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  1. added 2020-03-11
    The Making of Peacocks Treatise on Algebra: A Case of Creative Indecision.Menachem Fisch - 1999 - Archive for History of Exact Sciences 54 (2):137-179.
    A study of the making of George Peacock's highly influential, yet disturbingly split, 1830 account of algebra as an entanglement of two separate undertakings: arithmetical and symbolical or formal.
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  2. added 2019-12-05
    ¿Qué significa paraconsistente, indescifrable, aleatorio, computable e incompleto? Una revisión de’ la Manera de Godel: explota en un mundo indecible’ (Godel’s Way: Exploits into an Undecidable World) por Gregory Chaitin, Francisco A Doria, Newton C.A. da Costa 160p (2012) (revisión revisada 2019).Michael Richard Starks - 2019 - In Delirios Utópicos Suicidas en el Siglo 21 La filosofía, la naturaleza humana y el colapso de la civilización Artículos y reseñas 2006-2019 4a Edición. Las Vegas, NV USA: Reality Press. pp. 263-277.
    En ' Godel’s Way ', tres eminentes científicos discuten temas como la indecisión, la incompleta, la aleatoriedad, la computabilidad y la paracoherencia. Me acerco a estas cuestiones desde el punto de vista de Wittgensteinian de que hay dos cuestiones básicas que tienen soluciones completamente diferentes. Existen las cuestiones científicas o empíricas, que son hechos sobre el mundo que necesitan ser investigados Observacionalmente y cuestiones filosóficas en cuanto a cómo el lenguaje se puede utilizar inteligiblemente (que incluyen ciertas preguntas en matemáticas (...)
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  3. added 2019-09-04
    Hermann Grassmann and the Creation of Linear Algebra.Desmond Sander - 1979 - The American Mathematical Monthly 86:809-817.
    One may say without great exaggeration that Grassmann invented linear algebra and, with none at all, that he showed how properly to apply it in geometry.
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  4. added 2019-08-28
    असंभव, अपूर्णता, अनिर्णय, अनिर्णय, यादृच्छिकता, गणना, विरोधाभास, और चैटिन, विटगेनस्टीन, Hofstadter, Wolpert, डोरिया, दा कोस्टा, गोडेल, सीरले, Rodych, Berto, Floyd में अनिश्चितता पर टिप्पणी मोयाल-शररॉक और यानोफ्स्की.Michael Richard Starks - 2019 - Las Vegas, NV USA: Reality Press.
    यह आमतौर पर सोचा जाता है कि असंभवता, अपूर्णता, Paraconsistency, अनिर्णितता, Randomness, Computability, विरोधाभास, अनिश्चितता और कारण की सीमा अलग वैज्ञानिक शारीरिक या गणितीय मुद्दों में कम या कुछ भी नहीं कर रहे हैं आम. मेरा सुझाव है कि वे काफी हद तक मानक दार्शनिक समस्याओं (यानी, भाषा का खेल) जो ज्यादातर 80years पहले Wittgenstein द्वारा हल किए गए थे. -/- "क्या हम 'इस तरह के एक मामले में कहने के लिए' कर रहे हैं, ज़ाहिर है, दर्शन नहीं है, लेकिन (...)
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  5. added 2019-08-16
    Remarks on Wittgenstein, Gödel, Chaitin, Incompleteness, Impossiblity and the Psychological Basis of Science and Mathematics.Michael Richard Starks - 2019 - In Remarks on Impossibility, Incompleteness, Paraconsistency, Undecidability, Randomness, Computability, Paradox, Uncertainty and the Limits of Reason in Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, da Costa, Godel, Searle, Rodych, Berto, Floyd, Moyal. Las Vegas, NV USA: Reality Press. pp. 24-38.
    It is commonly thought that such topics as Impossibility, Incompleteness, Paraconsistency, Undecidability, Randomness, Computability, Paradox, Uncertainty and the Limits of Reason are disparate scientific physical or mathematical issues having little or nothing in common. I suggest that they are largely standard philosophical problems (i.e., language games) which were resolved by Wittgenstein over 80 years ago. -/- Wittgenstein also demonstrated the fatal error in regarding mathematics or language or our behavior in general as a unitary coherent logical ‘system,’ rather than as (...)
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  6. added 2019-08-14
    Iterated Reflection Over Full Disquotational Truth.Fischer Martin, Nicolai Carlo & Horsten Leon - 2017 - Journal of Logic and Computation 27 (8):2631-2651.
    Iterated reflection principles have been employed extensively to unfold epistemic commitments that are incurred by accepting a mathematical theory. Recently this has been applied to theories of truth. The idea is to start with a collection of Tarski-biconditionals and arrive by iterated reflection at strong compositional truth theories. In the context of classical logic, it is incoherent to adopt an initial truth theory in which A and ‘A is truen’ are inter-derivable. In this article, we show how in the context (...)
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  7. added 2019-06-06
    The Dignity of a Rule: Wittgenstein, Mathematical Norms, and Truth.Michael Hymers - 2003 - Dialogue 42 (3):419-446.
    RÉSUMÉ: Paul Boghossian soutient contre Wittgenstein que le normativisme au sujet de la logique et des mathématiques est incompatible avec le fait de tenir les énoncés logiques et mathématiques pour vrais et que le normativisme entraîne une régression indue. Je soutiens, pour ma part, que le normativisme n’entraîne pas une telle régression, parce que les normes peuvent être implicites et que le normativisme peut bien être «factualiste» si l’on rejette ce que Rockney Jacobsen appelle le «cognitivisme sémantique». Je tiens en (...)
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  8. added 2019-06-04
    The Truth Assignments That Differentiate Human Reasoning From Mechanistic Reasoning: The Evidence-Based Argument for Lucas' Goedelian Thesis.Bhupinder Singh Anand - 2016 - Cognitive Systems Research 40:35-45.
    We consider the argument that Tarski's classic definitions permit an intelligence---whether human or mechanistic---to admit finitary evidence-based definitions of the satisfaction and truth of the atomic formulas of the first-order Peano Arithmetic PA over the domain N of the natural numbers in two, hitherto unsuspected and essentially different, ways: (1) in terms of classical algorithmic verifiabilty; and (2) in terms of finitary algorithmic computability. We then show that the two definitions correspond to two distinctly different assignments of satisfaction and truth (...)
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  9. added 2019-06-04
    Do Goedel's Incompleteness Theorems Set Absolute Limits on the Ability of the Brain to Express and Communicate Mental Concepts Verifiably?Bhupinder Singh Anand - 2004 - Neuroquantology 2:60-100.
    Classical interpretations of Goedels formal reasoning, and of his conclusions, implicitly imply that mathematical languages are essentially incomplete, in the sense that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is, both, non-algorithmic, and essentially unverifiable. However, a language of general, scientific, discourse, which intends to mathematically express, and unambiguously communicate, intuitive concepts that correspond to scientific investigations, cannot allow its mathematical propositions to be interpreted ambiguously. Such a language must, therefore, define mathematical truth (...)
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  10. added 2019-04-04
    A Simple Theory Containing its Own Truth Predicate.Nicholas Shackel - 2018 - South American Journal of Logic 4 (1):121-131.
    Tarski's indefinability theorem shows us that truth is not definable in arithmetic. The requirement to define truth for a language in a stronger language (if contradiction is to be avoided) lapses for particularly weak languages. A weaker language, however, is not necessary for that lapse. It also lapses for an adequately weak theory. It turns out that the set of G{\"o}del numbers of sentences true in arithmetic modulo $n$ is definable in arithmetic modulo $n$.
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  11. added 2019-02-20
    Deflationism, Arithmetic, and the Argument From Conservativeness.Daniel Waxman - 2017 - Mind 126 (502):429-463.
    Many philosophers believe that a deflationist theory of truth must conservatively extend any base theory to which it is added. But when applied to arithmetic, it's argued, the imposition of a conservativeness requirement leads to a serious objection to deflationism: for the Gödel sentence for Peano Arithmetic is not a theorem of PA, but becomes one when PA is extended by adding plausible principles governing truth. This paper argues that no such objection succeeds. The issue turns on how we understand (...)
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  12. added 2019-01-28
    On Quantum Event Structures. III. Object of Truth Values.Elias Zafiris - 2004 - Foundations Of Physics Letters 17 (5):403-432.
    In this work we expand the foundational perspective of category theory on quantum event structures by showing the existence of an object of truth values in the category of quantum event algebras, characterized as subobject classifier. This object plays the corresponking role that the two-valued Boolean truth values object plays in a classical event structure. We construct the object of quantum truth values explicitly and argue that it constitutes the appropriate choice for the valuation of propositions describing the behavior of (...)
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  13. added 2018-12-22
    Plato’s Philosophy of Cognition by Mathematical Modelling.Roman S. Kljujkov & Sergey F. Kljujkov - 2014 - Dialogue and Universalism 24 (3):110-115.
    By the end of his life Plato had rearranged the theory of ideas into his teaching about ideal numbers, but no written records have been left. The Ideal mathematics of Plato is present in all his dialogues. It can be clearly grasped in relation to the effective use of mathematical modelling. Many problems of mathematical modelling were laid in the foundation of the method by cutting the three-level idealism of Plato to the single-level “ideism” of Aristotle. For a long time, (...)
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  14. added 2018-12-03
    Conservative Deflationism?Julien Murzi & Lorenzo Rossi - 2020 - Philosophical Studies 177 (2):535-549.
    Deflationists argue that ‘true’ is merely a logico-linguistic device for expressing blind ascriptions and infinite generalisations. For this reason, some authors have argued that deflationary truth must be conservative, i.e. that a deflationary theory of truth for a theory S must not entail sentences in S’s language that are not already entailed by S. However, it has been forcefully argued that any adequate theory of truth for S must be non-conservative and that, for this reason, truth cannot be deflationary :493–521, (...)
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  15. added 2018-11-01
    Hypatia's Silence. Truth, Justification, and Entitlement.Martin Fischer, Leon Horsten & Carlo Nicolai - manuscript
    Hartry Field distinguished two concepts of type-free truth: scientific truth and disquotational truth. We argue that scientific type-free truth cannot do justificatory work in the foundations of mathematics. We also present an argument, based on Crispin Wright's theory of cognitive projects and entitlement, that disquotational truth can do justificatory work in the foundations of mathematics. The price to pay for this is that the concept of disquotational truth requires non-classical logical treatment.
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  16. added 2017-11-01
    Can Mathematical Objects Be Causally Efficacious?Seungbae Park - 2019 - Inquiry: An Interdisciplinary Journal of Philosophy 62 (3):247–255.
    Callard (2007) argues that it is metaphysically possible that a mathematical object, although abstract, causally affects the brain. I raise the following objections. First, a successful defence of mathematical realism requires not merely the metaphysical possibility but rather the actuality that a mathematical object affects the brain. Second, mathematical realists need to confront a set of three pertinent issues: why a mathematical object does not affect other concrete objects and other mathematical objects, what counts as a mathematical object, and how (...)
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  17. added 2017-10-25
    Intuitionistic Logic and its Philosophy.Panu Raatikainen - 2013 - Al-Mukhatabat. A Trilingual Journal For Logic, Epistemology and Analytical Philosophy (6):114-127.
  18. added 2017-07-04
    Two Criticisms Against Mathematical Realism.Seungbae Park - 2017 - Diametros 52:96-106.
    Mathematical realism asserts that mathematical objects exist in the abstract world, and that a mathematical sentence is true or false, depending on whether the abstract world is as the mathematical sentence says it is. I raise two objections against mathematical realism. First, the abstract world is queer in that it allows for contradictory states of affairs. Second, mathematical realism does not have a theoretical resource to explain why a sentence about a tricle is true or false. A tricle is an (...)
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  19. added 2017-02-27
    Hilbert’s Program.Richard Zach - 2003 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab, Center for the Study of Language and Information, Stanford University.
    In the early 1920s, the German mathematician David Hilbert (1862–1943) put forward a new proposal for the foundation of classical mathematics which has come to be known as Hilbert's Program. It calls for a formalization of all of mathematics in axiomatic form, together with a proof that this axiomatization of mathematics is consistent. The consistency proof itself was to be carried out using only what Hilbert called “finitary” methods. The special epistemological character of finitary reasoning then yields the required justification (...)
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  20. added 2017-01-04
    Forms of Correspondence: The Intricate Route From Thought to Reality.Gila Sher - 2013 - In Nikolaj Jang Lee Linding Pedersen & Cory Wright (eds.), Truth and Pluralism: Current Debates. Oxford University Press. pp. 157--179.
    The paper delineates a new approach to truth that falls under the category of “Pluralism within the bounds of correspondence”, and illustrates it with respect to mathematical truth. Mathematical truth, like all other truths, is based on correspondence, but the route of mathematical correspondence differs from other routes of correspondence in (i) connecting mathematical truths to a special aspect of reality, namely, its formal aspect, and (ii) doing so in a complex, indirect way, rather than in a simple and direct (...)
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  21. added 2016-12-08
    Mathematical Instrumentalism Meets the Conjunction Objection.Hawthorne James - 1996 - Journal of Philosophical Logic 25 (4):363-397.
    Scientific realists often appeal to some version of the conjunction objection to argue that scientific instrumentalism fails to do justice to the full empirical import of scientific theories. Whereas the conjunction objection provides a powerful critique of scientific instrumentalism, I will show that mathematical instnrunentalism escapes the conjunction objection unscathed.
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  22. added 2016-10-23
    Hilbert's Program Revisited.Panu Raatikainen - 2003 - Synthese 137 (1):157-177.
    After sketching the main lines of Hilbert's program, certain well-known and influential interpretations of the program are critically evaluated, and an alternative interpretation is presented. Finally, some recent developments in logic related to Hilbert's program are reviewed.
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  23. added 2016-10-09
    The Kinds of Truth of Geometry Theorems.Michael Bulmer, Desmond Fearnley-Sander & Tim Stokes - 2001 - In Jürgen Richter-Gebert & Dongming Wang (eds.), LNCS: Lecture Notes In Computer Science. Springer Verlag. pp. 129-142.
    Proof by refutation of a geometry theorem that is not universally true produces a Gröbner basis whose elements, called side polynomials, may be used to give inequations that can be added to the hypotheses to give a valid theorem. We show that (in a certain sense) all possible subsidiary conditions are implied by those obtained from the basis; that what we call the kind of truth of the theorem may be derived from the basis; and that the side polynomials may (...)
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  24. added 2016-09-05
    Functions and Generality of Logic.Gabriel Sandu, Marco Panza & Hourya Benis-Sinaceur (eds.) - 2015 - Springer Verlag.
    Part I of Frege’s Grundgesetze is devoted to the “exposition [Darlegung]” of his formal system.
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  25. added 2016-08-26
    On Truth and Instrumentalisation.Chris Henry - 2016 - London Journal of Critical Thought 1:5-15.
    This paper makes two claims. Firstly, it shows that thinking the truth of any particular concept (such as politics) is founded upon an instrumental logic that betrays the truth of a situation. Truth cannot be thought ‘of something’, for this would fall back into a theory of correspondence. Instead, truth is a function of thought. In order to make this move to a functional concept of truth, I outline Dewey’s criticism, and two important repercussions, of dogmatically instrumental philosophy. I then (...)
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  26. added 2016-04-03
    Deflationary Truth and Pathologies.Cezary Cieśliński - 2010 - Journal of Philosophical Logic 39 (3):325-337.
    By a classical result of Kotlarski, Krajewski and Lachlan, pathological satisfaction classes can be constructed for countable, recursively saturated models of Peano arithmetic. In this paper we consider the question of whether the pathology can be eliminated; we ask in effect what generalities involving the notion of truth can be obtained in a deflationary truth theory (a theory of truth which is conservative over its base). It is shown that the answer depends on the notion of pathology we adopt. It (...)
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  27. added 2016-04-01
    How Tarski Defined the Undefinable.Cezary Cieśliński - 2015 - European Review 23 (01):139 - 149.
    This paper describes Tarski’s project of rehabilitating the notion of truth, previously considered dubious by many philosophers. The project was realized by providing a formal truth definition, which does not employ any problematic concept.
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  28. added 2015-10-07
    The Innocence of Truth.Cezary Cieśliński - 2015 - Dialectica 69 (1):61-85.
    One of the popular explications of the deflationary tenet of ‘thinness’ of truth is the conservativeness demand: the declaration that a deflationary truth theory should be conservative over its base. This paper contains a critical discussion and assessment of this demand. We ask and answer the question of whether conservativity forms a part of deflationary doctrines.
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  29. added 2015-09-09
    Malament–Hogarth Machines and Tait’s Axiomatic Conception of Mathematics.Sharon Berry - 2014 - Erkenntnis 79 (4):893-907.
    In this paper I will argue that Tait’s axiomatic conception of mathematics implies that it is in principle impossible to be justified in believing a mathematical statement without being justified in believing that statement to be provable. I will then show that there are possible courses of experience which would justify acceptance of a mathematical statement without justifying belief that this statement is provable.
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  30. added 2015-07-19
    Review of Danielle Macbeth, "Realizing Reason: A Narrative of Truth and Knowing". [REVIEW]Catherine Legg - 2015 - Notre Dame Philosophical Reviews:online.
  31. added 2014-11-10
    A Theory of Truth for a Class of Mathematical Languages and an Application.S. Heikkilä - manuscript
    In this paprer a class of so called mathematically acceptable (shortly MA) languages is introduced First-order formal languages containing natural numbers and numerals belong to that class. MA languages which are contained in a given fully interpreted MA language augmented by a monadic predicate are constructed. A mathematical theory of truth (shortly MTT) is formulated for some of these languages. MTT makes them fully interpreted MA languages which posses their own truth predicates, yielding consequences to philosophy of mathematics. MTT is (...)
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  32. added 2014-08-01
    On Saying What You Really Want to Say: Wittgenstein, Gödel and the Trisection of the Angle.Juliet Floyd - 1995 - In Jaakko Hintikka (ed.), From Dedekind to Gödel: The Foundations of Mathematics in the Early Twentieth Century, Synthese Library Vol. 251 (Kluwer Academic Publishers. pp. 373-426.
  33. added 2014-07-23
    Platonism by the Numbers.Steven M. Duncan - manuscript
    In this paper, I defend traditional Platonic mathematical realism from its contemporary detractors, arguing that numbers, understood as abstract, non-physical objects of rational intuition, are indispensable for the act of counting.
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  34. added 2014-04-02
    Hilary Putnam's Consistency Objection Against Wittgenstein's Conventionalism in Mathematics.P. Garavaso - 2013 - Philosophia Mathematica 21 (3):279-296.
    Hilary Putnam first published the consistency objection against Ludwig Wittgenstein’s account of mathematics in 1979. In 1983, Putnam and Benacerraf raised this objection against all conventionalist accounts of mathematics. I discuss the 1979 version and the scenario argument, which supports the key premise of the objection. The wide applicability of this objection is not apparent; I thus raise it against an imaginary axiomatic theory T similar to Peano arithmetic in all relevant aspects. I argue that a conventionalist can explain the (...)
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  35. added 2014-03-29
    Mathematical Truth Regained.Robert Hanna - 2010 - In Mirja Hartimo (ed.), Phenomenology and Mathematics. Springer. pp. 147--181.
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  36. added 2014-03-25
    On Some Much Maligned Remarks of Wittgenstein on Gödel.Charles Sayward - 2001 - Philosophical Investigations 24 (3):262–270.
    In "Remarks on the Foundations of Mathematics" Wittgenstein discusses an argument that goes from Gödel’s incompleteness result to the conclusion that some truths of mathematics are unprovable. Wittgenstein takes issue with this argument. Wittgenstein’s remarks in this connection have received very negative reaction from some very prominent people, for example, Gödel and Dummett. The paper is a defense of what Wittgenstein has to say about the argument in question.
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  37. added 2014-03-21
    Conceptions of Truth in Intuitionism.Panu Raatikainen - 2004 - History and Philosophy of Logic 25 (2):131--45.
    Intuitionism’s disagreement with classical logic is standardly based on its specific understanding of truth. But different intuitionists have actually explicated the notion of truth in fundamentally different ways. These are considered systematically and separately, and evaluated critically. It is argued that each account faces difficult problems. They all either have implausible consequences or are viciously circular.
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  38. added 2014-03-19
    Truthmakers Without Truth.Rognvaldur Ingthorsson - 2006 - Metaphysica 7 (2):53–71.
    It is often taken for granted that truth is mind-independent, i.e. that, necessarily, if the world is objectively speaking in a certain way, then it is true that it is that way, independently of anyone thinking that it is that way. I argue that proponents of correspondence-truth, in particular immanent realists, should not take the mind-independence of truth for granted. The assumption that the mind-independent features of the world, i.e. ‘facts’, determine the truth of propositions, does not entail that truth (...)
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  39. added 2014-03-09
    Benacerraf’s Dilemma and Informal Mathematics.Gregory Lavers - 2009 - Review of Symbolic Logic 2 (4):769-785.
    This paper puts forward and defends an account of mathematical truth, and in particular an account of the truth of mathematical axioms. The proposal attempts to be completely nonrevisionist. In this connection, it seeks to satisfy simultaneously both horns of Benacerrafs work on informal rigour. Kreisel defends the view that axioms are arrived at by a rigorous examination of our informal notions, as opposed to being stipulated or arrived at by trial and error. This view is then supplemented by a (...)
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  40. added 2014-03-09
    Catégories formelles, nombres et conceptualisme. La première philosophie de l’arithmétique de Husserl.Arkadiusz Chrudzimski - 2009 - Philosophiques 36 (2):427-445.
    Résumé -/- Dans son premier livre (Philosophie de l’arithmétique 1891), Husserl élabore une très intéressante philosophie des mathématiques. Les concepts mathématiques sont interprétés comme des concepts de « deuxième ordre » auxquels on accède par une réflexion sur nos opérations mentales de numération. Il s’ensuit que la vérité de la proposition : « il y a trois pommes sur la table » ne consiste pas dans une relation mythique quelconque avec la réalité extérieure au psychique (où le nombre trois doit (...)
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  41. added 2014-03-09
    Neil Tennant. The Taming of the True. Oxford: Clarendon Press, 1997. Pp. Xviii + 466. ISBN 0-19-823717-0 (Cloth), 0-19-925160-6 (Paper). [REVIEW]J. P. Burgess - 2005 - Philosophia Mathematica 13 (2):202-215.
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  42. added 2014-03-06
    Too Naturalist and Not Naturalist Enough: Reply to Horsten.Luca Incurvati - 2008 - Erkenntnis 69 (2):261 - 274.
    Leon Horsten has recently claimed that the class of mathematical truths coincides with the class of theorems of ZFC. I argue that the naturalistic character of Horsten’s proposal undermines his contention that this claim constitutes an analogue of a thesis that Daniel Isaacson has advanced for PA. I argue, moreover, that Horsten’s defence of his claim against an obvious objection makes use of a distinction which is not available to him given his naturalistic approach. I suggest a way out of (...)
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  43. added 2014-03-06
    Four Views of Arithmetical Truth.Charles Sayward - 1990 - Philosophical Quarterly 40 (159):155-168.
    Four views of arithmetical truth are distinguished: the classical view, the provability view, the extended provability view, the criterial view. The main problem with the first is the ontology it requires one to accept. Two anti-realist views are the two provability views. The first of these is judged to be preferable. However, it requires a non-trivial account of the provability of axioms. The criterial view is gotten from remarks Wittgenstein makes in Tractatus 6.2-6.22 . It is judged to be the (...)
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  44. added 2014-02-19
    What Mathematical Theories of Truth Should Be Like (and Can Be).Seppo Heikkilä - manuscript
    Hannes Leitgeb formulated eight norms for theories of truth in his paper [5]: `What Theories of Truth Should be Like (but Cannot be)'. We shall present in this paper a theory of truth for suitably constructed languages which contain the first-order language of set theory, and prove that it satisfies all those norms.
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  45. added 2014-02-19
    A Mathematical Theory of Truth and an Application to the Regress Problem.S. Heikkilä - forthcoming - Nonlinear Studies 22 (2).
    In this paper a class of languages which are formal enough for mathematical reasoning is introduced. Its languages are called mathematically agreeable. Languages containing a given MA language L, and being sublanguages of L augmented by a monadic predicate, are constructed. A mathematical theory of truth (shortly MTT) is formulated for some of those languages. MTT makes them fully interpreted MA languages which posses their own truth predicates. MTT is shown to conform well with the eight norms formulated for theories (...)
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  46. added 2012-10-10
    Does Truth Equal Provability in the Maximal Theory?Luca Incurvati - 2009 - Analysis 69 (2):233-239.
    According to the received view, formalism – interpreted as the thesis that mathematical truth does not outrun the consequences of our maximal mathematical theory – has been refuted by Goedel's theorem. In support of this claim, proponents of the received view usually invoke an informal argument for the truth of the Goedel sentence, an argument which is supposed to reconstruct our reasoning in seeing its truth. Against this, Field has argued in a series of papers that the principles involved in (...)
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  47. added 2012-04-09
    A Physicalist Account of Mathematical Truth.László Szabó - manuscript
    Realists, Platonists and intuitionists jointly believe that mathematical concepts and propositions have meanings, and when we formalize the language of mathematics, these meanings are meant to be reflected in a more precise and more concise form. According to the formalist understanding of mathematics (at least, according to the radical version of formalism I am proposing here) the truth, on the contrary, is that a mathematical object has no meaning; we have marks and rules governing how these marks can be combined. (...)
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  48. added 2012-04-09
    How Can Physics Account for Mathematical Truth?Laszlo E. Szabo - unknown
    If physicalism is true, everything is physical. In other words, everything supervenes on, or is necessitated by, the physical. Accordingly, if there are logical/mathematical facts, they must be necessitated by the physical facts of the world. In this paper, I will sketch the first steps of a physicalist philosophy of mathematics; that is, how physicalism can account for logical and mathematical facts. We will proceed as follows. First we will clarify what logical/mathematical facts actually are. Then, we will discuss how (...)
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  49. added 2012-04-09
    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 to (...)
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  50. added 2012-04-09
    Formal Systems as Physical Objects: A Physicalist Account of Mathematical Truth.E. Szabo´ La´Szlo´ - 2003 - International Studies in the Philosophy of Science 17 (2):117-125.
    This article is a brief formulation of a radical thesis. We start with the formalist doctrine that mathematical objects have no meanings; we have marks and rules governing how these marks can be combined. That's all. Then I go further by arguing that the signs of a formal system of mathematics should be considered as physical objects, and the formal operations as physical processes. The rules of the formal operations are or can be expressed in terms of the laws of (...)
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