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  1. An Elementary, Pre-formal, Proof of FLT: Why is x^n+y^n=z^n solvable only for n<3?Bhupinder Singh Anand - manuscript
    Andrew Wiles' analytic proof of Fermat's Last Theorem FLT, which appeals to geometrical properties of real and complex numbers, leaves two questions unanswered: (i) What technique might Fermat have used that led him to, even if only briefly, believe he had `a truly marvellous demonstration' of FLT? (ii) Why is x^n+y^n=z^n solvable only for n<3? In this inter-disciplinary perspective, we offer insight into, and answers to, both queries; yielding a pre-formal proof of why FLT can be treated as a true (...)
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  2. The Synthetic Concept of Truth and its Descendants.Boris Culina - manuscript
    The concept of truth has many aims but only one source. The article describes the primary concept of truth, here called the synthetic concept of truth, according to which truth is the objective result of the synthesis of us and nature in the process of rational cognition. It is shown how various aspects of the concept of truth -- logical, scientific, and mathematical aspect -- arise from the synthetic concept of truth. Also, it is shown how the paradoxes of truth (...)
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  3. Mathematics - an imagined tool for rational cognition.Boris Culina - manuscript
    Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial interpretation of the corresponding language. It follows from the analysis that (i) mathematical objects do not exist in the external world: they are our internally imagined objects, some of which, at least approximately, we can realize or represent; (ii) mathematical truths are not (...)
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  4. 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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  5. Is Euclid's proof of the infinitude of prime numbers tautological?Zeeshan Mahmud - manuscript
    Euclid's classic proof about the infinitude of prime numbers has been a standard model of reasoning in student textbooks and books of elementary number theory. It has withstood scrutiny for over 2000 years but we shall prove that despite the deceptive appearance of its analytical reasoning it is tautological in nature. We shall argue that the proof is more of an observation about the general property of a prime numbers than an expository style of natural deduction of the proof of (...)
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  6. 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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  7. Safety and Pluralism in Mathematics.James Andrew Smith - forthcoming - Erkenntnis:1-19.
    A belief one has is safe if either (i) it could not easily be false or (ii) in any nearby world in which it is false, it is not formed using the method one uses to form one’s actual belief. It seems our mathematical beliefs are safe if mathematical pluralism is true: if, loosely put, almost any consistent mathematical theory is true. It seems, after all, that in any nearby world where one’s mathematical beliefs differ from one’s actual beliefs, one (...)
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  8. (1 other version)Mathematics and society reunited: The social aspects of Brouwer's intuitionism.Kati Kish Bar-On - 2024 - Studies in History and Philosophy of Science 108:28-37.
    Brouwer's philosophy of mathematics is usually regarded as an intra-subjective, even solipsistic approach, an approach that also underlies his mathematical intuitionism, as he strived to create a mathematics that develops out of something inner and a-linguistic. Thus, points of connection between Brouwer's mathematical views and his views about and the social world seem improbable and are rarely mentioned in the literature. The current paper aims to challenge and change that. The paper employs a socially oriented prism to examine Brouwer's views (...)
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  9. Σ01 soundness isn’t enough: Number theoretic indeterminacy’s unsavory physical commitments.Sharon Berry - 2023 - British Journal for the Philosophy of Science 74 (2):469-484.
    It’s sometimes suggested that we can (in a sense) settle the truth-value of some statements in the language of number theory by stipulation, adopting either φ or ¬φ as an additional axiom. For example, in Clarke-Doane (2020b) and a series of recent APA presentations, Clarke-Doane suggests that any Σ01 sound expansion of our current arithmetical practice would express a truth. In this paper, I’ll argue that (given a certain popular assumption about the model-theoretic representability of languages like ours) we can’t (...)
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  10. Fishbones, Wheels, Eyes, and Butterflies: Heuristic Structural Reasoning in the Search for Solutions to the Navier-Stokes Equations.Lydia Patton - 2023 - In Lydia Patton & Erik Curiel (eds.), Working Toward Solutions in Fluid Dynamics and Astrophysics: What the Equations Don’t Say. Springer Verlag. pp. 57-78.
    Arguments for the effectiveness, and even the indispensability, of mathematics in scientific explanation rely on the claim that mathematics is an effective or even a necessary component in successful scientific predictions and explanations. Well-known accounts of successful mathematical explanation in physical science appeals to scientists’ ability to solve equations directly in key domains. But there are spectacular physical theories, including general relativity and fluid dynamics, in which the equations of the theory cannot be solved directly in target domains, and yet (...)
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  11. Modal Structuralism with Theoretical Terms.Holger Andreas & Georg Schiemer - 2021 - Erkenntnis 88 (2):721-745.
    In this paper, we aim to explore connections between a Carnapian semantics of theoretical terms and an eliminative structuralist approach in the philosophy of mathematics. Specifically, we will interpret the language of Peano arithmetic by applying the modal semantics of theoretical terms introduced in Andreas (Synthese 174(3):367–383, 2010). We will thereby show that the application to Peano arithmetic yields a formal semantics of universal structuralism, i.e., the view that ordinary mathematical statements in arithmetic express general claims about all admissible interpretations (...)
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  12. Stable and Unstable Theories of Truth and Syntax.Beau Madison Mount & Daniel Waxman - 2021 - Mind 130 (518):439-473.
    Recent work on formal theories of truth has revived an approach, due originally to Tarski, on which syntax and truth theories are sharply distinguished—‘disentangled’—from mathematical base theories. In this paper, we defend a novel philosophical constraint on disentangled theories. We argue that these theories must be epistemically stable: they must possess an intrinsic motivation justifying no strictly stronger theory. In a disentangled setting, even if the base and the syntax theory are individually stable, they may be jointly unstable. We contend (...)
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  13. 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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  14. How Can Abstract Objects of Mathematics Be Known?†.Ladislav Kvasz - 2019 - Philosophia Mathematica 27 (3):316-334.
    The aim of the paper is to answer some arguments raised against mathematical structuralism developed by Michael Resnik. These arguments stress the abstractness of mathematical objects, especially their causal inertness, and conclude that mathematical objects, the structures posited by Resnik included, are inaccessible to human cognition. In the paper I introduce a distinction between abstract and ideal objects and argue that mathematical objects are primarily ideal. I reconstruct some aspects of the instrumental practice of mathematics, such as symbolic manipulations or (...)
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  15. (1 other version)¿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 4TH Edición. 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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  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. 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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  17. 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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  18. Can Mathematical Objects Be Causally Efficacious?Seungbae Park - 2018 - 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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  19. 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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  20. 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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  21. 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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  22. 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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  23. 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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  24. On Truth and Instrumentalisation.Chris Henry - 2016 - London Journal in Critical Thought 1 (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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  25. XI- Naturalism and Placement, or, What Should a Good Quinean Say about Mathematical and Moral Truth?Mary Leng - 2016 - Proceedings of the Aristotelian Society 116 (3):237-260.
    What should a Quinean naturalist say about moral and mathematical truth? If Quine’s naturalism is understood as the view that we should look to natural science as the ultimate ‘arbiter of truth’, this leads rather quickly to what Huw Price has called ‘placement problems’ of placing moral and mathematical truth in an empirical scientific world-view. Against this understanding of the demands of naturalism, I argue that a proper understanding of the reasons Quine gives for privileging ‘natural science’ as authoritative when (...)
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  26. 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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  27. 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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  28. Danielle Macbeth, "Realizing Reason: A Narrative of Truth and Knowing". [REVIEW]Catherine Legg - 2015 - Notre Dame Philosophical Reviews:online.
    This substantial book is a highly original and thorough work of synthetic first philosophy. Although it has some recognizable roots in the Kantian/Sellarsian tradition of the Pittsburgh school, it adds a wealth of precise discussion of examples from science and mathematics, made possible by Macbeth's dual training in arts and sciences. It presents a developmental story of human reason bootstrapping itself towards greater power and clarity through the Western tradition (which is the sole purview of the discussion). This development is (...)
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  29. Functions and Generality of Logic: Reflections on Dedekind's and Frege's Logicisms.Gabriel Sandu, Marco Panza & Hourya Benis-Sinaceur (eds.) - 2015 - Cham, Switzerland: Springer Verlag.
    Part I of Frege’s Grundgesetze is devoted to the “exposition [Darlegung]” of his formal system.
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  30. 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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  31. 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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  32. Hilbert’s Program.Richard Zach - 2014 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. Stanford, CA: The Metaphysics Research Lab.
    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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  33. 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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  34. Intuitionistic logic and its philosophy.Panu Raatikainen - 2013 - Al-Mukhatabat. A Trilingual Journal For Logic, Epistemology and Analytical Philosophy (6):114-127.
  35. Aristotle on Mathematical Truth.Phil Corkum - 2012 - British Journal for the History of Philosophy 20 (6):1057-1076.
    Both literalism, the view that mathematical objects simply exist in the empirical world, and fictionalism, the view that mathematical objects do not exist but are rather harmless fictions, have been both ascribed to Aristotle. The ascription of literalism to Aristotle, however, commits Aristotle to the unattractive view that mathematics studies but a small fragment of the physical world; and there is evidence that Aristotle would deny the literalist position that mathematical objects are perceivable. The ascription of fictionalism also faces a (...)
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  36. 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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  37. Mathematical truth regained.Robert Hanna - 2010 - In Mirja Hartimo (ed.), Phenomenology and mathematics. London: Springer. pp. 147--181.
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  38. 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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  39. 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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  40. 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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  41. 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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  42. 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. 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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  44. Meršić o Hilbertovoj aksiomatskoj metodi [Meršić on Hilbert's axiomatic method].Srećko Kovač - 2006 - In E. Banić-Pajnić & M. Girardi Karšulin (eds.), Zbornik u čast Franji Zenku. pp. 123-135.
    The criticism of Hilbert's axiomatic system of geometry by Mate Meršić (Merchich, 1850-1928), presented in his work "Organistik der Geometrie" (1914, also in "Modernes und Modriges", 1914), is analyzed and discussed. According to Meršić, geometry cannot be based on its own axioms, as a logical analysis of spatial intuition, but must be derived as a "spatial concretion" using "higher" axioms of arithmetic, logic, and "rational algorithmics." Geometry can only be one, because space is also only one. It cannot be reduced (...)
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  45. (2 other versions)Making Sense of Questions in Logic and Mathematics: Mill vs. Carnap.Esther Ramharter - 2006 - Prolegomena 5 (2):209-218.
    Whether mathematical truths are syntactical (as Rudolf Carnap claimed) or empirical (as Mill actually never claimed, though Carnap claimed that he did) might seem merely an academic topic. However, it becomes a practical concern as soon as we consider the role of questions. For if we inquire as to the truth of a mathematical statement, this question must be (in a certain respect) meaningless for Carnap, as its truth or falsity is certain in advance due to its purely syntactical (or (...)
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  46. 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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  47. 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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  48. 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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  49. 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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  50. The Dignity of a Rule: Wittgenstein, Mathematical Norms, and Truth.Michael Hymers - 2003 - Dialogue 42 (3):419-446.
    RésuméPaul 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 outre (...)
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