Results for 'proof'

1000+ found
Order:
  1. On the concept of proof in elementary geometry Pirmin stekeler-weithofer.Proof In Elementary - 1992 - In Michael Detlefsen (ed.), Proof and Knowledge in Mathematics. Routledge.
     
    Export citation  
     
    Bookmark  
  2.  91
    Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - New York: Cambridge University Press. Edited by Jan Von Plato.
    Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics and computer science. The book contains a wealth of results on proof-theoretical systems, including extensions of such (...)
    Direct download  
     
    Export citation  
     
    Bookmark   116 citations  
  3.  9
    Proof theory.Gaisi Takeuti - 1975 - New York, N.Y., U.S.A.: Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co..
    This comprehensive monograph is a cornerstone in the area of mathematical logic and related fields. Focusing on Gentzen-type proof theory, the book presents a detailed overview of creative works by the author and other 20th-century logicians that includes applications of proof theory to logic as well as other areas of mathematics. 1975 edition.
    Direct download  
     
    Export citation  
     
    Bookmark   126 citations  
  4.  62
    Proof Analysis: A Contribution to Hilbert's Last Problem.Sara Negri & Jan von Plato - 2011 - Cambridge and New York: Cambridge University Press. Edited by Jan Von Plato.
    This book continues from where the authors' previous book, Structural Proof Theory, ended. It presents an extension of the methods of analysis of proofs in pure logic to elementary axiomatic systems and to what is known as philosophical logic. A self-contained brief introduction to the proof theory of pure logic is included that serves both the mathematically and philosophically oriented reader. The method is built up gradually, with examples drawn from theories of order, lattice theory and elementary geometry. (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   22 citations  
  5.  51
    Proof and Falsity: A Logical Investigation.Nils Kürbis - 2019 - Cambridge, UK: Cambridge University Press.
    This book argues that the meaning of negation, perhaps the most important logical constant, cannot be defined within the framework of the most comprehensive theory of proof-theoretic semantics, as formulated in the influential work of Michael Dummett and Dag Prawitz. Nils Kürbis examines three approaches that have attempted to solve the problem - defining negation in terms of metaphysical incompatibility; treating negation as an undefinable primitive; and defining negation in terms of a speech act of denial - and concludes (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   15 citations  
  6.  53
    Proof-theoretic semantics, paradoxes and the distinction between sense and denotation.Luca Tranchini - forthcoming - Journal of Logic and Computation 2014.
    In this paper we show how Dummett-Prawitz-style proof-theoretic semantics has to be modified in order to cope with paradoxical phenomena. It will turn out that one of its basic tenets has to be given up, namely the definition of the correctness of an inference as validity preservation. As a result, the notions of an argument being valid and of an argument being constituted by correct inference rules will no more coincide. The gap between the two notions is accounted for (...)
    Direct download  
     
    Export citation  
     
    Bookmark   20 citations  
  7. Proof Beyond a Reasonable Doubt: A Balanced Retributive Account.Alec Walen - 2015 - Louisiana Law Review 76 (2):355-446.
    The standard of proof in criminal trials in many liberal democracies is proof beyond a reasonable doubt, the BARD standard. It is customary to describe it, when putting a number on it, as requiring that the fact finder be at least 90% certain, after considering the evidence, that the defendant is guilty. Strikingly, no good reason has yet been offered in defense of using that standard. A number of non-consequentialist justifications that aim to support an even higher standard (...)
    Direct download  
     
    Export citation  
     
    Bookmark   8 citations  
  8. Evidence, Proofs, and Derivations.Andrew Aberdein - 2019 - ZDM 51 (5):825-834.
    The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice. Nonetheless, evidence, proof, and derivation are closely intertwined. This paper seeks to tease these concepts apart. It emphasizes the role of argumentation as a context shared by evidence, proofs, and derivations. The utility of argumentation theory, in general, and argumentation (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  9.  2
    Proof theory: sequent calculi and related formalisms.Katalin Bimbó - 2015 - Boca Raton: CRC Press, Taylor & Francis Group.
    Sequent calculi constitute an interesting and important category of proof systems. They are much less known than axiomatic systems or natural deduction systems are, and they are much less known than they should be. Sequent calculi were designed as a theoretical framework for investigations of logical consequence, and they live up to the expectations completely as an abundant source of meta-logical results. The goal of this book is to provide a fairly comprehensive view of sequent calculi -- including a (...)
    Direct download  
     
    Export citation  
     
    Bookmark   9 citations  
  10. Basic proof theory.A. S. Troelstra - 1996 - New York: Cambridge University Press. Edited by Helmut Schwichtenberg.
    This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   158 citations  
  11. New proofs for the existence of God: contributions of contemporary physics and philosophy.Robert J. Spitzer (ed.) - 2010 - Grand Rapids, Mich.: William B. Eerdmans.
    New Proofs for the Existence of God responds to these glaring omissions. / From universal space-time asymmetry to cosmic coincidences to the intelligibility of ...
    Direct download  
     
    Export citation  
     
    Bookmark   8 citations  
  12. Proof, Logic and Formalization.Michael Detlefsen (ed.) - 1992 - London, England: Routledge.
    The mathematical proof is the most important form of justification in mathematics. It is not, however, the only kind of justification for mathematical propositions. The existence of other forms, some of very significant strength, places a question mark over the prominence given to proof within mathematics. This collection of essays, by leading figures working within the philosophy of mathematics, is a response to the challenge of understanding the nature and role of the proof.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  13. Proofs and refutations: the logic of mathematical discovery.Imre Lakatos (ed.) - 1976 - New York: Cambridge University Press.
    Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre (...)
  14.  99
    Proof: Its nature and significance.Michael Detlefsen - 2008 - In Bonnie Gold & Roger A. Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematical Association of America. pp. 1.
    I focus on three preoccupations of recent writings on proof. -/- I. The role and possible effects of empirical reasoning in mathematics. Do recent developments (specifically, the computer-assisted proof of the 4CT) point to something essentially new as regards the need for and/or effects of using broadly empirical and inductive reasoning in mathematics? In particular, should we see such things as the computer-assisted proof of the 4CT as pointing to the existence of mathematical truths of which we (...)
    Direct download  
     
    Export citation  
     
    Bookmark   12 citations  
  15. 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 of (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   17 citations  
  16.  39
    Proof theory of modal logic.Heinrich Wansing (ed.) - 1996 - Boston: Kluwer Academic Publishers.
    Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.
    Direct download  
     
    Export citation  
     
    Bookmark   5 citations  
  17. Proof phenomenon as a function of the phenomenology of proving.Inês Hipólito - 2015 - Progress in Biophysics and Molecular Biology 119:360-367.
    Kurt Gödel wrote (1964, p. 272), after he had read Husserl, that the notion of objectivity raises a question: “the question of the objective existence of the objects of mathematical intuition (which, incidentally, is an exact replica of the question of the objective existence of the outer world)”. This “exact replica” brings to mind the close analogy Husserl saw between our intuition of essences in Wesensschau and of physical objects in perception. What is it like to experience a mathematical proving (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  18. Criminal Proof: Fixed or Flexible?Lewis Ross - 2023 - Philosophical Quarterly (4):1-23.
    Should we use the same standard of proof to adjudicate guilt for murder and petty theft? Why not tailor the standard of proof to the crime? These relatively neglected questions cut to the heart of central issues in the philosophy of law. This paper scrutinises whether we ought to use the same standard for all criminal cases, in contrast with a flexible approach that uses different standards for different crimes. I reject consequentialist arguments for a radically flexible standard (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  19. Proofs, pictures, and Euclid.John Mumma - 2010 - Synthese 175 (2):255 - 287.
    Though pictures are often used to present mathematical arguments, they are not typically thought to be an acceptable means for presenting mathematical arguments rigorously. With respect to the proofs in the Elements in particular, the received view is that Euclid's reliance on geometric diagrams undermines his efforts to develop a gap-free deductive theory. The central difficulty concerns the generality of the theory. How can inferences made from a particular diagrams license general mathematical results? After surveying the history behind the received (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   55 citations  
  20. The Proof-Structure of Kant's Transcendental Deduction.Dieter Henrich - 1969 - Review of Metaphysics 22 (4):640-659.
    Hence, there is still controversy over which of the two versions of the deduction deserves priority and whether indeed any distinction between them can be maintained that would go beyond questions of presentation and involve the structure of the proof itself. Schopenhauer and Heidegger held that the first edition alone fully expresses Kant's unique philosophy, while Kant himself, as well as many other Kantians, have only seen a difference in the method of presentation.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   51 citations  
  21. Criminal Proof: Fixed or Flexible?Lewis Ross - 2023 - The Philosophical Quarterly.
    Should we use the same standard of proof to adjudicate guilt for murder and petty theft? Why not tailor the standard of proof to the crime? These relatively neglected questions cut to the heart of central issues in the philosophy of law. This paper scrutinises whether we ought to use the same standard for all criminal cases, in contrast with a flexible approach that uses different standards for different crimes. I reject consequentialist arguments for a radically flexible standard (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  22. Proof-Theoretic Semantics, a Problem with Negation and Prospects for Modality.Nils Kürbis - 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 meanings (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   12 citations  
  23. Proof of an external world.George Edward Moore - 1939 - Proceedings of the British Academy 25 (5):273--300.
  24. Strategy-proof judgment aggregation.Franz Dietrich & Christian List - 2005 - Economics and Philosophy 23 (3):269-300.
    Which rules for aggregating judgments on logically connected propositions are manipulable and which not? In this paper, we introduce a preference-free concept of non-manipulability and contrast it with a preference-theoretic concept of strategy-proofness. We characterize all non-manipulable and all strategy-proof judgment aggregation rules and prove an impossibility theorem similar to the Gibbard--Satterthwaite theorem. We also discuss weaker forms of non-manipulability and strategy-proofness. Comparing two frequently discussed aggregation rules, we show that “conclusion-based voting” is less vulnerable to manipulation than “premise-based (...)
    Direct download (20 more)  
     
    Export citation  
     
    Bookmark   51 citations  
  25.  18
    Proofs and computations.Helmut Schwichtenberg - 2011 - New York: Cambridge University Press. Edited by S. S. Wainer.
    Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Gödel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11-CA0. Ordinal analysis and the (Schwichtenberg-Wainer) subrecursive hierarchies play a central (...)
    Direct download  
     
    Export citation  
     
    Bookmark   2 citations  
  26. Informal proofs and mathematical rigour.Marianna Antonutti Marfori - 2010 - Studia Logica 96 (2):261-272.
    The aim of this paper is to provide epistemic reasons for investigating the notions of informal rigour and informal provability. I argue that the standard view of mathematical proof and rigour yields an implausible account of mathematical knowledge, and falls short of explaining the success of mathematical practice. I conclude that careful consideration of mathematical practice urges us to pursue a theory of informal provability.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   19 citations  
  27. Proof-theoretic semantics for a natural language fragment.Nissim Francez & Roy Dyckhoff - 2010 - Linguistics and Philosophy 33 (6):447-477.
    The paper presents a proof-theoretic semantics (PTS) for a fragment of natural language, providing an alternative to the traditional model-theoretic (Montagovian) semantics (MTS), whereby meanings are truth-condition (in arbitrary models). Instead, meanings are taken as derivability-conditions in a dedicated natural-deduction (ND) proof-system. This semantics is effective (algorithmically decidable), adhering to the meaning as use paradigm, not suffering from several of the criticisms formulated by philosophers of language against MTS as a theory of meaning. In particular, Dummett’s manifestation argument (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   35 citations  
  28.  15
    Proof and the art of mathematics: examples and extensions.Joel David Hamkins - 2021 - Cambridge, Massachusetts: The MIT Press.
    An introduction to writing proofs, presented through compelling mathematical statements with interesting elementary proofs. This book offers an introduction to the art and craft of proof-writing. The author, a leading research mathematician, presents a series of engaging and compelling mathematical statements with interesting elementary proofs. These proofs capture a wide range of topics, including number theory, combinatorics, graph theory, the theory of games, geometry, infinity, order theory, and real analysis. The goal is to show students and aspiring mathematicians how (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  29.  99
    Proof-Theoretic Semantics.Peter Schroeder-Heister - forthcoming - Stanford Encyclopedia of Philosophy.
  30. On Proof-Theoretic Approaches to the Paradoxes: Problems of Undergeneration and Overgeneration in the Prawitz-Tennant Analysis.Seungrak Choi - 2019 - Dissertation, Korea University
    In this dissertation, we shall investigate whether Tennant's criterion for paradoxicality(TCP) can be a correct criterion for genuine paradoxes and whether the requirement of a normal derivation(RND) can be a proof-theoretic solution to the paradoxes. Tennant’s criterion has two types of counterexamples. The one is a case which raises the problem of overgeneration that TCP makes a paradoxical derivation non-paradoxical. The other is one which generates the problem of undergeneration that TCP renders a non-paradoxical derivation paradoxical. Chapter 2 deals (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  31. Five Proofs of The Existence of God.Edward Feser - 2017 - Ignatius Press.
    This book provides a detailed, updated exposition and defense of five of the historically most important (but in recent years largely neglected) philosophical proofs of God’s existence: the Aristotelian, the Neo-Platonic, the Augustinian, the Thomistic, and the Rationalist. It also offers a thorough treatment of each of the key divine attributes—unity, simplicity, eternity, omnipotence, omniscience, perfect goodness, and so forth—showing that they must be possessed by the God whose existence is demonstrated by the proofs. Finally, it answers at length all (...)
  32. The Proof-Theoretic Analysis of Transfinitely Iterated Fixed Point Theories.Gerhard Jager, Reinhard Kahle, Anton Setzer & Thomas Strahm - 1999 - Journal of Symbolic Logic 64 (1):53-67.
    This article provides the proof-theoretic analysis of the transfinitely iterated fixed point theories $\widehat{ID}_\alpha and \widehat{ID}_{<\alpha};$ the exact proof-theoretic ordinals of these systems are presented.
     
    Export citation  
     
    Bookmark   12 citations  
  33. Truth, Proof and Gödelian Arguments: A Defence of Tarskian Truth in Mathematics.Markus Pantsar - 2009 - Dissertation, University of Helsinki
    One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established (...)
    Direct download  
     
    Export citation  
     
    Bookmark   10 citations  
  34. Proof Paradoxes and Normic Support: Socializing or Relativizing?Marcello Di Bello - 2020 - Mind 129 (516):1269-1285.
    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.
    No categories
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  35.  9
    Proof Theory for Fuzzy Logics.George Metcalfe, Nicola Olivetti & Dov M. Gabbay - 2008 - Dordrecht, Netherland: Springer.
    Fuzzy logics are many-valued logics that are well suited to reasoning in the context of vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse areas such as fuzzy control, fuzzy databases, and fuzzy mathematics. This book provides an accessible and up-to-date introduction to this fast-growing and increasingly popular area. It focuses in particular on the development and applications of "proof-theoretic" presentations of fuzzy logics; the result of more than ten years of intensive work by (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  36.  6
    Mathematical proofs: a transition to advanced mathematics.Gary Chartrand - 2018 - Boston: Pearson. Edited by Albert D. Polimeni & Ping Zhang.
    For courses in Transition to Advanced Mathematics or Introduction to Proof. Meticulously crafted, student-friendly text that helps build mathematical maturity Mathematical Proofs: A Transition to Advanced Mathematics, 4th Edition introduces students to proof techniques, analyzing proofs, and writing proofs of their own that are not only mathematically correct but clearly written. Written in a student-friendly manner, it provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as optional excursions into fields such (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  37. Proofs, necessity and causality.Srećko Kovač - 2019 - In Enrique Alonso, Antonia Huertas & Andrei Moldovan (eds.), Aventuras en el Mundo de la Lógica: Ensayos en Honor a María Manzano. London: College Publications. pp. 239-263.
    There is a long tradition of logic, from Aristotle to Gödel, of understanding a proof from the concepts of necessity and causality. Gödel's attempts to define provability in terms of necessity led him to the distinction of formal and absolute (abstract) provability. Turing's definition of mechanical procedure by means of a Turing machine (TM) and Gödel's definition of a formal system as a mechanical procedure for producing formulas prompt us to understand formal provability as a mechanical causality. We propose (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  38. Proof Theory.Gaisi Takeuti - 1990 - Studia Logica 49 (1):160-161.
     
    Export citation  
     
    Bookmark   165 citations  
  39.  4
    Proofs 101: an introduction to formal mathematics.Joseph Kirtland - 2020 - Boca Raton: CRC Press, Taylor & Francis Group.
    Proofs 101: An Introduction to Formal Mathematics serves as an introduction to proofs for mathematics majors who have completed the calculus sequence (at least Calculus I and II) and Linear Algebra. It prepares students for the proofs they will need to analyse and write, the axiomatic nature of mathematics, and the rigors of upper-level mathematics courses. Basic number theory, relations, functions, cardinality, and set theory will provide the material for the proofs and lay the foundation for a deeper understanding of (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  40.  3
    Proof complexity.Jan Krajíček - 2019 - New York, NY: Cambridge University Press.
    Proof complexity is a rich subject drawing on methods from logic, combinatorics, algebra and computer science. This self-contained book presents the basic concepts, classical results, current state of the art and possible future directions in the field. It stresses a view of proof complexity as a whole entity rather than a collection of various topics held together loosely by a few notions, and it favors more generalizable statements. Lower bounds for lengths of proofs, often regarded as the key (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  41.  90
    A proof-theoretic defence of meaning-invariant logical pluralism.Bogdan Dicher - 2016 - Mind 125 (499):727-757.
    In this paper I offer a proof-theoretic defence of meaning-invariant logical pluralism. I argue that there is a relation of co-determination between the operational and structural aspects of a logic. As a result, some features of the consequence relation are induced by the connectives. I propose that a connective is defined by those rules which are conservative and unique, while at the same time expressing only connective-induced structural information. This is the key to stabilizing the meaning of the connectives (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   18 citations  
  42.  3
    Proof and the art of mathematics.Joel David Hamkins - 2020 - Cambridge, Massachusetts: The MIT Press.
    A textbook for students who are learning how to write a mathematical proof, a validation of the truth of a mathematical statement.
    Direct download  
     
    Export citation  
     
    Bookmark  
  43. Proof That Knowledge Entails Truth.Brent G. Kyle - forthcoming - Journal of Philosophy.
    Despite recent controversies surrounding the principle that knowledge entails truth (KT), this paper aims to prove that the principle is true. It offers a proof of (KT) in the following sense. It advances a deductively valid argument for (KT), whose premises are, by most lights, obviously true. Moreover, each premise is buttressed by at least two supporting arguments. And finally, all premises and supporting arguments can be rationally accepted by people who don’t already accept (KT).
    Direct download  
     
    Export citation  
     
    Bookmark  
  44.  12
    Proofs and types.Jean-Yves Girard - 1989 - New York: Cambridge University Press.
    This text is an outgrowth of notes prepared by J. Y. Girard for a course at the University of Paris VII. It deals with the mathematical background of the application to computer science of aspects of logic (namely the correspondence between proposition & types). Combined with the conceptual perspectives of Girard's ideas, this sheds light on both the traditional logic material & its prospective applications to computer science. The book covers a very active & exciting research area, & it will (...)
    Direct download  
     
    Export citation  
     
    Bookmark   57 citations  
  45. 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 (...)
    Direct download  
     
    Export citation  
     
    Bookmark   27 citations  
  46. Proof-Theoretic Semantics and the Interpretation of Atomic Sentences.Preston Stovall - 2020 - In Igor Sedlár & Martin Blicha (eds.), The Logica Yearbook 2019. Rickmansworth: College Publications. pp. 163-178.
    This essay addresses one of the open questions of proof-theoretic semantics: how to understand the semantic values of atomic sentences. I embed a revised version of the explanatory proof system of Millson and Straßer (2019) into the proof-theoretic semantics of Francez (2015) and show how to specify (part of) the intended interpretation of atomic sentences on the basis of their occurrences in the premises and conclusions of inferences to and from best explanations.
    Direct download  
     
    Export citation  
     
    Bookmark  
  47.  41
    Proofs and Refutations: The Logic of Mathematical Discovery.Imre Lakatos, John Worrall & Elie Zahar (eds.) - 1976 - Cambridge and London: Cambridge University Press.
    Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of (...)
  48.  30
    Proof theory: a selection of papers from the Leeds Proof Theory Programme, 1990.Peter Aczel, Harold Simmons & Stanley S. Wainer (eds.) - 1992 - New York: Cambridge University Press.
    This work is derived from the SERC "Logic for IT" Summer School Conference on Proof Theory held at Leeds University. The contributions come from acknowledged experts and comprise expository and research articles which form an invaluable introduction to proof theory aimed at both mathematicians and computer scientists.
    Direct download  
     
    Export citation  
     
    Bookmark  
  49.  49
    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   33 citations  
  50. A Proof of Gamma.Saul A. Kripke - 2022 - In Katalin Bimbó (ed.), Relevance Logics and other Tools for Reasoning. Essays in Honor of J. Michael Dunn. London: College Publications. pp. 261-265.
    This paper is dedicated to the memory of Mike Dunn. His untimely death is a loss not only to logic, computer science, and philosophy, but to all of us who knew and loved him. The paper gives an argument for closure under γ in standard systems of relevance logic (first proved by Meyer and Dunn 1969). For definiteness, I chose the example of R. The proof also applies to E and to the quantified systems RQ and EQ. The argument (...)
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
1 — 50 / 1000