Contrastive Empiricism
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Chapter 5: Methods of Proof for Boolean Logic
Chapter 5: Methods of Proof for Boolean Logic § 5.1 Valid inference steps Conjunction elimination Sometimes called simplification. From a conjunction, infer any of the conjuncts. • From P ∧ Q, infer P (or infer Q). Conjunction introduction Sometimes called conjunction. From a pair of sentences, infer their conjunction. • From P and Q, infer P ∧ Q. § 5.2 Proof by cases This is another valid inference step (it will form the rule of disjunction elimination in our formal deductive system and in Fitch), but it is also a powerful proof strategy. In a proof by cases, one begins with a disjunction (as a premise, or as an intermediate conclusion already proved). One then shows that a certain consequence may be deduced from each of the disjuncts taken separately. One concludes that that same sentence is a consequence of the entire disjunction. • From P ∨ Q, and from the fact that S follows from P and S also follows from Q, infer S. The general proof strategy looks like this: if you have a disjunction, then you know that at least one of the disjuncts is true—you just don’t know which one. So you consider the individual “cases” (i.e., disjuncts), one at a time. You assume the first disjunct, and then derive your conclusion from it. You repeat this process for each disjunct. So it doesn’t matter which disjunct is true—you get the same conclusion in any case. Hence you may infer that it follows from the entire disjunction. In practice, this method of proof requires the use of “subproofs”—we will take these up in the next chapter when we look at formal proofs. -
In Defence of Constructive Empiricism: Metaphysics Versus Science
To appear in Journal for General Philosophy of Science (2004) In Defence of Constructive Empiricism: Metaphysics versus Science F.A. Muller Institute for the History and Philosophy of Science and Mathematics Utrecht University, P.O. Box 80.000 3508 TA Utrecht, The Netherlands E-mail: [email protected] August 2003 Summary Over the past years, in books and journals (this journal included), N. Maxwell launched a ferocious attack on B.C. van Fraassen's view of science called Con- structive Empiricism (CE). This attack has been totally ignored. Must we con- clude from this silence that no defence is possible against the attack and that a fortiori Maxwell has buried CE once and for all, or is the attack too obviously flawed as not to merit exposure? We believe that neither is the case and hope that a careful dissection of Maxwell's reasoning will make this clear. This dis- section includes an analysis of Maxwell's `aberrance-argument' (omnipresent in his many writings) for the contentious claim that science implicitly and per- manently accepts a substantial, metaphysical thesis about the universe. This claim generally has been ignored too, for more than a quarter of a century. Our con- clusions will be that, first, Maxwell's attacks on CE can be beaten off; secondly, his `aberrance-arguments' do not establish what Maxwell believes they estab- lish; but, thirdly, we can draw a number of valuable lessons from these attacks about the nature of science and of the libertarian nature of CE. Table of Contents on other side −! Contents 1 Exordium: What is Maxwell's Argument? 1 2 Does Science Implicitly Accept Metaphysics? 3 2.1 Aberrant Theories . -
There Is No Pure Empirical Reasoning
There Is No Pure Empirical Reasoning 1. Empiricism and the Question of Empirical Reasons Empiricism may be defined as the view there is no a priori justification for any synthetic claim. Critics object that empiricism cannot account for all the kinds of knowledge we seem to possess, such as moral knowledge, metaphysical knowledge, mathematical knowledge, and modal knowledge.1 In some cases, empiricists try to account for these types of knowledge; in other cases, they shrug off the objections, happily concluding, for example, that there is no moral knowledge, or that there is no metaphysical knowledge.2 But empiricism cannot shrug off just any type of knowledge; to be minimally plausible, empiricism must, for example, at least be able to account for paradigm instances of empirical knowledge, including especially scientific knowledge. Empirical knowledge can be divided into three categories: (a) knowledge by direct observation; (b) knowledge that is deductively inferred from observations; and (c) knowledge that is non-deductively inferred from observations, including knowledge arrived at by induction and inference to the best explanation. Category (c) includes all scientific knowledge. This category is of particular import to empiricists, many of whom take scientific knowledge as a sort of paradigm for knowledge in general; indeed, this forms a central source of motivation for empiricism.3 Thus, if there is any kind of knowledge that empiricists need to be able to account for, it is knowledge of type (c). I use the term “empirical reasoning” to refer to the reasoning involved in acquiring this type of knowledge – that is, to any instance of reasoning in which (i) the premises are justified directly by observation, (ii) the reasoning is non- deductive, and (iii) the reasoning provides adequate justification for the conclusion. -
Truth, Rationality, and the Growth of Scientific Knowledge
....... CONJECTURES sense similar to that in which processes or things may be said to be parts of the world; that the world consists of facts in a sense in which it may be said to consist of (four dimensional) processes or of (three dimensional) things. They believe that, just as certain nouns are names of things, sentences are names of facts. And they sometimes even believe that sentences are some- thing like pictures of facts, or that they are projections of facts.7 But all this is mistaken. The fact that there is no elephant in this room is not one of the processes or parts ofthe world; nor is the fact that a hailstorm in Newfound- 10 land occurred exactIy I I I years after a tree collapsed in the New Zealand bush. Facts are something like a common product oflanguage and reality; they are reality pinned down by descriptive statements. They are like abstracts from TRUTH, RATIONALITY, AND THE a book, made in a language which is different from that of the original, and determined not only by the original book but nearly as much by the principles GROWTH OF SCIENTIFIC KNOWLEDGE of selection and by other methods of abstracting, and by the means of which the new language disposes. New linguistic means not only help us to describe 1. THE GROWTH OF KNOWLEDGE: THEORIES AND PROBLEMS new kinds of facts; in a way, they even create new kinds of facts. In a certain sense, these facts obviously existed before the new means were created which I were indispensable for their description; I say, 'obviously' because a calcula- tion, for example, ofthe movements of the planet Mercury of 100 years ago, MY aim in this lecture is to stress the significance of one particular aspect of carried out today with the help of the calculus of the theory of relativity, may science-its need to grow, or, if you like, its need to progress. -
Observational Determinism for Concurrent Program Security
Observational Determinism for Concurrent Program Security Steve Zdancewic Andrew C. Myers Department of Computer and Information Science Computer Science Department University of Pennsylvania Cornell University [email protected] [email protected] Abstract This paper makes two contributions. First, it presents a definition of information-flow security that is appropriate for Noninterference is a property of sequential programs that concurrent systems. Second, it describes a simple but ex- is useful for expressing security policies for data confiden- pressive concurrent language with a type system that prov- tiality and integrity. However, extending noninterference to ably enforces security. concurrent programs has proved problematic. In this pa- Notions of secure information flow are usually based on per we present a relatively expressive secure concurrent lan- noninterference [15], a property only defined for determin- guage. This language, based on existing concurrent calculi, istic systems. Intuitively, noninterference requires that the provides first-class channels, higher-order functions, and an publicly visible results of a computation do not depend on unbounded number of threads. Well-typed programs obey a confidential (or secret) information. Generalizing noninter- generalization of noninterference that ensures immunity to ference to concurrent languages is problematic because these internal timing attacks and to attacks that exploit informa- languages are naturally nondeterministic: the order of execu- tion about the thread scheduler. Elimination of these refine- tion of concurrent threads is not specified by the language se- ment attacks is possible because the enforced security prop- mantics. Although this nondeterminism permits a variety of erty extends noninterference with observational determin- thread scheduler implementations, it also leads to refinement ism. -
The Law and the Brain: Judging Scientific Evidence of Intent
The Journal of Appellate Practice and Process Volume 1 Issue 2 Article 4 1999 The Law and the Brain: Judging Scientific videnceE of Intent Erica Beecher-Monas Edgar Garcia-Rill Follow this and additional works at: https://lawrepository.ualr.edu/appellatepracticeprocess Part of the Evidence Commons, Jurisprudence Commons, and the Science and Technology Law Commons Recommended Citation Erica Beecher-Monas and Edgar Garcia-Rill, The Law and the Brain: Judging Scientific videnceE of Intent, 1 J. APP. PRAC. & PROCESS 243 (1999). Available at: https://lawrepository.ualr.edu/appellatepracticeprocess/vol1/iss2/4 This document is brought to you for free and open access by Bowen Law Repository: Scholarship & Archives. It has been accepted for inclusion in The Journal of Appellate Practice and Process by an authorized administrator of Bowen Law Repository: Scholarship & Archives. For more information, please contact [email protected]. THE LAW AND THE BRAIN: JUDGING SCIENTIFIC EVIDENCE OF INTENT Erica Beecher-Monas* and Edgar Garcia-Rill, Ph.D.** INTRODUCTION As evidentiary gatekeepers, judges must be ready to evaluate expert testimony about science and the brain. A wide variety of cases present issues of mental state, many doubtless with battling experts seeking to testify on these issues. This poses a dilemma for nonspecialist judges. How is a nonscientist to judge scientific evidence? How can a nonscientist decide if testimony about mental state meets the criteria of good science? This essay offers a general overview of the issue of evaluating scientific evidence and is aimed at exploring the issues involved, but not attempting easy answers. Of necessity, this requires thinking about how science works. -
1.) What Is the Difference Between Observation and Interpretation? Write a Short Paragraph in Your Journal (5-6 Sentences) Defining Both, with One Example Each
Observation and Response: Creative Response Template can be adapted to fit a variety of classes and types of responses Goals: Students will: • Practice observation skills and develop their abilities to find multiple possibilities for interpretation and response to visual material; • Consider the difference between observation and interpretation; • Develop descriptive skills, including close reading and metaphorical description; • Develop research skills by considering a visual text or object as a primary source; • Engage in creative response to access and communicate intellectually or emotionally challenging material. Observation exercises Part I You will keep a journal as you go through this exercise. This can be a physical notebook that pleases you or a word document on your computer. At junctures during the exercise, you will be asked to comment, define, reflect, and create in your journal on what you just did. Journal responses will be posted to Canvas at the conclusion of the exercise, either as word documents or as Jpegs. 1.) What is the difference between observation and interpretation? Write a short paragraph in your journal (5-6 sentences) defining both, with one example each. 2.) Set a timer on your phone or computer (or oven…) and observe the image provided for 1 minute. Quickly write a preliminary research question about it. At first glance, what are you curious about? What do you want to know? 3.) Set your timer for 5 minutes and write as many observations as possible about it. Try to keep making observations, even when you feel stuck. Keep returning to the question, “What do I see?” No observation is too big or too small, too obvious or too obscure. -
Persp V1n2 Final4pdf
MODERN SCIENCE AND THE SEARCH FOR TRUTH Brian Tonks—Department of Physics have pondered the question, “What is truth?” for many years. My I intellectual journey has convinced me that truth comes in many ways through a variety of sources. I began my schooling believing that scientists were searching for the truth, but my undergraduate training included classes in the history and philosophy of science that disillusioned me towards the scientific process. Then my service in the United States Navy showed me the practical utility of scientific principles, and my graduate studies provided real experience in how science really works. For five years I was involved in nearly all facets of the scientific process. My adult life spans the period of the Voyager missions to the outer planets, the Viking, Pathfinder, and Global Surveyor missions to Mars, and the Pioneer and Magellan missions to Venus. These missions demonstrated the power of scientific observation. Before Voyager, we knew little about the outer planets and even less about their satellites. Even in the largest ground-based telescopes, these appeared as mere pinpoints of light. Voyager revealed them as real worlds with actual, albeit bizarre, geology. Years of speculation were dispelled in a relative moment, reminding me of the Prophet Joseph Smith’s state- ment, “Could you gaze into heaven five minutes, you would know more than you would by reading all that was written on the subject” (History I have come full of the Church, 6:50). I have come full circle, believing today that science is an important source of truth. -
Achievements and Fallacies in Hume's Account of Infinite
-1- ACHIEVEMENTS AND FALLACIES IN HUME’S ACCOUNT OF INFINITE DIVISIBILITY James Franklin Hume Studies 20 (1994): 85-101 Throughout history,almost all mathematicians, physicists and philosophers have been of the opinion that space and time are infinitely divisible. That is, it is usually believedthat space and time do not consist of atoms, but that anypiece of space and time of non-zero size, howeversmall, can itself be divided into still smaller parts. This assumption is included in geometry,asinEuclid, and also in the Euclidean and non- Euclidean geometries used in modern physics. Of the fewwho have denied that space and time are infinitely divisible, the most notable are the ancient atomists, and Berkeleyand Hume. All of these assert not only that space and time might be atomic, but that theymust be. Infinite divisibility is, theysay, impossible on purely conceptual grounds. In the hundred years or so before Hume’s Tr eatise, there were occasional treatments of the matter,in places such as the Port Royal Logic, and Isaac Barrow’smathematical lectures of the 1660’s, 1 Theydonot add anything substantial to medievaltreatments of the same topic. 2 Mathematicians certainly did not take seriously the possibility that space and time might be atomic; Pascal, for example, instances the Chevalier de Me´re´’s belief in atomic space as proof of his total incompetence in mathematics. 3 The problem acquired amore philosophical cast when Bayle, in his Dictionary, tried to showthat both the assertion and the denial of the infinite divisibility of space led to contradictions; the problem thus appears as a general challenge to "Reason". -
Descartes' Arguments for Distinguishing Mind and Body
© Michael Lacewing Descartes’ arguments for distinguishing mind and body THE KNOWLEDGE ARGUMENT In Meditation II, having argued that he knows he thinks, Descartes then asks what kind of thing he is. Discussions of identity seek to establish the essential properties of something, what makes it the thing that it is. The question ‘what am I?’ can be answered by considering the question of what it is for me to exist. Descartes is trying to identify his essence, those properties which, if he lost them, would mean he was no longer what he is. (An island, for instance, must be surrounded by water. If the water dried up, joining it to the mainland, it would cease to be an island.) He remarks that he can continue to doubt whether he has a body; after all, he only believes he has a body as a result of his perceptual experiences, and so the demon could be deceiving him about this. But he cannot doubt that he has a mind, i.e. that he thinks. So he knows he exists even though he doesn’t know whether or not he has a body. From this Descartes concludes that it is possible for him to exist without a body. He is essentially a mind, not a body. He would not necessarily cease to be himself if he ceased to have a body, but he would necessarily cease to be himself if he didn’t have a mind. APPEAL TO GOD’S OMNIPOTENCE Descartes’ argument so far is that minds can exist without bodies. However, on its own, it doesn’t establish dualism. -
Deduction (I) Tautologies, Contradictions And
D (I) T, & L L October , Tautologies, contradictions and contingencies Consider the truth table of the following formula: p (p ∨ p) () If you look at the final column, you will notice that the truth value of the whole formula depends on the way a truth value is assigned to p: the whole formula is true if p is true and false if p is false. Contrast the truth table of (p ∨ p) in () with the truth table of (p ∨ ¬p) below: p ¬p (p ∨ ¬p) () If you look at the final column, you will notice that the truth value of the whole formula does not depend on the way a truth value is assigned to p. The formula is always true because of the meaning of the connectives. Finally, consider the truth table table of (p ∧ ¬p): p ¬p (p ∧ ¬p) () This time the formula is always false no matter what truth value p has. Tautology A statement is called a tautology if the final column in its truth table contains only ’s. Contradiction A statement is called a contradiction if the final column in its truth table contains only ’s. Contingency A statement is called a contingency or contingent if the final column in its truth table contains both ’s and ’s. Let’s consider some examples from the book. Can you figure out which of the following sentences are tautologies, which are contradictions and which contingencies? Hint: the answer is the same for all the formulas with a single row. () a. (p ∨ ¬p), (p → p), (p → (q → p)), ¬(p ∧ ¬p) b. -
The Critique of the Principle of Uniformitarianism and the Analysis
The Critique ofthe Principle ofUniformitarianism and the Analysis of High School Earth Science Textbooks Ho Jang Song and Hui Soo An Department ojEarth Science Education, Seoul National University Although uniformitarianism is widely recognized as the basic principle upon which the structure of historical geology has been erected, a closer investigation on the basis of present scientific knowledge and the philosophy of science reveals some of its invalid aspects. The concept of uniformitarianism wasdeveloped in a dual concept in Lyellian days. Substantive uniformitarianism (a testable theory of geologic change postulating uniformity of rates or material conditions) is false, ambiguous and stifling to hypotheses formation. Methodological uniformitarianism (a procedural principle asserting that former changes of the Earth's surface may be explained by reference to causes now in operation) belongs to the defmition of science and is not unique to geology. Moreover, it also has some methodological defects in forming bold and novel working hypotheses. Methodological uniformitarianism today should take the form of a much older and more general scientific principle: Occam's Razor, the principle of simplicity. Accordingly, substantive uniformitarianism, an incorrect theory, should be abandoned. Methodological uniformi tarianism, now a superfluous term, should be best confined to the historical roles in geology. In this connection, the presentation of uniformitarianism in high school textbooks was analyzed. It was revealed that text books were riddled with false and misleading statements as to what uniformi tarianism means. Since uniformitarianism, as presented in many textbooks, is in direct contradiction to the philosophy of Inquiry learning, it is important to rethink the direction of uniformitarianism presentation in Earth Science curriculum development.