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What is the Benacerraf Problem?

In Fabrice Pataut (ed.), New Perspectives on the Philosophy of Paul Benacerraf: Truth, Objects, Infinity. Springer Verlag (2017)

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  1. 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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  • The Benacerraf Problem as a Challenge for Ontic Structural Realism†.Majid Davoody Beni - forthcoming - Philosophia Mathematica:nkz022.
    ABSTRACT Benacerraf has presented two problems for the philosophy of mathematics. These are the problem of identification and the problem of representation. This paper aims to reconstruct the latter problem and to unpack its undermining bearing on the version of Ontic Structural Realism that frames scientific representations in terms of abstract structures. I argue that the dichotomy between mathematical structures and physical ones cannot be used to address the Benacerraf problem but strengthens it. I conclude by arguing that versions of (...)
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  • What is Field's Epistemological Objection to Platonism?Ylwa Sjölin Wirling - 2019 - In Robin Stenwall & Tobias Hansson Wahlberg (eds.), Maurinian Truths. pp. 123-133.
    This paper concerns an epistemological objection against mathematical platonism, due to Hartry Field.The argument poses an explanatory challenge – the challenge to explain the reliability of our mathematical beliefs – which the platonist, it’s argued, cannot meet. Is the objection compelling? Philosophers disagree, but they also disagree on (and are sometimes very unclear about) how the objection should be understood. Here I distinguish some options, and highlight some gaps that need to be filled in on the potentially most compelling version (...)
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  • Set-Theoretic Pluralism and the Benacerraf Problem.Justin Clarke-Doane - forthcoming - Philosophical Studies:1-18.
    Set-theoretic pluralism is an increasingly influential position in the philosophy of set theory (Balaguer [1998], Linksy and Zalta [1995], Hamkins [2012]). There is considerable room for debate about how best to formulate set-theoretic pluralism, and even about whether the view is coherent. But there is widespread agreement as to what there is to recommend the view (given that it can be formulated coherently). Unlike set-theoretic universalism, set-theoretic pluralism affords an answer to Benacerraf’s epistemological challenge. The purpose of this paper is (...)
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  • Is There a Reliability Challenge for Logic?Joshua Schechter - 2018 - Philosophical Issues 28 (1):325-347.
    There are many domains about which we think we are reliable. When there is prima facie reason to believe that there is no satisfying explanation of our reliability about a domain given our background views about the world, this generates a challenge to our reliability about the domain or to our background views. This is what is often called the reliability challenge for the domain. In previous work, I discussed the reliability challenges for logic and for deductive inference. I argued (...)
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  • Deflationary Nominalism and Puzzle Avoidance.David Mark Kovacs - 2019 - Philosophia Mathematica 27 (1):88-104.
    In a series of works, Jody Azzouni has defended deflationary nominalism, the view that certain sentences quantifying over mathematical objects are literally true, although such objects do not exist. One alleged attraction of this view is that it avoids various philosophical puzzles about mathematical objects. I argue that this thought is misguided. I first develop an ontologically neutral counterpart of Field’s reliability challenge and argue that deflationary nominalism offers no distinctive answer to it. I then show how this reasoning generalizes (...)
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  • A Reliability Challenge to Theistic Platonism.Dan Baras - 2017 - Analysis 77 (3):479-487.
    Many philosophers believe that when a theory is committed to an apparently unexplainable massive correlation, that fact counts significantly against the theory. Philosophical theories that imply that we have knowledge of non-causal mind-independent facts are especially prone to this objection. Prominent examples of such theories are mathematical Platonism, robust normative realism and modal realism. It is sometimes thought that theists can easily respond to this sort of challenge and that theism therefore has an epistemic advantage over atheism. In this paper, (...)
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  • Debunking Arguments: Mathematics, Logic, and Modal Security.Justin Clarke-Doane - forthcoming - In Robert Richards and Michael Ruse (ed.), The Cambridge Handbook of Evolutionary Ethics. Cambridge University Press.
    I discuss the structure of genealogical debunking arguments. I argue that they undermine our mathematical beliefs if they undermine our moral beliefs. The contrary appearance stems from a confusion of arithmetic truths with (first-order) logical truths, or from a confusion of reliability with justification. I conclude with a discussion of the cogency of debunking arguments, in light of the above. Their cogency depends on whether information can undermine all of our beliefs of a kind, F, without giving us direct reason (...)
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  • Objectivity and Reliability.Justin Clarke-Doane - 2017 - Canadian Journal of Philosophy 47 (6):841-855.
    Scanlon’s Being Realistic about Reasons (BRR) is a beautiful book – sleek, sophisticated, and programmatic. One of its key aims is to demystify knowledge of normative and mathematical truths. In this article, I develop an epistemological problem that Scanlon fails to explicitly address. I argue that his “metaphysical pluralism” can be understood as a response to that problem. However, it resolves the problem only if it undercuts the objectivity of normative and mathematical inquiry.
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  • Darwinism in Metaethics: What If the Universal Acid Cannot Be Contained?Eleonora Severini & Fabio Sterpetti - 2017 - History and Philosophy of the Life Sciences 39 (3):1-25.
    The aim of this article is to explore the impact of Darwinism in metaethics and dispel some of the confusion surrounding it. While the prospects for a Darwinian metaethics appear to be improving, some underlying epistemological issues remain unclear. We will focus on the so-called Evolutionary Debunking Arguments (EDAs) which, when applied in metaethics, are defined as arguments that appeal to the evolutionary origins of moral beliefs so as to undermine their epistemic justification. The point is that an epistemic disanalogy (...)
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  • What We Talk About When We Talk About Numbers.Richard Pettigrew - manuscript
    In this paper, I describe and motivate a new species of mathematical structuralism, which I call Instrumental Nominalism about Set-Theoretic Structuralism. As the name suggests, this approach takes standard Set-Theoretic Structuralism of the sort championed by Bourbaki and removes its ontological commitments by taking an instrumental nominalist approach to that ontology of the sort described by Joseph Melia and Gideon Rosen. I argue that this avoids all of the problems that plague other versions of structuralism.
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  • Mathematical Knowledge and Naturalism.Fabio Sterpetti - 2019 - Philosophia 47 (1):225-247.
    How should one conceive of the method of mathematics, if one takes a naturalist stance? Mathematical knowledge is regarded as the paradigm of certain knowledge, since mathematics is based on the axiomatic method. Natural science is deeply mathematized, and science is crucial for any naturalist perspective. But mathematics seems to provide a counterexample both to methodological and ontological naturalism. To face this problem, some naturalists try to naturalize mathematics relying on Darwinism. But several difficulties arise when one tries to naturalize (...)
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  • The Mystery of Moral Perception.Daniel Crow - 2016 - Journal of Moral Philosophy 13 (2):187-210.
    _ Source: _Page Count 24 Accounts of non-naturalist moral perception have been advertised as an empiricist-friendly epistemological alternative to moral rationalism. I argue that these accounts of moral perception conceal a core commitment of rationalism—to substantive a priori justification—and embody its most objectionable feature—namely, “mysteriousness.” Thus, accounts of non-naturalist moral perception do not amount to an interesting alternative to moral rationalism.
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  • Why Only Us? Language and Evolution By Robert C. Berwick and Noam Chomsky.Chris Daly - forthcoming - Analysis:any018.
    © The Author 2018. Published by Oxford University Press on behalf of The Analysis Trust. All rights reserved. For permissions, please email: journals.permissions@oup.comThis article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model...This is a clear and extremely stimulating book in which the authors present a series of innovative, even unorthodox, views on the relation between language and biology. It treats the study of language, and human cognition in general, as a matter of (...)
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  • Explanation in Ethics and Mathematics: Debunking and Dispensability. [REVIEW]David Faraci - 2018 - Analysis 78 (2):377-381.
    Explanation in Ethics and Mathematics: Debunking and Dispensability By LeibowitzUri D. and SinclairNeilOxford University Press, 2016. x + 258 pp. £45.00.
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  • Moral Skepticism and the Benacerraf Challenge.Tersman Folke - unknown
    The Benacerraf challenge is a well-known objection to Platonism in mathematics. Its proponent argues that, if mathematical entities are, as Platonists claim, mind-independent, causally inert, and existent beyond space and time, then we are led to a skeptical stance according to which it is not possible to explain how it is that we have cognitive access to the mathematical realm or how it is that our mathematical beliefs are reliable. It has been argued that a similar objection could be leveled (...)
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  • Why Only Us? Language and Evolution.Chris Daly - 2018 - Analysis 78 (2):381-383.
    Why Only Us? Language and Evolution By BerwickRobert C. and ChomskyNoamMassachusetts Institute of Technology, 2015. 224 pp. £17.95 paper.
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  • When Do Replies to the Evolutionary Debunking Argument Against Moral Realism Beg the Question?Justin Morton - 2018 - Australasian Journal of Philosophy 97 (2):265-280.
    ABSTRACTSome proponents of the evolutionary debunking argument against moral realism believe that replies that assume substantive moral claims beg the question. In this paper, I give a new account of what's wrong with such replies. On this account, many realists beg the question when they rely on substantive moral claims in their replies to the argument, but naturalists do not. While this account generalizes to some other domains, it allows perceptual and inductive realism to remain undebunked.
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  • Animal Cognition, Species Invariantism, and Mathematical Realism.Helen De Cruz - 2019 - In Andrew Aberdein & Matthew Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics. London: Bloomsbury Academic. pp. 39-61.
    What can we infer from numerical cognition about mathematical realism? In this paper, I will consider one aspect of numerical cognition that has received little attention in the literature: the remarkable similarities of numerical cognitive capacities across many animal species. This Invariantism in Numerical Cognition (INC) indicates that mathematics and morality are disanalogous in an important respect: proto-moral beliefs differ substantially between animal species, whereas proto-mathematical beliefs (at least in the animals studied) seem to show more similarities. This makes moral (...)
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  • Justification and Explanation in Mathematics and Morality.Justin Clarke-Doane - 2015 - In Russ Shafer-Landau (ed.), Oxford Studies in Metaethics: Volume 1. Oxford University Press.
    In an influential book, Gilbert Harman writes, "In explaining the observations that support a physical theory, scientists typically appeal to mathematical principles. On the other hand, one never seems to need to appeal in this way to moral principles [1977, 9 – 10]." What is the epistemological relevance of this contrast, if genuine? In this article, I argue that ethicists and philosophers of mathematics have misunderstood it. They have confused what I will call the justificatory challenge for realism about an (...)
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  • Objectivity in Ethics and Mathematics.Justin Clarke-Doane - 2015 - Proceedings of the Aristotelian Society: The Virtual Issue 3.
    How do axioms, or first principles, in ethics compare to those in mathematics? In this companion piece to G.C. Field's 1931 "On the Role of Definition in Ethics", I argue that there are similarities between the cases. However, these are premised on an assumption which can be questioned, and which highlights the peculiarity of normative inquiry.
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  • Qual a motivação para se defender uma teoria causal da memória?César Schirmer Dos Santos - 2018 - In Juliano Santos do Carmo & Rogério F. Saucedo Corrêa (eds.), Linguagem e cognição. Pelotas: NEPFil. pp. 63-89.
    Este texto tem como objetivo apresentar a principal motivação filosófica para se defender uma teoria causal da memória, que é explicar como pode um evento que se deu no passado estar relacionado a uma experiência mnêmica que se dá no presente. Para tanto, iniciaremos apresentando a noção de memória de maneira informal e geral, para depois apresentar elementos mais detalhados. Finalizamos apresentando uma teoria causal da memória que se beneficia da noção de veritação (truthmaking).
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  • The Access Problem for Knowledge of Logical Possibility.Sharon Berry - manuscript
    Accepting truth-value realism can seem to raise an explanatory problem: what can explain our accuracy about mathematics, i.e., the match between human psychology and objective mathematical facts? A range of current truth-value realist philosophies of mathematics allow one to reduce this access problem to a problem of explaining our accuracy about which mathematical practices are coherent -- in a sense which can be cashed out in terms of logical possibility. However, our ability to recognize these facts about logical possibility poses (...)
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  • Debunking and Disagreement.Folke Tersman - 2017 - Noûs 51 (4):754-774.
    The fact that debunkers can turn to the argument from disagreement for help is ofcourse not a surprise. After all, both types of challenge basically pursue the same,skeptical conclusion. What I have tried to show, however, is that they are related in amore intimate way.
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  • Epistemology Versus Non-Causal Realism.Jared Warren - 2017 - Synthese 194 (5).
    This paper formulates a general epistemological argument against what I call non-causal realism, generalizing domain specific arguments by Benacerraf, Field, and others. First I lay out the background to the argument, making a number of distinctions that are sometimes missed in discussions of epistemological arguments against realism. Then I define the target of the argument—non-causal realism—and argue that any non-causal realist theory, no matter the subject matter, cannot be given a reasonable epistemology and so should be rejected. Finally I discuss (...)
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