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Mathematical truth

Journal of Philosophy 70 (19):661-679 (1973)

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  1. Realistic Rationalism. [REVIEW]Mark Eli Kalderon - 2000 - Philosophical Review 109 (3):456-459.
    Philosophy of mathematics is in an alienated state. While regarded by the profession as a serious and legitimate subdiscipline, a passing knowledge of its subject matter is considered something of a luxury—or at least not required of a conscientious philosopher the way a passing knowledge of logic is. Philosophy of mathematics is thus regarded with a benign neglect: best left to the experts, whose opinions should be deferred to, but mostly irrelevant to the central concerns of the working philosopher. Its (...)
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  • From Metaphysics to Ethics: A Defence of Conceptual Analysis. [REVIEW]D. Gene Witmer - 2000 - Philosophical Review 109 (3):459-462.
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  • Real Realism: The Galilean Strategy.Philip Kitcher - 2001 - Philosophical Review 110 (2):151-197.
    This essay aims to disentangle various types of anti-realism, and to disarm the considerations that are deployed to support them. I distinguish empiricist versions of anti-realism from constructivist versions, and, within each of these, semantic arguments from epistemological arguments. The centerpiece of my defense of a modest version of realism - real realism - is the thought that there are resources within our ordinary ways of talking about and knowing about everyday objects that enable us to extend our claims to (...)
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  • Modal Metaphysics and the Existence of God.Joshua R. Sijuwade - 2022 - Metaphysica:1-70.
    In this article, I seek to assess the extent to which Theism, the claim that there is a God, can provide a true fundamental explanation for the existence of the infinite plurality of concrete and abstract possible worlds, posited by David K. Lewis and Alvin Plantinga. This assessment will be carried out within the (modified) explanatory framework of Richard Swinburne, which will lead to the conclusion that the existence of God provides a true fundamental explanation for these specific entities. And (...)
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  • The Price of Mathematical Scepticism.Paul Blain Levy - forthcoming - Philosophia Mathematica.
    This paper argues that, insofar as we doubt the bivalence of the Continuum Hypothesis or the truth of the Axiom of Choice, we should also doubt the consistency of third-order arithmetic, both the classical and intuitionistic versions. -/- Underlying this argument is the following philosophical view. Mathematical belief springs from certain intuitions, each of which can be either accepted or doubted in its entirety, but not half-accepted. Therefore, our beliefs about reality, bivalence, choice and consistency should all be aligned.
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  • Analysis and Interpretation in the Exact Sciences: Essays in Honour of William Demopoulos.Melanie Frappier, Derek Brown & Robert DiSalle (eds.) - 2011 - Dordrecht and London: Springer.
    The essays in this volume concern the points of intersection between analytic philosophy and the philosophy of the exact sciences. More precisely, it concern connections between knowledge in mathematics and the exact sciences, on the one hand, and the conceptual foundations of knowledge in general. Its guiding idea is that, in contemporary philosophy of science, there are profound problems of theoretical interpretation-- problems that transcend both the methodological concerns of general philosophy of science, and the technical concerns of philosophers of (...)
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  • Alethic Pluralism and the Role of Reference in the Metaphysics of Truth.Brian Ball - 2017 - Southern Journal of Philosophy 55 (1):116-135.
    In this paper, I outline and defend a novel approach to alethic pluralism, the thesis that truth has more than one metaphysical nature: where truth is, in part, explained by reference, it is relational in character and can be regarded as consisting in correspondence; but where instead truth does not depend upon reference it is not relational and involves only coherence. In the process, I articulate a clear sense in which truth may or may not depend upon reference: this involves (...)
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  • Can Metaphysical Structuralism Solve the Plurality Problem?Sophie R. Allen - 2018 - International Journal of Philosophical Studies 26 (5):722-746.
    ABSTRACTMetaphysics has a problem with plurality: in many areas of discourse, there are too many good theories, rather than just one. This embarrassment of riches is a particular problem for metaphysical realists who want metaphysics to tell us the way the world is and for whom one theory is the correct one. A recent suggestion is that we can treat the different theories as being functionally or explanatorily equivalent to each other, even though they differ in content. The aim of (...)
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  • Theories as Recipes: Third-Order Virtue and Vice.Michaela Markham McSweeney - 2020 - Philosophical Studies 177 (2):391-411.
    A basic way of evaluating metaphysical theories is to ask whether they give satisfying answers to the questions they set out to resolve. I propose an account of “third-order” virtue that tells us what it takes for certain kinds of metaphysical theories to do so. We should think of these theories as recipes. I identify three good-making features of recipes and show that they translate to third-order theoretical virtues. I apply the view to two theories—mereological universalism and plenitudinous platonism—and draw (...)
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  • International Handbook of Research in History, Philosophy and Science Teaching.Michael R. Matthews (ed.) - 2014 - Springer.
    This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the (...)
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  • An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Stucture.James Franklin - 2014 - London and New York: Palgrave MacMillan.
    An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and (...)
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  • Modality and Meaning.William G. Lycan - 1994 - Dordrecht: Kluwer Academic Publishers.
    MEANING POSTULATES REINSTATED If I am right in agreeing with Cresswell that the "logicarrlexicaT distinction is one of degree rather than one of kind, that in turn impugns the distinction between the official truth-rules that define logical ...
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  • Leśniewski's Systems of Logic and Foundations of Mathematics.Rafal Urbaniak - 2013 - Cham, Switzerland: Springer.
    With material on his early philosophical views, his contributions to set theory and his work on nominalism and higher-order quantification, this book offers a uniquely expansive critical commentary on one of analytical philosophy’s great ...
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  • Epistemic Modality and Hyperintensionality in Mathematics.Hasen Khudairi - 2021 - Dissertation, University of St Andrews
    This book concerns the foundations of epistemic modality. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality relates to the computational theory of mind; metaphysical modality; the types of mathematical modality; to the epistemic status of large cardinal axioms, undecidable propositions, and abstraction principles in the philosophy of mathematics; to the modal profile of rational intuition; and (...)
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  • Hilbert's Finitism: Historical, Philosophical, and Metamathematical Perspectives.Richard Zach - 2001 - Dissertation, University of California, Berkeley
    In the 1920s, David Hilbert proposed a research program with the aim of providing mathematics with a secure foundation. This was to be accomplished by first formalizing logic and mathematics in their entirety, and then showing---using only so-called finitistic principles---that these formalizations are free of contradictions. ;In the area of logic, the Hilbert school accomplished major advances both in introducing new systems of logic, and in developing central metalogical notions, such as completeness and decidability. The analysis of unpublished material presented (...)
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  • Truth and Scientific Change.Gila Sher - 2017 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 48 (3):371-394.
    The paper seeks to answer two new questions about truth and scientific change: What lessons does the phenomenon of scientific change teach us about the nature of truth? What light do recent developments in the theory of truth, incorporating these lessons, throw on problems arising from the prevalence of scientific change, specifically, the problem of pessimistic meta-induction?
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  • Abstracta and Possibilia: Modal Foundations of Mathematical Platonism.Hasen Khudairi - manuscript
    This paper aims to provide modal foundations for mathematical platonism. I examine Hale and Wright's (2009) objections to the merits and need, in the defense of mathematical platonism and its epistemology, of the thesis of Necessitism. In response to Hale and Wright's objections to the role of epistemic and metaphysical modalities in providing justification for both the truth of abstraction principles and the success of mathematical predicate reference, I examine the Necessitist commitments of the abundant conception of properties endorsed by (...)
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  • Infinity and the Foundations of Linguistics.Ryan M. Nefdt - 2019 - Synthese 196 (5):1671-1711.
    The concept of linguistic infinity has had a central role to play in foundational debates within theoretical linguistics since its more formal inception in the mid-twentieth century. The conceptualist tradition, marshalled in by Chomsky and others, holds that infinity is a core explanandum and a link to the formal sciences. Realism/Platonism takes this further to argue that linguistics is in fact a formal science with an abstract ontology. In this paper, I argue that a central misconstrual of formal apparatus of (...)
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  • Dummett on Abstract Objects.George Duke - 2012 - London, England: Palgrave-Macmillan.
    This book offers an historically-informed critical assessment of Dummett's account of abstract objects, examining in detail some of the Fregean presuppositions whilst also engaging with recent work on the problem of abstract entities.
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  • Rationality and the Structure of the Self Volume II: A Kantian Conception.Adrian M. S. Piper - 2013 - APRA Foundation.
    Adrian Piper argues that the Humean conception can be made to work only if it is placed in the context of a wider and genuinely universal conception of the self, whose origins are to be found in Kant’s Critique of Pure Reason. This conception comprises the basic canons of classical logic, which provide both a model of motivation and a model of rationality. These supply necessary conditions both for the coherence and integrity of the self and also for unified agency. (...)
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  • Evolutionary Debunking of Moral Realism.Katia Vavova - 2015 - Philosophy Compass 10 (2):104-116.
    Evolutionary debunking arguments move from a premise about the influence of evolutionary forces on our moral beliefs to a skeptical conclusion about those beliefs. My primary aim is to clarify this empirically grounded epistemological challenge. I begin by distinguishing among importantly different sorts of epistemological attacks. I then demonstrate that instances of each appear in the literature under the ‘evolutionary debunking’ title. Distinguishing them clears up some confusions and helps us better understand the structure and potential of evolutionary debunking arguments.
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  • The Reliability Challenge and the Epistemology of Logic.Joshua Schechter - 2010 - Philosophical Perspectives 24 (1):437-464.
    We think of logic as objective. We also think that we are reliable about logic. These views jointly generate a puzzle: How is it that we are reliable about logic? How is it that our logical beliefs match an objective domain of logical fact? This is an instance of a more general challenge to explain our reliability about a priori domains. In this paper, I argue that the nature of this challenge has not been properly understood. I explicate the challenge (...)
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  • Debunking Arguments.Dan Korman - 2019 - Philosophy Compass 14 (12).
    Debunking arguments—also known as etiological arguments, genealogical arguments, access problems, isolation objec- tions, and reliability challenges—arise in philosophical debates about a diverse range of topics, including causation, chance, color, consciousness, epistemic reasons, free will, grounding, laws of nature, logic, mathematics, modality, morality, natural kinds, ordinary objects, religion, and time. What unifies the arguments is the transition from a premise about what does or doesn't explain why we have certain mental states to a negative assessment of their epistemic status. I examine (...)
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  • Our Reliability is in Principle Explainable.Dan Baras - 2017 - Episteme 14 (2):197-211.
    Non-skeptical robust realists about normativity, mathematics, or any other domain of non- causal truths are committed to a correlation between their beliefs and non- causal, mind-independent facts. Hartry Field and others have argued that if realists cannot explain this striking correlation, that is a strong reason to reject their theory. Some consider this argument, known as the Benacerraf–Field argument, as the strongest challenge to robust realism about mathematics, normativity, and even logic. In this article I offer two closely related accounts (...)
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  • Rationality and the Structure of the Self, Volume I: The Humean Conception.Adrian M. S. Piper - 2008 - APRA Foundation Berlin.
    The Humean conception of the self consists in the belief-desire model of motivation and the utility-maximizing model of rationality. This conception has dominated Western thought in philosophy and the social sciences ever since Hobbes’ initial formulation in Leviathan and Hume’s elaboration in the Treatise of Human Nature. Bentham, Freud, Ramsey, Skinner, Allais, von Neumann and Morgenstern and others have added further refinements that have brought it to a high degree of formal sophistication. Late twentieth century moral philosophers such as Rawls, (...)
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  • Phenomenology and Mathematics.Mirja Hartimo (ed.) - 2010 - Dordrecht, Netherland: Springer.
    This volume aims to establish the starting point for the development, evaluation and appraisal of the phenomenology of mathematics.
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  • The Place of Probability in Science: In Honor of Ellery Eells (1953-2006).Ellery Eells & James H. Fetzer (eds.) - 2010 - Springer.
  • Skepticism About Other Minds.Anil Gomes - forthcoming - In Diego Machuca & Baron Reed (eds.), Skepticism: From Antiquity to the Present. Bloomsbury Academic.
    In this paper I distinguish two ways of raising a sceptical problem of others' minds: via a problem concerning the possibility of error or via a problem concerning sources of knowledge. I give some reason to think that the second problem raises a more interesting problem in accounting for our knowledge of others’ minds and consider proposed solutions to the problem.
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  • Tuples All the Way Down?Simon Thomas Hewitt - 2018 - Thought: A Journal of Philosophy 7 (3):161-169.
    We can introduce singular terms for ordered pairs by means of an abstraction principle. Doing so proves useful for a number of projects in the philosophy of mathematics. However there is a question whether we can appeal to the abstraction principle in good faith, since a version of the Caesar Problem can be generated, posing the worry that abstraction fails to introduce expressions which refer determinately to the requisite sort of object. In this note I will pose the difficulty, and (...)
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  • Lowe on Modal Knowledge.Joachim Horvath - 2014 - Thought: A Journal of Philosophy 3 (3):208-217.
    In recent work, E. J. Lowe presents an essence-based account of our knowledge of metaphysical modality that he claims to be superior to its main competitors. I argue that knowledge of essences alone, without knowledge of a suitable bridge principle, is insufficient for knowing that something is metaphysically necessary or metaphysically possible. Yet given Lowe's other theoretical commitments, he cannot account for our knowledge of the needed bridge principle, and so his essence-based modal epistemology remains incomplete. In addition to that, (...)
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  • On Explaining Knowledge of Necessity.Joel Pust - 2004 - Dialectica 58 (1):71–87.
    Moderate rationalists maintain that our rational intuitions provide us with prima facie justification for believing various necessary propositions. Such a claim is often criticized on the grounds that our having reliable rational intuitions about domains in which the truths are necessary is inexplicable in some epistemically objectionable sense. In this paper, I defend moderate rationalism against such criticism. I argue that if the reliability of our rational intuitions is taken to be contingent, then there is no reason to think that (...)
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  • Can Structuralism Solve the ‘Access’ Problem?Fraser MacBride - 2004 - Analysis 64 (4):309–317.
  • Is There a Good Epistemological Argument Against Platonism?David Liggins - 2006 - Analysis 66 (2):135–141.
    Platonism in the philosophy of mathematics is the doctrine that there are mathematical objects such as numbers. John Burgess and Gideon Rosen have argued that that there is no good epistemological argument against platonism. They propose a dilemma, claiming that epistemological arguments against platonism either rely on a dubious epistemology, or resemble a dubious sceptical argument concerning perceptual knowledge. Against Burgess and Rosen, I show that an epistemological anti- platonist argument proposed by Hartry Field avoids both horns of their dilemma.
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  • The Explainability of Intuitions.Nenad Miščević - 2004 - Dialectica 58 (1):43–70.
    Explaining intuitions in terms of "facts of our natural history" is compatible with rationally trusting them. This compatibilist view is defended in the present paper, focusing upon nomic and essentialist modal intuitions. The opposite, incompatibilist view alleges the following: If basic modal intuitions are due to our cognitive make-up or "imaginative habits" then the epistemologists are left with a mere non-rational feeling of compulsion on the side of the thinker. Intuitions then cannot inform us about modal reality. In contrast, the (...)
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  • Conceivability and Possibility: Chalmers on Modal Epistemology.Hamid Vahid - 2006 - Philosophical Explorations 9 (3):243-260.
    We often decide whether a state of affairs is possible by trying to mentally depict a scenario where the state in question obtains . These mental acts seem to provide us with an epistemic route to the space of possibilities. The problem this raises is whether conceivability judgments provide justification-conferring grounds for the ensuing possibility-claims . Although the question has a long history, contemporary interest in it was, to a large extent, prompted by Kripke's utilization of modal intuitions in the (...)
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  • An Argument for Completely General Facts.Landon D. C. Elkind - 2021 - Journal for the History of Analytical Philosophy 9 (7).
    In his 1918 logical atomism lectures, Russell argued that there are no molecular facts. But he posed a problem for anyone wanting to avoid molecular facts: we need truth-makers for generalizations of molecular formulas, but such truth-makers seem to be both unavoidable and to have an abominably molecular character. Call this the problem of generalized molecular formulas. I clarify the problem here by distinguishing two kinds of generalized molecular formula: incompletely generalized molecular formulas and completely generalized molecular formulas. I next (...)
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  • Immanence in Abundance.Chad Carmichael - forthcoming - Erkenntnis.
    In this paper, I develop a theory on which each of a thing’s abundant properties is immanent in that thing. On the version of the theory I will propose, universals are abundant, each instantiated universal is immanent, and each uninstantiated universal is such that it could have been instantiated, in which case it would have been immanent. After setting out the theory, I will defend it from David Lewis’s argument that such a combination of immanence and abundance is absurd. I (...)
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  • Shadows of Syntax: Revitalizing Logical and Mathematical Conventionalism.Jared Warren - 2020 - New York, USA: Oxford University Press.
    What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...)
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  • Knowledge of Abstract Objects in Physics and Mathematics.Michael J. Shaffer - 2017 - Acta Analytica 32 (4):397-409.
    In this paper a parallel is drawn between the problem of epistemic access to abstract objects in mathematics and the problem of epistemic access to idealized systems in the physical sciences. On this basis it is argued that some recent and more traditional approaches to solving these problems are problematic.
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  • A Pragmatic-Semiotic Defence of Bivalence.Marc Champagne - 2022 - History and Philosophy of Logic 43 (2):143-157.
    Since Peirce defined the first operators for three-valued logic, it is usually assumed that he rejected the principle of bivalence. However, I argue that, because bivalence is a principle, the strategy used by Peirce to defend logical principles can be used to defend bivalence. Construing logic as the study of substitutions of equivalent representations, Peirce showed that some patterns of substitution get realized in the very act of questioning them. While I recognize that we can devise non-classical notations, I argue (...)
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  • A Truthmaker Indispensability Argument.Sam Baron - 2013 - Synthese 190 (12):2413-2427.
    Recently, nominalists have made a case against the Quine–Putnam indispensability argument for mathematical Platonism by taking issue with Quine’s criterion of ontological commitment. In this paper I propose and defend an indispensability argument founded on an alternative criterion of ontological commitment: that advocated by David Armstrong. By defending such an argument I place the burden back onto the nominalist to defend her favourite criterion of ontological commitment and, furthermore, show that criterion cannot be used to formulate a plausible form of (...)
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  • Numbers and Functions in Hilbert's Finitism.Richard Zach - 1998 - Taiwanese Journal for History and Philosophy of Science 10:33-60.
    David Hilbert's finitistic standpoint is a conception of elementary number theory designed to answer the intuitionist doubts regarding the security and certainty of mathematics. Hilbert was unfortunately not exact in delineating what that viewpoint was, and Hilbert himself changed his usage of the term through the 1920s and 30s. The purpose of this paper is to outline what the main problems are in understanding Hilbert and Bernays on this issue, based on some publications by them which have so far received (...)
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  • A Metasemantic Challenge for Mathematical Determinacy.Jared Warren & Daniel Waxman - 2020 - Synthese 197 (2):477-495.
    This paper investigates the determinacy of mathematics. We begin by clarifying how we are understanding the notion of determinacy before turning to the questions of whether and how famous independence results bear on issues of determinacy in mathematics. From there, we pose a metasemantic challenge for those who believe that mathematical language is determinate, motivate two important constraints on attempts to meet our challenge, and then use these constraints to develop an argument against determinacy and discuss a particularly popular approach (...)
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  • Calling for Explanation.Dan Baras - 2022 - Oxford University Press.
    The idea that there are some facts that call for explanation serves as an unexamined premise in influential arguments for the inexistence of moral or mathematical facts and for the existence of a god and of other universes. This book is the first to offer a comprehensive and critical treatment of this idea. It argues that calling for explanation is a sometimes-misleading figure of speech rather than a fundamental property of facts.
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  • Could Evolution Explain Our Reliability About Logic.Joshua Schechter - 2013 - In Tamar Szabo Gendler & John Hawthorne (eds.), Oxford Studies in Epistemology 4. pp. 214.
    We are reliable about logic in the sense that we by-and-large believe logical truths and disbelieve logical falsehoods. Given that logic is an objective subject matter, it is difficult to provide a satisfying explanation of our reliability. This generates a significant epistemological challenge, analogous to the well-known Benacerraf-Field problem for mathematical Platonism. One initially plausible way to answer the challenge is to appeal to evolution by natural selection. The central idea is that being able to correctly deductively reason conferred a (...)
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  • How Can Necessary Facts Call for Explanation.Dan Baras - 2020 - Synthese 198 (12):11607-11624.
    While there has been much discussion about what makes some mathematical proofs more explanatory than others, and what are mathematical coincidences, in this article I explore the distinct phenomenon of mathematical facts that call for explanation. The existence of mathematical facts that call for explanation stands in tension with virtually all existing accounts of “calling for explanation”, which imply that necessary facts cannot call for explanation. In this paper I explore what theoretical revisions are needed in order to accommodate this (...)
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  • Nominalism in Metaphysics.Gonzalo Rodriguez-Pereyra - 2008 - Stanford Encyclopedia of Philosophy.
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  • Abstract Objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.
  • Dualism.Howard Robinson - 2008 - Stanford Encyclopedia of Philosophy.
    This entry concerns dualism in the philosophy of mind. The term ‘dualism’ has a variety of uses in the history of thought. In general, the idea is that, for some particular domain, there are two fundamental kinds or categories of things or principles. In theology, for example a ‘dualist’ is someone who believes that Good and Evil — or God and the Devil — are independent and more or less equal forces in the world. Dualism contrasts with monism, which is (...)
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  • Intuition.Joel Pust - 2017 - Stanford Encyclopedia of Philosophy.
    This entry addresses the nature and epistemological role of intuition by considering the following questions: (1) What are intuitions?, (2) What roles do they serve in philosophical (and other “armchair”) inquiry?, (3) Ought they serve such roles?, (4) What are the implications of the empirical investigation of intuitions for their proper roles?, and (5) What is the content of intuitions prompted by the consideration of hypothetical cases?
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