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  1. On Deductionism.Dan Bruiger - manuscript
    Deductionism assimilates nature to conceptual artifacts (models, equations), and tacitly holds that real physical systems are such artifacts. Some physical concepts represent properties of deductive systems rather than of nature. Properties of mathematical or deductive systems can thereby sometimes falsely be ascribed to natural systems.
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  2. 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].
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  3. Proof that Wittgenstein is correct about Gödel.P. Olcott - manuscript
    The conventional notion of a formal system is adapted to conform to the sound deductive inference model operating on finite strings. Finite strings stipulated to have the semantic property of Boolean true provide the sound deductive premises. Truth preserving finite string transformation rules provide valid the deductive inference. Conclusions of sound arguments are derived from truth preserving finite string transformations applied to true premises.
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  4. (4 other versions)Halting problem undecidability and infinitely nested simulation.P. Olcott - manuscript
    The halting theorem counter-examples present infinitely nested simulation (non-halting) behavior to every simulating halt decider. The pathological self-reference of the conventional halting problem proof counter-examples is overcome. The halt status of these examples is correctly determined. A simulating halt decider remains in pure simulation mode until after it determines that its input will never reach its final state. This eliminates the conventional feedback loop where the behavior of the halt decider effects the behavior of its input.
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  5. Refuting Tarski and Gödel with a Sound Deductive Formalism.P. Olcott - manuscript
    The conventional notion of a formal system is adapted to conform to the sound deductive inference model operating on finite strings. Finite strings stipulated to have the semantic value of Boolean true provide the sound deductive premises. Truth preserving finite string transformation rules provide the valid deductive inference. Sound deductive conclusions are the result of these finite string transformation rules.
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  6. (1 other version)Minimal Type Theory (MTT).P. Olcott - manuscript
    Minimal Type Theory (MTT) is based on type theory in that it is agnostic about Predicate Logic level and expressly disallows the evaluation of incompatible types. It is called Minimal because it has the fewest possible number of fundamental types, and has all of its syntax expressed entirely as the connections in a directed acyclic graph.
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  7. Tarski Undefinability Theorem Terse Refutation.P. Olcott - manuscript
    Both Tarski and Gödel “prove” that provability can diverge from Truth. When we boil their claim down to its simplest possible essence it is really claiming that valid inference from true premises might not always derive a true consequence. This is obviously impossible.
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  8. Defining Gödel Incompleteness Away.P. Olcott - manuscript
    We can simply define Gödel 1931 Incompleteness away by redefining the meaning of the standard definition of Incompleteness: A theory T is incomplete if and only if there is some sentence φ such that (T ⊬ φ) and (T ⊬ ¬φ). This definition construes the existence of self-contradictory expressions in a formal system as proof that this formal system is incomplete because self-contradictory expressions are neither provable nor disprovable in this formal system. Since self-contradictory expressions are neither provable nor disprovable (...)
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  9. A Theory of Implicit Commitment for Mathematical Theories.Mateusz Łełyk & Carlo Nicolai - manuscript
    The notion of implicit commitment has played a prominent role in recent works in logic and philosophy of mathematics. Although implicit commitment is often associated with highly technical studies, it remains so far an elusive notion. In particular, it is often claimed that the acceptance of a mathematical theory implicitly commits one to the acceptance of a Uniform Reflection Principle for it. However, philosophers agree that a satisfactory analysis of the transition from a theory to its reflection principle is still (...)
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  10. Substitutional Validity for Modal Logic.Marco Grossi - 2023 - Notre Dame Journal of Formal Logic 64 (3):291-316.
    In the substitutional framework, validity is truth under all substitutions of the nonlogical vocabulary. I develop a theory where □ is interpreted as substitutional validity. I show how to prove soundness and completeness for common modal calculi using this definition.
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  11. Finitist Axiomatic Truth.Sato Kentaro & Jan Walker - 2023 - Journal of Symbolic Logic 88 (1):22-73.
    Following the finitist’s rejection of the complete totality of the natural numbers, a finitist language allows only propositional connectives and bounded quantifiers in the formula-construction but not unbounded quantifiers. This is opposed to the currently standard framework, a first-order language. We conduct axiomatic studies on the notion of truth in the framework of finitist arithmetic in which at least smash function $\#$ is available. We propose finitist variants of Tarski ramified truth theories up to rank $\omega $, of Kripke–Feferman truth (...)
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  12. On the Logicality of Truth.Kentaro Fujimoto - 2022 - Philosophical Quarterly 72 (4):853-874.
    Deflationism about truth describes truth as a logical notion. In the present paper, I explore the implication of the alleged logicality of truth from the perspective of axiomatic theories of truth, and argue that the deflationist doctrine of the logicality of truth gives rise to two types of self-undermining arguments against deflationism, which I call the conservativeness argument from logicality and the topic-neutrality argument.
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  13. Semidisquotation and the infinitary function of truth.Camillo Fiore - 2021 - Erkenntnis 88 (2):851-866.
    The infinitary function of the truth predicate consists in its ability to express infinite conjunctions and disjunctions. A transparency principle for truth states the equivalence between a sentence and its truth predication; it requires an introduction principle—which allows the inference from “snow is white” to “the sentence ‘snow is white’ is true”—and an elimination principle—which allows the inference from “the sentence ‘snow is white’ is true” to “snow is white”. It is commonly assumed that a theory of truth needs to (...)
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  14. 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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  15. The SignalGlyph Project and Prime Numbers.Michael Joseph Winkler - 2021 - In Michael Winkler (ed.), The Image of Language. Northeast, NY: Artists Books Editions. pp. 158-163.
    An excerpt of "The SignalGlyph Project and Prime Numbers" (a chapter of the book THE IMAGE OF LANGUAGE) that attempts to illustrate how dimensional limitations of mathematical language have obscured recognition of the system of patterning in the distribution of prime numbers.
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  16. Conceptions of Set and the Foundations of Mathematics.Luca Incurvati - 2020 - Cambridge University Press.
    Sets are central to mathematics and its foundations, but what are they? In this book Luca Incurvati provides a detailed examination of all the major conceptions of set and discusses their virtues and shortcomings, as well as introducing the fundamentals of the alternative set theories with which these conceptions are associated. He shows that the conceptual landscape includes not only the naïve and iterative conceptions but also the limitation of size conception, the definite conception, the stratified conception and the graph (...)
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  17. 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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  18. Metamathematics and the Philosophical Tradition, by William Boos, ed. Florence S. Boos. Berlin: De Gruyter. 2018. [REVIEW]Lydia Patton - 2020 - Philosophia 48 (4):1-4.
    William Boos (1943–2014) was a mathematician, set theorist, and philosopher. His work is at the intersection of these fields. In particular, Boos looks at the classic problems of epistemology through the lens of the axiomatic method in mathematics and physics, or something resembling that method.
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  19. A Validation of Knowledge: A New, Objective Theory of Axioms, Causality, Meaning, Propositions, Mathematics, and Induction.Ronald Pisaturo - 2020 - Norwalk, Connecticut: Prime Mover Press.
    This book seeks to offer original answers to all the major open questions in epistemology—as indicated by the book’s title. These questions and answers arise organically in the course of a validation of the entire corpus of human knowledge. The book explains how we know what we know, and how well we know it. The author presents a positive theory, motivated and directed at every step not by a need to reply to skeptics or subjectivists, but by the need of (...)
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  20. Axiomatizing Changing Conceptions of the Geometric Continuum II: Archimedes-Descartes-Hilbert-Tarski†.John T. Baldwin - 2019 - Philosophia Mathematica 27 (1):33-60.
    In Part I of this paper we argued that the first-order systems HP5 and EG are modest complete descriptive axiomatization of most of Euclidean geometry. In this paper we discuss two further modest complete descriptive axiomatizations: Tarksi’s for Cartesian geometry and new systems for adding $$\pi$$. In contrast we find Hilbert’s full second-order system immodest for geometrical purposes but appropriate as a foundation for mathematical analysis.
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  21. Universes and univalence in homotopy type theory.James Ladyman & Stuart Presnell - 2019 - Review of Symbolic Logic 12 (3):426-455.
    The Univalence axiom, due to Vladimir Voevodsky, is often taken to be one of the most important discoveries arising from the Homotopy Type Theory research programme. It is said by Steve Awodey that Univalence embodies mathematical structuralism, and that Univalence may be regarded as ‘expanding the notion of identity to that of equivalence’. This article explores the conceptual, foundational and philosophical status of Univalence in Homotopy Type Theory. It extends our Types-as-Concepts interpretation of HoTT to Universes, and offers an account (...)
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  22. (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 OBSERVACIONES SOBRE IMPOSIBILIDAD, INCOMPLETA, PARACOHERENCIA,INDECISIÓN,ALEATORIEDAD, COMPUTABILIDAD, PARADOJA E INCERTIDUMBRE EN CHAITIN, WITTGENSTEIN, HOFSTADTER, WOLPERT, DORIA, DACOSTA, GODEL, SEARLE, RODYCH, BERTO,FLOYD, MOYAL-SHARROCK Y YANOFSKY. Reality Press. pp. 44-63.
    En ' Godel’s Way ', tres eminentes científicos discuten temas como la indecisión, la incompleta, la aleatoriedad, la computabilidad y la paraconsistencia. 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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  23. Axiomatizing Changing Conceptions of the Geometric Continuum I: Euclid-Hilbert†.John T. Baldwin - 2018 - Philosophia Mathematica 26 (3):346-374.
    We give a general account of the goals of axiomatization, introducing a variant on Detlefsen’s notion of ‘complete descriptive axiomatization’. We describe how distinctions between the Greek and modern view of number, magnitude, and proportion impact the interpretation of Hilbert’s axiomatization of geometry. We argue, as did Hilbert, that Euclid’s propositions concerning polygons, area, and similar triangles are derivable from Hilbert’s first-order axioms. We argue that Hilbert’s axioms including continuity show much more than the geometrical propositions of Euclid’s theorems and (...)
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  24. The Logical Strength of Compositional Principles.Richard Heck - 2018 - Notre Dame Journal of Formal Logic 59 (1):1-33.
    This paper investigates a set of issues connected with the so-called conservativeness argument against deflationism. Although I do not defend that argument, I think the discussion of it has raised some interesting questions about whether what I call “compositional principles,” such as “a conjunction is true iff its conjuncts are true,” have substantial content or are in some sense logically trivial. The paper presents a series of results that purport to show that the compositional principles for a first-order language, taken (...)
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  25. (1 other version)What Paradoxes Depend on.Ming Hsiung - 2018 - Synthese:1-27.
    This paper gives a definition of self-reference on the basis of the dependence relation given by Leitgeb (2005), and the dependence digraph by Beringer & Schindler (2015). Unlike the usual discussion about self-reference of paradoxes centering around Yablo's paradox and its variants, I focus on the paradoxes of finitary characteristic, which are given again by use of Leitgeb's dependence relation. They are called 'locally finite paradoxes', satisfying that any sentence in these paradoxes can depend on finitely many sentences. I prove (...)
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  26. Reflection Principles and the Liar in Context.Julien Murzi & Lorenzo Rossi - 2018 - Philosophers' Imprint 18.
    Contextualist approaches to the Liar Paradox postulate the occurrence of a context shift in the course of the Liar reasoning. In particular, according to the contextualist proposal advanced by Charles Parsons and Michael Glanzberg, the Liar sentence L doesn’t express a true proposition in the initial context of reasoning c, but expresses a true one in a new, richer context c', where more propositions are available for expression. On the further assumption that Liar sentences involve propositional quantifiers whose domains may (...)
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  27. Provably True Sentences Across Axiomatizations of Kripke’s Theory of Truth.Carlo Nicolai - 2018 - Studia Logica 106 (1):101-130.
    We study the relationships between two clusters of axiomatizations of Kripke’s fixed-point models for languages containing a self-applicable truth predicate. The first cluster is represented by what we will call ‘\-like’ theories, originating in recent work by Halbach and Horsten, whose axioms and rules are all valid in fixed-point models; the second by ‘\-like’ theories first introduced by Solomon Feferman, that lose this property but reflect the classicality of the metatheory in which Kripke’s construction is carried out. We show that (...)
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  28. The Epistemic Lightness of Truth: Deflationism and its Logic.Cezary Cieśliński - 2017 - Cambridge, United Kingdom: Cambridge University Press.
    This book analyses and defends the deflationist claim that there is nothing deep about our notion of truth. According to this view, truth is a 'light' and innocent concept, devoid of any essence which could be revealed by scientific inquiry. Cezary Cieśliński considers this claim in light of recent formal results on axiomatic truth theories, which are crucial for understanding and evaluating the philosophical thesis of the innocence of truth. Providing an up-to-date discussion and original perspectives on this central and (...)
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  29. 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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  30. Computability, Finiteness and the Standard Model of Arithmetic.Massimiliano Carrara, Enrico Martino & Matteo Plebani - 2016 - In Francesca Boccuni & Andrea Sereni (eds.), Objectivity, Realism, and Proof. FilMat Studies in the Philosophy of Mathematics. Cham, Switzerland: Springer International Publishing.
    This paper investigates the question of how we manage to single out the natural number structure as the intended interpretation of our arithmetical language. Horsten submits that the reference of our arithmetical vocabulary is determined by our knowledge of some principles of arithmetic on the one hand, and by our computational abilities on the other. We argue against such a view and we submit an alternative answer. We single out the structure of natural numbers through our intuition of the absolute (...)
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  31. 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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  32. Can the Cumulative Hierarchy Be Categorically Characterized?Luca Incurvati - 2016 - Logique Et Analyse 59 (236):367-387.
    Mathematical realists have long invoked the categoricity of axiomatizations of arithmetic and analysis to explain how we manage to fix the intended meaning of their respective vocabulary. Can this strategy be extended to set theory? Although traditional wisdom recommends a negative answer to this question, Vann McGee (1997) has offered a proof that purports to show otherwise. I argue that one of the two key assumptions on which the proof rests deprives McGee's result of the significance he and the realist (...)
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  33. Typed and Untyped Disquotational Truth.Cezary Cieśliński - 2015 - In T. Achourioti, H. Galinon, J. Martínez Fernández & K. Fujimoto (eds.), Unifying the Philosophy of Truth. Dordrecht: Imprint: Springer.
    We present an overview of typed and untyped disquotational truth theories with the emphasis on their (non)conservativity over the base theory of syntax. Two types of conservativity are discussed: syntactic and semantic. We observe in particular that TB—one of the most basic disquotational theories—is not semantically conservative over its base; we show also that an untyped disquotational theory PTB is a syntactically conservative extension of Peano Arithmetic.
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  34. 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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  35. Naive Infinitism: The Case for an Inconsistency Approach to Infinite Collections.Toby Meadows - 2015 - Notre Dame Journal of Formal Logic 56 (1):191-212.
    This paper expands upon a way in which we might rationally doubt that there are multiple sizes of infinity. The argument draws its inspiration from recent work in the philosophy of truth and philosophy of set theory. More specifically, elements of contextualist theories of truth and multiverse accounts of set theory are brought together in an effort to make sense of Cantor’s troubling theorem. The resultant theory provides an alternative philosophical perspective on the transfinite, but has limited impact on everyday (...)
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  36. Hilbert's axiomatic method and Carnap's general axiomatics.Michael Stöltzner - 2015 - Studies in History and Philosophy of Science Part A 53:12-22.
  37. Hilbert's Objectivity.Lydia Patton - 2014 - Historia Mathematica 41 (2):188-203.
    Detlefsen (1986) reads Hilbert's program as a sophisticated defense of instrumentalism, but Feferman (1998) has it that Hilbert's program leaves significant ontological questions unanswered. One such question is of the reference of individual number terms. Hilbert's use of admittedly "meaningless" signs for numbers and formulae appears to impair his ability to establish the reference of mathematical terms and the content of mathematical propositions (Weyl (1949); Kitcher (1976)). The paper traces the history and context of Hilbert's reasoning about signs, which illuminates (...)
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  38. The Ways of Hilbert's Axiomatics: Structural and Formal.Wilfried Sieg - 2014 - Perspectives on Science 22 (1):133-157.
    It is a remarkable fact that Hilbert's programmatic papers from the 1920s still shape, almost exclusively, the standard contemporary perspective of his views concerning (the foundations of) mathematics; even his own, quite different work on the foundations of geometry and arithmetic from the late 1890s is often understood from that vantage point. My essay pursues one main goal, namely, to contrast Hilbert's formal axiomatic method from the early 1920s with his existential axiomatic approach from the 1890s. Such a contrast illuminates (...)
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  39. Modality and axiomatic theories of truth I: Friedman-Sheard.Johannes Stern - 2014 - Review of Symbolic Logic 7 (2):273-298.
    In this investigation we explore a general strategy for constructing modal theories where the modal notion is conceived as a predicate. The idea of this strategy is to develop modal theories over axiomatic theories of truth. In this first paper of our two part investigation we develop the general strategy and then apply it to the axiomatic theory of truth Friedman-Sheard. We thereby obtain the theory Modal Friedman-Sheard. The theory Modal Friedman-Sheard is then discussed from three different perspectives. First, we (...)
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  40. Modality and axiomatic theories of truth II: Kripke-Feferman.Johannes Stern - 2014 - Review of Symbolic Logic 7 (2):299-318.
    In this second and last paper of the two part investigation on "Modality and Axiomatic Theories of Truth" we apply a general strategy for constructing modal theories over axiomatic theories of truth to the theory Kripke-Feferman. This general strategy was developed in the first part of our investigation. Applying the strategy to Kripke-Feferman leads to the theory Modal Kripke-Feferman which we discuss from the three perspectives that we had already considered in the first paper, where we discussed the theory Modal (...)
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  41. 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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  42. Axiomatic truth, syntax and metatheoretic reasoning.Graham E. Leigh & Carlo Nicolai - 2013 - Review of Symbolic Logic 6 (4):613-636.
    Following recent developments in the literature on axiomatic theories of truth, we investigate an alternative to the widespread habit of formalizing the syntax of the object-language into the object-language itself. We first argue for the proposed revision, elaborating philosophical evidences in favor of it. Secondly, we present a general framework for axiomatic theories of truth with theories of syntax. Different choices of the object theory O will be considered. Moreover, some strengthenings of these theories will be introduced: we will consider (...)
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  43. Are Mathematical Theories Reducible to Non-analytic Foundations?Stathis Livadas - 2013 - Axiomathes 23 (1):109-135.
    In this article I intend to show that certain aspects of the axiomatical structure of mathematical theories can be, by a phenomenologically motivated approach, reduced to two distinct types of idealization, the first-level idealization associated with the concrete intuition of the objects of mathematical theories as discrete, finite sign-configurations and the second-level idealization associated with the intuition of infinite mathematical objects as extensions over constituted temporality. This is the main standpoint from which I review Cantor’s conception of infinite cardinalities and (...)
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  44. Axioms in Mathematical Practice.Dirk Schlimm - 2013 - Philosophia Mathematica 21 (1):37-92.
    On the basis of a wide range of historical examples various features of axioms are discussed in relation to their use in mathematical practice. A very general framework for this discussion is provided, and it is argued that axioms can play many roles in mathematics and that viewing them as self-evident truths does not do justice to the ways in which mathematicians employ axioms. Possible origins of axioms and criteria for choosing axioms are also examined. The distinctions introduced aim at (...)
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  45. Axiomatic Theories of Truth.P. Smith - 2013 - Analysis 73 (1):163-168.
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  46. 8. Transcendental Arguments, Axiomatic Truth, and the Difficulty of Overcoming Idealism.Michael J. Olson - 2012 - In John Mullarkey & Anthony Paul Smith (eds.), Laruelle and Non-Philosophy. Edinburgh University Press. pp. 169-190.
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  47. V = L and intuitive plausibility in set theory. A case study.Tatiana Arrigoni - 2011 - Bulletin of Symbolic Logic 17 (3):337-360.
    What counts as an intuitively plausible set theoretic content (notion, axiom or theorem) has been a matter of much debate in contemporary philosophy of mathematics. In this paper I develop a critical appraisal of the issue. I analyze first R. B. Jensen's positions on the epistemic status of the axiom of constructibility. I then formulate and discuss a view of intuitiveness in set theory that assumes it to hinge basically on mathematical success. At the same time, I present accounts of (...)
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  48. T-equivalences for positive sentences.Cezary Cieśliński - 2011 - Review of Symbolic Logic 4 (2):319-325.
    Answering a question formulated by Halbach (2009), I show that a disquotational truth theory, which takes as axioms all positive substitutions of the sentential T-schema, together with all instances of induction in the language with the truth predicate, is conservative over its syntactical base.
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  49. Relative truth definability of axiomatic truth theories.Kentaro Fujimoto - 2010 - Bulletin of Symbolic Logic 16 (3):305-344.
    The present paper suggests relative truth definability as a tool for comparing conceptual aspects of axiomatic theories of truth and gives an overview of recent developments of axiomatic theories of truth in the light of it. We also show several new proof-theoretic results via relative truth definability including a complete answer to the conjecture raised by Feferman in [13].
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  50. The gödel paradox and Wittgenstein's reasons.Francesco Berto - 2009 - Philosophia Mathematica 17 (2):208-219.
    An interpretation of Wittgenstein’s much criticized remarks on Gödel’s First Incompleteness Theorem is provided in the light of paraconsistent arithmetic: in taking Gödel’s proof as a paradoxical derivation, Wittgenstein was drawing the consequences of his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. It is shown that the features of paraconsistent arithmetics match (...)
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