Results for 'proof'

960 found
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  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.
     
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  2. 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 (...)
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  3.  75
    Proof Methods for Modal and Intuitionistic Logics.Melvin Fitting - 1985 - Journal of Symbolic Logic 50 (3):855-856.
  4.  26
    Identifying future-proof science.Peter Vickers - 2023 - Oxford: Oxford University Press.
    Explores how to identify future-proof science. Peter Vickers takes a transdisciplinary approach in his analysis of 'scientific fact' in order to defend science against potentially dangerous scepticism.
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  5. Proof and Truth.Stewart Shapiro - 1998 - Journal of Philosophy 95 (10):493-521.
  6. Proof Theory.Gaisi Takeuti - 1990 - Studia Logica 49 (1):160-161.
     
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  7. (1 other version)Proof-Theoretic Semantics.Peter Schroeder-Heister - 2024 - Stanford Encyclopedia of Philosophy.
  8. 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 (...)
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  9.  30
    Evidence Matters: Science, Proof, and Truth in the Law.Susan Haack - 2014 - New York, NY: Cambridge University Press.
    Is truth in the law just plain truth - or something sui generis? Is a trial a search for truth? Do adversarial procedures and exclusionary rules of evidence enable, or impede, the accurate determination of factual issues? Can degrees of proof be identified with mathematical probabilities? What role can statistical evidence properly play? How can courts best handle the scientific testimony on which cases sometimes turn? How are they to distinguish reliable scientific testimony from unreliable hokum? These interdisciplinary essays (...)
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  10.  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, (...)
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  11.  53
    What is future-proof science?Peter Vickers - 2023 - In Identifying future-proof science. Oxford: Oxford University Press.
    Is science getting at the truth? The sceptics – those who spread doubt about science – often employ a simple argument: scientists were sure in the past, and then they ended up being wrong. Such sceptics draw on dramatic quotes from eminent scientists such as Lord Kelvin, who reportedly stated at the turn of the 20th century “There is nothing new to be discovered in physics now,” shortly before physics was dramatically transformed. They ask: given the history of science, wouldn’t (...)
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  12. 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 (...)
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  13.  50
    Advances in Proof-Theoretic Semantics.Peter Schroeder-Heister & Thomas Piecha (eds.) - 2015 - Cham, Switzerland: Springer Verlag.
    This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, and the defence of model theory. The field of proof-theoretic semantics has existed for almost 50 years, (...)
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  14.  84
    Godel's Proof.S. R. Peterson - 1961 - Philosophical Quarterly 11 (45):379.
    In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system and had radical implications that have echoed throughout many fields. A gripping combination of science and accessibility, Godel’s Proof by Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and (...)
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  15. 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 (...)
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  16.  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 (...)
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  17.  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 (...)
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  18.  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 (...)
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  19.  25
    (1 other version)Language, Proof and Logic.Patrick Grim - 2001 - Bulletin of Symbolic Logic 7 (3):377-379.
  20.  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 (...)
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  21.  68
    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 (...)
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  22. Uniform proof-theoretic semantics for logical constants.Peter Schroeder-Heister - 1991 - Journal of Symbolic Logic 56:1142.
  23. 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 (...)
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  24.  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 (...)
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  25. (1 other version)Minimum propositional proof length is NP-Hard to linearly approximate.Michael Alekhnovich, Sam Buss, Shlomo Moran & Toniann Pitassi - 2001 - Journal of Symbolic Logic 66 (1):171-191.
    We prove that the problem of determining the minimum propositional proof length is NP- hard to approximate within a factor of 2 log 1 - o(1) n . These results are very robust in that they hold for almost all natural proof systems, including: Frege systems, extended Frege systems, resolution, Horn resolution, the polynomial calculus, the sequent calculus, the cut-free sequent calculus, as well as the polynomial calculus. Our hardness of approximation results usually apply to proof length (...)
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  26.  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, (...)
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  27.  70
    Proof and Paradox.Neil Tennant - 1982 - Dialectica 36 (2‐3):265-296.
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  28. 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 (...)
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  29.  60
    Provability algebras and proof-theoretic ordinals, I.Lev D. Beklemishev - 2004 - Annals of Pure and Applied Logic 128 (1-3):103-123.
    We suggest an algebraic approach to proof-theoretic analysis based on the notion of graded provability algebra, that is, Lindenbaum boolean algebra of a theory enriched by additional operators which allow for the structure to capture proof-theoretic information. We use this method to analyze Peano arithmetic and show how an ordinal notation system up to 0 can be recovered from the corresponding algebra in a canonical way. This method also establishes links between proof-theoretic ordinal analysis and the work (...)
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  30. A constructive proof of the Peter-Weyl theorem.B. Spitters & G. Coquand - 2005 - Mathematical Logic Quarterly 51 (4):351.
  31. Intuitionism, religious belief, and proof in the papers of the metaphysical society.William Sweet - 2019 - In Catherine Marshall, Bernard V. Lightman & Richard England, The Metaphysical Society (1869-1880): intellectual life in mid-Victorian England. New York, NY: Oxford University Press.
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  32. Proof and truth.Christopher Peacocke - 1993 - In John Haldane & Crispin Wright, Reality, representation, and projection. New York: Oxford University Press. pp. 165--190.
     
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  33. Shifting the burden of proof?Michael Rescorla - 2009 - Philosophical Quarterly 59 (234):86-109.
    Dialectical foundationalists, including Adler, Brandom, Leite, and Williams, claim that some asserted propositions do not require defense just because an interlocutor challenges them. By asserting such a proposition, the speaker shifts the burden of proof to her interlocutor. Dialectical egalitarians claim that all asserted propositions require defense when challenged. I elucidate the dispute between dialectical foundationalists and egalitarians, and I defend a broadly egalitarian stance against several prominent objections.
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  34.  67
    Proof with and without probabilities.Bart Verheij - 2017 - Artificial Intelligence and Law 25 (1):127-154.
    Evidential reasoning is hard, and errors can lead to miscarriages of justice with serious consequences. Analytic methods for the correct handling of evidence come in different styles, typically focusing on one of three tools: arguments, scenarios or probabilities. Recent research used Bayesian networks for connecting arguments, scenarios, and probabilities. Well-known issues with Bayesian networks were encountered: More numbers are needed than are available, and there is a risk of misinterpretation of the graph underlying the Bayesian network, for instance as a (...)
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  35.  25
    Reductive Logic, Proof-Search, and Coalgebra: A Perspective from Resource Semantics.Alexander V. Gheorghiu, Simon Docherty & David J. Pym - 2023 - In Alessandra Palmigiano & Mehrnoosh Sadrzadeh, Samson Abramsky on Logic and Structure in Computer Science and Beyond. Springer Verlag. pp. 833-875.
    The reductive, as opposed to deductive, view of logic is the form of logic that is, perhaps, most widely employed in practical reasoning. In particular, it is the basis of logic programming. Here, building on the idea of uniform proof in reductive logic, we give a treatment of logic programming for BI, the logic of bunched implications, giving both operational and denotational semantics, together with soundness and completeness theorems, all couched in terms of the resource interpretation of BI’s semantics. (...)
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  36. 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 (...)
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  37.  5
    Sūgaku ni okeru shōmei to shinri: yōsō ronri to sūgaku kisoron = Proof and truth in mathematics: modal logic and the foundations of mathematics.Katsuhiko Sano (ed.) - 2016 - Tōkyō-to Bunkyō-ku: Kyōritsu Shuppan.
    正しいから証明できるのか、証明できるから正しいのか。数学にとって証明とは何か、正しさとは何なのかは数学基礎論の根本的な問題である。様相論理を軸とした、証明と真理に関わる数学基礎論の古典的な結果から最先 端の議論までを解説した。.
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  38. Kant on the ontological proof.Uygar Abaci - 2023 - In Ina Goy, Kant on Proofs for God's Existence. Boston: De Gruyter.
     
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  39.  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 (...)
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  40. Civil liability and the 50%+ standard of proof.Martin Smith - 2021 - International Journal of Evidence and Proof 25 (3):183-199.
    The standard of proof applied in civil trials is the preponderance of evidence, often said to be met when a proposition is shown to be more than 50% likely to be true. A number of theorists have argued that this 50%+ standard is too weak – there are circumstances in which a court should find that the defendant is not liable, even though the evidence presented makes it more than 50% likely that the plaintiff’s claim is true. In this (...)
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  41. The History of Mathematical Proof in Ancient Traditions.Karine Chemla (ed.) - 2012 - Cambridge University Press.
    This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship. It documents the existence of proofs in ancient mathematical writings about numbers and shows that practitioners of mathematics in Mesopotamian, Chinese and Indian cultures knew how to (...)
     
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  42. Computer proof.Paul Teller - 1980 - Journal of Philosophy 77 (12):797-803.
  43.  36
    Proof Systems for 3-valued Logics Based on Gödel’s Implication.Arnon Avron - 2022 - Logic Journal of the IGPL 30 (3):437-453.
    The logic $G3^{<}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$ was introduced in Robles and Mendéz as a paraconsistent logic which is based on Gödel’s 3-valued matrix, except that Kleene–Łukasiewicz’s negation is added to the language and is used as the main negation connective. We show that $G3^{<}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$ is exactly the intersection of $G3^{\{1\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$ and $G3^{\{1,0.5\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$, the two truth-preserving 3-valued logics which are based on the same truth tables. We then construct a Hilbert-type system which has for $\to $ as its sole rule of inference, and is (...)
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  44. Proof Theory and Meaning.B. G. Sundholm - unknown
     
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  45.  80
    Leibniz’s Ontological Proof of the Existence of God and the Problem of »Impossible Objects«.Wolfgang Lenzen - 2017 - Logica Universalis 11 (1):85-104.
    The core idea of the ontological proof is to show that the concept of existence is somehow contained in the concept of God, and that therefore God’s existence can be logically derived—without any further assumptions about the external world—from the very idea, or definition, of God. Now, G.W. Leibniz has argued repeatedly that the traditional versions of the ontological proof are not fully conclusive, because they rest on the tacit assumption that the concept of God is possible, i.e. (...)
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  46. Slip-Proof Actions.Santiago Amaya - 2015 - In Roman Altshuler & Michael J. Sigrist, Time and the Philosophy of Action. New York: Routledge. pp. 21-36.
    Most human actions are complex, but some of them are basic. Which are these? In this paper, I address this question by invoking slips, a common kind of mistake. The proposal is this: an action is basic if and only if it is not possible to slip in performing it. The argument discusses some well-established results from the psychology of language production in the context of a philosophical theory of action. In the end, the proposed criterion is applied to discuss (...)
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  47.  18
    Paradoxes, Intuitionism, and Proof-Theoretic Semantics.Reinhard Kahle & Paulo Guilherme Santos - 2024 - In Thomas Piecha & Kai F. Wehmeier, Peter Schroeder-Heister on Proof-Theoretic Semantics. Springer. pp. 363-374.
    In this note, we review paradoxes like Russell’s, the Liar, and Curry’s in the context of intuitionistic logic. One may observe that one cannot blame the underlying logic for the paradoxes, but has to take into account the particular concept formations. For proof-theoretic semantics, however, this comes with the challenge to block some forms of direct axiomatizations of the Liar. A proper answer to this challenge might be given by Schroeder-Heister’s definitional freedom.
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  48.  77
    Proof and Understanding in Mathematical Practice.Danielle Macbeth - 2012 - Philosophia Scientiae 16 (1):29-54.
    Prouver des théorèmes est une pratique mathématique qui semble clairement améliorer notre compréhension mathématique. Ainsi, prouver et reprouver des théorèmes en mathématiques, vise à apporter une meilleure compréhension. Cependant, comme il est bien connu, les preuves mathématiques totalement formalisées sont habituellement inintelligibles et, à ce titre, ne contribuent pas à notre compréhension mathématique. Comment, alors, comprendre la relation entre prouver des théorèmes et améliorer notre compréhension mathématique. J'avance ici que nous avons d'abord besoin d'une notion différente de preuve (formelle), qui (...)
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  49.  25
    Proof and Explanation: The Virginia Lectures.John Wisdom - 1991 - University Press of America.
    This book is based on previously unpublished lectures that Wisdom delivered at the University of Virginia. Its content goes significantly beyond that of his other books. Here he is concerned with how misunderstandings about what it is to prove something or what it is to explain something can infect our thinking in many different fields.
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  50. Informal proof, formal proof, formalism.Alan Weir - 2016 - Review of Symbolic Logic 9 (1):23-43.
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