Results for 'PROOF VS DEDUCTION'

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  1. REVIEW OF 1988. Saccheri, G. Euclides Vindicatus (1733), Edited and Translated by G. B. Halsted, 2nd Ed. (1986), in Mathematical Reviews MR0862448. 88j:01013.John Corcoran - 1988 - MATHEMATICAL REVIEWS 88 (J):88j:01013.
    Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are devoted. (...)
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  2. Prove It! The Burden of Proof Game in Science Vs. Pseudoscience Disputes.Massimo Pigliucci & Maarten Boudry - 2014 - Philosophia 42 (2):487-502.
    The concept of burden of proof is used in a wide range of discourses, from philosophy to law, science, skepticism, and even in everyday reasoning. This paper provides an analysis of the proper deployment of burden of proof, focusing in particular on skeptical discussions of pseudoscience and the paranormal, where burden of proof assignments are most poignant and relatively clear-cut. We argue that burden of proof is often misapplied or used as a mere rhetorical gambit, with (...)
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  3.  59
    The Proof Structure of Kant's A-Edition Objective Deduction.Corey W. Dyck - forthcoming - In Giuseppe Motta & Dennis Schulting (eds.), Kant’s Deduction From Apperception: An Essay on the Transcendental Deduction of the Categories. Berlin: DeGruyter.
    Kant's A-Edition objective deduction is naturally (and has traditionally been) divided into two arguments: an " argument from above" and one that proceeds " von unten auf." This would suggest a picture of Kant's procedure in the objective deduction as first descending and ascending the same ladder, the better, perhaps, to test its durability or to thoroughly convince the reader of its soundness. There are obvious obstacles to such a reading, however; and in this chapter I will argue (...)
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  4. How Fundamental is the Fundamental Assumption?Nils Kurbis - 2012 - Teorema: International Journal of Philosophy 2 (2):5-19.
    The fundamental assumption of Dummett’s and Prawitz’ proof-theoretic justification of deduction is that ‘if we have a valid argument for a complex statement, we can construct a valid argument for it which finishes with an application of one of the introduction rules governing its principal operator’. I argue that the assumption is flawed in this general version, but should be restricted, not to apply to arguments in general, but only to proofs. I also argue that Dummett’s and Prawitz’ (...)
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  5.  82
    Discourse Grammars and the Structure of Mathematical Reasoning III: Two Theories of Proof,.John Corcoran - 1971 - Journal of Structural Learning 3 (3):1-24.
    ABSTRACT This part of the series has a dual purpose. In the first place we will discuss two kinds of theories of proof. The first kind will be called a theory of linear proof. The second has been called a theory of suppositional proof. The term "natural deduction" has often and correctly been used to refer to the second kind of theory, but I shall not do so here because many of the theories so-called are not (...)
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  6. Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value.John Corcoran - 1971 - Journal of Structural Learning 3 (2):1-16.
    1971. Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value, Journal of Structural Learning 3, #2, 1–16. REPRINTED 1976. Structural Learning II Issues and Approaches, ed. J. Scandura, Gordon & Breach Science Publishers, New York, MR56#15263. -/- This is the second of a series of three articles dealing with application of linguistics and logic to the study of mathematical reasoning, especially in the setting of a concern for improvement (...)
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  7. A Note on Harmony.Nissim Francez & Roy Dyckhoff - 2012 - Journal of Philosophical Logic 41 (3):613-628.
    In the proof-theoretic semantics approach to meaning, harmony , requiring a balance between introduction-rules (I-rules) and elimination rules (E-rules) within a meaning conferring natural-deduction proof-system, is a central notion. In this paper, we consider two notions of harmony that were proposed in the literature: 1. GE-harmony , requiring a certain form of the E-rules, given the form of the I-rules. 2. Local intrinsic harmony : imposes the existence of certain transformations of derivations, known as reduction and expansion (...)
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  8. Argumentaciones y lógica.J. Corcoran - 1994 - Agora 13 (1):27.
    Argumentations are at the heart of the deductive and the hypothetico-deductive methods, which are involved in attempts to reduce currently open problems to problems already solved. These two methods span the entire spectrum of problem-oriented reasoning from the simplest and most practical to the most complex and most theoretical, thereby uniting all objective thought whether ancient or contemporary, whether humanistic or scientific, whether normative or descriptive, whether concrete or abstract. Analysis, synthesis, evaluation, and function of argumentations are described. Perennial philosophic (...)
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  9. Review of Macbeth, D. Diagrammatic Reasoning in Frege's Begriffsschrift. Synthese 186 (2012), No. 1, 289–314. Mathematical Reviews MR 2935338.John Corcoran - 2014 - MATHEMATICAL REVIEWS 2014:2935338.
    A Mathematical Review by John Corcoran, SUNY/Buffalo -/- Macbeth, Danielle Diagrammatic reasoning in Frege's Begriffsschrift. Synthese 186 (2012), no. 1, 289–314. ABSTRACT This review begins with two quotations from the paper: its abstract and the first paragraph of the conclusion. The point of the quotations is to make clear by the “give-them-enough-rope” strategy how murky, incompetent, and badly written the paper is. I know I am asking a lot, but I have to ask you to read the quoted passages—aloud if (...)
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  10. Proof in Mathematics: An Introduction.James Franklin - 1996 - Sydney, Australia: Quakers Hill Press.
    A textbook on proof in mathematics, inspired by an Aristotelian point of view on mathematics and proof. The book expounds the traditional view of proof as deduction of theorems from evident premises via obviously valid steps. It deals with the proof of "all" statements, "some" statements, multiple quantifiers and mathematical induction.
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  11. Proof-Theoretic Semantics, a Problem with Negation and Prospects for Modality.Nils Kurbis - 2015 - Journal of Philosophical Logic 44 (6):713-727.
    This paper discusses proof-theoretic semantics, the project of specifying the meanings of the logical constants in terms of rules of inference governing them. I concentrate on Michael Dummett’s and Dag Prawitz’ philosophical motivations and give precise characterisations of the crucial notions of harmony and stability, placed in the context of proving normalisation results in systems of natural deduction. I point out a problem for defining the meaning of negation in this framework and prospects for an account of the (...)
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  12. Kant's Subjective Deduction.Nathan Bauer - 2010 - British Journal for the History of Philosophy 18 (3):433-460.
    In the transcendental deduction, the central argument of the Critique of Pure Reason, Kant seeks to secure the objective validity of our basic categories of thought. He distinguishes objective and subjective sides of this argument. The latter side, the subjective deduction, is normally understood as an investigation of our cognitive faculties. It is identified with Kant’s account of a threefold synthesis involved in our cognition of objects of experience, and it is said to precede and ground Kant’s (...) of the validity of the categories in the objective deduction. I challenge this standard reading of the subjective deduction, arguing, first, that there is little textual evidence for it, and, second, that it encourages a problematic conception of how the deduction works. In its place, I present a new reading of the subjective deduction. Rather than being a broad investigation of our cognitive faculties, it should be seen as addressing a specific worry that arises in the course of the objective deduction. The latter establishes the need for a necessary connection between our capacities for thinking and being given objects, but Kant acknowledges that his readers might struggle to comprehend how these seemingly independent capacities are coordinated. Even worse, they might well believe that in asserting this necessary connection, Kant’s position amounts to an implausible subjective idealism. The subjective deduction ismeant to allay these concerns by showing that they rest on a misunderstanding of the relation between these faculties. This new reading of the subjective deduction offers a better fit with Kant’s text. It also has broader implications, for it reveals the more philosophically plausible account of our relation to the world as thinkers that Kant is defending – an account that is largely obscured by the standard reading of the subjective deduction. (shrink)
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  13.  65
    Commentary and Illocutionary Expressions in Linear Calculi of Natural Deduction.Moritz Cordes & Friedrich Reinmuth - 2017 - Logic and Logical Philosophy 26 (2).
    We argue that the need for commentary in commonly used linear calculi of natural deduction is connected to the “deletion” of illocutionary expressions that express the role of propositions as reasons, assumptions, or inferred propositions. We first analyze the formalization of an informal proof in some common calculi which do not formalize natural language illocutionary expressions, and show that in these calculi the formalizations of the example proof rely on commentary devices that have no counterpart in the (...)
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  14.  32
    Proof Theory of Finite-Valued Logics.Richard Zach - 1993 - Dissertation, Technische Universität Wien
    The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory (...)
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  15. Natural Deduction for Modal Logic with a Backtracking Operator.Jonathan Payne - 2015 - Journal of Philosophical Logic 44 (3):237-258.
    Harold Hodes in [1] introduces an extension of first-order modal logic featuring a backtracking operator, and provides a possible worlds semantics, according to which the operator is a kind of device for ‘world travel’; he does not provide a proof theory. In this paper, I provide a natural deduction system for modal logic featuring this operator, and argue that the system can be motivated in terms of a reading of the backtracking operator whereby it serves to indicate modal (...)
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  16. Natural Deduction for Three-Valued Regular Logics.Yaroslav Petrukhin - 2017 - Logic and Logical Philosophy 26 (2):197–206.
    In this paper, I consider a family of three-valued regular logics: the well-known strong and weak S.C. Kleene’s logics and two intermedi- ate logics, where one was discovered by M. Fitting and the other one by E. Komendantskaya. All these systems were originally presented in the semantical way and based on the theory of recursion. However, the proof theory of them still is not fully developed. Thus, natural deduction sys- tems are built only for strong Kleene’s logic both (...)
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  17. Proof-Theoretic Semantics for Subsentential Phrases.Nissim Francez, Roy Dyckhoff & Gilad Ben-Avi - 2010 - Studia Logica 94 (3):381-401.
    The paper briefly surveys the sentential proof-theoretic semantics for fragment of English. Then, appealing to a version of Frege’s context-principle (specified to fit type-logical grammar), a method is presented for deriving proof-theoretic meanings for sub-sentential phrases, down to lexical units (words). The sentential meaning is decomposed according to the function-argument structure as determined by the type-logical grammar. In doing so, the paper presents a novel proof-theoretic interpretation of simple type, replacing Montague’s model-theoretic type interpretation (in arbitrary Henkin (...)
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  18. Aristotle's Demonstrative Logic.John Corcoran - 2009 - History and Philosophy of Logic 30 (1):1-20.
    Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing a chain of reasoning showing (...)
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  19. Is Euclid's Proof of the Infinitude of Prime Numbers Tautological?Zeeshan Mahmud - manuscript
    Euclid's classic proof about the infinitude of prime numbers has been a standard model of reasoning in student textbooks and books of elementary number theory. It has withstood scrutiny for over 2000 years but we shall prove that despite the deceptive appearance of its analytical reasoning it is tautological in nature. We shall argue that the proof is more of an observation about the general property of a prime numbers than an expository style of natural deduction of (...)
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  20.  98
    Hypersequents and the Proof Theory of Intuitionistic Fuzzy Logic.Matthias Baaz & Richard Zach - 2000 - In Peter G. Clote & Helmut Schwichtenberg (eds.), Computer Science Logic. 14th International Workshop, CSL 2000. Berlin: Springer. pp. 187– 201.
    Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the first-order Gödel logic based on the truth value set [0,1]. The logic is known to be axiomatizable, but no deduction system amenable to proof-theoretic, and hence, computational treatment, has been known. Such a system is presented here, based on previous work on hypersequent calculi for propositional Gödel logics by Avron. It is shown that the system is sound and (...)
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  21. Why Simpler Arguments Are Better.Moti Mizrahi - 2016 - Argumentation 30 (3):247-261.
    In this paper, I argue that, other things being equal, simpler arguments are better. In other words, I argue that, other things being equal, it is rational to prefer simpler arguments over less simple ones. I sketch three arguments in support of this claim: an argument from mathematical proofs, an argument from scientific theories, and an argument from the conjunction rule.
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  22. Argumentations and Logic.John Corcoran - 1989 - ARGUMENTAION 3 (1):17-43.
    Argumentations are at the heart of the deductive and the hypothetico-deductive methods, which are involved in attempts to reduce currently open problems to problems already solved. These two methods span the entire spectrum of problem-oriented reasoning from the simplest and most practical to the most complex and most theoretical, thereby uniting all objective thought whether ancient or contemporary, whether humanistic or scientific, whether normative or descriptive, whether concrete or abstract. Analysis, synthesis, evaluation, and function of argumentations are described. Perennial philosophic (...)
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  23. Stable Harmony.Nils Kurbis - 2008 - In Peliš Michal (ed.), Logica Yearbook 2007.
    In this paper, I'll present a general way of "reading off" introduction/elimination rules from elimination/introduction rules, and define notions of harmony and stability on the basis of it.
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  24. A Farewell Letter To My Students.John Corcoran - 2012 - Philosophy Now 92:18-18.
    I am saying farewell after more than forty happy years of teaching logic at the University of Buffalo. But this is only a partial farewell. I will no longer be at UB to teach classroom courses or seminars. But nothing else will change. I will continue to be available for independent study. I will continue to write abstracts and articles with people who have taken courses or seminars with me. And I will continue to honor the LogicLifetimeGuarantee™, which is earned (...)
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  25. Semantic Arithmetic: A Preface.John Corcoran - 1995 - Agora 14 (1):149-156.
    SEMANTIC ARITHMETIC: A PREFACE John Corcoran Abstract Number theory, or pure arithmetic, concerns the natural numbers themselves, not the notation used, and in particular not the numerals. String theory, or pure syntax, concems the numerals as strings of «uninterpreted» characters without regard to the numbe~s they may be used to denote. Number theory is purely arithmetic; string theory is purely syntactical... in so far as the universe of discourse alone is considered. Semantic arithmetic is a broad subject which begins when (...)
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  26. Gap? What Gap?—On the Unity of Apperception and the Necessary Application of the Categories.Dennis Schulting - 2017 - In Udo Thiel & Giuseppe Motta (eds.), Immanuel Kant: Die Einheit des Bewusstseins (Kant-Studien Ergänzungshefte). Berlin, Boston: De Gruyter. pp. 89-113.
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  27. Critical Thinking and Pedagogical License.John Corcoran - 1999 - Manuscrito 22 (2):109.
    Critical thinking involves deliberate application of tests and standards to beliefs per se and to methods used to arrive at beliefs. Pedagogical license is authorization accorded to teachers permitting them to use otherwise illicit means in order to achieve pedagogical goals. Pedagogical license is thus analogous to poetic license or, more generally, to artistic license. Pedagogical license will be found to be pervasive in college teaching. This presentation suggests that critical thinking courses emphasize two topics: first, the nature and usefulness (...)
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  28. Ancient Logic and its Modern Interpretations Proceedings of the Buffalo Symposium on Modernist Interpretations of Ancient Logic, 21 and 22 April, 1972. [REVIEW]John Corcoran (ed.) - 1974 - Reidel.
    Articles by Ian Mueller, Ronald Zirin, Norman Kretzmann, John Corcoran, John Mulhern, Mary Mulhern,Josiah Gould, and others. Topics: Aristotle's Syllogistic, Stoic Logic, Modern Research in Ancient Logic.
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  29.  40
    Expressing Truth Directly Within a Formal System with No Need for Model Theory.Pete Olcott - manuscript
    Because formal systems of symbolic logic inherently express and represent the deductive inference model formal proofs to theorem consequences can be understood to represent sound deductive inference to deductive conclusions without any need for other representations.
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  30. An Alternative Proof of the Universal Propensity to Evil.Pablo Muchnik - 2010 - In Sharon Anderson-Gold & Pablo Muchnik (eds.), Kant's Anatomy of Evil. Cambridge University Press.
    In this paper, I develop a quasi-transcendental argument to justify Kant’s infamous claim “man is evil by nature.” The cornerstone of my reconstruction lies in drawing a systematic distinction between the seemingly identical concepts of “evil disposition” (böseGesinnung) and “propensity to evil” (Hang zumBösen). The former, I argue, Kant reserves to describe the fundamental moral outlook of a single individual; the latter, the moral orientation of the whole species. Moreover, the appellative “evil” ranges over two different types of moral failure: (...)
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  31. Can Kants Deduction of Judgments of Taste Be Saved?Miles Rind - 2002 - Archiv für Geschichte der Philosophie 84 (1):20-45.
    Kant’s argument in § 38 of the *Critique of Judgment* is subject to a dilemma: if the subjective condition of cognition is the sufficient condition of the pleasure of taste, then every object of experience must produce that pleasure; if not, then the universal communicability of cognition does not entail the universal communicability of the pleasure. Kant’s use of an additional premise in § 21 may get him out of this difficulty, but the premises themselves hang in the air and (...)
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  32. Questions About Proof Theory Vis-À-Vis Natural Language Semantics (2007).Anna Szabolcsi - manuscript
    Semantics plays a role in grammar in at least three guises. (A) Linguists seek to account for speakers‘ knowledge of what linguistic expressions mean. This goal is typically achieved by assigning a model theoretic interpretation2 in a compositional fashion. For example, No whale flies is true if and only if the intersection of the sets of whales and fliers is empty in the model. (B) Linguists seek to account for the ability of speakers to make various inferences based on semantic (...)
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  33. Logical Consequence in Modal Logic II: Some Semantic Systems for S4.George Weaver - 1974 - Notre Dame Journal of Formal Logic 15:370.
    ABSTRACT: This 1974 paper builds on our 1969 paper (Corcoran-Weaver [2]). Here we present three (modal, sentential) logics which may be thought of as partial systematizations of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of these three logics coincide with one another and with those of standard formalizations of Lewis's S5. These logics, when regarded as logistic systems (cf. Corcoran [1], p. 154), are seen to be equivalent; (...)
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  34. Proofs Are Programs: 19th Century Logic and 21st Century Computing.Philip Wadler - manuscript
    As the 19th century drew to a close, logicians formalized an ideal notion of proof. They were driven by nothing other than an abiding interest in truth, and their proofs were as ethereal as the mind of God. Yet within decades these mathematical abstractions were realized by the hand of man, in the digital stored-program computer. How it came to be recognized that proofs and programs are the same thing is a story that spans a century, a chase with (...)
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  35.  91
    The Reasonable and the Relevant: Legal Standards of Proof.Georgi Gardiner - 2019 - Philosophy and Public Affairs 47 (3):288-318.
    According to a common conception of legal proof, satisfying a legal burden requires establishing a claim to a numerical threshold. Beyond reasonable doubt, for example, is often glossed as 90% or 95% likelihood given the evidence. Preponderance of evidence is interpreted as meaning at least 50% likelihood given the evidence. -/- In light of problems with the common conception, I propose a new ‘relevant alternatives’ framework for legal standards of proof. Relevant alternative accounts of knowledge state that a (...)
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  36. Nelsons Kritik der Erkenntnistheorie und ihre Konsequenzen.Kay Herrmann - 1999 - In Wolfram Hogrebe Kay Herrmann (ed.), Jakob Friedrich Fries – Philosoph, Naturwissenschaftler und Mathematiker. Verhandlungen des Symposions „Probleme und Perspektiven von Jakob Friedrich Fries’ Erkenntnislehre und Naturphilosophie“ vom 9. bis 11. Oktober 1997 an der Friedrich-Schiller-Univer. Peter Lang. pp. 353–368.
    Nelson's Proof of the Impossibility of the Theory of Knowledge -/- In addressing the possibility of a theory of knowledge, Leonard Nelson noted the contradiction of an epistemological criterion that one would require in order to differentiate between valid and invalid knowledge. Nelson concluded that the inconsistency of such a criterion proves the impossibility of the theory of knowledge. -/- Had the epistemological criterion had a perception, then it would presume to adjudicate on its own truth (thus epistemological circular (...)
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  37. Kant on Perception: Naive Realism, Non-Conceptualism, and the B-Deduction.Anil Gomes - 2014 - Philosophical Quarterly 64 (254):1-19.
    According to non-conceptualist interpretations, Kant held that the application of concepts is not necessary for perceptual experience. Some have motivated non-conceptualism by noting the affinities between Kant's account of perception and contemporary relational theories of perception. In this paper I argue (i) that non-conceptualism cannot provide an account of the Transcendental Deduction and thus ought to be rejected; and (ii) that this has no bearing on the issue of whether Kant endorsed a relational account of perceptual experience.
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  38. Legal Burdens of Proof and Statistical Evidence.Georgi Gardiner - forthcoming - In James Chase & David Coady (eds.), The Routledge Handbook of Applied Epistemology. Routledge.
    In order to perform certain actions – such as incarcerating a person or revoking parental rights – the state must establish certain facts to a particular standard of proof. These standards – such as preponderance of evidence and beyond reasonable doubt – are often interpreted as likelihoods or epistemic confidences. Many theorists construe them numerically; beyond reasonable doubt, for example, is often construed as 90 to 95% confidence in the guilt of the defendant. -/- A family of influential cases (...)
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  39.  35
    Takeuti's Proof Theory in the Context of the Kyoto School.Andrew Arana - 2019 - Jahrbuch Für Philosophie Das Tetsugaku-Ronso 46:1-17.
    Gaisi Takeuti (1926–2017) is one of the most distinguished logicians in proof theory after Hilbert and Gentzen. He extensively extended Hilbert's program in the sense that he formulated Gentzen's sequent calculus, conjectured that cut-elimination holds for it (Takeuti's conjecture), and obtained several stunning results in the 1950–60s towards the solution of his conjecture. Though he has been known chiefly as a great mathematician, he wrote many papers in English and Japanese where he expressed his philosophical thoughts. In particular, he (...)
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  40. Aristotle's Natural Deduction System.John Corcoran - 1974 - In Ancient Logic and its Modern Interpretations. Boston: Reidel. pp. 85--131.
    This presentation of Aristotle's natural deduction system supplements earlier presentations and gives more historical evidence. Some fine-tunings resulted from conversations with Timothy Smiley, Charles Kahn, Josiah Gould, John Kearns,John Glanvillle, and William Parry.The criticism of Aristotle's theory of propositions found at the end of this 1974 presentation was retracted in Corcoran's 2009 HPL article "Aristotle's demonstrative logic".
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  41. Is Kant’s Transcendental Deduction of the Categories Fit for Purpose?Anil Gomes - 2010 - Kantian Review 15 (2):118-137.
    James Van Cleve has argued that Kant’s Transcendental Deduction of the categories shows, at most, that we must apply the categories to experience. And this falls short of Kant’s aim, which is to show that they must so apply. In this discussion I argue that once we have noted the differences between the first and second editions of the Deduction, this objection is less telling. But Van Cleve’s objection can help illuminate the structure of the B Deduction, (...)
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  42.  32
    On the Alleged Simplicity of Impure Proof.Andrew Arana - 2017 - In Roman Kossak & Philip Ording (eds.), Simplicity: Ideals of Practice in Mathematics and the Arts. pp. 207-226.
    Roughly, a proof of a theorem, is “pure” if it draws only on what is “close” or “intrinsic” to that theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure proof is one that avoids what is “extrinsic,” “extraneous,” “distant,” “remote,” “alien,” or “foreign” to the problem or theorem under investigation. In the background of these attributions is the view that there is a distance measure (or a variety of such measures) between mathematical (...)
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  43. Nonexistence of Gods: An Inductive Proof.Christian Buth - manuscript
    I prove the nonexistence of gods. The proof is based on three axioms: Ockham’s razor (OR), religiosity is endogenous in humans, and, there are no miracles. The OR is formulated operationally, to remove improper postulates, such that it yields not only a plausible argument but truth. The validity of the second and the third axiom is established empirically by inductive reasoning relying on a thorough analysis of the psychiatric literature and skeptical publications. With these axioms I prove that gods (...)
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  44.  60
    Forall X: Calgary. An Introduction to Formal Logic.P. D. Magnus, Tim Button, Aaron Thomas-Bolduc, Richard Zach & Robert Trueman - 2019 - KDP.
    forall x: Calgary is a full-featured textbook on formal logic. It covers key notions of logic such as consequence and validity of arguments, the syntax of truth-functional propositional logic TFL and truth-table semantics, the syntax of first-order (predicate) logic FOL with identity (first-order interpretations), translating (formalizing) English in TFL and FOL, and Fitch-style natural deduction proof systems for both TFL and FOL. It also deals with some advanced topics such as truth-functional completeness and modal logic. Exercises with solutions (...)
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  45. The Content of Deduction.Mark Jago - 2013 - Journal of Philosophical Logic 42 (2):317-334.
    For deductive reasoning to be justified, it must be guaranteed to preserve truth from premises to conclusion; and for it to be useful to us, it must be capable of informing us of something. How can we capture this notion of information content, whilst respecting the fact that the content of the premises, if true, already secures the truth of the conclusion? This is the problem I address here. I begin by considering and rejecting several accounts of informational content. I (...)
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  46. Why the Transcendental Deduction is Compatible with Nonconceptualism.Sacha Golob - 2016 - In Dennis Schulting (ed.), Kantian Nonconceptualism. Palgrave-Macmillan. pp. 27-52.
    One of the strongest motivations for conceptualist readings of Kant is the belief that the Transcendental Deduction is incompatible with nonconceptualism. In this article, I argue that this belief is simply false: the Deduction and nonconceptualism are compatible at both an exegetical and a philosophical level. Placing particular emphasis on the case of non-human animals, I discuss in detail how and why my reading diverges from those of Ginsborg, Allais, Gomes and others. I suggest ultimately that it is (...)
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  47.  85
    Stoic Sequent Logic and Proof Theory.Susanne Bobzien - 2019 - History and Philosophy of Logic 40 (3):234-265.
    This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. (...)
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  48. Single Premise Deduction and Risk.Maria Lasonen-Aarnio - 2008 - Philosophical Studies 141 (2):157 - 173.
    It is tempting to think that multi premise closure creates a special class of paradoxes having to do with the accumulation of risks, and that these paradoxes could be escaped by rejecting the principle, while still retaining single premise closure. I argue that single premise deduction is also susceptible to risks. I show that what I take to be the strongest argument for rejecting multi premise closure is also an argument for rejecting single premise closure. Because of the symmetry (...)
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  49. The Dogmatist, Moore's Proof and Transmission Failure.Luca Moretti - 2014 - Analysis 74 (3):382-389.
    According to Jim Pryor’s dogmatism, if you have an experience as if P, you acquire immediate prima facie justification for believing P. Pryor contends that dogmatism validates Moore’s infamous proof of a material world. Against Pryor, I argue that if dogmatism is true, Moore’s proof turns out to be non-transmissive of justification according to one of the senses of non-transmissivity defined by Crispin Wright. This type of non-transmissivity doesn’t deprive dogmatism of its apparent antisceptical bite.
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  50.  55
    Proof Paradoxes and Normic Support: Socializing or Relativizing?Marcello Di Bello - forthcoming - Mind:fzz021.
    Smith argues that, unlike other forms of evidence, naked statistical evidence fails to satisfy normic support. This is his solution to the puzzles of statistical evidence in legal proof. This paper focuses on Smith’s claim that DNA evidence in cold-hit cases does not satisfy normic support. I argue that if this claim is correct, virtually no other form of evidence used at trial can satisfy normic support. This is troublesome. I discuss a few ways in which Smith can respond.
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