Results for 'Proofs'

167 found
Order:
  1. Proofs of God in Early Modern Europe.Lloyd Strickland - 2018 - Waco, TX, USA: Baylor University Press.
    Proofs of God in Early Modern Europe offers a fascinating window into early modern efforts to prove God’s existence. Assembled here are twenty-two key texts, many translated into English for the first time, which illustrate the variety of arguments that philosophers of the seventeenth and eighteenth centuries offered for God. These selections feature traditional proofs—such as various ontological, cosmological, and design arguments—but also introduce more exotic proofs, such as the argument from eternal truths, the argument from universal (...)
    Download  
     
    Export citation  
     
    Bookmark  
  2. Philosophical Proofs Against Common Sense.Bryan Frances - forthcoming - Analysis.
    Many philosophers are sceptical about the power of philosophy to refute commonsensical claims. They look at the famous attempts and judge them inconclusive. I prove that even if those famous attempts are failures, there are alternative successful philosophical proofs against commonsensical claims. After presenting the proofs I briefly comment on their significance.
    Download  
     
    Export citation  
     
    Bookmark  
  3. Oppy and Modal Theistic Proofs.Richard Davis - 2009 - Philosophia Christi 11 (2):437-444.
    I argue that Graham Oppy’s attempt to redefend his charge that all modal theistic arguments “must be question-begging” is unsuccessful. Oppy’s attempt to show that theism and modal concretism are compatible is not only tangential for his purposes, it is marred by a misunderstanding of theism, and vulnerable to a counterexample that actually demonstrates incompatibility. Moreover, the notion of begging the question employed by Oppy against the theist is seen to be far too permissive.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  4. Formal Logic: Classical Problems and Proofs.Luis M. Augusto - 2019 - London, UK: College Publications.
    Not focusing on the history of classical logic, this book provides discussions and quotes central passages on its origins and development, namely from a philosophical perspective. Not being a book in mathematical logic, it takes formal logic from an essentially mathematical perspective. Biased towards a computational approach, with SAT and VAL as its backbone, this is an introduction to logic that covers essential aspects of the three branches of logic, to wit, philosophical, mathematical, and computational.
    Download  
     
    Export citation  
     
    Bookmark  
  5. Edward Feser: Five Proofs of the Existence of God. [REVIEW]Logan Paul Gage - 2019 - Philosophia Christi 21 (1):228-232.
    A review of Edward Feser's Five Proofs of the Existence of God.
    Download  
     
    Export citation  
     
    Bookmark  
  6. 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 (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  7. Explanation in Mathematics: Proofs and Practice.William D'Alessandro - 2019 - Philosophy Compass 14 (11).
    Mathematicians distinguish between proofs that explain their results and those that merely prove. This paper explores the nature of explanatory proofs, their role in mathematical practice, and some of the reasons why philosophers should care about them. Among the questions addressed are the following: what kinds of proofs are generally explanatory (or not)? What makes a proof explanatory? Do all mathematical explanations involve proof in an essential way? Are there really such things as explanatory proofs, and (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  8.  24
    Informal and Formal Proofs, Metalogic, and the Groundedness Problem.Mario Bacelar Valente - manuscript
    When modeling informal proofs like that of Euclid’s Elements using a sound logical system, we go from proofs seen as somewhat unrigorous – even having gaps to be filled – to rigorous proofs. However, metalogic grounds the soundness of our logical system, and proofs in metalogic are not like formal proofs and look suspiciously like the informal proofs. This brings about what I am calling here the groundedness problem: how can we decide with certainty (...)
    Download  
     
    Export citation  
     
    Bookmark  
  9. Teaching and Learning Guide For: Explanation in Mathematics: Proofs and Practice.William D'Alessandro - 2019 - Philosophy Compass 14 (11).
    This is a teaching and learning guide to accompany "Explanation in Mathematics: Proofs and Practice".
    Download  
     
    Export citation  
     
    Bookmark  
  10. Beyond the Paralogisms: The Proofs of Immortality in the Lectures on Metaphysics.Corey W. Dyck - 2015 - In Robert Clewis (ed.), Reading Kant's Lectures. De Gruyter. pp. 115-134.
    Considered in light of the reader’s expectation of a thoroughgoing criticism of the pretensions of the rational psychologist, and of the wealth of discussions available in the broader 18th century context, which includes a variety of proofs that do not explicitly turn on the identification of the soul as a simple substance, Kant’s discussion of immortality in the Paralogisms falls lamentably short. However, outside of the Paralogisms (and the published works generally), Kant had much more to say about the (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  11. 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 schemes, in (...)
    Download  
     
    Export citation  
     
    Bookmark  
  12.  34
    Review of John Stillwell, Reverse Mathematics: Proofs From the Inside Out. [REVIEW]Benedict Eastaugh - 2020 - Philosophia Mathematica 28 (1):108-116.
    Review of John Stillwell, Reverse Mathematics: Proofs from the Inside Out. Princeton, NJ: Princeton University Press, 2018, pp. 200. ISBN 978-0-69-117717-5 (hbk), 978-0-69-119641-1 (pbk), 978-1-40-088903-7 (e-book).
    Download  
     
    Export citation  
     
    Bookmark  
  13. Proofs Versus Experiments: Wittgensteinian Themes Surrounding the Four-Color Theorem.G. D. Secco - 2017 - In Marcos Silva (ed.), How Colours Matter to Philosophy. Cham: Springer. pp. 289-307.
    The Four-Colour Theorem (4CT) proof, presented to the mathematical community in a pair of papers by Appel and Haken in the late 1970's, provoked a series of philosophical debates. Many conceptual points of these disputes still require some elucidation. After a brief presentation of the main ideas of Appel and Haken’s procedure for the proof and a reconstruction of Thomas Tymoczko’s argument for the novelty of 4CT’s proof, we shall formulate some questions regarding the connections between the points raised by (...)
    Download  
     
    Export citation  
     
    Bookmark  
  14. Simulation Models of the Evolution of Cooperation as Proofs of Logical Possibilities. How Useful Are They?Eckhart Arnold - 2013 - Ethics and Politics 2 (XV):101-138.
    This paper discusses critically what simulation models of the evolution of cooperation can possibly prove by examining Axelrod’s “Evolution of Cooperation” (1984) and the modeling tradition it has inspired. Hardly any of the many simulation models in this tradition have been applicable empirically. Axelrod’s role model suggested a research design that seemingly allowed to draw general conclusions from simulation models even if the mechanisms that drive the simulation could not be identified empirically. But this research design was fundamentally flawed. At (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  15. Teaching Proving by Coordinating Aspects of Proofs with Students' Abilities.Annie Selden & John Selden - 2009 - In Despina A. Stylianou, Maria L. Blanton & Eric J. Knuth (eds.), Teaching and Learning Proof Across the Grades: A K-16 Perspective. New York, USA: Routledge. pp. 339--354.
    In this chapter we introduce concepts for analyzing proofs, and for analyzing undergraduate and beginning graduate mathematics students’ proving abilities. We discuss how coordination of these two analyses can be used to improve students’ ability to construct proofs. -/- For this purpose, we need a richer framework for keeping track of students’ progress than the everyday one used by mathematicians. We need to know more than that a particular student can, or cannot, prove theorems by induction or contradiction (...)
    Download  
     
    Export citation  
     
    Bookmark  
  16. Corcoran Reviews Boute’s 2013 Paper “How to Calculate Proofs”.John Corcoran - 2014 - MATHEMATICAL REVIEWS 14:444-555.
    Corcoran reviews Boute’s 2013 paper “How to calculate proofs”. -/- There are tricky aspects to classifying occurrences of variables: is an occurrence of ‘x’ free as in ‘x + 1’, is it bound as in ‘{x: x = 1}’, or is it orthographic as in ‘extra’? The trickiness is compounded failure to employ conventions to separate use of expressions from their mention. The variable occurrence is free in the term ‘x + 1’ but it is orthographic in that term’s (...)
    Download  
     
    Export citation  
     
    Bookmark  
  17. Co-Constructive Logic for Proofs and Refutations.James Trafford - 2014 - Studia Humana 3 (4):22-40.
    This paper considers logics which are formally dual to intuitionistic logic in order to investigate a co-constructive logic for proofs and refutations. This is philosophically motivated by a set of problems regarding the nature of constructive truth, and its relation to falsity. It is well known both that intuitionism can not deal constructively with negative information, and that defining falsity by means of intuitionistic negation leads, under widely-held assumptions, to a justification of bivalence. For example, we do not want (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  18. Simulation Models of the Evolution of Cooperation as Proofs of Logical Possibilities. How Useful Are They?Eckhart Arnold - 2013 - Etica E Politica 15 (2):101-138.
    This paper discusses critically what simulation models of the evolution ofcooperation can possibly prove by examining Axelrod’s “Evolution of Cooperation” and the modeling tradition it has inspired. Hardly any of the many simulation models of the evolution of cooperation in this tradition have been applicable empirically. Axelrod’s role model suggested a research design that seemingly allowed to draw general conclusions from simulation models even if the mechanisms that drive the simulation could not be identified empirically. But this research design was (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  19. Eliminating the Ordinals From Proofs. An Analysis of Transfinite Recursion.Edoardo Rivello - 2014 - In Proceedings of the conference "Philosophy, Mathematics, Linguistics. Aspects of Interaction", St. Petersburg, April 21-25, 2014. pp. 174-184.
    Transfinite ordinal numbers enter mathematical practice mainly via the method of definition by transfinite recursion. Outside of axiomatic set theory, there is a significant mathematical tradition in works recasting proofs by transfinite recursion in other terms, mostly with the intention of eliminating the ordinals from the proofs. Leaving aside the different motivations which lead each specific case, we investigate the mathematics of this action of proof transforming and we address the problem of formalising the philosophical notion of elimination (...)
    Download  
     
    Export citation  
     
    Bookmark  
  20. Algorithmic Structuring of Cut-Free Proofs.Matthias Baaz & Richard Zach - 1993 - In Egon Börger, Hans Kleine Büning, Gerhard Jäger, Simone Martini & Michael M. Richter (eds.), Computer Science Logic. CSL’92, San Miniato, Italy. Selected Papers. Berlin: Springer. pp. 29–42.
    The problem of algorithmic structuring of proofs in the sequent calculi LK and LKB ( LK where blocks of quantifiers can be introduced in one step) is investigated, where a distinction is made between linear proofs and proofs in tree form. In this framework, structuring coincides with the introduction of cuts into a proof. The algorithmic solvability of this problem can be reduced to the question of k-l-compressibility: "Given a proof of length k , and l ≤ (...)
    Download  
     
    Export citation  
     
    Bookmark  
  21. Short Proofs of Tautologies Using the Schema of Equivalence.Matthias Baaz & Richard Zach - 1994 - In Egon Börger, Yuri Gurevich & Karl Meinke (eds.), Computer Science Logic. 7th Workshop, CSL '93, Swansea. Selected Papers. Berlin: Springer. pp. 33-35.
    It is shown how the schema of equivalence can be used to obtain short proofs of tautologies A , where the depth of proofs is linear in the number of variables in A .
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  22.  43
    Hegel on the Proofs and Personhood of God: Studies in Hegel's Logic and Philosophy of Religion by Robert R. Williams. [REVIEW]Kevin J. Harrelson - 2017 - Journal of the History of Philosophy 55 (4):739-740.
    Hegel endorsed proofs of the existence of God, and also believed God to be a person. Some of his interpreters ignore these apparently retrograde tendencies, shunning them in favor of the philosopher's more forward-looking contributions. Others embrace Hegel's religious thought, but attempt to recast his views as less reactionary than they appear to be. Robert Williams's latest monograph belongs to a third category: he argues that Hegel's positions in philosophical theology are central to his philosophy writ large. The book (...)
    Download  
     
    Export citation  
     
    Bookmark  
  23. From Display to Labelled Proofs for Tense Logics.Agata Ciabattoni, Tim Lyon & Revantha Ramanayake - 2018 - In Anil Nerode & Sergei Artemov (eds.), Logical Foundations of Computer Science. Springer International Publishing. pp. 120 - 139.
    We introduce an effective translation from proofs in the display calculus to proofs in the labelled calculus in the context of tense logics. We identify the labelled calculus proofs in the image of this translation as those built from labelled sequents whose underlying directed graph possesses certain properties. For the basic normal tense logic Kt, the image is shown to be the set of all proofs in the labelled calculus G3Kt.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  24. Fitting Feelings and Elegant Proofs: On the Psychology of Aesthetic Evaluation in Mathematics.Cain Todd - 2017 - Philosophia Mathematica:nkx007.
    ABSTRACT This paper explores the role of aesthetic judgements in mathematics by focussing on the relationship between the epistemic and aesthetic criteria employed in such judgements, and on the nature of the psychological experiences underpinning them. I claim that aesthetic judgements in mathematics are plausibly understood as expressions of what I will call ‘aesthetic-epistemic feelings’ that serve a genuine cognitive and epistemic function. I will then propose a naturalistic account of these feelings in terms of sub-personal processes of representing and (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  25.  68
    From Bi-Facial Truth to Bi-Facial Proofs.Stefan Wintein & Reinhard A. Muskens - 2015 - Studia Logica 103 (3):545-558.
    In their recent paper Bi-facial truth: a case for generalized truth values Zaitsev and Shramko [7] distinguish between an ontological and an epistemic interpretation of classical truth values. By taking the Cartesian product of the two disjoint sets of values thus obtained, they arrive at four generalized truth values and consider two “semi-classical negations” on them. The resulting semantics is used to define three novel logics which are closely related to Belnap’s well-known four valued logic. A syntactic characterization of these (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  26. Towards an Evolutionary Account of Conceptual Change in Mathematics: Proofs and Refutations and the Axiomatic Variation of Concepts.Thomas Mormann - 2002 - In G. Kampis, L.: Kvasz & M. Stöltzner (eds.), Appraising Lakatos: Mathematics, Methodology and the Man. Kluwer Academic Publishers. pp. 1--139.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  27.  92
    Deductively Sound Formal Proofs.P. Olcott - manuscript
    Could the intersection of [formal proofs of mathematical logic] and [sound deductive inference] specify formal systems having [deductively sound formal proofs of mathematical logic]? All that we have to do to provide [deductively sound formal proofs of mathematical logic] is select the subset of conventional [formal proofs of mathematical logic] having true premises and now we have [deductively sound formal proofs of mathematical logic].
    Download  
     
    Export citation  
     
    Bookmark  
  28. Validations of Proofs Considered as Texts: Can Undergraduates Tell Whether an Argument Proves a Theorem?Annie Selden - 2003 - Journal for Mathematics Education Research 34 (1):4-36.
    We report on an exploratory study of the way eight mid-level undergraduate mathematics majors read and reflected on four student-generated arguments purported to be proofs of a single theorem. The results suggest that mid-level undergraduates tend to focus on surface features of such arguments and that their ability to determine whether arguments are proofs is very limited -- perhaps more so than either they or their instructors recognize. We begin by discussing arguments (purported proofs) regarded as texts (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  29.  53
    Persuasion and Evidence in The Proofs of Faith.Ekrem Sefa Gül - 2018 - Tasavvur - Tekirdag Theology Journal 4 (2):726 - 758.
    Faith is the highest truth that ensures the happiness and salvation of man in the world and in the Hereafter. But the essence of superstitious is invalid and wrong. The realization of this happiness and salvation is possible by having a true faith. Another consequence of the true faith is the ability to recognize that this belief is right. Believing in true faith, ensures rightness and makes possible to prove and disclose this truth. It is important to have true faith (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  30.  49
    Deepening the Automated Search for Gödel's Proofs.Adam Conkey - unknown
    Gödel's incompleteness theorems establish the stunning result that mathematics cannot be fully formalized and, further, that any formal system containing a modicum of number or set theory cannot establish its own consistency. Wilfried Sieg and Clinton Field, in their paper Automated Search for Gödel's Proofs, presented automated proofs of Gödel's theorems at an abstract axiomatic level; they used an appropriate expansion of the strategic considerations that guide the search of the automated theorem prover AProS. The representability conditions that (...)
    Download  
     
    Export citation  
     
    Bookmark  
  31. There Must Be A First: Why Thomas Aquinas Rejects Infinite, Essentially Ordered, Causal Series.Caleb Cohoe - 2013 - British Journal for the History of Philosophy 21 (5):838 - 856.
    Several of Thomas Aquinas's proofs for the existence of God rely on the claim that causal series cannot proceed in infinitum. I argue that Aquinas has good reason to hold this claim given his conception of causation. Because he holds that effects are ontologically dependent on their causes, he holds that the relevant causal series are wholly derivative: the later members of such series serve as causes only insofar as they have been caused by and are effects of the (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  32. Wittgenstein Sobre as Provas Indutivas.André Porto - 2009 - Dois Pontos 6 (2).
    This paper offers a reconstruction of Wittgenstein's discussion on inductive proofs. A "algebraic version" of these indirect proofs is offered and contrasted with the usual ones in which an infinite sequence of modus pones is projected.
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  33.  34
    Automated Theorem Proving and Its Prospects. [REVIEW]Desmond Fearnley-Sander - 1995 - PSYCHE: An Interdisciplinary Journal of Research On Consciousness 2.
    REVIEW OF: Automated Development of Fundamental Mathematical Theories by Art Quaife. (1992: Kluwer Academic Publishers) 271pp. Using the theorem prover OTTER Art Quaife has proved four hundred theorems of von Neumann-Bernays-Gödel set theory; twelve hundred theorems and definitions of elementary number theory; dozens of Euclidean geometry theorems; and Gödel's incompleteness theorems. It is an impressive achievement. To gauge its significance and to see what prospects it offers this review looks closely at the book and the proofs it presents.
    Download  
     
    Export citation  
     
    Bookmark  
  34.  31
    The Correctness of Reasoning, Logical Models, and the Faithfulness Problem.Mario Bacelar Valente - manuscript
    When adopting a sound logical system, reasonings made within this system are correct. The situation with reasonings expressed, at least in part, with natural language is much more ambiguous. One way to be certain of the correctness of these reasonings is to provide a logical model of them. To conclude that a reasoning process is correct we need the logical model to be faithful to the reasoning. In this case, the reasoning inherits, so to speak, the correctness of the logical (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  35. “Truth-Preserving and Consequence-Preserving Deduction Rules”,.John Corcoran - 2014 - Bulletin of Symbolic Logic 20 (1):130-1.
    A truth-preservation fallacy is using the concept of truth-preservation where some other concept is needed. For example, in certain contexts saying that consequences can be deduced from premises using truth-preserving deduction rules is a fallacy if it suggests that all truth-preserving rules are consequence-preserving. The arithmetic additive-associativity rule that yields 6 = (3 + (2 + 1)) from 6 = ((3 + 2) + 1) is truth-preserving but not consequence-preserving. As noted in James Gasser’s dissertation, Leibniz has been criticized for (...)
    Download  
     
    Export citation  
     
    Bookmark  
  36. Descartes's Method of Doubt.Leslie Allan - manuscript
    Enlightenment philosopher, René Descartes, set out to establish what could be known with certainty, untainted by a deceiving demon. With his method of doubt, he rejected all previous beliefs, allowing only those that survived rigorous scrutiny. In this essay, Leslie Allan examines whether Descartes's program of skeptical enquiry was successful in laying a firm foundation for our manifold beliefs. He subjects Descartes's conclusions to Descartes's own uncompromising methodology to determine whether Descartes escaped from a self-imposed radical skepticism.
    Download  
     
    Export citation  
     
    Bookmark  
  37.  82
    Some Basic Studies About Trigonometry.Luiz Antonio Freire - manuscript
    A guide to the first steps into the world of Geometry, Trigonometry and their lines-of-reasoning widely used through the high school and first years of college, in the exact-sciences context.
    Download  
     
    Export citation  
     
    Bookmark  
  38. Constructing the World.David Chalmers - 2012 - Oxford University Press.
    Inspired by Rudolf Carnap's Der Logische Aufbau Der Welt, David J. Chalmers argues that the world can be constructed from a few basic elements. He develops a scrutability thesis saying that all truths about the world can be derived from basic truths and ideal reasoning. This thesis leads to many philosophical consequences: a broadly Fregean approach to meaning, an internalist approach to the contents of thought, and a reply to W. V. Quine's arguments against the analytic and the a priori. (...)
    Download  
     
    Export citation  
     
    Bookmark   151 citations  
  39. How Can Necessary Facts Call for Explanation?Dan Baras - forthcoming - Synthese:1-18.
    While there has been much discussion about what makes some mathematical proofs more explanatory than others, and what are mathematical coincidences, in this article I explore the distinct phenomenon of mathematical facts that call for explanation. The existence of mathematical facts that call for explanation stands in tension with virtually all existing accounts of “calling for explanation”, which imply that necessary facts cannot call for explanation. In this paper I explore what theoretical revisions are needed in order to accommodate (...)
    Download  
     
    Export citation  
     
    Bookmark  
  40.  82
    Proof, Explanation, and Justification in Mathematical Practice.Moti Mizrahi - forthcoming - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie:1-18.
    In this paper, I propose that applying the methods of data science to “the problem of whether mathematical explanations occur within mathematics itself” (Mancosu 2018) might be a fruitful way to shed new light on the problem. By carefully selecting indicator words for explanation and justification, and then systematically searching for these indicators in databases of scholarly works in mathematics, we can get an idea of how mathematicians use these terms in mathematical practice and with what frequency. The results of (...)
    Download  
     
    Export citation  
     
    Bookmark  
  41. Kant’s Religious Argument for the Existence of God: The Ultimate Dependence of Human Destiny on Divine Assistance.Stephen R. Palmquist - 2009 - Faith and Philosophy 26 (1):3-22.
    After reviewing Kant’s well-known criticisms of the traditional proofs of God’s existence and his preferred moral argument, this paper presents a detailedanalysis of a densely-packed theistic argument in Religion within the Bounds of Bare Reason. Humanity’s ultimate moral destiny can be fulfilled only through organized religion, for only by participating in a religious community can we overcome the evil in human nature. Yet we cannot conceive how such a community can even be founded without presupposing God’s existence. Viewing God (...)
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  42. Reasoning About Uncertain Conditionals.Niki Pfeifer - 2014 - Studia Logica 102 (4):849-866.
    There is a long tradition in formal epistemology and in the psychology of reasoning to investigate indicative conditionals. In psychology, the propositional calculus was taken for granted to be the normative standard of reference. Experimental tasks, evaluation of the participants’ responses and psychological model building, were inspired by the semantics of the material conditional. Recent empirical work on indicative conditionals focuses on uncertainty. Consequently, the normative standard of reference has changed. I argue why neither logic nor standard probability theory provide (...)
    Download  
     
    Export citation  
     
    Bookmark   12 citations  
  43. Proving Quadratic Reciprocity: Explanation, Disagreement, Transparency and Depth.William D'Alessandro - 2020 - Synthese:1-44.
    Gauss’s quadratic reciprocity theorem is among the most important results in the history of number theory. It’s also among the most mysterious: since its discovery in the late 18th century, mathematicians have regarded reciprocity as a deeply surprising fact in need of explanation. Intriguingly, though, there’s little agreement on how the theorem is best explained. Two quite different kinds of proof are most often praised as explanatory: an elementary argument that gives the theorem an intuitive geometric interpretation, due to Gauss (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  44.  38
    Sellars' Exam Question Trilemma - Are Kant's Premises Analytic, or Synthetic A Priori, or A Posterior.James O'Shea - 2019 - British Journal for the History of Philosophy 27 (2):402-421.
    ABSTRACT Wilfrid Sellars argued that Kant’s account of the conceptual structures involved in experience can be given a linguistic turn so as to provide an analytic account of the resources a language must have in order to be the bearer of empirical knowledge. In this paper I examine the methodological aspects of Kant’s transcendental philosophy that Sellars took to be fundamental to influential themes in his own philosophy. My first aim here is to clarify and argue for the plausibility of (...)
    Download  
     
    Export citation  
     
    Bookmark  
  45.  27
    Starting Rational Reconstruction of Spinoza's Metaphysics by "a Formal Analogy to Elements of 'de Deo' (E1)".Friedrich Wilhelm Grafe - manuscript
    We aim to compile some means for a rational reconstruction of a named part of the start-over of Baruch (Benedictus) de Spinoza's metaphysics in 'de deo' (which is 'pars prima' of the 'ethica, ordine geometrico demonstrata' ) in terms of 1st order model theory. In so far, as our approach will be judged successful, it may, besides providing some help in understanding Spinoza, also contribute to the discussion of some or other philosophical evergreen, e.g. 'ontological commitment'. For this text we (...)
    Download  
     
    Export citation  
     
    Bookmark  
  46. 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.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  47. A Horse is a Horse, of Course, of Course, but What About Horseness?Necip Fikri Alican - 2015 - In Debra Nails & Harold Tarrant (eds.), Second Sailing: Alternative Perspectives on Plato. Helsinki: Societas Scientiarum Fennica. pp. 307–324.
    Plato is commonly considered a metaphysical dualist conceiving of a world of Forms separate from the world of particulars in which we live. This paper explores the motivation for postulating that second world as opposed to making do with the one we have. The main objective is to demonstrate that and how everything, Forms and all, can instead fit into the same world. The approach is exploratory, as there can be no proof in the standard sense. The debate between explaining (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  48. Triviality Results and the Relationship Between Logical and Natural Languages.Justin Khoo & Matthew Mandelkern - 2019 - Mind 128 (510):485-526.
    Inquiry into the meaning of logical terms in natural language (‘and’, ‘or’, ‘not’, ‘if’) has generally proceeded along two dimensions. On the one hand, semantic theories aim to predict native speaker intuitions about the natural language sentences involving those logical terms. On the other hand, logical theories explore the formal properties of the translations of those terms into formal languages. Sometimes, these two lines of inquiry appear to be in tension: for instance, our best logical investigation into conditional connectives may (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  49.  38
    The ILLTP Library for Intuitionistic Linear Logic.Carlos Olarte, Valeria Correa Vaz De Paiva, Elaine Pimentel & Giselle Reis - manuscript
    Benchmarking automated theorem proving (ATP) systems using standardized problem sets is a well-established method for measuring their performance. However, the availability of such libraries for non-classical logics is very limited. In this work we propose a library for benchmarking Girard's (propositional) intuitionistic linear logic. For a quick bootstrapping of the collection of problems, and for discussing the selection of relevant problems and understanding their meaning as linear logic theorems, we use translations of the collection of Kleene's intuitionistic theorems in the (...)
    Download  
     
    Export citation  
     
    Bookmark  
  50. Supervaluationism and Classical Logic.Pablo Cobreros - 2011 - In Rick Nouwen, Robert van Rooij, Hans-Christian Schmitz & Uli Sauerland (eds.), Vagueness in Communication, Lecture Notes in Computer Science, Vol. 6517. Springer.
    This paper is concerned with the claim that supervaluationist consequence is not classical for a language including an operator for definiteness. Although there is some sense in which this claim is uncontroversial, there is a sense in which the claim must be qualified. In particular I defend Keefe's position according to which supervaluationism is classical except when the inference from phi to Dphi is involved. The paper provides a precise content to this claim showing that we might provide complete (and (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
1 — 50 / 167