Pluralisms About Truth and Logic Nathan Kellen University of Connecticut - Storrs, [email protected]
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Logical Truth, Contradictions, Inconsistency, and Logical Equivalence
Logical Truth, Contradictions, Inconsistency, and Logical Equivalence Logical Truth • The semantical concepts of logical truth, contradiction, inconsistency, and logi- cal equivalence in Predicate Logic are straightforward adaptations of the corre- sponding concepts in Sentence Logic. • A closed sentence X of Predicate Logic is logically true, X, if and only if X is true in all interpretations. • The logical truth of a sentence is proved directly using general reasoning in se- mantics. • Given soundness, one can also prove the logical truth of a sentence X by provid- ing a derivation with no premises. • The result of the derivation is that X is theorem, ` X. An Example • (∀x)Fx ⊃ (∃x)Fx. – Suppose d satisfies ‘(∀x)Fx’. – Then all x-variants of d satisfy ‘Fx’. – Since the domain D is non-empty, some x-variant of d satisfies ‘Fx’. – So d satisfies ‘(∃x)Fx’ – Therefore d satisfies ‘(∀x)Fx ⊃ (∃x)Fx’, QED. • ` (∀x)Fx ⊃ (∃x)Fx. 1 (∀x)Fx P 2 Fa 1 ∀ E 3 (∃x)Fx 1 ∃ I Contradictions • A closed sentence X of Predicate Logic is a contradiction if and only if X is false in all interpretations. • A sentence X is false in all interpretations if and only if its negation ∼X is true on all interpretations. • Therefore, one may directly demonstrate that a sentence is a contradiction by proving that its negation is a logical truth. • If the ∼X of a sentence is a logical truth, then given completeness, it is a theorem, and hence ∼X can be derived from no premises. 1 • If a sentence X is such that if it is true in any interpretation, both Y and ∼Y are true in that interpretation, then X cannot be true on any interpretation. -
Misconceived Relationships Between Logical Positivism and Quantitative Research: an Analysis in the Framework of Ian Hacking
DOCUMENT RESUME ED 452 266 TM 032 553 AUTHOR Yu, Chong Ho TITLE Misconceived Relationships between Logical Positivism and Quantitative Research: An Analysis in the Framework of Ian Hacking. PUB DATE 2001-04-07 NOTE 26p. PUB TYPE Opinion Papers (120) ED 2S PRICE MF01/PCO2 Plus Postage. 'DESCRIPTORS *Educational Research; *Research Methodology IDENTIFIERS *Logical Positivism ABSTRACT Although quantitative research methodology is widely applied by psychological researchers, there is a common misconception that quantitative research is based on logical positivism. This paper examines the relationship between quantitative research and eight major notions of logical positivism:(1) verification;(2) pro-observation;(3) anti-cause; (4) downplaying explanation;(5) anti-theoretical entities;(6) anti-metaphysics; (7) logical analysis; and (8) frequentist probability. It is argued that the underlying philosophy of modern quantitative research in psychology is in sharp contrast to logical positivism. Putting the labor of an out-dated philosophy into quantitative research may discourage psychological researchers from applying this research approach and may also lead to misguided dispute between quantitative and qualitative researchers. What is needed is to encourage researchers and students to keep an open mind to different methodologies and apply skepticism to examine the philosophical assumptions instead of accepting them unquestioningly. (Contains 1 figure and 75 references.)(Author/SLD) Reproductions supplied by EDRS are the best that can be made from the original document. Misconceived relationships between logical positivism and quantitative research: An analysis in the framework of Ian Hacking Chong Ho Yu, Ph.D. Arizona State University April 7, 2001 N N In 4-1 PERMISSION TO REPRODUCE AND DISSEMINATE THIS MATERIALHAS BEEN GRANTED BY Correspondence: TO THE EDUCATIONAL RESOURCES Chong Ho Yu, Ph.D. -
Some Unnoticed Implications of Churchland's Pragmatic Pluralism
Contemporary Pragmatism Editions Rodopi Vol. 8, No. 1 (June 2011), 173–189 © 2011 Beyond Eliminative Materialism: Some Unnoticed Implications of Churchland’s Pragmatic Pluralism Teed Rockwell Paul Churchland’s epistemology contains a tension between two positions, which I will call pragmatic pluralism and eliminative materialism. Pragmatic pluralism became predominant as his episte- mology became more neurocomputationally inspired, which saved him from the skepticism implicit in certain passages of the theory of reduction he outlined in Scientific Realism and the Plasticity of Mind. However, once he replaces eliminativism with a neurologically inspired pragmatic pluralism, Churchland (1) cannot claim that folk psychology might be a false theory, in any significant sense; (2) cannot claim that the concepts of Folk psychology might be empty of extension and lack reference; (3) cannot sustain Churchland’s critic- ism of Dennett’s “intentional stance”; (4) cannot claim to be a form of scientific realism, in the sense of believing that what science describes is somehow realer that what other conceptual systems describe. One of the worst aspects of specialization in Philosophy and the Sciences is that it often inhibits people from asking the questions that could dissolve long standing controversies. This paper will deal with one of these controversies: Churchland’s proposal that folk psychology is a theory that might be false. Even though one of Churchland’s greatest contributions to philosophy of mind was demonstrating that the issues in philosophy of mind were a subspecies of scientific reduction, still philosophers of psychology have usually defended or critiqued folk psychology without attempting to carefully analyze Churchland’s theory of reduction. -
The Analytic-Synthetic Distinction and the Classical Model of Science: Kant, Bolzano and Frege
Synthese (2010) 174:237–261 DOI 10.1007/s11229-008-9420-9 The analytic-synthetic distinction and the classical model of science: Kant, Bolzano and Frege Willem R. de Jong Received: 10 April 2007 / Revised: 24 July 2007 / Accepted: 1 April 2008 / Published online: 8 November 2008 © The Author(s) 2008. This article is published with open access at Springerlink.com Abstract This paper concentrates on some aspects of the history of the analytic- synthetic distinction from Kant to Bolzano and Frege. This history evinces con- siderable continuity but also some important discontinuities. The analytic-synthetic distinction has to be seen in the first place in relation to a science, i.e. an ordered system of cognition. Looking especially to the place and role of logic it will be argued that Kant, Bolzano and Frege each developed the analytic-synthetic distinction within the same conception of scientific rationality, that is, within the Classical Model of Science: scientific knowledge as cognitio ex principiis. But as we will see, the way the distinction between analytic and synthetic judgments or propositions functions within this model turns out to differ considerably between them. Keywords Analytic-synthetic · Science · Logic · Kant · Bolzano · Frege 1 Introduction As is well known, the critical Kant is the first to apply the analytic-synthetic distinction to such things as judgments, sentences or propositions. For Kant this distinction is not only important in his repudiation of traditional, so-called dogmatic, metaphysics, but it is also crucial in his inquiry into (the possibility of) metaphysics as a rational science. Namely, this distinction should be “indispensable with regard to the critique of human understanding, and therefore deserves to be classical in it” (Kant 1783, p. -
John P. Burgess Department of Philosophy Princeton University Princeton, NJ 08544-1006, USA [email protected]
John P. Burgess Department of Philosophy Princeton University Princeton, NJ 08544-1006, USA [email protected] LOGIC & PHILOSOPHICAL METHODOLOGY Introduction For present purposes “logic” will be understood to mean the subject whose development is described in Kneale & Kneale [1961] and of which a concise history is given in Scholz [1961]. As the terminological discussion at the beginning of the latter reference makes clear, this subject has at different times been known by different names, “analytics” and “organon” and “dialectic”, while inversely the name “logic” has at different times been applied much more broadly and loosely than it will be here. At certain times and in certain places — perhaps especially in Germany from the days of Kant through the days of Hegel — the label has come to be used so very broadly and loosely as to threaten to take in nearly the whole of metaphysics and epistemology. Logic in our sense has often been distinguished from “logic” in other, sometimes unmanageably broad and loose, senses by adding the adjectives “formal” or “deductive”. The scope of the art and science of logic, once one gets beyond elementary logic of the kind covered in introductory textbooks, is indicated by two other standard references, the Handbooks of mathematical and philosophical logic, Barwise [1977] and Gabbay & Guenthner [1983-89], though the latter includes also parts that are identified as applications of logic rather than logic proper. The term “philosophical logic” as currently used, for instance, in the Journal of Philosophical Logic, is a near-synonym for “nonclassical logic”. There is an older use of the term as a near-synonym for “philosophy of language”. -
Yuji NISHIYAMA in This Article We Shall Focus Our Attention Upon
The Notion of Presupposition* Yuji NISHIYAMA Keio University In this article we shall focus our attention upon the clarificationof the notion of presupposition;First, we shall be concerned with what kind of notion is best understood as the proper notion of presupposition that grammars of natural languageshould deal with. In this connection,we shall defend "logicalpresupposi tion". Second, we shall consider how to specify the range of X and Y in the presuppositionformula "X presupposes Y". Third, we shall discuss several difficultieswith the standard definition of logical presupposition. In connection with this, we shall propose a clear distinction between "the definition of presupposi tion" and "the rule of presupposition". 1. The logical notion of presupposition What is a presupposition? Or, more particularly, what is the alleged result of a presupposition failure? In spite of the attention given to it, this question can hardly be said to have been settled. Various answers have been suggested by the various authors: inappropriate use of a sentence, failure to perform an illocutionary act, anomaly, ungrammaticality, unintelligibility, infelicity, lack of truth value-each has its advocates. Some of the apparent disagreementmay be only a notational and terminological, but other disagreement raises real, empirically significant, theoretical questions regarding the relationship between logic and language. However, it is not the aim of this article to straighten out the various proposals about the concept of presupposition. Rather, we will be concerned with one notion of presupposition,which stems from Frege (1892)and Strawson (1952),that is: (1) presupposition is a condition under which a sentence expressing an assertive proposition can be used to make a statement (or can bear a truth value)1 We shall call this notion of presupposition "the statementhood condition" or "the conditionfor bivalence". -
Recent Work on Ontological Pluralism
Recent Work on Ontological Pluralism Jason Turner November 15, 2018 Ontological Pluralism is said in many ways, at least if two counts as ‘many’. On one disambiguation, to be an ‘ontological pluralist’ is to be accommodating about theories with different ontologies. This is the pluralism of Carnap (1950) and Putnam (1987) who grant that there are competing ontological visions of reality but deny that any has an objectively better claim to correctness. We are free to accept an ontology of numbers or not, and there’s no good philosoph- ical debate to be had about whether there really are any numbers. This is the pluralism of the pluralistic society, where opposing ontological visions need to learn to just get along. We will discuss the other disambiguation of ‘Ontological Pluralism’ here. According to it, there are different ways of being. In The Problems of Philosophy, for instance, Betrand Russell (1912: 90, 98) tells us that, while there are relations as well as people, relations exist in a deeply different way than people do.1 The way in which the world grants being to relations is radically different, on this picture, then the way in which it grants it to people. Despite its pedigree, during the 20th century analytic philosophers grew suspicious of the notion. Presumably, when the logical positivists tried to kill metaphysics, the idea things could exist in different ways was supposed to die with it. Quine’s resurrection of metaphysics linked ontology with quantifiers, making it hard to see what ‘things exist in different ways’ could mean. Zoltán Szabó puts it this way: The standard view nowadays is that we can adequately capture the meaning of sentences like ‘There are Fs’, ‘Some things are F’, or ‘F’s exist’ through existential quantification. -
The Development of Mathematical Logic from Russell to Tarski: 1900–1935
The Development of Mathematical Logic from Russell to Tarski: 1900–1935 Paolo Mancosu Richard Zach Calixto Badesa The Development of Mathematical Logic from Russell to Tarski: 1900–1935 Paolo Mancosu (University of California, Berkeley) Richard Zach (University of Calgary) Calixto Badesa (Universitat de Barcelona) Final Draft—May 2004 To appear in: Leila Haaparanta, ed., The Development of Modern Logic. New York and Oxford: Oxford University Press, 2004 Contents Contents i Introduction 1 1 Itinerary I: Metatheoretical Properties of Axiomatic Systems 3 1.1 Introduction . 3 1.2 Peano’s school on the logical structure of theories . 4 1.3 Hilbert on axiomatization . 8 1.4 Completeness and categoricity in the work of Veblen and Huntington . 10 1.5 Truth in a structure . 12 2 Itinerary II: Bertrand Russell’s Mathematical Logic 15 2.1 From the Paris congress to the Principles of Mathematics 1900–1903 . 15 2.2 Russell and Poincar´e on predicativity . 19 2.3 On Denoting . 21 2.4 Russell’s ramified type theory . 22 2.5 The logic of Principia ......................... 25 2.6 Further developments . 26 3 Itinerary III: Zermelo’s Axiomatization of Set Theory and Re- lated Foundational Issues 29 3.1 The debate on the axiom of choice . 29 3.2 Zermelo’s axiomatization of set theory . 32 3.3 The discussion on the notion of “definit” . 35 3.4 Metatheoretical studies of Zermelo’s axiomatization . 38 4 Itinerary IV: The Theory of Relatives and Lowenheim’s¨ Theorem 41 4.1 Theory of relatives and model theory . 41 4.2 The logic of relatives . -
Introduction to the Philosophy of Cognitive Science by Dr
Introduction to the Philosophy of Cognitive Science By Dr. Charles Wallis Last revision: 1/23/2013 Chapter 2 Greek Metaphysical Speculation: Philosophical Materialisms and Dualisms 2.1 Introduction It may seem odd to the contemporary thinker to suppose that people did not always have a clear conception of the mind and of mental phenomena. Nevertheless, like most contemporary western concepts the development of the notion of the mind and of mental phenomena actually occurs over the course of centuries. Indeed, the development of the notion of “the mind” arguably traces back to the development of the Greek notion of the soul. For most of Greek history the conception of the soul bears little resemblance to its contemporary western counterpart. In fact, the Greeks develop their notion of the soul as part of the development of general ontological frameworks for scientific and metaphysical speculation. Three features of the development of the Greek notion of the soul figure prominently in this rather superficial history. First, the development of the Greek notion of the soul represents a slow accretion of properties and processes associated with three different contemporary distinctions into a single ontological entity; living vs non-living, animate vs inanimate, and mental vs non-mental. Second, as the soul becomes more distinct both in its nature and in its functions, the Greeks begin to more actively debate whether the soul constitutes a fundamental kind of stuff (a distinct substance) or merely one of many permutations of more fundamental kinds of stuff (substances). For instance, early Greek thinkers often supposed that the universe consists of various permutations of one or more fundamental elements. -
An Introduction to Philosophy
An Introduction to Philosophy W. Russ Payne Bellevue College Copyright (cc by nc 4.0) 2015 W. Russ Payne Permission is granted to copy, distribute and/or modify this document with attribution under the terms of Creative Commons: Attribution Noncommercial 4.0 International or any later version of this license. A copy of the license is found at http://creativecommons.org/licenses/by-nc/4.0/ 1 Contents Introduction ………………………………………………. 3 Chapter 1: What Philosophy Is ………………………….. 5 Chapter 2: How to do Philosophy ………………….……. 11 Chapter 3: Ancient Philosophy ………………….………. 23 Chapter 4: Rationalism ………….………………….……. 38 Chapter 5: Empiricism …………………………………… 50 Chapter 6: Philosophy of Science ………………….…..… 58 Chapter 7: Philosophy of Mind …………………….……. 72 Chapter 8: Love and Happiness …………………….……. 79 Chapter 9: Meta Ethics …………………………………… 94 Chapter 10: Right Action ……………………...…………. 108 Chapter 11: Social Justice …………………………...…… 120 2 Introduction The goal of this text is to present philosophy to newcomers as a living discipline with historical roots. While a few early chapters are historically organized, my goal in the historical chapters is to trace a developmental progression of thought that introduces basic philosophical methods and frames issues that remain relevant today. Later chapters are topically organized. These include philosophy of science and philosophy of mind, areas where philosophy has shown dramatic recent progress. This text concludes with four chapters on ethics, broadly construed. I cover traditional theories of right action in the third of these. Students are first invited first to think about what is good for themselves and their relationships in a chapter of love and happiness. Next a few meta-ethical issues are considered; namely, whether they are moral truths and if so what makes them so. -
Logical Consequence: a Defense of Tarski*
GREG RAY LOGICAL CONSEQUENCE: A DEFENSE OF TARSKI* ABSTRACT. In his classic 1936 essay “On the Concept of Logical Consequence”, Alfred Tarski used the notion of XU~@~ZC~~NIto give a semantic characterization of the logical properties. Tarski is generally credited with introducing the model-theoretic chamcteriza- tion of the logical properties familiar to us today. However, in his hook, The &ncel>f of Lugid Consequence, Etchemendy argues that Tarski’s account is inadequate for quite a number of reasons, and is actually incompatible with the standard mod&theoretic account. Many of his criticisms are meant to apply to the model-theoretic account as well. In this paper, I discuss the following four critical charges that Etchemendy makes against Tarski and his account of the logical properties: (1) (a) Tarski’s account of logical consequence diverges from the standard model-theoretic account at points where the latter account gets it right. (b) Tarski’s account cannot be brought into line with the model-thcorctic account, because the two are fundamentally incompatible. (2) There are simple countcrcxamples (enumerated by Etchemcndy) which show that Tarski’s account is wrong. (3) Tarski committed a modal faIlacy when arguing that his account captures our pre-theoretical concept of logical consequence, and so obscured an essential weakness of the account. (4) Tarski’s account depends on there being a distinction between the “log- ical terms” and the “non-logical terms” of a language, but (according to Etchemendy) there are very simple (even first-order) languages for which no such distinction can be made. Etchemcndy’s critique raises historica and philosophical questions about important foun- dational work. -
What Is Meant by “Christian Dualism” (Genuine Separation
Jeremy Shepherd October 15, 2004 The Friday Symposium Dallas Baptist University “Christian Enemy #1: Dualism Exposed & Destroyed” “The Fear of the Lord is the beginning of knowledge, but fools despise wisdom and discipline.” - Proverbs 1:7 “Christianity is not a realm of life; it’s a way of life for every realm”1 Introduction When I came to Dallas Baptist University I had a rather violent reaction to what I thought was a profound category mistake. Coming from the public school system, I had a deeply embedded idea of how “religious” claims ought to relate, or should I say, ought not to relate, with “worldly affairs.” To use a phrase that Os Guinness frequently uses, I thought that “religion might be privately engaging but publicly irrelevant.”2 I was astonished at the unashamed integration of all these “religious” beliefs into other realms of life, even though I myself was a Christian. The key word for me was: unashamed. I thought to myself, “How could these people be so shameless in their biases?” My reaction to this Wholistic vision of life was so serious that I almost left the university to go get myself a “real” education, one where my schooling wouldn’t be polluted by all of these messy assumptions and presuppositions, even if they were Christian. My worldview lenses saw “education” as something totally separate from my “faith.” I was a model student of the American public school system, and like most other students, whether Christian or not, the separation of “church/state” and “faith/education” was only a small part of something much deeper and much more profound, the separation of my “faith” from the rest of my “life.” Our public schools are indoctrinating other students who have this same split-vision3, in which “faith” is a private thing, which is not to be integrated into the classroom.