statement is a law. Contrast

, this law with the accidental generalization "All birds in

the species B lack red feathers" where there is genetic

evidence that red feathered B-birds could have arisen if the

species had not become extinct. Such evidence might consist

of the presence of a recessive gene for red feathers in some

of the birds but in such a low frequency that as a matter of

fact no birds were conceived with two of these genes and

hence no birds were born with red feathers. The generalization

"All members of species 1} lack red feathers" is not lawful

since there could have been counter instances but there just

were none. But the generalization does not mention that

It is true of only a certain geographic region or that it

is true of only a certain span of time. So the philosophers

who propose their criterion to distinguish between accidental

and lawful generalizations are mistaken. Lawful generalizations

support counterfactuals because counterfactuals are simply

other ways of stating laws. Accidental generalizations do not

support counterfactuals because the generalization is true 109 only because it holds for each individual while counterfactuals, like lawful generalizations, are not true simply because they hold for each individual; their logic is intensional. Accidental generalizations will support counterfactuals which depend upon counterfactual identities as explained above. But, if the purported counterfactual inferred from an accidental generali­ zation does not depend upon a counter identity, the generalization supports no counterfactual. This point will be explored below where consideration is given to the question of how to construe subjunctive statements about entities where it is not intended that the new entities be identical to any entity already in the extension of the generalization.

Extensional logic which dominates twentieth century views of logic was developed to handle the inferences which arise in mathematical arguments. It should not be surprising that such logic may not be adequate to handle the inferences which arise in the empirical sciences. The philosophical hope is that one logic will be useful in both the empirical and the mathematical sciences. That the logic of mathematical inference as developed in Principle Mathematics does not work for empirical science does not squash the hope. The problem has to be tackled from the opposite direction. A logic for the empirical sciences has to be developed and then applied to mathematics. In

Chapter One, it was argued that the logic of Principle Mathematics would not do for empirical science since empirical science 110

presupposed an extension for each term which it employed. The

logic developed there was extensional. The classical theory, as extended by Chisholm, argues that no extensional logic will handle scientific inferences. In view of the analysis of counterfactuals developed above it can now be seen that

Chisholm's point is unfair. No scientist asks the question whether a new thing in the universe has the property of the old things. This is a philosophical and not a scientific question. A scientist may ask if a new thing to be examined has the properties of things already examined, but logically speaking, the new thing to be examined is already in the universe. Only the philosophers ask questions about things not in the observed universe, things not in the model. It will be seen below that the philosophic question is queer indeed. So that the question of how evidence about new things affects our belief in previously accepted generalizations has to be treated as a scientific problem. New things to be considered follow lawful generalizations. They do so because all things follow lawful generalizations. Fart of the evidence that all things follow a particular lawful generalization is that all things examined up to now have followed that generali­ zation. The evidence is inductively related to the generalization.

From a generalization and a statement of how many things there are in the universe, the extensional form of the generali­ zation may be deductively derived. If the extension of the Ill

generalization has the same meaning as the generalization,

then it should be derivable from the extension. If it is not

derivable, then they have different meanings. If the premises

of an argument have the same meaning as its conclusion, then

the premises are derivable from the conclusion. For some

inferences, the premise may be deductively derived from

the conclusion. In such a case they are logically equivalent.

But this does not hold for a generalization and its extension.

To simplify matters, consider a universe with two members where (1), below, is a generalization, (2), below, is the

statement that exactly two things exist, and the conclusion of the argument is the extension of the generalization.

1. (x)(Fx3Gx)

2. (x)(x»a v x«*b)

3. FaoGa 1, UI

il. FtoGb I, UI

$. (FaoGa) *(Fb3Gb) 3/1* conj

But the inference from 5 to 1 and 2 is invalid since 5 clearly

does not entail 2. 5 does entail 2 3 1. However the converse

does not hold, 5 does not entail 1 3 2 . ^ Since 5 entails

2 3 1, if 5 entailed 1 3 2, it would also entail 2=1. The

inference from 5 to 1 3 2 is invalid,hence the inference from

5 to 2 i 1 is invalid. If 5 entailed 1 and 2, It would also ...

^ I t may easily be proven invalid in a three-membered universe. 112 entail 2=1. Since the inference from 5 to 2 = 1 is invalid, this is a second proof that 5 does not entail 1 and 2.

5 also does not entail 1 by itself since that would be a violation of universal generalization. The inference can be clearly shown to be invalid in any universe with more than two members.

Since these inferences are invalid, 5 cannot express all of the meaning of a generalization. Hence the extensional interpretation of a generalization is only a partial interpretation.

If a generalization and its extension were synonomous, then they would each imply the other. Since they do not, they cannot have the same meaning. The partial interpretation is adequate for use in providing models by which to prove invalidity of arguments but it is not adequate to deal with the issue of counterfactuals since the Inference from the extensional interpretation of the generalization to the generalization itself is deductively invalid. When it is asked of a non­ heated piece of copper whether it would expand if heated, the question is not: Suppose that the properties of this piece of copper when heated were added to the evidence about the generalization "all copper when heated expands" then would the generalization still hold? There is no way to answer the question except to argue inductively that the generalization is a scientific law and hence applies to anything which is a piece of copper. Put in other words, if this piece of non­ heated copper is construed as standing in for heated copper 113

In a scientific model, then clearly it would expand when heated for that is what heated copper does. But if the question is to be taken literally, if it is meant that a piece of copper is not to be taken as standing in for a heated piece of copper, then it is not clear at all what is being asked for to suppose that the piece were heated is to suppose that the piece were standing in for the heated piece of copper in the model.

The only evidence that can be brought to bear on the issue of the truth of a counterfactual is the evidence for - the scientific law which it expresses in an oblique way.

The evidence is, in the explicit case, a conjunction of instances. The causal law (x)(Fx o Gx) is inductively supported by evidence like (Fa • Ga) • (Fb • Gb) . . .

(Fn * Gn); i.e., each thing examined is both an F and a G, or perhaps evidence like (Fa d Ga) (Fb 3 Gb) . . . (Fn d G n ) ; i.e., each thing examined is a G if it is an F. Such a conjunction is also the extensional interpretation of the generalization. Chisholm and his followers seem to have been confused by the fact that the epistemological evidence for a law is identical to the extensional interpretation of the law so that deciding about the truth of a counterfactual has to be construed in terms of a derivation in extensional logic.

Since the counterfactual is not extensional but rather intensional, he and others become perplexed about its analysis. 114

(Chisholm, of course, is aware of this.) The classical theory

is put forth to provide a way of dealing with counterfactuals

in extensional logic. But the question of the meaning of a

counterfactual cannot be decided in that way for that is to misconstrue the English form of the sentence as its meaning.

The counterfactual expresses a law since the individual which it seems to be about in English is really just a place holder for something else in the model. If what it is about in English is construed as a new individual to be added to

the law's extensional equivalent, then the problem becomes trivial.

If the thing is added to the extension as a new name for an individual already treated in the extension, then the position is like the one defended in this essay but without any reasons to make the identification (which is "cheap" procedure). On

the other hand, if the individual is to be added to the extension, and then the generalization is to be deductively inferred from the extension, no counterfactual is supported since no extension entails its generalization. If it is allowed that the extension is to be used as inductive evidence for the generalization, then the issue is still not clear.

The new individual adds a fact to the extension. But there are no subjunctive states of affairs; so it is not evident how to use it to support the generalization. The only way to use it is to interpret it as an indicative. But this requires that the individual be construed as standing in for a member already present in the extension. 115

The only way to avoid the trivialization of the problem

is to construe the extension as being, on this issue, inductive

evidence for the generalization where the "new" individual

stands in for something already in the model. But once again

the counterfactual does not introduce a new fact; it merely

restates the generalization. The question of the truth, or

of the meaning, of the counterfactual is just the question of

. the truth, or the meaning, of the lawful generalization which

it asserts. The truth of a generalization is known by means

of inductive arguments. Before this can be proved, a paradox

about confirmation has to be considered. This will be done

in the next chapter. Induction itself will be considered in

Chapter Four. The semantics for scientific laws has already

been examined in the first chapter.

The problem of counterfactuals arises out of a mistaken

analysis of the extension of the terms employed in the English

expression of the counterfactual. Once the correct extension

has been made clear, it is seen that the issue is only made more

muddy by bringing extensional logic to bear on it. Extensional

interpretations have their usefulness, but not on this issue.

A counterfactual is expressed subJunetively to indicate a

special emphasis, to assert the law which it expresses in the

strongest possible way. Counterfactuals express laws. In

spite of the failure of counterfactuals to have a (correct)

analysis in extensional logic, the application of extensional logic to the problem has emphasized the issue of how evidence is used to support scientific laws. This issue will be explored in the remaining chapters. CHAPTER THREE

THE PARADOX OF CONFIRMATION

The paradox of confirmation la important in two quite different ways for this study. First, clarification of what leads to the paradox paves the way for a (partial) solution

to the problem of induction. Second, since the dissolution of the paradox requires the sort of logic developed in Chapter

O n e , it further shows the power of the ideas developed there.

In effect, it will be shown how a misconception about the extension of the terms employed in scientific discourse gave rise to the paradox. The present Chapter will develop a concise statement of the paradox in addition to a solution to the paradox. Some alternatives to the proposed solution will, of course, be considered.

3.1 Paradox of Confirmation

The Paradox is generated within the context of developing a purely formal theory of confirmation.^ The quest is to state

^For such formal developments see Carl Hempel's original paper "Studies in the Logic of Confirmation" Part I, M i n d , LIV (January, 1945), 1-26; Part II, 97-120. Hempel's development was stimulated by Janina Hosiasson-Lindenbaum's paper "On Confirmation," The Journal of Symbolic Logic, V (1940), 133-148, (see Hempel, p. 21, 22). Hempel's paper is an attack on the work of. Jean Nicod, especially Foundations of Geometry and Induction (New York: The

117 118

exactly how a statement like "(individual) a_ has (property)

F" affects the probability of a generalization such as "All

individuals of the same kind as £ have property F". The

study is formal and hence, for Hempel, the criteria are purely syntactical.* The traditional example of the generali­ zation is "All Ravens are Black". Hence the problem is to

find out which statements about individuals substantiate or confirm this generalization. The paradox arises in this way:

The Equivalence Condition is accepted. This condition states

that a given state of affairs confirms or disconfirms a generalization independent of how it is expressed. Interestingly, it does not matter whether the generalization is given in English,

French, German or any other language since they are all considered equivalent; they mean the same thing, that this raven is black confirms them all equally. But the condition applies to any

equivalent way of formulating the generalization, Hence any

proposition which is logically equivalent to the original

Humanities Press, 1950). Patrick Suppes has a formal development of the paradox in "A Bayesian Approach to the Paradoxes of Confirmation," Aspects of Inductive Logic, ed. J. Hintikka and P. Suppes, (Amsterdam: North Holland Publishing Co., 1966), 199-207. (Below this collection will be cited as Aspects.) An informal development of the paradox may be found in Nelson Goodman, Fact, 70.

^For the purpose here, two formal expressions are equivalent if the statement that they are materially equivalent is a tautology; if each can be transformed into the other by the used manipulative techniques. 119

generalization will also be equally confirmed (diaconfirmed) by a state of affairs which confirms (diaconfirms) the

original generalization. In a symbolic language of the IM

type:

(A) All ravens are black

is symbolized by

(B) (x) (Rx ^ Bx ) .

(B) is logically equivalent to

(C) (x) ( „ Bx>, Rx) or "All non-black things are nonravens".

The statement that this is a white piece of chalk confirms (C) since the chalk is both nonblack and nonraven.

Since (C) is logically equivalent to (B), a white piece of chalk confirms (B) as well by the equivalence condition. To put this formally, the sentence that this piece of chalk is white,

Wa • Ca which amounts to^

(D) w Ba . #v Ra • or "this is not black and this is not a raven", confirms both

(C) and (B). From this it may be inferred that a statement about ravens may be confirmed without ever looking at a raven, which is paradoxical. How can knowledge about ravens be gained

^The true generalizations "(x) (Wx D ~ Bx)" and "(x) (Cx o ~ Rx)" are implicitly employed here. Of course these are not empirical generalizations but their exact status is not of concern now. 120

by not examining any ravens? The Equivalence Condition allows

for the possibility but the Equivalence Condition seems

plausible.^ There must be a mistake somewhere, but where?

It is a paradox for it is a seemingly false conclusion. The

paradox has to be removed by showing that the equivalence

condition is mistaken, or by showing that (D) does not confirm

(C), or by showing that (D) does not allow for the confirmation

, of (B) unless some ravens are examined. The third approach

may be accomplished by showing that (A) is not merely about

ravens so that there is no paradox in allowing statements

about pieces of chalk and the like to confirm (B). As was

stated above, the Equivalence Condition is not to be attacked, or

at least only at last resort. Philosophers have taken both

of the other ways out. It shall be argued here that the second

way out, as it has appeared in the literature to be discussed,

is less plausible than the third way out which shall be opted

for below.^

The equivalence condition was proposed by Nicod, Foundations.... It is criticized by my advisor Charles Kielkopf "The Paradox of Confirmation and the Existential Import of A Propositions," (Columbus, Ohio: mimeograph, 1964). See p.]3>£f below.

^Among the articles which are in the tradition of the second way [(D) does not confirm (C) ] are: Israel Scheffler, The Anatomy of Inquiry. (New York: Alfred A. Knopf, 1963). G. H. Von Wright, The Logical Problem of Induction, 2nd rev. ed., (New York: Macmillan, 1957). And, Max Black, "Notes on the Paradoxes of Confirmation," Aspects. Among the articles advocating the third way [(A) is not merely about ravens ) is C. Hempel, Mind. LIV. See also Section 3.4 below. 3.2 The Paradox Dissolved

The paradox, as stated above, is that a proposition about ravens may be confirmed without our having ever examined any ravens. In part the paradox arises because (C) and (B) may be true in a FM type of logic if there are no ravens. Hence a PM type logic cannot be used in science. Indeed (B) cannot be the symbolization for (A) since (A) entails that there are ravens while (B) does not. Interpreting (A) in Boolean logic will also not do since a proposition like (A) is true in Boolean logic just in case there are no ravens. What is needed is a logic in which (A) may be analyzed and which requires that there are ravens. The Aristotelian type logic developed in

Chapter One is such a logic. The symbolization of (A) in this logic looks very much like (B).^ It is:

(E) (x) (Rx 3 B x ) .

But from (E), it follows that there are ravens. The expansion of (E) in an n. membered universe is

(F) (Ra 3 Ba) ■ ... • (Rn 3 Bn) * (Ra ^ .•• y Rn) *

(Ba v ... y Bn) •

Suppose that there are ravens as (F) requires. Suppose further that all the nonblack things have been examined. What color are the ravens? If all the.nonblack things are nonravens, the only

£ The reader should remember that bold face predicates are Aristotelian in that every bold face predicate has a non-empty extension. However, not every problem discussed in this chapter depends upon which symbolization is employed. Such non-dependent symbolizations will be noted. . 122

choice is that the ravens are themselves black. Since no raven has been found among the nonblack things, the ravens must be

among the black things. Hence, all ravens are black.

Nothing in the above requirement depends upon the logic developed in Chapter One, it might be argued. So this pulling away the veil of puzzlement from the conclusion of the paradox does not require the new Aristotelian type logic. However,

this is not quite true. If there is no supposition that there are ravens, the rest of the argument still follows in a PM

type logic since any generalization where the subject term has an empty extension will be true in a HI type logic. In short,

if no ravens are found among the nonblack objects, it follows

in a HI type logic that A is true. Why? Well, if there are ravens, then the only place they could be is among the black objects since they are not among the nonblack ones. But, if

there are no ravens then (A) is still true since (B) is true,

for its antecedent is false for every x. The Hi type logic

still allows for the possibility of confirming (A) without ever examining any ravens.? For the Aristotelian type logic,

7 Among the problems for which FM logic was developed is the one of denotation. In "On Denoting," Mind. XIV, (October, 1905), Russell seems to argue that the proposition 'The present king of France is bald' is true because there is no present king of France. But 'The present king of France is not bald' may also be true if it is not construed as the denial of the previous proposition but rather construed as the assertion that he has hair. There too Russell seems to have in mind that each is true because if the world were split into two piles, the bald and the nonbald, each could be confirmed by the failure to find the king in the pile where he would have to be if the 123

the move to showing that the ravens are among the black objects

since they are not among the nonblack ones cannot be made

unless there are ravens. In such a logic, a predicate cannot

be introduced unless it has a nonempty extension. The paradox

is eliminated because (A) cannot be confirmed without there o being guarantees that there are ravens. Once the symbolization

and equivalence have been drawn by means of the Aristotelian

type logic, it is Been that the conclusion of the paradox is

not false after all. (A) is not confirmed unless ravens are

examined.

But should (D) be considered at all when considering

(A)? Is (A) about ravens and no other things? Should

statements about chalk or other nonravens ever be considered

when confirming generalizations like (A)?

Consider what is usually taken to be a paradigm of an

inductive argument: it has a series of premises which state that

a large number of individuals of a certain kind, say ravens, also

have a certain property, say blackness, and its conclusion iB

that all things of that kind have the property. assertion were false. For example, the first proposition is true because the king is not located in the pile of nonbald entities. Perhaps, then, the paradox of confirmation has its origins in this early piece by Russell.

®The guarantees themselves would have to be spelled out. Sufficient guarantees would be actual observation or use as a parameter of the state equations. There may perhaps be others as well. But remember, if there are ravens (whose color has not been observed) and they are not among the nonblack things, they must be among the black ones. 124

(G) (1) Ra • Ba

(li) Rn • Bn

/\ (tn) (x) (Rx d Bx)9

Let It be taken for granted for the moment that 1 generalizations do inductively follow from such premises.

(m) does follow from (1) - (h) but only because it deductively follows from another generalization which does inductively follow from (1) - (h). The premises in (G) state that each thing examined is both a raven and black. Formally this is the only evidence. So the premises, in fact, inductively warrant a conclusion much stronger than (m). They warrant the conclusion

(H) (x) (Rx • Bx)'

If the only evidence is that everything examined is both a raven and black, then since the sample is intended to reflect the ' properties in the world as a whole, it must be that everything, anything at all, is a raven and black. A conclusion like (H) is in fact not drawn from premises like (1) - (h) because it is already known that (H) is false, but it could be drawn since

9Argument (G) and lines (H) and (I) below could occur in either PM notation or Aristotelian-type notation, see note 6 above. Among the standard works in the philosophy of science which employ the model are: David Hume.. Treatise.... Book I, Part III, Section VII; N. Goodman, Fact.... 23-74; and Rudolph Carnap, The Logical....

lOjust let 'h' be a sufficiently large number, so that the sample is large enough to warrant the generalization. 125

(1) - (h) is Che only stated evidence. Instead a conclusion like

(m) is drawn. (H) deductively implies (m), so (m) does

inductively follow from (1) - (h) but not in the way it is intended

if (G) is a paradigm of an enumerative inductive inference. What

this shows is that every correct inductive argument must use both

11 enumerative and eliminative techniques. What is needed is

additional evidence in the premises to exclude the conclusion (H).

. When the inductive paradigm is presented formally, it is readily

seen that the person using argument (G) is sneaking evidence

into the premises which is not stated. The problem is to state

the evidence. When this is done, the unstated evidence turns out

to be statements like (D). The paradox arises because (D) seems

irrelevant to the tenets of (A), but it will now be seen that

it is inductively required for the support of (A) [(m) ] instead

of (H).

The argument to follow for proving the need for

eliminative inductive techniques in addition to enumerative

depends upon construing any nomological relations between two

properties as analysable by one of the sixteen possible (two­

valued) truth functional connections. The evidence presented in

inductive arguments will be treated as confirming or disconfirming

* . all but one of the sixteen possibilities. In all but two of these

possibilities disconfirmation works by counter-example. The other

two work by induction. The deductive logic discussed on these

^But also see Steven Barker, Induction and Hypothesis, (Ithica, New York: Cornell University Press, 1957). 126

pages depends upon the assumption that any universally held

relation between two properties Is analysed by one of the sixteen

logical relations. Hence any evidence about the relation can be

analysed for its relevance in terms of the meaning of the logical

relation, the truth table. The evidence for the relation, if it

is universal, will be inconsistent with the distribution of values

in all but one of the sixteen truth tables. The correct

, inductive argument, in effect, selects the one remaining table by

inductively supporting the existence of that relation. The

argument is relevant to the paradox of confirmation because such

an Inductive argument requires the kind of evidence which the

paradox finds puzzling. Since the evidence is required, the

puzzle is removed.

A consideration of all possible truth tables for binary

connectives helps then to decide which truth function on two

properties is supported by evidence about the distribution of

those properties in the sample. The statements in the premises

reflect the distribution of two properties in a sample of things.

The size of the sample is h, where h is the number of instances

in the inductive arguemnt. There are sixteen different binary

connectives which can relate the truth functions 'Rx' and rBx*.

The evidence presented in the premises eliminates, presumably, all

but one of those connections. If the '0' in

(I) Rx 0 Bx

is a variable for connectives with 1,...,16 representing the

sixteen different binary connectives, then what the evidence in 127

TABLE 1

THE INCOMPATIBILITY TABLE*

Ra TTFF

Ba T F TF

Connective

1 i c c c

2 c i c c

3 c c i c

4 c c c i

5 i i c c

6 i c i c

7 i c c i

8 c i i c

9 c i c i

10 c c i i

11 i i i c

12 i i c i

13 i c i i

14 c i i i

15 i i i i

16 c c c c

*'i' means the evidence is inconsistent with that connective being the proper one in (I) and 'c' means that the evidence is consistent with that function being the one. 'i' and 'c' may also ' be interpreted as 'false1 and 'true1 respectively. The top row lists the instances of the sixteen truth functions. Hencef 'i' means that the evidence is not an actual instance (truth making) of the function while 'c* means that it is an actual instance. I.

128

(1) - (h) does is to support the claim that the proper number to

put into the 'O' in (I) is such and such. If the law to be

derived is nomological and not statistical, then, presumably, it

can be represented as the universal closure of one of the sixteen

truth functional relations among the two properties at issue. As

will be illustrated below, the positive evidence of the sort

presented in the paradigm (6) will disconfirm all but four

possibilities. Eliminative inductive techniques will now be

necessary to disconfirm all but one of these. The one remaining

is the relation which the evidence supports. If all possibilities

are eliminated, and a different but analogous procedure has to be

employed in such a case, then the relationship must be statistical.

The evidence presented in the premises of (G) is

consistent with functions 2, 3, 4, 8, 9, 10, 14 and 16, where 2

would give (m) and 14 would give (H). What is needed are premises

to eliminate all but one of these eight different possibilities

for the correct relationship between Rx and Bx. If (D), with a

suitable change of the name for the individual, is used as

evidence, then 4, 9, 10 and 14 are also eliminated leaving

2, 3, 8 and 16 as possibilities. 3 and 8 are eliminated by

evidence like Ra • Ba, for example, the existence of a black

automobile since it is black and not a raven. There remain only

two possibilities, 2 and 16. Every state of affairs is consistent

with 16. 16 is compatible with everything. Why, then, choose 2

over 16? 2 is incompatible with some states of affairs, ones which

make the function 'Rx'Bx* true. To decide between the functions, 129 it has to be that some state lacks an occurrence. If one state of affairs does not occur, then 16 cannot be the function. The preponderance of evidence in (G) is that the state of affairs

Ra*Ba does not occur. Hence 16 is eliminated inductively. The other 14 functions cannot be the case, but their elimination follows deductively from the offered evidence as an example consider the relation between (D) and, say, 14,

The conclusion of (G) is, of course, the denial of what would be the case if everything had truth function 14 between 'R' and 'B*. If the state of affairs which eliminates a possible function is the premise of an argument which has the denial of the universal quantification of that function as its conclusion, then the argument is valid. This can be proven by reduction methods.

This procedure also works for function 16 since the denial of its universal quantification is a contradiction.

What has been shown by this long discussion of the incompatibility table is that it is a mistake to claim that the existence of white sheets of paper, say, is irrelevant to (m).

Evidence like that is needed to eliminate all but one of the possible truth functional relations between being a raven and being black. Without such evidence, that generalization follows from the inductive evidence only because it is evidence for a much stronger generalization, (H), and (H) entails the generaliza­ tion in issue. The paradox is dissolved because it depends in part on the conmon sense conviction that the existence of white pieces of paper and the like are irrelevent to (m), but since it 130

is now seen to not be the case, such evidence is required.

Further it has been seen that only in a logic which required

that each predicate have an extension does it remain impossible

to verify (m) without ever examining any ravens. If there is

evidence that nothing is a raven, then in a logic such as PM,

it follows that all ravens are black. So in the logic commonly accepted, the paradox, in this sense, holds. To eliminate the possibility that (m) can be verified without ever examining any ravens, it is necessary to adopt the "newHlogic developed in Chapter One.

3.3 Existential Import

Carl Hempel was one of the first philosophers to give the paradoxes extensive treatment in print. In his classic article, "Studies in the Logic of Confirmation", he states that the paradoxes may be avoided in an Aristotelian logic. ^

Nevertheless, he provides what he considers compelling reasons to reject this way out. In what follows his reasons for allowing that there is an Aristotelian way out of the paradoxes and his reasons for rejecting it will be explored and criticized.

Hempel's discussion may be divided into two parts. The first part consists of his remarks directed againBt the symboli­ zation which he adopts to analyse Aristotelian logic. Since

l^Hempel (Mind. LIV) cites Ho siasson-Lindenbaum (The Journal of Symbolic Logic, V) as being the first to publish an attempted solution to the paradox. 131

the symbolism employed in these pages is far superior to his, it

will turn out that these objections may be dealt with easily.

The second, and more serious, set of objections can be construed

as being against any attempt to interpret scientific discourse

by means of an Aristotelian logic.

Hempel symbolizes (A) in the Aristotelian mode; my (E), as

' (K) (x) (Rx 3 Bx) • (3 x)Rx

. and its contrapositive (B) by

(L) (x) ( « B x > Rx) . ( 3 x) ~ Bx

He considers the four states of affairs

(Ma) Ra • Ba (Mb) Rb Bb (Me) « Rc • Be (Md) „ R d Bd

(where the subscripts on the M's indicate his labeling for the

states of affairs). (Md) serves as Hempel's version of (D) above.

He says of them that "Only [M]a might reasonably be said to confirm

...[ K ] and only [M]d is to confirm...[L ]." I believe he maintains

that this follows because only (Ma) confirms both conjuncts of (K)

and only (Md) confirms both conjuncts of (L). Unfortunately his

statement is too strong. (Ma), (Me), and (Md) all confirm, on some

pre-analytic concept of confirmation, the left conjuncts of both

(K) and (L). [(Mb) confirms the right conjunct of (L) but it

disconfirms the left conjunct so that we can ignore it. ] Presumably,

since (Ma) confirms both conjuncts of (K) while the other two

states of affairs only confirm the left conjunct, it confirms (K)

more in an intuitive sense of degrees of confirmation than they do. 132

A similar condition holds between (Md) and (L). So Hempel should

have expressed the Aristotelian way out in relative terms "(Ma)

confirms (K) more than the other states of affairs and so too for

(Md) and (Xj)." But since the other states of affairs also confirm

(K) and (L), the Aristotelian way out does not seem very attractive

as Hempel presents it. In fact it now reduces to the way out

adopted by Janla Hosiasson-Lindenbaum which will be discussed below

, in Section 3.4.

Hempel has gotten into difficulty here, in part, because he

tried to state the existential import of (A) in PM logic, a logic

without existential import. As a consequence he does this by

conjoining the PM symbolization of (A) to the PM symbolization for

the nonempty extension of its subject term. He correctly points out..

that such a symbolization does not in fact capture Aristotelian

logic since, for Aristotle, (A) and its contrapositive are logically * equivalent while (K) and (L) are not. (This is his criticism of the

program which depends upon his mistaken symbolization.^) There is,

however, a further mistake here. (L) is not a good symbolization

for the contrapositive of (A) even in PM logic. The point has to

do with the kind of predicates which have existential import. It

is related to the second of his objections to the program. It is

worthwhile to quote it in full.

*^See also P. F. Strawson, Introduction to Logical Theory. (London: University Paperbacks, 19630, Chapter 6; as well as Alan Hausman, "Strawson On the Tradition Logic," Inquiry. (Summer, 1969). 133

Second, the customary formulation of general hypotheses in empirical science clearly does not contain an existential clause, nor doeB it, as a rule, ever indirectly determine such a clause unambiguously. Thus, consider the hypothesis that if a person after receiving an injection of a certain test substance has a positive skin reaction, he has diptheria. Should we construe the existential clause here as referring to persons, to persons receiving the injection, or to persons who, upon receiving the injection, show a positive skin reaction? A more or less arbitrary decision has to be made; each of the possible decisions gives a different interpretation to the hypothesis, and none of them seems to be really implied by the latter. ^

To make the discussion clearer the following distinction is required. The distinction is between atomic and molecular properties. In 'Ra', 'R' is an atomic property of 'a* since the statement 'Ra1 involves no logical constants. In '~Ra', '~R' is a molecular property of 'a' since the statement '~Ra' involves a logical constant. Molecular properties are constructed out of atomic properties. The atomic properties are the variables of the state equations or are the ones employed in the model. The molecular properties are constructed out of them. 'Mass' and

'velocity' are atomic properties while 'density' and 'raven' are molecular. Existential import only holds for the atomic properties in a generalization. For example, from the left conjunct in (L), it follows that the properties 'B' and 'R' have non-empty extensions.

That a molecular property has an extension has to be derived. The derivation for many molecular properties is attainable in PM itself

1^Hempel, Mind. LIV, 16. 134

where '(x)Fx' entails '(3x)Fx.' If 'F' is a molecular property,

such as Mx is a B, if it is an R" then ' (3x)Fx' says that 'F* has a nonempty extension. Consider,

(w) (x) (y) (z) ( (Pw *Ixy *Tyz *Dz *Rwx) d ((3u) (Su *Fuz *Hwu) z>Hwz) ) which is the symbolization for Hempel's sentence about the diptheria test where the following holds:

Px -- x is a person Ixy -- x is an injection of y Dx -- x is diptheria Txy -- x is a test for y Sx -- x is a positive Rxy — x receives y skin test Fxy -- x is for y Hxy -- x has y it follows from this only that there is at least one person, case of diptheria, positive skin reaction, and acts of injection, testing, receiving, being for and having in the model. The instances of these properties and relations would have to be such that there are no laws, logical or scientific, operative in the model which would permit the derivation of a contradiction. The laws might allow for a derivation of a molecular property. For example, there might be a law which enables the derivation of the claim that at least one person has had the injection and so on.

In general, this would be the case since such a law would not be introduced into the model without some ^experimental basis and hence without the existence of a person in the model who actually had the test. If it is allowed that a law guarantees an instance of the molecular property in its antecedent, then difficulties immediately arise. Consider the law:

(Na) (x) ((Ax *Bx) 3 Cx) 135

which is logically equivalent to each of the following:

(Nb)(x)(Ax d (Bx d Cx )) (Ne) (x) (~Cxi>~(Ax *Bx ) )

(Nc) (x) ( Ax d (~Cx d ~Px ) ) (Nf) (x) ((Px*~Cx) d ~Ax )

(Nd) (x) ((Ax»~Cx) d~Px) (Ng) (x) (((Ax»Px) »~Cx)o ( Px*~Bx))

If each of these antecedents have an instance, then it would

follow that each of these consequents would also have an instance

since the generalization could be universally instantiated to the

, individual for which the antecedent has an instance and the

instance of the consequent could be derived by modus ponens.

This presents various problems, for example, the consequent of the

last of the logically equivalent formulas is a contradiction which,

presumably, lacks an instance. Further antecedents or consequents

can be constructed such that the molecular property which is

solely the negation of an atomic property occurs. From this it

may be derived that there is an individual which lacks any given

atomic property. It would follow from this that no property is

had by all things. This is an uncomfortable consequence. It

would seem strange indeed that it would be a logical consequence

that Newton was wrong in postulating that every physical object

had a mass. But this could be derived as examples (Nd), (Ne), and

(Nf) indicate. The alternative is that no sequence of laws can

f describe the behavior of all objects in the universe. For

example, Newton's laws would hold only for physical objects; non­

physical objects would not be scientifically describable. But if -

all of reality is to modeled in science, then this possibility

cannot be actual. Hempel's views on Existential Import lead to the conclusion that no property can be had by all things and this

follows logically. But, to summarize, it seems odd that it is

a logical consequence of a semantical theory that science cannot

incorporate all of reality into one model. To disprove the

possibility that all reality cannot be fit into a single model, it

is necessary to find a counter example to the claim that no

atomic property is had by everything. In a Newtonian physical

.■ model every object has a mass and a spatial position, but

not every object in a quantum mechanical model has these

properties. But every object in a quantum mechanical model has

associated with it a quantum number. No object lacks a quantum

number. Even macro objects have a quantum number for in a quantum

model their relations are only held with probability of almost one.

Perhaps this will do for a counter example.

The problem presented by the Hempelian conception of

existential import is like the problem of negative properties. If

I look at the table, I see an instance of the property brown; do I

also see an instance of the property nonred or do I "deduce" from

seeing that the table is brown that it is not red? In short, are

the properties nonred and brown the same kind of property or are

they different kinds of properties? Suppose that I list all the

properties which an object has, in the ordinary sense, do I

thereby know what the object is or do I have to also list all

the properties which it lacks7 Suppose that there is a color

that I have never seen, have I misapprehended the table because I

have not realized that it is not an instance of that color? To 137

give an affirmative answer to the last question is to commit ones'

self to holism with respect to properties. According to holism,

to be acquainted with an instance of one property is to be

acquainted with all other properties, for to recognize that an

object has a property is to recognize that it lacks all

properties incompatible with the property that it has. For

example, to recognize that the table is brown would be to

✓ recognize that it also has the properties nonred, nonblue, and so

on for all, other colors but brown and that it 1b also non-C#,

non-C^, and so on for all pitches, and so on for every kind of

property which an object must lack if it has a color.

It has to be kept in mind that the only issue is whether

a claim like "x is nonred" is an observation report or whether it

is derived from one. Holists argue the former, I argue the

latter in what follows. For some person who has not seen all

colors or heard all pitches it is not the case that he has

misapprehended the table because he does not realize that the

table is not an instance of a property which he has never apprehended.

This suggests that there is difference between being an instance

of an atomic property and being an instance of the negation of

an atomic property. The former may be revealed perceptually but

the latter may not be seen but rather only inferred from what

is seen.

This point is captured in the logical requirement that the * J nonempty extension of an atomic property follows from the

employment of the property in the statement of a scientific law, 138

while the nonempty extension of a molecular property does not

follow from such employment but that a molecular property has an

Instance must be deduced In some other way. In particular, a

molecular property may only be Introduced Into the model If there

are no laws which enable the derivation of a contradiction from

its introduction. To illustrate, take an example which Hempel

employs in an attempt to refute the claim that an Aristotelian

, logic is adequate for science. He asks us to

consider a biological hypothesis to the effect that whenever man and ape are crossed, the offspring will have such and such characteristics. This is a general hypothesis; it might be contemplated as a mere conjecture, or as a consequence of a broader genetic theory, other implications of which may already have been tested with positive results; but unquestionably the hypothesis does not imply an existential clause asserting that the contemplated kind of cross-breeding referred to will, at some time, actually take place.15

The last bit is, of course, correct, it only follows that there

are men and there are apes, if they are atomic properties in the *

model. But it must be remembered that in VK logic, with which

Hempel desires to solve the paradox, the truth of the conjecture

follows immediately from the fact that the cross-breeding does

not take place. The point here is that the conjecture is only

allowable if it can be modeled, if the man-ape can be modeled in

a model which the broader genetic theory governs. Models for

conjecture will not be, in general, scientific models for actual

ISHempel, Mind, LIV, 16. 139

reality. The final scientific model for our world may or may

not permit the conjecture. If it does, but the cross-breeding

never occurs, the model would have to be such that an accident of

history did not permit the cross-breeding. A conjecture is

interesting only if it can be given extension in an accepted

model, otherwise the conjecture is not offered with the intention

of asserting its truth and hence that it is a law; it is only a

• conjecture. But-the claim about the man-ape is more than a

conjecture since its properties follow from a well-established

genetic theory. It is only a conjecture in the sense that an

actual physical, man-ape has never been examined. It is a

conjecture like the one offered in the 19th century that there

is a planet beyond Jupiter because Newtonian mechanics predicts

it— given the irregularities in the orbit of Saturn. For the

conjecture to be true, the genetic model must contain a man-

ape with just those characteristics whose generation was

governed by genetic theory applied to the characteristics of

the parents. If it did, the conjecture would be true and the

model would contain a non-empty extension for the term 'man-ape1.

The only way such a conjecture could be proven false is if

later evidence showed that the genetic theory was itself false.

In any event, Hempel is just holding to a naive theory of

existential import.

It has to be remembered that in a logic with existential

import the thesis that every atomic predicate has a non-empty 140

extension is not an afterthought; it is an integral part of

the logic. An attempt to express the import in a PM logic

inevitably makes the existential assumption an afterthought.

(K) , for example, conjoins the symbolization for the generalization

to an existential clause. But in a logic with existential import,

the existence of at least one thing with the property follows

from the employment of a symbol for 'R' in the symbolization.

As noted below, that a property has an occurrence in a scientific

law and hence occurs in the symbolization for the law, shows

that the property has an instance in the model and therefore

that existential import holds. (K) can be derived from the

symbolization for the generalization in a logic which makes

the Aristotelian assumption and it is, in fact, logically

equivalent to the symbolization for the generalization in such

a logic, but then in such a logic since the formulas are

equivalent, there is no need to symbolize the generalization

by (K). In such a logic the existential conjunction is

superfluous, just as in a Ri logic *( 3 x) (Fx*Gx) 1 and 1( 3 x)

(Fx*Gx). ( 3 x) Fx 1 are logically equivalent and the second

conjunction in the latter formula is superfluous.

Hempel is also wrong in a second view of his about how

one might be led to the Aristotelian assumption'in an attempt

to eliminate the paradox. He says about the relevance of (Ma),

(Mb), (Me), and (Md) that: 141

the paradoxical character of the cases...may be said to grow out of the feeling that the hypothesis that all ravens are black is about ravens, and not about non-black things, nor about all things. The use of an existential clause was one attempt at expressing this presumed peculiarity of the hypothesis,16

Hempel rejects the claim that the generalization requires a

restricted field of application. He simply argues against it

by npting that it is not scientific practice to restrict the r field of application of a generalization. He fails, however,

to note a much more basic mistake in the program. The mistake

is akin to the one explored above that the usual paradigm for

an inductive argument is too weak since the evidence stated in

its premises in fact supports a much stronger claim than the

usual generalization in the conclusion. If the field of

application is restricted to ravens, then while it is true

that facts about non-ravens would be irrelevant to a generalization

with restricted application, it is still true that within the

field of application, if all ravens are black the correct

conclusion to be drawn is not one like (m) or (K) but rather

1(x) (Rx*Bx)', (H), for within that field of application

everything is a raven and everything is black. If the field

of application is widened to, say, birds, then the original

paradox arises once again since a white swan, for example,

will confirm the generalization. But as explained above, this

is what is to be expected. It is not paradoxical that this

occurs because evidence about nonravens and about nonblack .....

16Hempel, Mind, LIV, 17. 142

things is needed to eliminate an induction to a claim stronger

than the generalization.

To summarize the above discussion) a logic with

existential import does solve the paradox because it does

not permit the verification of a generalization like "all

ravens are black" without the examination of ravens since the

predicate "raven" cannot be introduced into the logic without

strong guarantees that it has a non-empty extension. Further,

the paradox itself only arises from the mistaken common sense i view that facts about nonblack things and nonravens are irrelevant

to the generalization. Such facts are relevant for without

them it would be possible to induce the conclusion that everything is a raven and everything is black. Since the paradox only arises because of this misconception of common sense, the paradox has been dissolved. But the formalist approach to inductive logic adopted by Hempel has proven its power for, without it, noticing that the usual paradigms for induction are illicit because not all the premises are stated

» . would have been extremely difficult. The formalization made the illicit introduction of evidence perspicuous.

3.4 Other Approaches

Hempel, among others, has taken a way out not too dissimilar to the one taken above but without realizing all of its implications. He points out that a generalization like

"Every R is B" does indeed apply to everything since, if it 143

Is true, nothing has the characteristic 'r ' without also having

the characteristic *B1. All objects may therefore be placed in

one of two classes, the class of objects which lack the

characteristic 'R' or the class of objects which have the

characteristic 'B1. To put this another way, one who asserts

"Every R is B" advances the hypothesis that the union of the

class whose members lack R with the class whose members have

, B is the universal class. Since every object falls into one.

or the other of these two classes, facts about anything at

all may confirm or disconfirm the generalization. So those

who accept the paradox are misled in their thinking that the

existence of things which are neither R nor B is irrelevant

to the truth of the generalization.

He illustrates his point by arguing that the paradox

seems only to arise if "extra information" is employed in

the inductive premise. The information is extra in the sense

that it is not explicitly stated in the premises. He asks us

to consider an experiment in support of the assertion "all

sodium salt burns yellow". The experiment consists of placing

a piece of pure ice in a colorless flame and observing that

it does not turn the flame yellow. Since the experiment confirms

the contrapositive of the assertion at issue, "Whatever does

not burn yellow is not sodium salt", by the equivalence condition

it also confirms the original assertion. Hempel argues that

this aeems paradoxical because we already know that pure ice 144

is not: a sodium salt. Since we already know that pure ice

contains no sodium, whether it burned yellow or not, it would

not disconfirm the original assertion. It is paradoxical to

confirm a generalization with an experiment which requires no risk since it cannot possibly disconfirm the original thesis.

But, Hempel argues, in such circumstances "we fail to observe

the 'methodological fiction', characteristic of every case of confirmation, that we have no relevant evidence for (hypothesis)

H other than that included in (premises) E. But, when an object is picked for the purpose of testing an hypothesis, it is picked, supposedly, at random. In short, there should be prior knowledge of the constitution of the object. If an object is picked, and it doet, not burn with a yellow flame, then if upon analysis it turns out to not contain a salt of sodium, Hempel asserts that there is nothing paradoxical about allowing this to be a confirming instance of the generalization.

Even if the object turns out, upon analysis, to be pure ice, there is no paradox. The paradox arises only when the knowledge that a piece of pure ice is being examined is allowed into the premises of the inductive argument prior to the burning test, or so he claims.

Nevertheless, in spite of this plausible presentation, conviction does not come. Suppose that a large number of objects are presented and each burns without a yellow flame....

17Hempel, Mind. LIV, 20. 145

and each, upon analysis, turns out to not be a sodium salt,

then in spite of considerable previous confirmation for the

generalization, it is not comforting since there is yet no

evidence that there are sodium salts (where the intention

is that sodium salts in the model will have a physical inter­

pretation). That is, both enumerative and eliminative induction

have to be employed. But in logic this does not matter,

for such a large sample without the presence of sodium salts

would indicate that there are none and if there are none, the

generalization is true. The paradox still arises even on

Hempel's way out.

A better approach to the difficulties inherent in the

paradox was presented by Hosiasson-Lindenbaum in her discussion

of the paradox which predates Hempel's.^-® Her approach has been followed by others who have held to divergent theories of

probability.^ Even though each presentation of the viewpoint has been embedded in a theory of probability, since the point against the paradox has been presented in the context of

several different theories of probability it should be able to

stand on its own. In spite of this, the approach of Patrick

Suppes shall be followed. For example Suppes takes her tack

l^See note 12 above.

l^Among these are H. G. Alexander, "The Paradoxes of Confirmation,11 British Journal for the Philosophy of Science, IX, (November, 1958), 227-233; and I. J. Good, "The Paradox ... . of Confirmation," British Journal for the Philosophy of Science. IX, (August, 1960), 145-149. 146

but employs a subjective probability theory.^ 0 His view shall

be examined since a subjective probability theory seems very

close to actual scientific practice.21 The basic consideration

is that since there are more nonblack things than ravens,

sampling a raven confirms (m) more than sampling a nonblack

thing does. The paradox is dissolved because evidence about

nonblack things does confirm the raven generalization but the

common sense objection is not entirely without merit since

such evidence confirms the generalization to a lesser extent

than evidence about ravens. Suppes asks us to consider the

prior probabilities that a given thing fall into a given one

of the four mutually exclusive classes (represented above by

the objects which fall into the four different possible states

of affairs in the confirmation table).

P( fx:Rx-Bxlf ) « p ±

P( ^x:Rx*«>Bx3r) “ P 2

P( ) B P 3

P( £ x :~Rx »~Bx ’}‘ ) =

where the sum of the p^ equals 1. And, he also asks us to assume

that for each p, p i* o. Then in our universe p^ should be much

larger than p^, since there are more nonraven nonblack things

than ravens. The prior probabilities represent the percentage

Bayesian...," Aspects.

^ F o r a background into, subjective theories of probability see: Studies in Subjective Probability, ed. H. Kyburg and H. Smokier, (New York: John Wiley and Sons, 1964). , 147

of the total population found in each of the four disjoint

classes. The probabilities that things are ravens or black is

represented by the respective formulas

P( £ x :Rx J ) “ Pi + P2

P( { x : E x ^ ) = p1 +

and hence

P( B | R) - Pi/Pi+P2

• and

p (~r |~b ) =

Now the point of all this is to justify the presumption that

greater degrees of confirmation are obtained by examining R's

than by examining B's or the assumption that P(B|R)< P(~R|Bv B);

that is, if the probability that something is black given that

it is a raven is less than the probability that something is not

a raven given that it is not black. Given the above equations,

this amounts to the inequality pi . pu PJ. + P2 < P2 + Pj,

which holds if and only if

Pi < Pk

This last inequality is the assertion that there are fewer black

ravens than nonblack nonravens and hence fewer black ravens than

nonblack things in general. So it is a consequence of this

arithmetical relationship that the probability that something is

black given that it is a raven is less than the probability that 148

something is not a raven given that it is nonblack. In fact with the numerical assignments employed by Suppes to illustrate the point,

the following results are obtained.

P( b |r ) “ 0.909,090,9

when

Pl = 10"6

P2 = IQ"7

P3 “ io“4

P4 - 1-10"4-10"6-10'7

He points out that, in this example, F(-/r(''B) is so high that, under usual circumstances, it would be more efficient to raise the prior, subjective, probability of P(B/R). Since the numerical assignments to p^ - are subjective, I would like to offer a different set. Since the existence of any members in the set

£c:Rx*'uBx3 would reduce the probability of (m) to zero, the subjective prior probability that there would be anything at all in this set has to be smaller than p^ by more than a factor of 10, as in Suppes1 example. In the long run, according to Subjectivists, whatever prior probabilities are initially adopted will not matter for with increasing evidence the calculated probabilities will approach the actual frequency of distribution. Nevertheless, it is illuminating to see what is the probability that something is black given that it is a raven when reasonable subjective prior probabilities are assigned. In this example leave p^ and p^ 149

unchanged and assign P2 the value 10 ^ and adjust accordingly. -4 Now p^ is greater than p2 by a factor of 10 which agrees much

better with the supposition that there are no nonblack ravens.

Under these circumstances

P(B/R) =0.999900009999...

In fact as more evidence accumulates the size of P2 becomes

vanishingly small and after not much evidence at all it becomes

. zero. At this point

P(B|R) = 1

or at least it can be made as close to 1 as desirable.

Suppes finds his example artificial, not on the grounds

presented above but rather on the ground that almost anything I counts as confirming that something is a nonraven given that it

is nonblack. As he puts it even nonblack thoughts add confirmation.

Actual scientific practice does not allow for such a wide variety

of trivial confirmations to be introduced. The scientist limits

the actual range of objects which he introduces. In such a case

p^ is not so close to one in value and P(*»r |^B) is far enough

away from one in value to make consideration of raising its value

worthwhile. In fact Suppes contrived a plausible example where

it is more efficient to try to raise its value than to raise the

value of P(B)R) where it is desired to confirm a generalization

of the form "All R are B".

Hempel criticizes this approach because the ability to

get relative frequency probability assignments depends upon the

fact that there are a finite number of ravens in the universe, 150 22 otherwise a probability cannot be assigned to p^. He suggests

that if the scientific language be modified so that it is now

incidences of ravens occupying places at moments that are what

we count, that is, space-time points containing ravens, then since

the cardinality of the set of all such moments is of the order of

the continuum as is the cardinality of the set of all other

places, there is no longer any advantage to examing black

■ ravens rather than examining nonblack nonravens. The ability to

generate the kinds of probabilities which Suppes used to remove

the paradox are not available in a language in which there are

as many ways to raise p^ as there are to raise p^. In such a

language, assuming P2 to be zero, P]_ = P 3 = P4* So Suppes1 program

is not very general; the paradoxes can be regenerated simply by

describing our world with a different language. Even though

Hempel would not push the scientist and Suppes to support using

his language as opposed to their language, rationale for

preferring one language to another will be taken up in the last

section. There Nelson Goodman's new problem of induction will

be examined for it too raises the question of the defense for a

preference for one language as opposed to another. For now, let

it just be said that the Suppes-like retort to the paradox does

recognize that sentences other than those like (Ma) confirm (m)

and in the usual circumstances, nevertheless, sentences like this

add more confirmation to (m) than sentences like (Me) and (Md).

^2His argument was, of course, against Hosiasson- Lindenbaum, see M i n d , LIV, 21, n2. /

151

Since the latter holds, in usual circumstances, it is more

expeditious to examine reavens for blackness than to examine

nonblack things for nonravenhood. However, this approach still

does not recognize that sentences like (Me) and (Md) have to be

presented in order to defend the claim that truth function 2 holds

between being and 'R1 and being a 'B1 and that no other truth

function does so hold. The Suppes-like approach recognizes that

sentences other than those like (Ma) may be examined in order to

confirm (m) contrary to the paradox, but the approach does not

recognize that such facts must be examined in order to confirm (m).

The Suppes-like approach defends a weakened version of this: in

usual circumstances, sentences like (Ma) give more confirmation to

(m) than other kinds of sentences. Thus in usual circumstances,

in order to confirm (m) quickly, seek out information like that

stated in (Ma). Since the paradox only arises with the stronger

common-sense presumption, the Suppes-like approach does remove it.

Another attack on the paradox comes from challenging the

equivalence condition since no one theory of confirmation has

received wide-spread agreement. At this stage of the development

of the theory of confirmation, it is only a highly plausible

conjecture for parts of the theory have to be modified. If it is

refuted or modified as such not much of the theory of confirmation

will have to be changed. So not much is lost by giving it up. What

is lost, in a scientific context is that once a statement is

confirmed, a scientist may not employ any logically equivalent

version of the statement because, without the equivalence 152

condition, it does not follow that the equivalent statement has also

been confirmed. Each logically equivalent version of the statement

will have to be confirmed separately. This is an extremely high

price to pay but, below, a version of the equivalence condition will

be presented which avoids the paradox and for which this price does

not have to be paid. If the equivalence condition can be weakened

sufficiently to prevent the generation of the paradox but kept

strong enough to avoid paying the above mentioned price, Nicod's version of the equivalence condition is not such a central part of confirmation theory to make keeping it desirable.

An analogy employed by Charles Kielkopf is suggestive.

a truth table array which justifies us in saying that P is a tautology may be of no help in justifying our claim that Q is a tautology but of course all tautologies are logically equivalent.^3

His point is that "Truth table array A justifies the claim that

P is a tautology" provides an intentional context for *P', one where it is not possible always to substitute a logically equivalent expression for 'P' and preserve the truth value of the entire claim. Since some valuation concepts provide intentional contexts, there is the possibility that the concept of confirmation

is such a valuation concept.

Consider the formula

(P) pv~p

It can be proven to be a tautology by the truth table method....

23»ihe Paradox..." Professor Kielkopf is ray advisor on this work. I

153

This formula is logically equivalent to

(Q) (PV~P) v (P-P2 *P3'-"-Pl,000,000>

which has 1,000,000 distinct propositional signs and hence, if

its truth table were constructed would have 2X rows, which is too

large for anyone to construct. But the two propositions may be

easily proved to be logically equivalent by transforming each into

the other by the usual techniques. Since the formulas are

,• logically equivalent and (P) is a tautology, (Q) is also a

tautology. The truth table for (P) is used to defend the claim

that (Q) is a tautology because it is proved the (P) and (Q) are

logically equivalent. But the truth table by itself does not

prove that (Q) is a tautology, the proof that (P) and (Q) are

logically equivalent is also required.

Such a program applies also to the paradoxes of confirmation.

(Md) is evidence for (C). But if (C) is confirmed then (m) is

also since they are logically equivalent. The evidence for (m)

is not (Md) by itself but rather (Md) and the proof that (m) and

(C) are logically equivalent. This is analogous to the former

case where the truth table by itself was not evidence that (Q)

is a tautology, but rather the truth table plus the proof that (P)

and (Q) are logically equivalent was the adequate evidence that

(Q) is a tautology. That a given proposition is confirmed can be

proven by showing that it is logically.equivalent to a previously

confirmed proposition. The evidence that the given proposition is -

confirmed consists of both the (true) sentences which confirm the

other proposition and the proof that they are logically equivalent. 154

Put in another way, sentences like (Md) confirm (m) only when

coupled with the equivalence condition, neither (Md) nor the

equivalence condition by themselves confirm (m) but their

conjunction does.

The paradox itself still stands since (Md) can be used

to confirm(m); the previous discussion is still needed to remove

the paradox. But much of the perplexing nature of the paradox

. has been removed since (Md) alone cannot add confirmation to (m).

The final perplexity is removed once it is seen that (Md) is

required to confirm (m) since without sentences like (Md) the

obviously false statement (H) would be confirmed. The weakened

form of the equivalence condition not only removes much of the

perplexity but there is no need to pay a high price for its

adoption. To see this, examine the formal statement of the

weakened equivalence condition.

If evidence E confirms statement S to degree D, then if S and S' are logically equivalent, then S' is confirmed to degree D.

Note that, unlike the equivalence condition offered by Nicod

and discussed by Hempel, it does not require that the evidence for

S also be evidence for S'. Once this evidence relation is

removed, much of the puzzle is removed because the evidence

requires argumentation before it can confirm S': The argumentation

comes with the proof that S and S' are logically equivalent. But

an Aristotelian-type logic is still required in order to avoid the

possibility of confirming a generalization which has an antecedent 155

with a vacuous extension.

3.5 Choosing a Language

Previously there was mentioned a Hempelian attack upon

the Suppes-type way out from the paradox of confirmation. Hempel1

attack involves adopting a scientific vocabulary other than the

one which is normally employed. The new scientific vocabulary

takes as primitive instances of space-time points. (In such a

language, the location of these points are atomic properties.)

Since a finite number of objects will occupy during their history a set of (such) points of cardinality equal to that of the continuum, probability considerations cannot be used to analyse

their distribution. With such a language the Suppes-type approach

to the paradoxes collapses.

Another philosophical problem which is engendered by

language considerations is Nelson Goodman's "New Problem of

Induction". Goodman introduces the predicates 'Grue' and 'Bleen

x is Grue if and only if x is green before time t^ and x is blue at and after time t^

x is Bleen if and only if x is blue before time t^ and x is green at and after time t^

(For ' tj_' any appropriate date remotely in the future may be substituted. Often the date is the year '2000'.) Of a green emerald he asks: It is green now but what color will it have in

the year 2000? If it is green now and in the year 2000, the

24Fact,. 156

emerald has Che ordinary property green. But If the emerald

turns blue In the year 2000, It has this new property grue. If

there Is abundant evidence that every emerald In a collection is

now green, there seems to be no way of deciding whether.they will

be blue or green in 2001. The evidence that they are now green

is compatable with either outcome, so it cannot be used to

distinguish between them. What the example raises is the problem

, of the kind of predicates with which observation or science deals.

Part of the point is that with the new kind of predicate, any

outcome in the future is consistent with the inductive evidence

so that the problem of induction cannot be just one of finding

regularities. Since any outcome in the future is consistent with

the existence of regularities, the problem of induction is not to

prove that there are regularities. Goodman calls this the problem

of projection: Which predicates may be projected as being held

by an object in the future given that the object now has them?

Goodman quickly dismisses the attempt to settle his quest

in favor of the traditional green/blue predicate on the gound

that the definition of 'grue1 and 'bleen' involve a temporal .

reference. He does this by pointing out that 'grue' and 'bleen'

can be taken as primitive observational predicates and 'green'

and 'blue1 defined in terms of them.

X is green if and only if x is grue before time and x is bleen at and after time t^

X is blue if and only if x is bleen before time t^ and x is grue at and after time t^ 157

In effect, a choice has to be made now between competing

descriptive languages without knowing which of incompatible

observational inferences are true. If the usual language is

employed, the emerald will be green in 2001; if Goodman's new

language is employed, the emerald will be blue in 2001. Hence

the decision has to be made in terms of the languages themselves and not the veracity of their competing observational reports.

The problem can be made perspicuous in another way.

Consider the following two inductive arguments with incompatible conclusions.

emerald 1 is green at tQ emerald 2 is green at tQ

emerald n Is green at tn / .*. all emeralds are green

emerald 1 is green at tQ

4 emerald n is green at t^ /.*. all emeralds are grue

The conclusions are incompatible because the first one entails that emerald 1 will be green at t^ while the latter conclusion entails that it will be blue (assuming that tQ is earlier than t^). Since both arguments have the same premises, one has to be incorrect. But which one is illicit? The first is illicit if the property green is not projectable while the second 158

Is illicit if the property grue is not projectable. The difference between the arguments cannot lie with the evidence since they both depend upon the same evidence. The only difference lies in that one of the predicates, green or grue, is ''queer", is not projectable, is not subject to inductive inference. The decision has to be made in terms of choosing an appropriate language with which to do science.

I turn now to a word about Goodman's calling his problem a "new" one for induction theorists. One way of justifying the claim of newness is to notice that some of the old attacks upon justifying inductive inference, even if successful on all other grounds, fail to solve Goodman's problem. To illustrate, consider Goodman's problem as it arises for those who maintain that the problem of induction is solved by postulating the existence of natured objects.25 for a nature theorist,

C causes E is justified only by pointing out that it is in the nature of G to cause E, that is, there is a real connection between C and E, and E does not merely follow C. Since a real connection only exists between kinds of objects, if this instance of kind C causes this instance of kind E, then the causal relation is grounded in the kinds themselves and hence in the natures of C and E. If it is in the nature of C to have property P, then every instance of the kind has the property,

25see for example E.. J. Nelson, "Causal Necessity and Induction," Proceedings of the Aristotelian Society, New Series, LXIV, (June, 1964), 289-300. 159 there being a real or necessary connection between being a C and having property P. This solves the "traditional" problem of induction for if there is evidence that a sample of things of kind C have a property F and that it is in the nature of constituents of the sample to have the property then every instance of the kind will also have the property. Hence if there are real connections among things grounded in natures, a justification of induction is possible. The nature theorist has proven that there are regularities. Of course, David

Hume was presented with a problem once he realized that there was no experimental evidence for the existence of real or necessary connections between cause and effect. As he would put it, "I do not see the connection and it is not a contradiction to deny that the cause, G, occurs and its effect, E, does not" which connection, he claims, the nature theorist requires.

Ignoring Hume's critique of this defense for the legitimacy of inductive inference, the nature theorist flounders on the rock of Goodman's new problem. For the followers of Goodman, the question would arise whether it is in the nature of emeralds to be green or to be grue. If it is in the nature of emeralds to be green, then emeralds will be green in 2001, but if it is in the nature of emeralds to be grue, they will be blue in 2001. Since whether emeralds are green or grue, they will now appear green, the nature theorist has no way within his present theory of deciding which is true; the 160

prediction that "the emeralds will be green in 2001" or the

prediction that "the emeralds will be blue in 2001". In short

he cannot tell which of two incompatible inductive conclusions

is true and hence he has not justified induction for from

natures we are not able to distinguish between projectable and

non-projectable properties. This is further illustrated by

the incompatible inductive arguments presented above.

In terms of the model, introduction of bleen/grue

predicates would amount to the claim that objects with surfaces

which have the characteristic of reflecting light waves of

frequency will change their surfaces at t^ such that

they then reflect light of frequency ^2* This is the case

because bleen/grue predicates are defined by means of observational

predicates and incorporation of visible observational predicates

occurs in the model via surface characteristics of light frequency

absorption. The introduction of such predicates into the model

amounts, then, to the introduction of an additional scientific

law for governance of the model. The law states that surface

characteristics of objects change at t]_. For convenience, a

distinction can be drawn between M 2, t^ie model with the grue/bleen

predicates and M^, the model with the usual predicates. M^ and

M 2 have the same physical interpretation now, that is, there are

no current observational differences between them. Observational

differences only occur at and after tj_. At t^ they no longer

have the same physical interpretation. There isi a clear sense in 161 which Mi is simpler than M 2~~M2 contains one additional law that Mi lacks. The additional law is the one governing the change in surface-structure at ti. Model Mi is preferable to

M2 because it is simpler— it can be as readily given the same physical interpretation now, before ti, bb M 2 but without employing one of the laws in M2* In the absence of any observational differences between the models which are presently available, the choice of a model has to be made on pragmatic grounds, on the basis of simplicity. Remember that the observational difference occurs remotely in the future and that M 2 is more complex than Mi because M 2 has one additional law. For the combination of these reasons Mi is preferable now. Later, after the observational difference has been settled, M 2 may be preferred. Nevertheless, even if scientists had started with grue/bleen predicates, the intro­ duction of green/blue predicates could have been required on the grounds of simplicity for those latter predicates give a model Ml for the world as it is currently without the assumption that its appearance will change at ti, without one of the laws of M 2> Goodman maintains, correctly, that the ability to define 'green' and 'blue' in terms of 'grue' and 'bleen' shows that neither pair is more basic than the other. But on the level of models there is a difference for the grue/bleen model, M2» has one more law than the green/blue model, Mi» and simplicity is a proper consideration for choosing one model over another. 162

A slightly different approach is needed to defend the choice of the usual model over Hempel's model. Hempel's model is rejected because probability theory does not apply to it.

Remember that Hempel chooses it for just this reason, since he wishes to eliminate the probability theory based way out of the paradox. A model in which probability theory may be employed is preferable to one in which it may not be employed simply on the basis that it solves more problems. After all, a model is chosen in order to be able to unify diverse events in the observed world, it is chosen in order to eliminate problems, not in order to preserve them.

Two reasons for choosing one model over another are these, the preferable model solves more problems, and the preferable model does so with a smaller number of laws.

Obviously, the former reason is the stronger. The latter reason is employed in the grue/bleen case only because, by hypothesis, there are no problems which either model can now solve which the other cannot and there will be none until t^.

It can now be seen that once the nonempty extension of scientific predicates is made clear, the paradox of confirmation is eliminated for no generalization may be confirmed unless at least one instance of its subject term has been examined. Further, once the forms of premises requisite for an inductive argument to a generalization are stated, then it is seen that the premises are , required to be of three different forms. 163

Ex'Bx

~Rx*Fx

~Rx»~Bx

Without premises of these different forms, false conclusions,

(x)(Rx*Bx)j much stronger than the usual generalizations

(x )(ILj o Bx ), may be drawn. Finally, other approaches to the dissolution of the paradoxes have been explored. Though they help, none of them appreciate the previous point. Now attention may be turned to the problem of induction itself. This is done in the next chapter, Chapter Four. CHAPTER FOUR

THE PROBLEM OF INDUCTION AND ITS SOLUTION

Before a problem can be solved, the exact nature of the problem must be explicit. Indeed, there is merit in the suggestion that the hardest part of solving any problem is figuring out the nature of the problem. For example, Kepler was able to give laws for the description of celestial motion only when he realized that astronomy was not the science of describing the movements of the stars by means of circles but merely the science of describing the movements of the stars. So too, with the problem of induction. Much work will be done below to make the problem clear. In particular, work has to be done to explicate the notion of justifying induction by a particular inductive inference rule. To justify induction is to demonstrate that most or almost all inductive arguments which use the same inductive rule and which have true premises also have a true conclusion.

The explication presupposes a satisfactory analysis of what such a demonstration is and what differentiates inductive argument from other kinds. Once this is done, che solution to the problem of induction will appear obvious. The central thesis of the chapter is that the same sort of techniques required for the analysis of deduction are required for the analysis of 165 induction. The new twist here is to see the problem of justifying an inductive inference as being identical in kind to that of justifying a deductive inference. Below it will be seen that much confusion exists about the relation between the premises of an inductive argument and its conclusion. The proper relation will only become clear by means of a semantics like the one adopted in previous chapters. In order to properly understand the relation among the propositions employed in scientific discourse, it must be understood that they have existential import.

4.1 The Characterization of Induction

Whatever characterization is given to induction, it should be the case that it is analytic that induction can be justified.

This is the main principle of analysis employed in this section.

Since serious philosophical issues cannot be settled by definition alone, it cannot be the case that induction is or is not justified by definition. Whatever induction is, it is certainly a technique employed in the sciences to establish generalizations. Two such basic techniques employed in the science are sampling procedures and what philosophers call the hypothetica1 -deduetive technique.

Sampling procedures utilize a sample or a small number of members of a large class of objects about which it is desired to find the distribution of a property within the class. By actual observation the distribution of the property is determined for the sample and then various techniques are used to project this observed distribution onto the large class. Examples come to mind: 166

TV racings, The Gallup Poll, and the traditional problems in

statistics which use the drawing of colored balls from urns--all of these involves sampling procedures. Samples can be selected at random where there is no prior information about the sample used in its selection. "Stir up the urn of balls, close your eyes, and pick ten." Samples may also be weighted. For example, since women are about one-half of the electorate, a political poll which sampled only men would be inaccurate, for sex is related to voting patterns. Any trustworthy poll will weight its sample so that its composition reflects the distribution in the total population of all factors known to be, or suspected on good grounds to be, correlated with the occurrence or non-occurrence of the property under investigation. In this way sampling in the social sciences is seen to depend upon the results of earlier inductions. Below this will be seen to hold in the natural sciences as well.

The hypothetical-deductive technique has been explored above, in part, in Section 2.6 on covering law model explanations.

Suppose that a scientist wishes to confirm or to disconfirm a conjecture or proposed scientific law; he adds to it already verified laws and statements of initial conditions and deduces from this conjunction what would be the case if the conjecture or proposed lav/ were the case. Of course, the derivation has to be such that it could not be reconstructed without the conjecture by using only the accepted hypotheses and initial conditions, and yet the conclusion still follows. That is, the 167 conjecture must play an essential role in the derivation. ^

If the prediction, the deduced claim, is true, the conjecture is confirmed; if it is false, the conjecture is disconfirmed, or at least, one of the premises of the deduction is false. (It might be one of the previously well-established hypotheses.) To illustrate: suppose that a scientist wishes to confirm or disconfirm the conjecture that mechanical motion by itself is sufficient to produce heat, then from the conjecture together with statements correlating rise in temperature with the presence of heat, the initial temperatures of the apparatus, and statements describing the motion of the heat, he could deduce that after the apparatus has been moved for a time, its temperature would rise. Count Rumford who made the conjecture did observe a rise in temperature of his apparatus, a stationary cannon barrel which A was being reamed, and concluded that his conjecture was confirmed 2 since the deduced consequence was observed to be true. Similarily,

Newton claimed that his universal law of gravitation is true since both Galileo's law for falling bodies near the earth's surface and O Kepler's law for planetary motion could be deduced from it. If the deduced consequence is false, it follows only that at least

■*"The reader should consult the notes in Secti011 2.6 for a brief bibliography of the literature on the hypothetical- deductive method.

~H and R , Chapter 19. The authors remark that Rumford's experiments by themselves were not enough to "convert the calorists and topple their views, for the simple reason that there was no well-developed conceptual scheme to offer instead." This is another illustration of the need for models in science.

3H and R, 133. 163

one of the premises of the derivation is false; it docs not have to be the conjecture. The conjecture might be correct but

the present experiment is the first one to cast doubt upon some previously well-accepted hypothesis. In any event, the interest for now is in confirmation.

While the first kind of inductive procedure stressed that many observations are necessary before confirmation is obtained, the hypothetical-deductive method stresses only one. The method, in effect, allows for the acceptance of any hypothesis which is consistent with already accepted laws in the model since the model pictures the observed world by only using the primary qualities; the qualities required for the statement of the accepted laws. In the interesting case, the model is the one for the world in which we live. So, there, the method allows for the acceptance of any hypothesis which is consistent with already accepted law-like statements in our world. That is, ones from which, as far as we know, no false deductive consequences follow. The laws govern behavior in the model. If the model has a physical interpretation, then the laws govern the behavior of whatever is used to interpret the model. At every level of science there is an interplay between what is observed and the model. By logical manipulation and convention any law can be introduced into the model, but the test of truth is whether the model with that law can be given a physical interpretation.

A law is tested by first being integrated into a model; then, together with the other laws whicu govern the model and the initial 169

conditions of an experimental situation, a prediction about a new

state of the system is made: if the observable event which is

used to interpret that state occurs the law is confirmed; if

it fails to occur then either the new law-like statement is false,

or some of the other laws in the model are.

The two methods are not as diverse as the above discussion makes them appear since the hypothetical-deductive method makes use

of the observations which were used to confirm the previously accepted hypotheses. The method seems to rely upon a single observation but in fact relies also upon the observations needed

to confirm what is already accepted. Both methods amount to the claim that "nothing known shows the new generalization is false and there is positive evidence for it." The sampling procedure does

this, if the experimenter is honest, by not including previously known disconfirming evidence in the sample. The honesty provision is added because it is only this which allows the inference that 4 there is no disconfirming evidence which is being hidden. For a

^The honesty provision may be compared to the deductive requirement that a term must not be equivocated on in an argument. If the validity of an argument whose subject matter is unfamiliar is being judged, one can only rely upon an expert in the field of the subject matter, usually the asserter of the argument, that no technical term being employed is used equivocally. Specialized knowledge on the part of the logician would avoid the need for an honesty requirement. But the logician is presumably in no position to judge equivocations for that takes technical, nonlogical, know­ ledge. For example, only a user of English would know that a red herring is not (usually) a fish. Some logicians do, however, claim that validity depends only upon logical form and hence even an argument whose subject matter is unknown may be evaluated. See H. Kahanc, Logic and Philosophy, (Belmont, California: Wadsworth, 1969), Chapter One. 170

logically correct induction there can be no disconfirming evidence

about which the experimenter is aware but which lie is hiding

from the readers. The hypothetical-deductive method meets this

condition by actually using previously accepted hypotheses as

part of the inductive support for the conjecture. This provision

is important for it will be seen below that several paradigms for

inductive arguments have violated it.

Hume's characterization of induction, the first to be

rejected, is also the first important one in modern philosophy.

For Hume, the conclusion of an inductive argument is law-like;

that is, for him, a statement of causal connection.

We remember to have had frequent instances of the existence of one species of objects; and also remember that the individuals of another species of objects have always attended them and have existed in a regular order of contiguity and succession with regard to them....Without any further ceremony, we call the one cause and the other effect, and infer the existence of the one from that of the other.

But no causal connection is perceived nor is it reasoned

to by means of the mind's reflection on the data presented by the senses. Hence, the causal inference exceeds the testimony of the senses. This characterization of induction as leading to a conclusion which exceeds the "testimony" of the premises is faulty because it leads necessarily to the inference that no inductive argument is ever justified. To see this, consider the

-*Tron ti so. . . , Boole I, Part III, Section VI. The emphasis is in the original. deductive inference that since paper is white, it is white or yellow. Someone could believe the premise without believing the

conclusion drawn from it, especially if he were.a beginning

student in logic. So the fact that the inference can be deductively drawn does not guarantee that it will be made. Similarly then for induction, if the sensory evidence available to an observer inductively justifies a conclusion it does not follow that the observer will believe that conclusion. Now, in the deductive case, the conclusion certainly exceeds the testimony of the senses, if what is meant is that believing the premises guarantees believing the conclusion. But Kume surely meant to hold that deductive inferences do not exceed the testimony of their premises.

Hence this approach cannot be what Hume had in mind. Since Hume maintained that inductive inferences are neither observed to be true, nor products of deductive reasoning from what is observed, he seems to mean rather that there is no legitimate inference from the data of the senses to the inductive conclusions drawn from them. The conclusion of an inductive argument exceeds the data of its premises only if that conclusion neither repeats the premises nor follows from them. The deductive inference considered above does not have a conclusion which exceeds the testimony of its premises since the conclusions follows from those premises.

To characterize induction in this way is then to make it analytic that induction is unjustified for no conclusion which fails to follow legitimately from its premises, which exceeds the testimony of its premises, is ever justifiably drawn. 172

There are two parts to an inference: the logic and the

content. Formal logic is the study of the logical relations among

sentences ignoring their content.^ Whatever content does eventually

arrive in the conclusion is solely a function of the content that

is originally in the premises. The role of the logic is simply

to convey it there. Put in another way, given the content in

the premises, the logical relations among the premises guarantees

the content of the conclusion. In the case of a valid deductive

argument the guarantee is ironclad; if the premises are true,

the conclusion must be true. In an inductive argument the

guarantee is not absolute but the content can still only come

from that placed in the premises from the beginning. For Hume

to say that the content exceeds the testimony of the senses is

to mislead for his comment makes it sound as if the content of

the inductive argument is unjustified. If the content of the

inductive conclusion is not warranted by the content of the

inductive premises, then it must have come from something which

played no role in the formal argument. This would make the

argument illicit. It is therefore necessary to find a different

characterization of induction.

To bring home this anti-Humean point consider a modern day

Humean on this issue: Wesley Salmon tells us that, "The content

of the conclusion of a correct (valid) deductive argument is

°Most books on logic make this point. See, for example, A. N. Prior, Formal Logic, 2nd ed., (Oxford: Clarendon Press, 1962), Part I, Section I. present in the premises."^ And speaking of a particular valid argument he says, "All of the information or factual content in the conclusion was already contained, at least implicitly, in the premises." While of a particular inductive argument he says,

"The conclusion contains the information not present, even implicitly, in the premises,"^ He means, most likely, that the premises of an inductive argument are about the properties of a few observed things while the conclusion, since it is a generaliza­ tion, is about all things or at least about all things of the same kind as those things which are described in the premises. In short there are more things in the extension of the inductive conclusion than in the extension of the conjunction of the inductive premises. Suppose that this is true; then the question to be faced is: Where does this extra content come from? This is like the question just asked of Hume: If the conclusion of an inductive argument exceeds the testimony of the senses, where does this excess come from? Hume answers that it comes from a habit of mind. He does this after rejecting the alternatives that it comes directly from the senses or that it comes via deductive inference from the premises. But he overlooks the third possibility that it comes via inductive inference from the premises. For example, if the premises of an inductive argument justify our

^Logic, (Englewood Cliffs, New Jersey: Prentice-Hali, 1963), 16.

^Logic, 14. 9 Lo^ic, 14. 174 adding the content to the inductive conclusion, then the premises

justify the added content themselves. If I justify your taking

the money, then I justify the taking of the money. So, too,

if inductive premises justify the inferer in adding content to

the conclusion, the premises justify the added content. Note:

the extra content in the conclusion must come from somewhere. If

it does not come from the premises, it comes from some other place.

If it comes from some other place, then clearly the inference is

is unjustified for it is not based upon the premises alone. Any justified inference must proceed from only its premises. So an inference which obtains content from someplace other than its premises would, by necessity, be unjustified. If an inductive conclusion contains content which is neither in the premises nor obtained from them, but rather comes from some other place, then such inductive arguments, by definition, are unjustified. If it is not to be analytic that induction is unjustified, then the content in the conclusion must be obtained from the premises alone.

The content of the conclusion of a deductive argument is deduced from its premises. Similarly, the content of the conclusion of an inductive argument is inductively inferred from its premises. To explore this further consider a typical example of deduction, modus ponens.

a )

(2) J.

A (3) '

The content of its conclusion is not identical to the content of 175

its premises since the premises also entail propositions which

are clearly aistince from (3). For example, those same premises

entail

(1;) AvC

whose content is clearly disjoint from the content of (3).^ That

(3) and (4) lack a common content is further evidenced by the fact

that neither "If (3), then (4)" nor "If (4), then (3)” is valid.

Since (3) and (4) fail to have the same content and since they are both deductive consequences of (1) and (2), it follows that a deductive consequence of a set of premises need not have the same content as the premises from which it is derived.

Another argument to the same effect comes from the (presumed)

transitivity of the "sameness of the content11 relation. Above,

the (false) claim that (3) has the same content as "(1) and (2)" was drawn from the fact that (3) follows deductively from them.

But (3) also follows deductively from many other sets of premises.

Among these sets are nlif C, then B 1 and *C111 as well as all contradictory sets. But quite clearly 11 (1) and (2) 11 does not have the same content as these latter sets. Let ,DI be a contradiction.

(3) follows validly from ID1. By the theory under criticism, (3) would have the same content as 'D1. Further, since "(1) and (2)n has the same content as (3), it would seem that they also have the same content as 'D1. Indeed, since any proposition at all is deduc-

^-®To see this clearly just let A be 'Bertrand Russell is Pope', let B_ be 'The moon is made of green cheese, ', and let C_ be 'Most Ohio State University scudents are not interested in football1. 176 ible from'D', it would turn out that every proposition has the same content. Surely this is false. Once again it seems that the deductive conclusion of a set of premises may have content not identical to that of the set of premises from which it is deduced.

Again, (3) does not have the same content as (1) nor does it deductively follow from (1) alone. Similarly, (3) docs not have the same content as (2 ) nor does it deductively follow from (2) alone. How then is the content of (3) generated from (1) and (2)?

The possibilities that the content of (3) is identical to both (1) and (2) or to either of them separately have been eliminated. The only choice left is that the content comes from the logical relationship between (1) and (2). In general, the content of a conclusion deductively inferred from a set of premises is a product of the logical relationships among that set of premises.

In the case of deduction, the content of the conclusion is deduced from that of the premises. In this sense, its content does not exceed that of the premises. But for similar reasons, the content of the inductive conclusion must be inductively inferred from the premises. If the content exceeded that of the premises, it would have to get into the conclusion in some extra-logical way, which by definition, would make all inductive inferences unjustified. Hence, the solution to our problem will not be found in distinguishing between induction and deduction by means of the notion of the content of the conclusion as it compares to the content of the premises from which it has been inferred. 177

Other approaches to characterizing the distinction by means of content lead up different paths. Mill is famous for

remarking that the syllogism begs the question.

It must be granted that in every syllogism, considered as an argument to prove the conclusion, there is a petitio princippl. Wien we say,

[ 5.. j All men are mortal

[C:] Socrates is a man, therefore

i. 7 j Socrates is mortal;

it is unanswerably urged by the adversaries of the syllogistic theory, that the proposition, Socrates is mortal, is presupposed in the more general assumption, All men are mortal. ^

The issue here is the sense in which [7] is "presupposed in the more general assumption" I Si- [Si is more general than

L7] in the sense that the extension on IS] includes Socrates as well as other individuals. While the extension of L7] includes

Socrates and no other individuals. The extensions of [SI and [7] respectively, are

(5I-0 (ilcob.a) • (hbr>; .h )*...• ( HsdXs)

(7F) Xs

One sense of 'presuppose' would be that (S'S) entailed

(7h) , but that clearly does not hold. Another sense might be that

(7-w entailed (bh) That too does not obtain but (7E) does entail that part of (5^) in virture of which Socrates can be said to be in the extension of i.bj> 'LsiX.s1. is it that L b J presupposes

^Quoted in W. Kneale and M. Kneale, The Development of Logic, (Oxford; Clarendon Press, 1962), 375. 173

■ 7 ] in the sense that the one individual in the extension of

i, 7 j j (7-u) j i-s also one of the individuals in the extension of

i $ ]) (£-0 ? 11 this were all that counted, then the extension of

'Socrates is Snub-nosed1 which is 1Ss ' would also be presupposed by :5] * This is not the case since [£] could be true even if nothing were snub-nosed. None of the senses of 'presuppose' seems to work.

The only deductive relation between (7L) and ($l ) is the one previously alluded to: ('71) entails in a PM tvpe of logic. In the Aristotelian logic developed above, this is not true unless there is a guarantee that the property '11' has a non­ empty extension. This shows that in the Aristotelian logic, (710 does not, by itself, entail a conjunctive part of (^ii). But in

PM logic, the derivation is trivial.

What Kill may of had in mind was that the truth of 1.Si is purportedly established by examining single instances of the generalization and i7] seems to be such an instance. Since

Socrates is a man, it seems as if 'Socrates is mortal' is an instance of the general claim 'All men are mortal'. Clearly 'this man is mortal' or 'that man is mortal' are instances of the generalization. But it is one thing to realize that this man is mortal and quite another to realize that Socrates is mortal even when this man is Socrates. What Mill has relied upon is an extra piece of information; he has illicitly employed the information that Socrates is a man. Among the individuals which could be examined in order to provide evidence for [£] is Socrates. But the evidence in no way turns upon the name 'Socrates', all that

counts is that this man is mortal. That this is so is indicated by the fact that in the deduction, premise i.6] is required to

indicate that 'Socrates' names a man.

Mill seems to be implying that one could not know [£j unless one already knew [7 j; hence the syllogistic argument begs

the question for one of the premises would not be believed unless the conclusion were already believed. Even if Mill were right in that those premises could not be known unless the conclusion were already known, the inference he draws does not in fact follow. It does not follow since knowing is a psychological attitude and an attitude may be justified for a person to have without the person having the attitude. For example, X may have evidence for the belief that Jones murdered Smith without realizin that is is evidence and hence without having the belief.

Michaelson and Morley had the evidence that there was no aether 12 but never realized it. It is one thing to have evidence and quite another to realize it. Someone may have examined Socrates as part of the evidence for his belief that all men are mortal while realizing neither that the person being examined was named

'Socrates' nor that 'Socrates' is the name of a person. Even though he has all the evidence needed to justify the claim that

Socrates is mortal, he does not know it since he does not believe that 'Socrates' names a man or that Socrates is one of the men

12Compare, A. Einstein, Relativity, (New York: Crown, 1961), 147. 130 whom he has examined.

Further, if Mill is right, then deduction is characterized by the fact that if the premises are known then the conclusion is also known. But Mill's intention is that induction lacks this characteristic. Since induction is used to provide evidence for its conclusion, by Mill's characterization the evidence relation could never be strong enough to defend a knowledge claim. Mill's characterization, then, is to be rejected for it makes induction unjustified by definition.

For induction to be justified it has to be the sort of inference technique which can be used to make knowledge claims.

Science uses inductive argumentation to support claims of law- likeness. If induction could not yield knowledge, then scientists could never properly claim to know the laws of nature. Hence, any characterization of induction on which it turned out that inductive conclusions could not be known (if the only evidence for them was inductive) would for this reason be rejected. The only clear expositions of the notion of inclusion either have led to the point that both kinds of arguments, inductive and deductive, include the content of their conclusion in their premises or have led to the point that this is true of neither kind of argument. Since this happens in Mill's and Salmon's and

Hume's characterizations of induction, they have been rejected.

Below we will consider philosophers who look at a successful inductive logic as one which goes from true premises to true conclusions most of the time. For them, presumably, since induction lbl

rarely goes wrong, ic can be relied on to yield knowledge. But

before they are considered, the source of the Humean confusion

is worth pursuing.

Salmon says of valid deduction that "The conclusion must

be true if the premises are true, because the conclusion says

nothing which was not already stated by the premises. " ^ His

reasoning may be rejected, but it cannot be doubted that the

conclusion must be true in a valid deductive argument if the

premises are true. This holds because of the logical structure of the valid deductive argument. Hence deductive arguments may be analysed by means of their logical form; there is no need, in

general, to ever examine their factual content. Deduction is

simply characterized as an argument structure in which if the

premises are true, then the conclusion must be true. The force of 'must* is that a logically necessary relationship holds between

the premises and conclusion of a valid deductive argument. This

is further evidenced by the fact that a logically necessary if-then

sentence is formed by taking as its antecedent the conjunction of

the premises of a valid deductive argument and by taking as its consequent the conclusion of the argument.

13 Correct inductive arguments are probablistic as Hume and Salmon^ among others have remarked. The premises of correct

12t . Logic, 15. 13 Treatise..., Book I, Part III, Section II.

1 4Logic, T • 114 / . 1S2 inductive arguments provide evidence for the conclusion and hence affect its probability. If the premises of a correct inductive argument are true, its conclusion is probably true. (If an inductive argument is intended to cast doubt on the claim that a proposition is true, it is really an argument whose conclusion is the denial of the proposition at issue. This kind of argument also fits the characterization. Such an argument might be designed to prove that, say, the butler did not do it.) The nature of the probability as it relates to inductive reasoning will be explored below. First, however, it will be necessary to further explore misunderstandings about the characterization of induction.

It has sometimes been held that every inductive argument can be transformed into a deductive argument by adding to it, as a premise, a principle of inductive logic. Hume, for example, considerers and rejects this possibility.^ The arguments against this position usually are directed against some particular formulation of the principle. Hume rejects the proposed inductive principle that "instances, of which we have had no experience, 1 fi must resemble those, of which we have had experience." What is needed is a general argument since refuting only particular proposals always leaves open the possibility that some such principle may eventually be found. In what follows it is important that induction be a form of reasoning which cannot be reduced

^Treatise..., book I, Part III, Section VI.

^Treatise..., Book I, Part III, Section VI. to deduction.

If the reduction could be carried out, then the sentence version of the inductive principle of reasoning would be on equal

level with sentence versions of deductive principles of reasoning

since, by hypothesis, there is only one kind of reasoning. The

sentence versions of deductive inference principles (formed by

transforming p/\ Q into Pn Q) are themselves analytic. Hence, on this supposition, the sentence formulation of the principle of inductive inference is itself analytic. But any inference with a logically true premise is also valid without that

premise. That is, if a set of premises entails a conclusion and a subset of the premises are tautologies, then those

premises which are not tautologies alone entail the conclusion.

If 'P]_1 through 'Pn ' are the premises of a valid deductive argument which has the conclusion 1Q1 and if some of those premises are tautologies then 1(P^*...• Pn)3 Q 1 is a tautology for there is no way to make the antecedent true and the consequent false. Similarly, given a conditional statement which is a

tautology and whose antecedent is a sequence of conjunctions, like the above example, then the argument which has as premises

the conjuncts in the antecedent and which has as conclusion the consequent is valid. But if some of the say Pj,...,Pk , are

tautologies, then the argument with only the non-tautologous premises and the same conclusion is also valid. This follows because ’ (P pj-l*Pk+i pn)=fl' is still a tautology. 184

Hence, if there is a tautologies 1 premise which when added to

(correct) inductive arguments transposes them into (correct) deductive arguments, then the premises of the (correct) inductive argument by themselves already entail the inductive conclusion.

If the supposition that inductive arguments can be rewritten as deductive arguments entails that the missing premise is

itself analytic, then the supposition is false for the inductive arguments so transformed would have to be valid deductive arguments without the additional analytic premise.

The only alternative is that the statement form of the principle of inductive reasoning be contingent. What would it be for an inference principle to be contingent? This would mean that the principle would apply to some logically possible worlds but not to all. For an inference principle to apply to a possible world it would either have to be usually successful or be capable of uncovering past mistakes. In the interesting case, the principle would apply to our actual world although other worlds could be imagined in which the principle went from true premises to a false conclusion. The thesis here is that the principle of induction is such a rule. To defend this claim it will be necessary to examine the paradigms of mistaken inductive inference and see whether they are to the credit or discredit of induction. This is done in the next section. 135

4.2 Counter Examples to Induction

As shall be seen below, the counter examples to induction fall into two distinct groups. The first group consists of experiments of the imagination. Here what counts is that there has been imagined an instance in which inductive arguments have true premises and false conclusions. The second group consists of alleged instances of historically actual inductive arguments with true premises and a false conclusion. Since this second group is rarely discussed in the literature, most of these examples are original. The point of either kind of example is that induction is not trustworthy since it can lead from true premises to a false conclusion. In the interesting cases, inductive arguments are employed to support scientific laws. The very claim that scientific laws are known rests upon the ability to infer them from evidence. Some of this process has been explored above. If the logical structure which leads from evidence to the laws of physics can have within it true premises and a false conclusion, then man has no reason to claim that this is not the case in the inductive arguments which have led to the presently accepted laws of physics and other sciences, or so the critics claim. _

The force of either kind of "counter example" is to cast doubt upon the principle that the future will resemble the past.

For the future to resemble the past there have to be some indicators in the past of the events to come in the future. The future resembles the past because the indicators forewarn of the future. If the future docs not, somehow, resemble the past, then there is no way to predict what the future will be like and hence inductive logic cannot so predict. Of course, the future will not be like the past in every respect. I am now in doubt as to whether there will be a nuclear war during the next year, but once the year is over there will no longer be any doubt. So, one way in which the future will be unlike the past is that some of my doubts will be resolved. More interesting, however, is the issue of whether all regularities now exhibited by the world will continue in the future. Will the future resemble the past in virtue of exhibiting all regularities which have been exhibited up to now? The answer is a clear

"NO.1". For example, every time x has driven to work in his car, he has not had an accident. This regularity is the sort which is broken every day. Indeed, according to insurance companies, it is quite unlikely to be preserved in the future assuming that x drives to work four or five times a week. Again, the regularity

"everytime boy B looks at girl G, B's blood pressure rises" is the sort which rarely is preserved because love is an attitude which is difficult to sustain, as divorce rates indicate. The latter case is extremely interesting since it would ordinarily be said by the layman that B's looking at G causes B's blood pressure to rise and yet almost no one would seriously believe that the causal law would continue to hold throughout B's life. 137

This, than, is an example of a causal relationship which holds

for a short span of time. It is a causal regularity which

will most likely not hold in the future.

Such regularities are important for they would serve as"counter examples" to induction since, by the paradigm of

inductive reasoning, argument 3G, the occurrence of sufficient

instances of the regularity would provide evidence for the generalization. For example,

1. at ti, B looked at G and B's blood pressure rose

2. at t2 , B looked at G and B's blood pressure rose

3. at t3 , B looked at G and B's blood pressure rose I I 1 h . at t^. . .

Therefore, whenever B looks at G, B's blood pressure

rises.

Since that conclusion is manifestly false, the argument serves to prove, or so it seems, that an inductive argument can proceed from true premises to false conclusions. Discussion of alleged counter examples to the justification of inductive logic will then proceed in terms of regularities such as these which occur for a while and then cease. (It might have been thought that such regularities are all accidental but the second of the two examples is clearly a causal one.)

From the discussion of the paradigm for induction given in Chapter Three, it should be apparent that the above argument proves too much: its premises justify the conclusion "At every time B looks at G and B's blood pressure rises." The inference as presented above relies upon information not stated in the premises. What information? In this extra information there is surely the point that "there are times when B does not look at G." Hence the argument presupposes knowledge of B ’s behavior when not in the presence of G. But the argument also has to eliminate the possibility of B's looking at G and not having his blood pressure rise. That is, the argument has to provide evidence on the point of whether all "times when B looks at G" are "times when B exhibits blood pressure rise." In order to eliminate the possibility that disconfirming instances of the inductive conclusion have not been found only because they have not been sought after diligently enough, evidence has to be brought on this possibility from another source. That is, there has to be considered evidence on the likelihood that further search would turn up an instance in the future when

B looked at G and B's blood pressure did not rise. Now, attention turns to the model. Does the generalization for which there is some evidence fit into the model--is it consistent with all previously established laws? Further, are there other already established laws which can be deduced from it? Once attention turns to the model, it is noticed that such regularities are not longlasting since love is not longlasting. In the model, presumably there is a law which states (some of) the conditions 139

under which love dies and from which law it follows that the

regularity at issue will cease.

Models thus serve to eliminate bad from good inductive

arguments. The conclusion (and premises) of a good inductive

argument can be integrated into the model. Such use of the

model eliminates some supposed counter examples to induction.

These eliminated counter examples include all those where the

conclusion is intuitively false.^ Such are the pedagogically

sound cases "Since only Irishmen are seen on the bench,

sitting on the bench causes one to be Irish" and "Since I have

on a tie everytime I come through the door, I cannot come

through the door unless I have on a tie."

Another alleged kind of counter example does not allow

for such ease in eliminating the difficulty. Until the discovery

of black swans in Australia, no European had ever seen a non­

white swan.

1. Swan 1 is white

2. Swan 2 is white 1

T

f h. Swan h is white

/.*. h+1. All swans are white

Such an argument would have been acceptable to Europeans even

though it seems to go from true premises to a false conclusion.

^ See for example, M. Beardsley and E. Beardsley, Philosophical. Thinking: An Introduction, (New York: Harcourt, Brace and World, 1965), 229. 190

However, there is no low governing the model which conflicts with this generalization. But also, presumably, there is nothing in

the model which makes this generalization intelligible. If

the conclusion is true, then there is something about the makeup of swans which requires that they be white. Even if contemporary genetic theory is grafted onto the European's model, there is no explanation of why the generalization is true since at this point in the development of the model not enough is known about the genetic structure of birds to explain such occurrences. Hence there is nothing in the model which either supports or contradicts this generalization. Here the use of the model cannot distinguish between good and bad inductive arguments. Is there, then, anything wrong with this argument other than it has true premises and a false conclusion?

In order to answer this last question it is necessary to pursue part of Hume’s attack on induction. The relevance is just this: The inductive argument is not convincing because it is easy to imagine its premises to be true and its conclusion to be false. This is true since a nonwhite swan can be imagined.

Hence, there is no connection between being a swan and being white. This consideration, Hume might have argued, is relevant since, in the example under consideration, it is known that the premises do not exlcude known relevant evidence and it is known, now, that the conclusion is false. Hence even for "alleged" laws linking species and color, in the absence of a comprehensive 191 genetic model which accounts for the linkage, there is no evidence which justifies the lawlikeness of generalizations connecting species and color. What we think are laws connecting, say, ravens and black, are no more laws than the "law" connecting swans with white. All the positive instances of these laws are irrelevant since in the case of the swan they were misleading.

Since the evidence about species and color is like the evidence about swans and white, the (former) evidence is not useful.

This sceptical argument has to be accepted. Without a model to make the generalization intelligible, there is no reason to believe the generalization. The whole point of introducing models was to make the distinction between generali­ zations and laws (see Chapter One). Past experience may lead to conjectures about lawful relationships which in turn may lead to new models. But without the new model, the generalization is unintelligible; we do not know why it occurs, and, hence, there is no legitimate reason for accepting it. The model provides intelligibility since it provides a connection between the regularly linked properties. Proper induction requires the consideration of all relevant evidence. But the only way to insure that this requirement has been met is to have the argument consider all evidence, to have the generalization at issue integrated into the model. It is conceivable that two properties are regularly linked without there being a connection between them but that such occurs in fact will always be unknown since the 192

history of properties expires with the history of the world

and hence with the history of knowers. All counter examples to

the claim that induction is justified which rely upon the

falsity of previously accepted generalizations which were never made part of science, which were never incorporated into the

scientific model, are for that failure to be rejected. It is

only by means of a model that knowers are able to know the

future history of two linked characteristics since the model establishes that there is a connection between the properties.

Every proper inductive argument requires that its conclusion be incorporated in the model in order to have all available evidence considered and in order to make the linkage of the properties intelligible and hence projectable.

The serious counter examples to the claim of inductive justification can lie only in the falsity of law-like statements which have had support in the model. Since science changes, and since science rejects what once were accepted as laws and hence rejects what once was made acceptable in the model, there seem to be inductive arguments which have led from true premises to a false conclusion. Put in bold language: The fact that the model has had to be changed indicates that induction is an inadequate tool for investigating the future. Counter examples which arise from imaginary cases are to be rejected since such examples do not depend upon a mistaken model. Counter examples which depend upon false generalizations which never received 193

support in the model are to be rejected for that very reason.

The only counter examples which have to be taken seriously arc

those which have drawn from the history of science for their

inspiration. Only these now proven false law-like statements which were once supported in the model provide serious

counter examples to the claim that induction is a legitimate

inference method. This holds because only such cases draw upon the full logical resources of inductive inference.

The transition from Newtonian Mechanics to Relativity and Quantum Mechanics provides a striking example of the overthrow of a well-developed model. In effect, the inductive argument supports a generalization only if the scientific model makes the generalization understandable. The impact of this by now trite remark is that the inductive argument really supports the model as an interpretation of phenomenal reality.

By incorporating a "mechanism" in the model which provides a connection between the correlated phenomena, there is an implicit claim that the correlate holds between the phenomena wherever they occur, that the correlation is projectable. The inductive argument which first, perhaps, was the source of intellectual interest in the generalization now becomes support for the claim that the model does interpret reality, that the invariable relationships between "concepts" in the model also hold in reality since the same logical structure occurs there. An example should make this clear. Phenomenally, mixing blue and yellow paint produces green paint. Is the relationship

projectable? Is, "whenever blue and yellow paint are mixed, green paint results" a scientific law? The first step on the way to answering this question would be to try mixing blue and yellow paint under various conditions. This would lead to an inductive argument whose conclusion is the generalization at issue. But, the generalization is only understood completely if it fits into the physical model of reality, into atomic theory. The model is changed or extended to incorporate a

"mechanism" which explains or provides a connection between mixing blue and yellow on one hand and producing green on the other. But the claim that the model interprets reality depends upon the claim that the relationships among what is interpreted in the model as blue, yellow, and green hold in reality. If they do not, then the model "paints" a false picture of reality and has to be rejected. But if the relations do hold, then it is plausible that the model does picture reality. Hence the inductive argument is now seen as providing evidence that the model has a physical interpretation. Since the formal inductive argument consists of both the results of experimentation and the results of incorporating the generalization into the model, an investigation of a new generalization may begin either with the experimentation or with the model. Sampling procedure stresses the former and the hypothetical-deductive method the latter. Since experimenta­ tion provides a link between the model and reality as perceived, it also provides the justification for the claim that the model 195

is of reality. Experimentation indicates that a generalization

holds and the model indicates that it holds lawfully. The model

is, thus, ultimately a mathematical tool which receives an

interpretation by moans of inductive arguments.

How then can a model go wrong? Newtonian mechanics in

its astrophysics went wrong. Newtonian mechanics in its

astrophysics went wrong because it was not a close enough

approximation to reality. Relativity theory replaced it. From

the point of view of relativity theory Newtonian mechanics is

just a special case. Newtonian mechanics was proven wrong when

it was shown that predictions based upon it were not as accurate

as those based upon relativity considerations. But over a large

field of predictability the predictions are within the range of

error of measurement. Within this field there are no measurements

which show the inaccuracy of Newtonian mechanics. It is for this

reason that Newtonian mechanics is considered an (acceptable)

approximation to reality.

Could, however, a model be entirely wrong and not just

wrong in the sense that it is a special case of a more general

theory? The development of relativity theory, in part, came about because of the failure to experimentally detect the presence

of an aether. Newtonian mechanics presupposed that a wave

traveled in a medium. The medium in the space between stellar

objects is the aether. Indeed the aether extended throughout the

universe. Wherever there is no matter there is aether. Therefore,

a wave will exhibit a velocity with respect to the aether. The 196

theory held that a wave should exhibit the Doppler effect due

to its motion relative to the aether. The effect is due to

the fact that small velocities are additive. The frequency of

propagation of a wave on a slowly moving source is the algebraic

sum of their velocities. For example, the whistle of a moving

train changes pitch when the train passes a person standing

next to the track for the frequency of propagation of the sound

wave is greater when the train travels toward the observer than

when the train travels away from him. Light should exhibit

the same effect when travelling through a constant medium.

Michelson and Morley set up an experiment to measure the effect.

From the measurement it would be possible to calculate the

velocity of the aether. But their experiment instead showed

that light does not so exhibit the Doppler effect. (Light will

exhibit the Doppler effect under other conditions.) There was

no way to explain this within the context of Newtonian mechanics

except to assume that their apparatus changed its size as it

moved, and that the change was just enough to compensate for 1R the change in velocity of the light due to the Doppler effect. °

Einstein proposed an alternative which seemed simpler. Light has a constant speed in a given medium. Using this assumption

it could be proved that the apparatus would change its size

just as the ad hoc patch on Newtonian theory required. Newtonian

theory appeared as a special case of Einstein's more general

18See M. B. Hesse, Forces and Fields, (Totawa, New Jersey: Littlefield, Adams, and Company, 1965), Chapter IX. 197

theory which explained Newtonian Mechanic's predictive powers.

However, since relativity is a more general theory, there were

cases of distinct differences in the consequences of the theories,

hence a crucial experiment was possible. The experiment justified

Einstein's physics.

The model has three important logical functions. It

shows that all law-like statements are consistent because they

each have an interpretation in a consistent logical model. The

logical model is also the scientific model. The model helps

to show that the set of law-like statements contains only true

statements since it shows that the set is consistent. Consistency

is a property of the set of lawful statements. Hence the set of

law-like statements meets a necessary condition for being in

the set of laws. The second logical function has been explored above. It is the job of making the generalization intelligible.

Without the model there is no way of distinguishing between laws and accidental generalizations. The third function will be further explored below. It is the function of insuring that an inductive argument meets a total evidence condition.

The generalizations of Newtonian Mechanics were well tested with countless verified predictions. They were integrated with each other because of the model. For both of these reasons, it was only experiments in new areas which prompted the theory's rejection and the adoption of a more general theory. But are there cases when the model lent support to a theory which was 198

replaced by something not more general but rather something

entirely different? Have there been accepted law-like statements

which were totally false and not just special cases of more

general theories? To raise this question at all indicates a

gross misunderstanding of the change to relativity theory.

Newtonian mechanics is a special case of relativity theory

only in that its equations are special cases of those in

relativity theory. The Newtonian model of wave propagation was rejected in toto. The model can support a generalization which is finally rejected and not replaced by a more general

law.

Inductive logic does, therefore, on occasion, lead from

true premises to a false conclusion. In spite of the usefulness of the model, actual scientific procedure does lead astray.

But, this is only a worry if it happens often. If an inductive argument has true premises and a false conclusion, one of two

things has gone wrong. Either something relevant was left out of the premises or there is something wrong with the

(inductive) logic. If it is assumed that there is something wrong with the logic, then there is no need to have more experimentation in the area; what is needed is a better logic.

For example, if the difference between deductive and inductive logic is just that induction, unlike deduction, occasionally leads to a false conclusion, then in any case where it does this, the scientist can simply say that it is the fault of

the logic and not of the data that he inferred from. But 199 scientists do not do this; when a false conclusion is obtained, they go back and re-examine their data, they conduct new experiments, they assume that there is some factual mistake which has led to error. If the counter examples are due to a fault in inductive logic, there would be no need to re-examine the facts, only re-examination of the logic is necessary.

That scientists in fact find overlooked data to account for their previously accepting false law-like statements indicates that there is nothing wrong with inductive logic, it is justified. When an inductive procedure leads to error, the scientist assumes that there is some system parameter which was previously unknown and hence looks for the new variable.

In short, the scientist looks for a new factor to be placed in the model. The basic sort of change in science is towards the integration of new results with older, better established ones. New results mean changes in the model. Radical changes in atomic theory are to be expected since scientists argue about whether mesons, electrons, and the like are particles, waves, or even about whether the controversy is useful. But proof that the numerical values of Kepler’s laws are wrong is not expected. In this last sense the future will (mostly) be like the past because inductive reasoning leads to few undetected mis takes.

Another way of looking at this is to note that inductive arguments are not finite. At any given time, the evidence on a given issue can be stated. But a model is needed, since the 200 generalization supported by the evidence has also to be supported by the model; the evidence is never fully in until science is complete. The history of science is the history of induction.

A good scientific argument integrates its results with the model and hence takes account of all the evidence that scientists have ever considered. Each inductive argument meets a total evidence condition. All relevant evidence considered by other scientists is brought to bear once the model is employed. All remaining relevant evidence is brought to bear to the limit of the ingenuity of the scientist making the argument. The latter is done through his experimentation. Conflicts arise between experiments which indicate an invariable relationship and a model which cannot accommodate it. Since reality lacks contra­ dictions, either the experiments are wrong or the model is.

Through this tension, the model is under constant scrutiny and science uncovers past errors. Inductive logic, however, is not to be faulted for leading from true premises to false conclusions. If such instances were the fault of the logic, there would be no need to examine the factual content of the premises for overlooked relevant events; there would only be need to dismiss the false conclusion as being what has to be occasionally expected since induction is illicit. If induction is unjustified, it can be expected to occasionally lead from true premises to a false conclusion. When such an instance arose, one could simply dismiss it as the expected outcome of 201 employing an unjustified logical technique. In the white swan case, that nonwhite swans were eventually discovered shows that the inductive conclusion is false but it does not show that there is something wrong with inductive logic. If the mistake in inferring from only white swans observed to only white swans existant were a logical one, if it were the kind of case where all relevant evidence was considered in constructing the premises, then-once the falsity of the conclusion was known there would have been no reason to conduct further investigation of the connection between being a swan and having a particular color for the error would have been only in using an illicit logic to reason from perfectly acceptable premises. It would be unjust to hold the reasoner responsible for overlooking relevant data which he was not aware of as being relevant, but nevertheless this was the mistake made. No one is, perhaps, to be held responsible for the mistake but it was made. All that an inductive reasoner can do is attempt to consider all relevant data and one way of doing this is to integrate the data into the already accepted model; that is, integrate it into a system with all known truths since nothing else relevant is known. Inability to do this shows that either the new generalization is not law-like or that one of the previously accepted generalizations is not law-like (or both). But if this can be done, the generalization becomes intelligible and hence is law-like. 202

4.3 Inductive Support^

One of the most important results of the previous two

sections has been the increasingly apparent point that the

issue of whether induction is justified is much like a factual

question. The issue cannot be settled by definition or stipulation.

What is needed are facts about a logic, facts about induction.

The only way to settle the issue of whether a logic is justified

is to reason about the logic. What the logic is capable of doing has to be examined and inference drawn from the results

of the examination as to whether the logic is truth preserving-- whether it always leads from true premises to a true conclusion.

There have been historically important philosophers who have

recognized that the justification issue was quasi-factual and who use factual techniques to approach the issue. What is recognized is that some inductive arguments which seem proper

in all respects nevertheless have true premises and a false conclusion. This holds even though at the time when the arguments were first offered it could not be known that the conclusion was false. If this had been known at that time,

then there would have been available relevant evidence not considered in the premises and the argument would have not been logically proper. Hence, the only acceptable counterexamples

IQ An earlier version of this and the following section appeared as" 1 Self-Supporting' Inductive Arguments," Boston Studies in The Philosophy of Science, Vol. VIII, ed. R. Cohen and R, Buck, (Boston: Boston University, 1971). It was read at the Second Biennual Meeting of the Philosophy of Science Association in Boston, October, 1970. 203

to the justification claim are inductive arguments which have

had widespread historical approval but which led to conclusions

which were later overthrown by other scientists. The only

serious attack upon induction arises from the evaluating

characteristic of science. What is needed now are facts about

induction which will show that inductive procedures will

continue to lead towards the truth. This shall be done by

first examining two other attempts which have recognized this

approach and by learning how they went wrong.

Before beginning, however, an assumption buried in the

above paragraph deserves to be evaluated. It was stated above

that there have been successful inductive arguments. These

would be arguments which have led from true premises to true

conclusions. Indeed these arguments would provide sufficient

reason for a claim that these conclusions are known. The

issue that will be examined below is the prospects that such arguments will continue to be available in the future. A sceptic or someone adopting the Humean position would challenge this assumption. Philosophically, they would claim, there is no reason to accept any inductive argument. As ordinary people, we have to accept then, they are the basis of many of our actions. But as philosophers, we see that they are not justified arguments. If the sceptics are allowed to establish the starting point of arguments about induction, then such arguments cannot depend upon any non-analytic generalization. But contingent 204

genera lizations are supported only by inductive arguments. To

challenge inductive arguments as such is then to challenge

contingent generalizations. The arguments about induction

could only depend upon atomic facts and deductive logic for

inductive arguments and all that rests upon them are to be

defended in the argument. The conclusion could not be

"induction is justified" because that is a contingent generali­

zation according to a prior argument and deductive logic can

only prove contingent generalizations from other contingent

generalizations. So any attempt to start with the sceptical

position and build deductively to "induction is justified"

is doomed to failure. Put another way, any attempt to so

build gets to the desired conclusion only if it begs the question.

The sceptic has made it analytic that induction is unjustified.

The starting point here is to assume that scientists are using

efficacious methods for predicting the future and that the

philosophic job is to prove that they are justified methods.

The philosopher does not challenge the scientist's results;

his methods have worked, they are efficacious. The philosopher

asks: Given that they have worked, will they continue to work?

The first approach to the problem is that of Max Black.^0

He assumes that the question of the justification of induction

is itself a question which may be answered by means of an

^.The basic paper is "Self-Supporting Inductive Arguments," Journal of Philosophy. Vol. LV (August, 1958). 205

inductive argument. This approach was criticised even by Hume.21

Indeed, Black stands almost alone among philosophers in claiming

that the problem of induction may be solved through an inductive

examination of previous inductive arguments. Black investigates

the rule.

Rl To argue from Most instances of A's examined under a wide variety of conditions have been B to (probably) The next A to be encountered will be B .

It can be granted that this is an inductive rule of inference. There may be many other inductive rules, but if this one rule can be justified, philosophers will have done a lot.

Certainly a rule very much like it could have been employed by most scientists. Their rule would have probably had a stronger conclusion, but then in any argument in which their rule worked successfully so too would have Rl. This, or any other inference rule is successful in a particular application, if and only if in that application it proceeds from true premises to a true conclusion. It does not matter whether the success was fortuitous or rational. Even a rule like

To argue from The last flip of coin C is heads (tails') to The next A to be encountered is (not) B . may be successful on an occasional application.

Black reasons inductively about Rl in the argument

A1 In most instances of the use of Rl in arguments with true premises examined in a wide variety of conditions, Rl has been successful.

Hence (probably) .

2 treatise. .., Book I, Part III, Section XII. 206

In the next instance to be encountered of the use of Rl in an argument with a true premise, Rl will be successful.

This argument, itself, used Rl as its rule of inference. So, of course, it is an inductive argument.

The critics of this approach, going back to Hume, have argued that it is circular. It used induction (Rl) to argue about itself and hence presupposes that induction is justified-- the very point in issue.

The conclusion of the argument would only be believed if it logically followed from the premises. To believe that the conclusion so follows is to accept the use of Rl in Al as justified. But it is the justification of Rl which is the issue. Hence, the critics claim that Black has begged the question.

Black counters by pointing out that the premise of Al is not identical with its conclusion nor does it follow from the conclusion. These are the two usual reasons in support of a claim of a circular argument. Either one of the premises is the same as the conclusion or the premise follows from the conclusion--if either of these hold, then the argument is circular. Since the conditions are not met, Black argues that the argument is not circular.

Nevertheless, there is a third more general criterion for circularity which Black has overlooked. Fortunately, it does not vitiate his general claim. The third criterion is that an argument is circular if the premise would be believed

only by someone who already believes the conclusion. However,

Al is clearly not circular on this ground either. Furthermore,

the employment of Rl in Al is not itself one of the uses of Rl

to which the conclusion alludes since it is not the next

application of Rl. The acceptance of the premise of Al depends

upon the existence of successful uses of Rl. Is the use of Rl

in Al one of these? The question can be divided into two

parts: First, is the use of Rl in Al successful? And second,

is this use of Rl one of the instances of Rl upon which the

premise of Al depends? As noted above, an inference rule is

successful if it leads from true premises to a true conclusion.

In this section induction will be justified. This amounts to

the claim that most applications of inductive procedures to

true premises (probably) yield a true conclusion and where this does not happen, relevant data are missing from the premises.

Hence, being a conclusion of an inductive argument with true premises justifies the claim of truth. If this were all that counted, then, if induction were justified, every application of inductive inference would be successful. But this is not the case. Even though inductive reasoning is one way of establishing the truth of a claim, it is not the way which is required in a proof of success. There only direct comparison of the claim with the world will do. That is, success depends upon correspondence. A rule is successful in application if 203 and only if its conclusion actually occurs. This topic will be returned to below. Hence, the application of Rl in Al is successful only if the conclusion of Al corresponds to the world, only if the next application of Rl is successful. Since the next application of Rl has yet to occur, it is now not known whether the application of Rl in Al is successful. It therefore cannot be one of the uses of Rl examined in order to establish the premise of Al. This would be still another piece of evidence in support of Black's thesis that he has not argued in a circle.

In effect, Black's defense against the charge of circularity rests upon the point that he is only arguing about the next application of Rl. Since the argument in no way depends upon sneaking into the argument a premise which depends for its truth upon the success of the next employment of Rl nor upon sneaking into it an inference rule which depends for its acceptance upon the success of the next employment of Rl, Black holds that he has committed no logical fallacies.

The critics treat this as a subterfuge. For them, the issue of defending logic is not one of the legitimacy of this or that application of Rl (inductive logic) but rather Rl itself.

Either all uses of Rl are justified or none are. For them, the issue is not the success of each application, but rather the success of most applications of the rule. A rule is justified if most applications of it are successful. To bring home their point, they try to show that Black's method is erroneous by 209

showing that it can be used to "justify" what are clearly

unjustified inference rules. They consider rules which are

clearlymistaken and use one application of the rule to justify

the next. If the procedure employed by Black will defend what

are clearly unjustified rules, then it is not adequate when dealing with induction. 22 Wesley Salmon, for example, used the counter inductive rule

R2 To argue from Most instances of A ’s examined in a wide variety of conditions have been B to (probably) The next A to be encountered will be B .

This rule is counter inductive since it clearly presupposes

that the future will not be like the past. It is also important because from the same body of evidence, R2 and Rl will lead to contradictory predictions. Since not both Rl and R2 can hold in the same universe, any procedure which justified both of them would be logically incoherent. If Black's procedure justifies R2, then the argument in defense of Rl is simply unacceptable. Salmon presents an argument about R2 which employs R2 as its rule of inference.

A2 In most instances of the use of R2 in arguments with true premises examined in a wide variety of conditions, R2 has been unsuccessful.

Hence (probably)

In the next instance to be encountered of the use of R2 in an argument with a true premise, R2 will be successful. . .

9 9 Among his basic papers on this topic is "Should We Attempt to Justify Induction?" Philosophical Studies, Vol. VIII, (April, 210

In the past, the future has been like the past. Prior to now,

if anyone had used R2 to make predictions, he would have

predicted wrongly quite often. But R2 predicts that the future

will be unlike the past. Since R2 has previously been usually

wrong, its next use will lead to a true conclusion. Black's

procedure seems to be capable of defending R2. Since it also

defends Rl and the two rules are logically incompatible, the

justification procedure itself must be mistaken.

23 Peter Achinstein , who sides with Salmon against Black,

uses a somewhat different sort of incorrect inference rule for a counter-example to Black's procedure. His fallacious inference rule is deductive.

R3 To argue from No F is G and Some G is H to All F is H .

This rule would permit the invalid syllogism IEA-1. He justifies

it by means of an IEA-1 syllogism.

A3 No argument using R3 as its rule of inference is an argument which contains a premise beginning with the term "All".

Some arguments containing a premise beginning with the term "All" are valid.

1957). But see also note 24 below.

2-hiis contribution is "The Circularity of A Self-Supporting Inductive Argument", Analysis, Vol. 22, (June, 1962). The three previously cited papers are all reprinted in The Philosophy of Science, ed. P. H. Nidditch, (London: Oxford University Press, 1968). Black's reply to Achinstein is "Self-Support and Circularity: A Reply to Mr. Achinstein," Analysis. Vol.23, (October, .1962). See ilso his "Comments on Salmon's Paper," Induction: Some Current Issues, ed. H. Kyburg and E. Nagel, (Middletown, Connecticut: Wesleyan University, 1963). 211

/.*• All arguments using R3 as their rule of inference are valid.

The usual techniques for the metalogic of deduction can be used to show that R3 is a rule which allows for inference from true premises to a false conclusion. Such an example is A3. Xf

Black's procedure justifies Rl then it must justify R3 too.

Since R3 is not justified, neither is Rl.

Black seems to be bested by his critics so that his approach cannot work unless there is a reason for restricting the justifying argument to the use of Rl. Below, the work of

Hans Reichenbach will be construed to take this step,

Reichenbach^ gave up the attempt to justify induction.

He rather tried to justify the use of induction. Since he accepted the Humean critique of induction, he felt that attempts to justify induction would be fruitless. There could be no guarantee that there is a way of predicting the future. But he reasoned that if there is a way of predicting the future, the pragmatic choice would be to stick with induction. A means of predicting the future would be a rule which uses markers observable now to predict the future. (One sense of the thesis that the future resembles the past is that there are such markers.)

What is needed are the markers in the past and present which

^ Experience and Prediction. (Chicago: University of Chicago, 1938), 348-363. Salmon's work is a continuation of Reichenbach's. In this connection,, see the discussion of Salmon in Current Issues in the Philosophy of Science, ed. H. Feigl and G. Maxwell, (New York: Holt, Rinehart and Winston, 1961). 212 point to the future. Induction looks to past regularities as the markers. R2 looks to past irregularities as the marker.

Fortune tellers look to crystal balls or tea leaves as the markers. But all inference techniques for dealing with the future look to some kind of marker or other. If there are no markers at all, then the inference rules for predicting the future are equally useless; however, there being no way to predict the future, each inference technique is also as useful as any other. The user of induction is no worse off (or better off) than the user of any other method. But in a world which contains markers, the user of induction has an advantage. If the markers are the sort which induction picks out, then induction can be used to predict the future. If the markers are not the sort which induction picks out, then induction will not predict the future, but it will pick out a correlation between application of the correct method and the success of its prediction. Here induction is not used to infer about the world but rather about inference techniques. The advantage of using induction over any other method is that if it cannot be used to infer the future, it can still be used to pick the successful method from among all the others. Reichenbach says that induction is the best bet because it cannot lead you astray if there is no way of predicting the future and if there is a way of predicting the future, induction is either that method 213 25 or will find the successful method.

Reichenbach1s method, however, also proves too much.

Like Black's procedure, Reichenbach's can be used todefend

other rules than Rl. A tea leaf reader could argue: If there

is no way of predicting the future, then the user of tea leaf

reading is no worse off (or better off) than the user of any

other method. But, if there is a way of predicting the future,

then it is either tea leaf reading or, if it is some other method, then the correct method can be found by reading the leaves since "everything is found in the leaves." The tea leaf reader would then conclude that even if tea leaf reading is not justifiable, the use of tea leaf readingis justified.Once again, if the procedure could be restricted toRl as the inference rule, then the problem would be solved.

Both Black and Reichenbach have employed induction to reason about logic without invoking the basic logical distinction between using a logic and talking about a logic. Logicians distinguish between the object language which contains the language which is the object of discussion and the metalanguage which is used to talk about the object language. One of the sources of the distinction is the liar paradox. In modern dress it occurs thusly:

(A) Sentence B is true (B) Sentence A is false . . .

Compare Reichenbach's development of the point with H. Feigl, "De Principiis Non Disputandum.. . Philosophical Analysis. ed. M. Black, (Englewood Cliffs, N.J.: Prentice-Hall, 1950). 214

If (A) is true, then (B) is true. But if (B) is true, then

(A) is false. On the other hand, if (A) is false, then (B)

is false. But if (B) is false, then (A) is true. So that (A)

is true if and only if (A) is false. The last sentence, of

course, is a contradiction. Yet the sentences seem meaningful

and hence the sentences seem to be either true or false. But

if either sentence has one truth value it has the other as well.

The basic way of removing the paradox is to structure

languages into a referential hierarchy. No language may be

used to refer to itself or to languages "above" it in the

hierarchy. The lowest level language is the object language.

On the next level is the metalanguage. Then there is the

metametalanguage. The process need not terminate depending

upon the needs of the logician discussing the object language.

There are ways, however, of circumventing the hierarchy.

Kurt Godel devised a way of constructing an analogue of a

language within the language itself. The language could

be used to talk about itself by means of expressions in the

analogue. Even then, nevertheless, the dictionary to translate

between the analogue and the language can only be stated in

the metalanguage. Also, the analogue can only be used to talk

about the language under some interpretations. It was a key

^ A n informal development of Godel's result may be found in E. Nagel and J. R. Newman, Godel's Proof, (New York: New York University, 1960). 215

result of Godel that no analogue could be used under every 27 interpretation. In any event, the level of language

distinction or, as it is sometimes termed, the use/mention

distinction, solves the liar paradox. If sentence (A) refers

to sentence (B), then (A) must occur in the metalanguage for the

language in which (B) occurs. But, then, (B) cannot refer

to (A). Whatever (B) does refer to, if it can be construed

as meaningful, it is not (A). The paradox is removed because

(B) is either meaningless or it does not refer to (A).

The distinction is, perhaps, more useful in the

formalization of a logic. The difficulty in a formal approach

is that it is not only necessary to prove things with a logic

but it is also necessary to prove things about the logic. Proofs

with a logic are not convincing unless the logic, speaking

roughly, is free from contradictions--it is consistent. If a

logic could be used to prove every sentence, then the logic is epistemologically useless for a logic which will go from

i true premises to a false conclusion is not convincing. Since among the totality of sentences are false ones, if a logic could prove every sentence, it would lack conviction. The usual procedure is to prove that a logic is rich enough to be capable of having formulated within it all the truths of the subject matter under discussion. But it is also proven that some nontruths are expressible but not provable with the logic.

27 See H. DcLong, A Profile of Mathematical Logic, (Princeton: Van Nostrand, 1965), Chapter 4, Section 23, Part C. 216

This is sufficient to prove that the logic is free from contradiction. Since not every meaningful sentence is provable, it is also desirable to show that not only are all truths of interest expressable in the logic but that they are also provable.

This consititues a proof that the logic is complete.

The proof cannot be contained within the logic itself for it is about the logic. As one contemporary logician expresses the point;

It is important to observe that a proof of the completeness of a deductive system is not itself a deduction within the system, though the fact that certain deductions, and certain kinds of deduction are possible within the system, will be an important part of it. The proof of completeness is a proof of something about the system; it involves viewing the

system, as it were, from the o u t s i d e .26

If a man said to you that he always tells the truth, his merely asserting the words would not prove their authenticity, for even a liar can assert them. So too with a logic. If a logic could be used to prove of itself that it was consistent, that would not count for an inconsistent logic could do the same. What is needed is a proof in a different logic. The lowest level logic usually discussed is propositional logic or the prepositional calculus, PC. Many formulations of it can be proven both consistent and complete. The metalanguage in which this is done contains a logic much more powerful than propositional logic. Yet propositional logic is the basis of most reasoning in formal systems.

2^a . N. Prior, Forma 1..., 64. 217

Rules such as modus ponens and hypothetical syllogism are constantly invoked. The metalogic contains arguments about propositional

logic which seem to use such rules. If they were the same rules,

then the process would be circular. The metalogic is informal. It contains expressions in natural language which are about the consequences of the existence of certain proofs in the object language, and these consequences are proven to follow. The metaproofs employ what look like the same inference rules as those in the object language. But the process is not circular so the inferences do not employ propositional logic.

A typical consistency proof for the propositional calculus

(PC) might look like

(8) If there is an interpretation of the axioms of PC under which they are all true, then if the rules of inference for PC only go (under the intended interpretation) from true premises to a true conclusion, then PC is consistent.

(9) The standard truth tables give an interpretation for PC under which the axioms are all true.

(10) Therefore, if the rules of inference for PC only go (under the intended interpretation) from true premises to a true conclusion, then PC is consistent.

(11) The rules of inference for PC only go (under the intended interpretation) from true premise to a true conclusion.

/.'. (12) Therefore, PC is consistent.

The inferences from (3) and (9) to (10) and from (10) and (11) to

(12) appear to be instances of modus ponens. If they were, then the whole argument would beg the question since one of the things that (12) shows is that modus ponens is a legitimate inference 213

rule. The issue in the metalanguage is the legitimacy of modus

ponens and all the other propositional proof procedures. If they

are the inference rules by which conclusions are informally

drawn in the metalanguage, the arguments will lack all conviction.

If one of the subsystems of the logic employed in the metalanguage

were the propositional calculus, the entire usefulness of the

formal approach to logic would be eliminated.

Both Black and Reichenbach are logicians. It is a howler

that they have not invoked this fundamental distinction in their

discussions of inductive logic. Perhaps this is due to their not

thinking of inductive logic as being formalizeable. One can write

the form of modus ponens. But, what is the form of an inductive argument? Above it was shown how poorly even the paradigm captures the inductive approach. Nevertheless, courses in inductive logic (sampling theory) are often taught in universities.

Even if the logic is not formalized with symbols on these pages, basic logical distinctions should be observed. After all, if a procedure can be followed when justifying deduction, then it can be followed when justifying induction, assuming that all other factors are the same. No philosopher has doubts about deduction because its foundation has been examined. But if the level of language distinctions were not observed, then the examination would be circular and deduction could not ever be justified. Hence, it is not only permissible, but necessary to observe this distinction in discussions of induction.

In our object language there will be inductive logic in 219

addition to any other alleged method of predicting the future. Our

object language contains all sorts of applications of these

methods. There will be many successful applications of inductive

logic, but few successful ones of R2 as well as, presumably, few

of card reading and crystal ball gazing.

The metalanguage presents more of a problem. It will

contain deductive logic but, as was seen above, that is.not enough.

' The goal of the metalanguage arguments Is to find a successful

furture predicting rule. Reichenbach has provided a criterion

for induction in our hunt for the successful rule. If there is a

successful rule, then a good proportion of the times that It is

applied to true premises it will lead to a true conclusion.

Induction certainly would pick out the object language rule which

had a high degree of success, if it could occur in the metalanguage

aB a principle of selection for object language success.

Unfortunately, it cannot for it is already in the object language.

What is needed in the metalanguage is simply a metarule that an

object rule is justified if more often than not its applications

are successful. (The exact proportion is a mathematical detail

which need not be considered here.) That is, the metarule would

be one like Rl. For this kind of reason a metarule similar

to R2 is unacceptable since it would pass over an object rule

which had a high degree of success. But the metarule adopted here

would pick out R2 in the object language if R2 had a high degree

of success.

However, there still reamins the question of the criterion 220

of success. A tea leaf reader might argue that success was

finding the name of the rule In the tea leaves and hence tea

leaf reading should be a metaprocedure. Nevertheless, even

people who believe in tea leaf reading do not.take the tea

leaves as success itself, they are only the mark of success to

come. If I ask who will win the race and the tea leave show "Ajax",

then that does not allow me to now collect the bets. The race has

to be won before there is success. A rule is successful not

because its name appears in the leaves, even though a tea leaf

reader would claim that it is a sign of success. Success has to do

with truth.

A rule is only successful if it often leads from true

premises to a true conclusion. The measure is actually examining

the application of the rule, not examining tea leaves or crystal

balls. So that the ubusI criterion for truth operates on both

the object language level and on the metalanguage level. The

above metarule needs to be modified in light of this to read: . .

R4 An object language rule is justified which has a high degree of success of application as measured by actual correspondence between the conclusion of the application and the world.

.This rule is inductive-like in that if induction were a meta­

principle, it would pick out the same rule as the metarule will

pick out.

Presumably, this metarule will pick induction as a justified

object rule. For example, If the Justified rulb is termed 'R5',

then the metaargument would be 221

A5 In most Instances of the use of R5 In arguments with true premises examined In a wide variety of conditions, R5 has been successful

. Hence (probably)

In the next Instance to be encountered of the use of R5 In an argument with a true premise, R5 will be successfult

The argument Is much like Black's A1 and Is, as a matter of fact,

what Reichenbach1s argument pointed at, Inductive (here Induetive-

✓ like) Inference can pick out any justified method of predicting

the future, If there be any, A5 uses a metarule like Rl, R4, as its

rule of inference. Black's and Reichenbach's positions are very

similar once their positions are restated using the object language/

metalanguage distinction. They only differ in that Reichenbach

unlike Black allows for the possibility that a noninductive rule

will be Justified.^

In any event, induction has been justified in the

metaargument. In a noncircular way it has been proved that ■ m induction leads, most of the time, from true premises to a true

conclusion. In those cases from the history of science where all

experimentation pointed at a, now known to be, false conclusion,

29 The examples of metaarguments have been couched in terms of induction to the next case while much of the discussion has centered on induction to generalizations. The "next case" examples have been used because they are the ones which appear in the literature, particularly in Black's essays. On the other hand, Reichenbach almost always talks about generalizations. If the discrepancy bothers the reader, he may simply translate all examples into ones about inference to generalisations, the same arguments Kork in either situation.

1 222

the error was the experimenter's and not the logic's. If the

fault lay with the logic, then further examination of the data

for the overlooked parameters of the system woul.d be foolish

since the logic operated on acceptable premises. (If the premises

were unacceptable, then the mistaken conclusion is their

responsibility and not the method of Inference.) Integrating the

result with the model helps eliminate the possibility of overlooking

✓ relevant data by insuring that new findings are consistent with

everything else known about the world. Hence, even difficulties

in the problem of induction arise through lack of appreciation

of the central role that models play in science.

4.4 Some Misconceptions Clarified

Two main sources of misconception need to be avoided. The

first sort raises the old Humean attack on Induction against the

metarule. This cannot be entirely answered except in that It

leads to scepticism about deduction. The other source attacks not'

the metarule but rather the notion of success. Could not

philosophers construct so many unsuccessful applications of any

object language rule that more of them are unsuccessful than not?

. If some unsuccessful applications are known, could not more be

constructed? A careful re-examination of the results of the

section on counter examples entirely removes the brunt of this

attack.

The first kind of misconception arises from the following

considerations: The metarule picks out the object rule which in 223

the past has had a high degree of success. It uses past success

as the mark of future success. In the past the criterion has

worked. What reason Is there to believe that this will continue

to be the mark in the future? Hume worried about whether the

future will be like the past. He wondered whether past physical

regularities would be preserved in the future. About inductive

logic, it can be wondered whether past correlation of successful

, application will continue to hold in the future. In deductive

metatheory, proof is given by a deductive-like metalogic that

deduction as used in the object language is truth preserving. In

inductive metatheory, proof is given by an inductive-like

metalogic that induction as used in the object language is

truth preserving.

For example, there could be a point in time at which all

(previously) justified methods of predicting the future no longer

are successful in application and at which all unjustified methods

of predicting the future are successful in application. This

time would also mark an enormous physical upheaval since all

previous regular physical processes would cease. It could be

a time after which no one object rule worked continuously. Each

rule would work at certain times and not at others. Any meta­

rule which looked for regularities would be systematically misled.

Only a metarule which looked for systematized changing efficacy

would ever pick out which object rule to use where. In shortt

what is needed is a metametarule for picking out the metarule.

Indeed, the argument above for the metarule is a metametaargument. 4

224

There is no reason to suppose, however) that thia is the

case. The metarule adopted was chosen just because it would pick

out a justified object rule. Its choice was on pragmatic grounds.

What is being looked for is a usually successful rule for dealing

with physical relations. The above challenge looks instead for

a logical rule which will be successful in its next application.

The rule which Is successful next need not be justified since it

, may be rarely successful. The challenge depends upon changing

the quest of the metarule. What is done in the metalanguage

depends upon the desires of logicians. One problem is Bolved

abovef but the challenge asks for a solution to another.

The challenge could be raised in a different way. What

has been done above is to justify induction on the object level.

How can induction be justified on the metalevel? That is,

how can reassurance be given that metainduction will continue to

pick out the object rule which is successful in application more

often than not? If the arguments above are not satisfactory on

this point, then the kind of reassurance required depends upon a

metametainductlve .principle which is to be defended in the same

way as was the metainductive principle. Similarly, if the

deductive logic in the metalogic for deductions is challenged

(If, for example, it is asked whether the metaloglc is consistent)

the answer depends upon metametalogic. For example, the R2-like

rule was eliminated from the metalanguage on the metametagrounds

s • that is would not select any successful future predicting object

language rule. If escalation to the me tame talevel and beyond 225

raises doubts about the satisfactoriness of the solution to the

inductive problem, then the analogous move about deduction should

raise analogous doubts about deduction. Attacks upon the meta-

approach to induction seem to also be attacks upon the meta­

approach to deduction. The approach is either acceptable in both

cases or to be rejected in both cases. Philosophers who are

uncomfortable about induction should also be uncomfortable about

, deduction.

Perhaps eliminating the second kind of misconception will

alleviate the last lingering doubts. A justified method of

predicting the future has far more successful applications than

unsuccessful ones, but there are unsuccessful ones. Even laws

which are supported in the model may later prove wrong. Could

not the unsuccessful ones be used as guides to the construction

of more unsuccessful ones? Ultimately, so many unsuccessful

applications could be constructed that induction, or any other

method, would have far more unsuccessful applications than

successful ones. By constructing these unsuccessful applications

any once justified inference technique could be turned into an

unjustified one. As attractive an objection as this might seem,

the program cannot be carried out. Unsuccessful applications have

to occur in scientific practice, they cannot just be Imagined as

Hume held. The requirement for proper application of induction

are two fold. First, the scientist must draw upon all information

that his experiments elicit. But, more important, for the present

purposes, the generalisation that his experiments support must be 226

fit into the model. Until this is done there is no reason to

suppose that it is nothing more than an accidental generalization 30 such as the Bode-Titus "law". In short, the unsuccessful

application would have to support what scientists would accept

as a law but which law-like sentence later turned out to be

false. If the argument constructor already knew that the law was

false,'he would be leaving relevant information out of the

, inductive argument and hence it would be logically incorrect. The

only unsuccessful applications of interest go wrong for no other

reason than they have a false conclusion (which can later be

traced to relevant facts missing from the premises). Here the

Integration into the model proved an unreliable guide to the

inclusion of all relevant evidence since the model was itself

incorrect. Unsuccessful applications can not be constructed

willfully because that would involve violating the condition of

using all available relevant evidence. 4 Consideration of the distinction between an accidental

\ generalization and a scientific law led to the realization of the

importance of the model in science. It was further realized that

every scientific law had its extension in the model because in

science no generalization is true simply because its subject has

an empty extension. Several important problems in the philosophy

of science were cleared up with the aid of these realizations.. ..

^This "law" relates the distances of the. planets from the sun to distance of the Earth to the sun. See H and R . ^ Chapter 12, Section 8. 227

These problems Included those of the status of counter-factual

conditionals as well as the paradox of confirmation. Finally,

the problem of induction itself was tackled. Once again the

realization of the Importance of the model proved paramount. The

model insures the Integration of each discovered law into one

science. Hence, Inductive logic meets a total evidence condition.

Consequently, the only acceptable counter examples to the claim

. that Induction is justified are the past mistakes of science. But

since the model insures that future evidence will be brought to

bear on previously accepted (but false) generalizations; occasional

lack of success of application is not a problem; Induction discovers

the conclusions which are wrong but were once accepted. The

mistaken conclusion was inferred to because relevant information

was left out of the premises. If the logic were faulty, if it

were the case that an otherwise correct Inductive argument went

from true premises to a false conclusion, then when such a case * arose there would be no need to re-examine the premises since by

hypothesis they are correct. But scientists do re-examine the

premises in such cases. They search for and find relevant

information previously overlooked. Allowing induction occasionally

to yield mistaken results due to faulty logic undercuts the

experimental drive; hence, induction leads to a false conclusion

only when relevant data is left out of the premises. Integration

of the inductive results with past laws in the model will continue

to be a mark of having employed all relevant evidence in the

premises because It has been in the past* This is not arguing In

• ' * i ■*- > (

* V L ' 4 ' I r ' ' ' ■ -j. • 228 a circle because the last statement depends upon a metalinguistic argument. No metalanguage contains for its rules of reasoning any rules which occur in the object language. The adoption of an inductive-like rule in the metalanguage is defensible on the pragmatic grounds that it will pick out any justified method for predicting the future, if there is one. Since the metarule picks out induction, induction is finally justified. BIBLIOGRAPHY

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