Results for 'proof'

951 found
Order:
  1. On the concept of proof in elementary geometry Pirmin stekeler-weithofer.Proof In Elementary - 1992 - In Michael Detlefsen, Proof and Knowledge in Mathematics. New York: Routledge.
     
    Export citation  
     
    Bookmark  
  2.  75
    Proof Methods for Modal and Intuitionistic Logics.Melvin Fitting - 1985 - Journal of Symbolic Logic 50 (3):855-856.
  3. The Proof ‘Ex Motu’ for the Existence of God.Jan Salamucha - 1958 - New Scholasticism 32 (3):334-372.
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  4.  76
    A Proof of the Independence of the Continuum Hypothesis.Dana Scott - 1968 - Journal of Symbolic Logic 33 (2):293-293.
  5. (1 other version)Proof-Theoretic Semantics.Peter Schroeder-Heister - 2024 - Stanford Encyclopedia of Philosophy.
  6. Proof and Truth.Stewart Shapiro - 1998 - Journal of Philosophy 95 (10):493-521.
  7. Proof Theory.Gaisi Takeuti - 1990 - Studia Logica 49 (1):160-161.
     
    Export citation  
     
    Bookmark   166 citations  
  8. Godel's Proof.Ernest Nagel & James Roy Newman - 1958 - New York, NY, USA: Routledge. Edited by James Roy Newman.
    _'Nagel and Newman accomplish the wondrous task of clarifying the argumentative outline of Kurt Godel's celebrated logic bomb.'_ _– The Guardian_ In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of physicist Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system. The importance of Godel's Proof rests upon its radical implications and has echoed throughout many fields, from (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   93 citations  
  9. Ideas and Results in Proof Theory.Dag Prawitz & J. E. Fenstad - 1971 - Journal of Symbolic Logic 40 (2):232-234.
  10.  65
    Tracking Reason: Proof, Consequence, and Truth.Jody Azzouni - 2005 - Oxford, England: Oup Usa.
    When ordinary people - mathematicians among them - take something to follow from something else, they are exposing the backbone of our self-ascribed ability to reason. Jody Azzouni investigates the connection between that ordinary notion of consequence and the formal analogues invented by logicians. One claim of the book is that, despite our apparent intuitive grasp of consequence, we do not introspect rules by which we reason, nor do we grasp the scope and range of the domain, as it were, (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   36 citations  
  11. Mathematical Explanation beyond Explanatory Proof.William D’Alessandro - 2017 - British Journal for the Philosophy of Science 71 (2):581-603.
    Much recent work on mathematical explanation has presupposed that the phenomenon involves explanatory proofs in an essential way. I argue that this view, ‘proof chauvinism’, is false. I then look in some detail at the explanation of the solvability of polynomial equations provided by Galois theory, which has often been thought to revolve around an explanatory proof. The article concludes with some general worries about the effects of chauvinism on the theory of mathematical explanation. 1Introduction 2Why I Am (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   19 citations  
  12.  90
    Semantics and Proof Theory of the Epsilon Calculus.Richard Zach - 2017 - In Ghosh Sujata & Prasad Sanjiva, Logic and Its Applications. ICLA 2017. Springer. pp. 27-47.
    The epsilon operator is a term-forming operator which replaces quantifiers in ordinary predicate logic. The application of this undervalued formalism has been hampered by the absence of well-behaved proof systems on the one hand, and accessible presentations of its theory on the other. One significant early result for the original axiomatic proof system for the epsilon-calculus is the first epsilon theorem, for which a proof is sketched. The system itself is discussed, also relative to possible semantic interpretations. (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  13.  88
    The Semantics and Proof Theory of Linear Logic.Arnon Avron - 1988 - Theoretical Computer Science 57 (2):161-184.
    Linear logic is a new logic which was recently developed by Girard in order to provide a logical basis for the study of parallelism. It is described and investigated in Gi]. Girard's presentation of his logic is not so standard. In this paper we shall provide more standard proof systems and semantics. We shall also extend part of Girard's results by investigating the consequence relations associated with Linear Logic and by proving corresponding str ong completeness theorems. Finally, we shall (...)
    Direct download  
     
    Export citation  
     
    Bookmark   64 citations  
  14. Uniform proof-theoretic semantics for logical constants.Peter Schroeder-Heister - 1991 - Journal of Symbolic Logic 56:1142.
  15.  46
    Model Theory and Proof Theory of the Global Reflection Principle.Mateusz Zbigniew Łełyk - 2023 - Journal of Symbolic Logic 88 (2):738-779.
    The current paper studies the formal properties of the Global Reflection Principle, to wit the assertion “All theorems of$\mathrm {Th}$are true,” where$\mathrm {Th}$is a theory in the language of arithmetic and the truth predicate satisfies the usual Tarskian inductive conditions for formulae in the language of arithmetic. We fix the gap in Kotlarski’s proof from [15], showing that the Global Reflection Principle for Peano Arithmetic is provable in the theory of compositional truth with bounded induction only ($\mathrm {CT}_0$). Furthermore, (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  16.  62
    Handbook of proof theory.Samuel R. Buss (ed.) - 1998 - New York: Elsevier.
    This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth. The chapters are arranged so that the two introductory (...)
    Direct download  
     
    Export citation  
     
    Bookmark   34 citations  
  17. Mathematical Method and Proof.Jeremy Avigad - 2006 - Synthese 153 (1):105-159.
    On a traditional view, the primary role of a mathematical proof is to warrant the truth of the resulting theorem. This view fails to explain why it is very often the case that a new proof of a theorem is deemed important. Three case studies from elementary arithmetic show, informally, that there are many criteria by which ordinary proofs are valued. I argue that at least some of these criteria depend on the methods of inference the proofs employ, (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   29 citations  
  18.  58
    Mill's "proof" of the principle of utility.Neil Cooper - 1969 - Mind 78 (310):278-279.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  19.  88
    Confronting Ideals of Proof with the Ways of Proving of the Research Mathematician.Norma B. Goethe & Michèle Friend - 2010 - Studia Logica 96 (2):273-288.
    In this paper, we discuss the prevailing view amongst philosophers and many mathematicians concerning mathematical proof. Following Cellucci, we call the prevailing view the “axiomatic conception” of proof. The conception includes the ideas that: a proof is finite, it proceeds from axioms and it is the final word on the matter of the conclusion. This received view can be traced back to Frege, Hilbert and Gentzen, amongst others, and is prevalent in both mathematical text books and logic (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   32 citations  
  20. Von Neumann’s impossibility proof: Mathematics in the service of rhetorics.Dennis Dieks - 2017 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 60:136-148.
    According to what has become a standard history of quantum mechanics, von Neumann in 1932 succeeded in convincing the physics community that he had proved that hidden variables were impossible as a matter of principle. Subsequently, leading proponents of the Copenhagen interpretation emphatically confirmed that von Neumann's proof showed the completeness of quantum mechanics. Then, the story continues, Bell in 1966 finally exposed the proof as seriously and obviously wrong; this rehabilitated hidden variables and made serious foundational research (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   12 citations  
  21. Paratheism: A Proof that God neither Exists nor Does Not Exist.Steven James Bartlett - 2016 - Willamette University Faculty Research Website: Http://Www.Willamette.Edu/~Sbartlet/Documents/Bartlett_Paratheism_A%20Proof%20that%20God%20neither%2 0Exists%20nor%20Does%20Not%20Exist.Pdf.
    Theism and its cousins, atheism and agnosticism, are seldom taken to task for logical-epistemological incoherence. This paper provides a condensed proof that not only theism, but atheism and agnosticism as well, are all of them conceptually self-undermining, and for the same reason: All attempt to make use of the concept of “transcendent reality,” which here is shown not only to lack meaning, but to preclude the very possibility of meaning. In doing this, the incoherence of theism, atheism, and agnosticism (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  22.  76
    Audience role in mathematical proof development.Zoe Ashton - 2020 - Synthese 198 (Suppl 26):6251-6275.
    The role of audiences in mathematical proof has largely been neglected, in part due to misconceptions like those in Perelman and Olbrechts-Tyteca which bar mathematical proofs from bearing reflections of audience consideration. In this paper, I argue that mathematical proof is typically argumentation and that a mathematician develops a proof with his universal audience in mind. In so doing, he creates a proof which reflects the standards of reasonableness embodied in his universal audience. Given this framework, (...)
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  23. IV*—On Putnam's Proof that We are not Brains-in-a-Vat1.Crispin Wright - 1992 - Proceedings of the Aristotelian Society 92 (1):67-94.
    Crispin Wright; IV*—On Putnam's Proof that We are not Brains-in-a-Vat1, Proceedings of the Aristotelian Society, Volume 92, Issue 1, 1 June 1992, Pages 67–94, h.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   40 citations  
  24. Open texture, rigor, and proof.Benjamin Zayton - 2022 - Synthese 200 (4):1-20.
    Open texture is a kind of semantic indeterminacy first systematically studied by Waismann. In this paper, extant definitions of open texture will be compared and contrasted, with a view towards the consequences of open-textured concepts in mathematics. It has been suggested that these would threaten the traditional virtues of proof, primarily the certainty bestowed by proof-possession, and this suggestion will be critically investigated using recent work on informal proof. It will be argued that informal proofs have virtues (...)
    No categories
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  25. Existence, proof and truth-making: A perspective on the intuitionistic conception of truth.Göran Sundholm - 1994 - Topoi 13 (2):117-126.
    Truth-maker analyses construe truth as existence of proof, a well-known example being that offered by Wittgenstein in theTractatus. The paper subsumes the intuitionistic view of truth as existence of proof under the general truth-maker scheme. Two generic constraints on truth-maker analysis are noted and positioned with respect to the writings of Michael Dummett and theTractatus. Examination of the writings of Brouwer, Heyting and Weyl indicates the specific notions of truth-maker and existence that are at issue in the intuitionistic (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   32 citations  
  26.  18
    Burdens of Proof in Modern Discourse.Richard H. Gaskins - 1992 - Yale University Press.
    Public and professional debates have come to rely heavily on a special type of reasoning: the argument-from-ignorance, in which conclusions depend on the _lack_ of compelling information. "I win my argument," says the skillful advocate, "unless you can prove that I am wrong." This extraordinary gambit has been largely ignored in modern rhetorical and philosophical studies. Yet its broad force can be demonstrated by analogy with the modern legal system, where courts have long manipulated burdens of proof with skill (...)
    Direct download  
     
    Export citation  
     
    Bookmark   24 citations  
  27. Diversity in proof appraisal.Matthew Inglis & Andrew Aberdein - 2016 - In Brendan Larvor, Mathematical Cultures: The London Meetings 2012-2014. Springer International Publishing. pp. 163-179.
    We investigated whether mathematicians typically agree about the qualities of mathematical proofs. Between-mathematician consensus in proof appraisals is an implicit assumption of many arguments made by philosophers of mathematics, but to our knowledge the issue has not previously been empirically investigated. We asked a group of mathematicians to assess a specific proof on four dimensions, using the framework identified by Inglis and Aberdein (2015). We found widespread disagreement between our participants about the aesthetics, intricacy, precision and utility of (...)
    Direct download  
     
    Export citation  
     
    Bookmark   8 citations  
  28. The Burden of Proof and Its Role in Argumentation.Ulrike Hahn & Mike Oaksford - 2007 - Argumentation 21 (1):39-61.
    The notion of “the burden of proof” plays an important role in real-world argumentation contexts, in particular in law. It has also been given a central role in normative accounts of argumentation, and has been used to explain a range of classic argumentation fallacies. We argue that in law the goal is to make practical decisions whereas in critical discussion the goal is frequently simply to increase or decrease degree of belief in a proposition. In the latter case, it (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   29 citations  
  29.  91
    Newman, Anselm and Proof of the Existence of God.Leslie Armour - 1986 - International Journal for Philosophy of Religion 19 (1/2):87 - 93.
  30. A completeness proof for Porte's S°a and Sa.C. F. Kielkopf - 1982 - Logique Et Analyse 25:435.
     
    Export citation  
     
    Bookmark  
  31. Pragmatic encroachment and legal proof.Sarah Moss - 2021 - Philosophical Issues 31 (1):258-279.
    This paper uses some modest claims about knowledge to identify a significant problem for contemporary American trial procedure. First, suppose that legal proof requires knowledge. In particular, suppose that the defendant in a jury trial is proven guilty only if the jury knows that the defendant is guilty. Second, suppose that knowledge is subject to pragmatic encroachment. In particular, whether the jury knows the defendant is guilty depends on what’s at stake in their decision to convict, including the consequences (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  32.  70
    From Collapse Theorems to Proof-Theoretic Arguments.Alessandro Rossi - 2023 - Australasian Journal of Logic 20 (1):1-31.
    On some views, we can be sure that parties to a dispute over the logic of ‘exists’ are not talking past each other if they can characterise ‘exists’ as the only monadic predicate up to logical equivalence obeying a certain set of rules of inference. Otherwise, we ought to be suspicious about the reality of their disagreement. This is what we call a proof- theoretic argument. Pace some critics, who have tried to use proof-theoretic arguments to cast doubts (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  33. Truth Through Proof: A Formalist Foundation for Mathematics.Alan Weir - 2010 - Oxford, England: Oxford University Press.
    Truth Through Proof defends an anti-platonist philosophy of mathematics derived from game formalism. Alan Weir aims to develop a more satisfactory successor to game formalism utilising a widely accepted, broadly neo-Fregean framework, in which the proposition expressed by an utterance is a function of both sense and background circumstance.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  34.  60
    Mathematical Intuitionism. Introduction to Proof Theory.A. G. Dragalin & E. Mendelson - 1990 - Journal of Symbolic Logic 55 (3):1308-1309.
  35.  18
    Hybrid Logic and its Proof-Theory.Torben Braüner - 2010 - Dordrecht and New York: Springer.
    This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model. This is useful for many applications, for example when reasoning about time one often wants to formulate a series of statements about what happens at specific times. There is little consensus about proof-theory for ordinary modal logic. Many modal-logical proof systems lack important properties and the relationships (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  36.  60
    Meta-uncertainty and the proof paradoxes.Katie Steele & Mark Colyvan - 2023 - Philosophical Studies 180 (7):1927-1950.
    Various real and imagined criminal law cases rest on “naked statistical evidence”. That is, they rest more or less entirely on a probability for guilt/liability derived from a single statistical model. The intuition is that there is something missing in these cases, high as the probability for guilt/liability may be, such that the relevant standard for legal proof is not met. Here we contribute to the considerable debate about how this intuition is best explained and what it teaches us (...)
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  37.  65
    Wang Hao. Alternative proof of a theorem of Kleene.J. C. E. Dekker - 1962 - Journal of Symbolic Logic 27 (1):81-82.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  38.  8
    Ordinals and Functionals in Proof Theory.Solomon Feferman - 1975 - Journal of Symbolic Logic 40 (4):625-626.
  39.  33
    A theistic proof of perfection.Thomas V. Morris - 1987 - Sophia 26 (2):31-35.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  40.  35
    On Synonymy in Proof-Theoretic Semantics: The Case of 2Int\mathtt{2Int}.Sara Ayhan & Heinrich Wansing - 2023 - Bulletin of the Section of Logic 52 (2):187-237.
    We consider an approach to propositional synonymy in proof-theoretic semantics that is defined with respect to a bilateral G3-style sequent calculus SC2Int\mathtt{SC2Int} for the bi-intuitionistic logic 2Int\mathtt{2Int}. A distinctive feature of SC2Int\mathtt{SC2Int} is that it makes use of two kind of sequents, one representing proofs, the other representing refutations. The structural rules of SC2Int\mathtt{SC2Int}, in particular its cut rules, are shown to be admissible. Next, interaction rules are defined that allow transitions from proofs to refutations, and vice versa, mediated (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  41. Fitch's proof, verificationism, and the knower paradox.J. C. Beall - 2000 - Australasian Journal of Philosophy 78 (2):241 – 247.
    I have argued that without an adequate solution to the knower paradox Fitch's Proof is- or at least ought to be-ineffective against verificationism. Of course, in order to follow my suggestion verificationists must maintain that there is currently no adequate solution to the knower paradox, and that the paradox continues to provide prima facie evidence of inconsistent knowledge. By my lights, any glimpse at the literature on paradoxes offers strong support for the first thesis, and any honest, non-dogmatic reflection (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   35 citations  
  42.  81
    Peter Schroeder-Heister on Proof-Theoretic Semantics.Thomas Piecha & Kai F. Wehmeier (eds.) - 2024 - Springer.
    This open access book is a superb collection of some fifteen chapters inspired by Schroeder-Heister's groundbreaking work, written by leading experts in the field, plus an extensive autobiography and comments on the various contributions by Schroeder-Heister himself. For several decades, Peter Schroeder-Heister has been a central figure in proof-theoretic semantics, a field of study situated at the interface of logic, theoretical computer science, natural-language semantics, and the philosophy of language. -/- The chapters of which this book is composed discuss (...)
  43.  61
    Wittgenstein on Proof and Concept-Formation.Sorin Bangu - forthcoming - Philosophical Quarterly.
    In his Remarks on the Foundations of Mathematics, Wittgenstein claims, puzzlingly, that ‘the proof creates a new concept’ (RFM III-41). This paper aims to contribute to clarifying this idea, and to showing how it marks a major break with the traditional conception of proof. Moreover, since the most natural way to understand his claim is open to criticism, a secondary goal of what follows is to offer an interpretation of it that neutralizes the objection. The discussion proceeds by (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  44. Truth Values and Proof Theory.Greg Restall - 2009 - Studia Logica 92 (2):241-264.
    I present an account of truth values for classical logic, intuitionistic logic, and the modal logic S5, in which truth values are not a fundamental category from which the logic is defined, but rather, an idealisation of more fundamental logical features in the proof theory for each system. The result is not a new set of semantic structures, but a new understanding of how the existing semantic structures may be understood in terms of a more fundamental notion of logical (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   22 citations  
  45. 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.
    Direct download (10 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  46.  59
    A short proof of Glivenko theorems for intermediate predicate logics.Christian Espíndola - 2013 - Archive for Mathematical Logic 52 (7-8):823-826.
    We give a simple proof-theoretic argument showing that Glivenko’s theorem for propositional logic and its version for predicate logic follow as an easy consequence of the deduction theorem, which also proves some Glivenko type theorems relating intermediate predicate logics between intuitionistic and classical logic. We consider two schemata, the double negation shift (DNS) and the one consisting of instances of the principle of excluded middle for sentences (REM). We prove that both schemata combined derive classical logic, while each one (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  47.  27
    Propositional proof systems based on maximum satisfiability.Maria Luisa Bonet, Sam Buss, Alexey Ignatiev, Antonio Morgado & Joao Marques-Silva - 2021 - Artificial Intelligence 300 (C):103552.
  48. Aristotle’s Completeness Proof.Timothy Smiley - 1994 - Ancient Philosophy 14 (S1):25-38.
  49.  17
    Focusing Gentzen’s LK Proof System.Chuck Liang & Dale Miller - 2024 - In Thomas Piecha & Kai F. Wehmeier, Peter Schroeder-Heister on Proof-Theoretic Semantics. Springer. pp. 275-313.
    Gentzen’s sequent calculi LK and LJ are landmark proof systems. They identify the structural rules of weakening and contraction as notable inference rules, and they allow for an elegant statement and proof of both cut elimination and consistency for classical and intuitionistic logics. Among the undesirable features of those sequent calculi is that their inferences rules are low-level and frequently permute over each other. As a result, large-scale structures within sequent calculus proofs are hard to identify. In this (...)
    Direct download  
     
    Export citation  
     
    Bookmark   3 citations  
  50.  18
    Ludic Proof: Greek Mathematics and the Alexandrian Aesthetic.Reviel Netz - 2009 - Cambridge University Press.
    This book represents a new departure in science studies: an analysis of a scientific style of writing, situating it within the context of the contemporary style of literature. Its philosophical significance is that it provides a novel way of making sense of the notion of a scientific style. For the first time, the Hellenistic mathematical corpus - one of the most substantial extant for the period - is placed centre-stage in the discussion of Hellenistic culture as a whole. Professor Netz (...)
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   6 citations  
1 — 50 / 951