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  1. added 2018-10-01
    Deflationary Nominalism and Puzzle Avoidance.David Mark Kovacs - forthcoming - Philosophia Mathematica:nky019.
    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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  2. added 2018-02-18
    Conjoining Mathematical Empiricism with Mathematical Realism: Maddy’s Account of Set Perception Revisited.Alex Levine - 2005 - Synthese 145 (3):425-448.
    Penelope Maddy's original solution to the dilemma posed by Benacerraf in his 'Mathematical Truth' was to reconcile mathematical empiricism with mathematical realism by arguing that we can perceive realistically construed sets. Though her hypothesis has attracted considerable critical attention, much of it, in my view, misses the point. In this paper I vigorously defend Maddy's account against published criticisms, not because I think it is true, but because these criticisms have functioned to obscure a more fundamental issue that is well (...)
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  3. added 2018-02-17
    On Field’s Epistemological Argument Against Platonism.Ivan Kasa - 2010 - Studia Logica 96 (2):141-147.
    Hartry Field's formulation of an epistemological argument against platonism is only valid if knowledge is constrained by a causal clause. Contrary to recent claims (e.g. in Liggins (2006), Liggins (2010)), Field's argument therefore fails the very same criterion usually taken to discredit Benacerraf's earlier version.
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  4. added 2018-02-17
    Uma Solução para o Problema de Benacerraf.Eduardo Castro - 2009 - Principia: An International Journal of Epistemology 13 (1):7-28.
    The Benacerraf’s problem is a problem about how we can attain mathematical knowledge: mathematical entities are entities not located in space-time; we exist in spacetime; so, it does not seem that we could have a causal connection with mathematical entities in order to attain mathematical knowledge. In this paper, I propose a solution to the Benacerraf’s problem supported by the Quinean doctrines of naturalism, confirmational holism and postulation. I show that we have empirical knowledge of centres of mass and of (...)
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  5. added 2017-11-20
    Autonomy Platonism and the Indispensability Argument. By Russell Marcus. Lanham, Md.: Lexington Books, 2015. Pp. Xii + 247. [REVIEW]Nicholas Danne - 2017 - Metaphilosophy 48 (4):591-594.
  6. added 2017-10-17
    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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  7. added 2017-10-17
    Coincidence Avoidance and Formulating the Access Problem.Sharon Berry - manuscript
    In this paper I discuss a trivialization worry for currently popular formulations of the `access problem' in philosophy of mathematics. I argue that we can avoid this worry by relating access worries to general epistemic norms of coincidence avoidance. Specifically, I propose that a realist theory of some domain of investigation (such as mathematics or morals) \textit{faces an access problem} to the extent that accepting this theory commits one to positing \textit{any} extra unexplained coincidence beyond those required by competing deflationary (...)
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  8. added 2017-10-05
    Rejecting Mathematical Realism While Accepting Interactive Realism.Seungbae Park - 2018 - Analysis and Metaphysics 17:7-21.
    Indispensablists contend that accepting scientific realism while rejecting mathematical realism involves a double standard. I refute this contention by developing an enhanced version of scientific realism, which I call interactive realism. It holds that interactively successful theories are typically approximately true, and that the interactive unobservable entities posited by them are likely to exist. It is immune to the pessimistic induction while mathematical realism is susceptible to it.
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  9. added 2017-06-20
    Review of Leibowtiz and Sinclair (Eds.) Explanation in Ethics and Mathematics: Debunking and Dispensability. [REVIEW]Karl Schafer - 2017 - Notre Dame Philosophical Reviews 2017.
  10. added 2017-06-14
    The Modal Status of Contextually A Priori Arithmetical Truths.Markus Pantsar - 2016 - In Andrea Sereni & Francesca Boccuni (eds.), Objectivity, Realism, and Proof. Springer International Publishing. pp. 67-79.
    In Pantsar (2014), an outline for an empirically feasible epistemological theory of arithmetic is presented. According to that theory, arithmetical knowledge is based on biological primitives but in the resulting empirical context develops an essentially a priori character. Such contextual a priori theory of arithmetical knowledge can explain two of the three characteristics that are usually associated with mathematical knowledge: that it appears to be a priori and objective. In this paper it is argued that it can also explain the (...)
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  11. added 2016-12-08
    Epistemological Challenges to Mathematical Platonism.Øystein Linnebo - 2006 - Philosophical Studies 129 (3):545-574.
    Since Benacerraf’s “Mathematical Truth” a number of epistemological challenges have been launched against mathematical platonism. I first argue that these challenges fail because they unduely assimilate mathematics to empirical science. Then I develop an improved challenge which is immune to this criticism. Very roughly, what I demand is an account of how people’s mathematical beliefs are responsive to the truth of these beliefs. Finally I argue that if we employ a semantic truth-predicate rather than just a deflationary one, there surprisingly (...)
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  12. added 2016-01-12
    To Bridge Gödel’s Gap.Eileen S. Nutting - 2016 - Philosophical Studies 173 (8):2133-2150.
    In “Mathematical Truth,” Paul Benacerraf raises an epistemic challenge for mathematical platonists. In this paper, I examine the assumptions that motivate Benacerraf’s original challenge, and use them to construct a new causal challenge for the epistemology of mathematics. This new challenge, which I call ‘Gödel’s Gap’, appeals to intuitive insights into mathematical knowledge. Though it is a causal challenge, it does not rely on any obviously objectionable constraints on knowledge. As a result, it is more compelling than the original challenge. (...)
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  13. added 2016-01-08
    Debunking Arguments: Mathematics, Logic, and Modal Security.Justin Clarke-Doane - forthcoming - In Robert Richards and Michael Ruse (ed.), 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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  14. added 2015-12-01
    Reliability in Mathematical Physics.Michael Liston - 1993 - Philosophy of Science 60 (1):1-21.
    In this paper I argue three things: (1) that the interactionist view underlying Benacerraf's (1973) challenge to mathematical beliefs renders inexplicable the reliability of most of our beliefs in physics; (2) that examples from mathematical physics suggest that we should view reliability differently; and (3) that abstract mathematical considerations are indispensable to explanations of the reliability of our beliefs.
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  15. added 2015-07-10
    Debunking and Dispensability.Justin Clarke-Doane - 2016 - In Uri D. Leibowitz & Neil Sinclair (eds.), Explanation in Ethics and Mathematics: Debunking and Dispensability. Oxford University Press.
    In his précis of a recent book, Richard Joyce writes, “My contention…is that…any epistemological benefit-of-the-doubt that might have been extended to moral beliefs…will be neutralized by the availability of an empirically confirmed moral genealogy that nowhere…presupposes their truth.” Such reasoning – falling under the heading “Genealogical Debunking Arguments” – is now commonplace. But how might “the availability of an empirically confirmed moral genealogy that nowhere… presupposes” the truth of our moral beliefs “neutralize” whatever “epistemological benefit-of-the-doubt that might have been extended (...)
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  16. added 2014-06-21
    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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  17. added 2014-03-17
    Mathematical Knowledge.Mary Leng, Alexander Paseau & Michael Potter (eds.) - 2007 - Oxford University Press.
    What is the nature of mathematical knowledge? Is it anything like scientific knowledge or is it sui generis? How do we acquire it? Should we believe what mathematicians themselves tell us about it? Are mathematical concepts innate or acquired? Eight new essays offer answers to these and many other questions. Written by some of the world's leading philosophers of mathematics, psychologists, and mathematicians, Mathematical Knowledge gives a lively sense of the current state of debate in this fascinating field. Contents 1. (...)
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  18. added 2014-03-08
    What is the Benacerraf Problem?Justin Clarke-Doane - 2017 - In Fabrice Pataut (ed.), New Perspectives on the Philosophy of Paul Benacerraf: Truth, Objects, Infinity.
    In "Mathematical Truth", Paul Benacerraf articulated an epistemological problem for mathematical realism. His formulation of the problem relied on a causal theory of knowledge which is now widely rejected. But it is generally agreed that Benacerraf was onto a genuine problem for mathematical realism nevertheless. Hartry Field describes it as the problem of explaining the reliability of our mathematical beliefs, realistically construed. In this paper, I argue that the Benacerraf Problem cannot be made out. There simply is no intelligible problem (...)
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  19. added 2014-03-07
    Epistemological Objections to Platonism.David Liggins - 2010 - Philosophy Compass 5 (1):67-77.
    Many philosophers posit abstract entities – where something is abstract if it is acausal and lacks spatio-temporal location. Theories, types, characteristics, meanings, values and responsibilities are all good candidates for abstractness. Such things raise an epistemological puzzle: if they are abstract, then how can we have any epistemic access to how they are? If they are invisible, intangible and never make anything happen, then how can we ever discover anything about them? In this article, I critically examine epistemological objections to (...)
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  20. added 2013-05-08
    Moral Epistemology: The Mathematics Analogy.Justin Clarke-Doane - 2014 - Noûs 48 (2):238-255.
    There is a long tradition comparing moral knowledge to mathematical knowledge. In this paper, I discuss apparent similarities and differences between knowledge in the two areas, realistically conceived. I argue that many of these are only apparent, while others are less philosophically significant than might be thought. The picture that emerges is surprising. There are definitely differences between epistemological arguments in the two areas. However, these differences, if anything, increase the plausibility of moral realism as compared to mathematical realism. It (...)
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  21. added 2013-02-08
    Between Mathematics and Physics.Michael D. Resnik - 1990 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1990:369 - 378.
    Nothing has been more central to philosophy of mathematics than the distinction between mathematical and physical objects. Yet consideration of quantum particles shows the inadequacy of the popular spacetime and causal characterizations of the distinction. It also raises problems for an assumption used recently by Field, Hellman and Horgan, namely, that the mathematical realm is metaphysically independent of the physical one.
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  22. added 2013-01-05
    Mathematics, Science and Ontology.Thomas Tymoczko - 1991 - Synthese 88 (2):201 - 228.
    According to quasi-empiricism, mathematics is very like a branch of natural science. But if mathematics is like a branch of science, and science studies real objects, then mathematics should study real objects. Thus a quasi-empirical account of mathematics must answer the old epistemological question: How is knowledge of abstract objects possible? This paper attempts to show how it is possible.The second section examines the problem as it was posed by Benacerraf in Mathematical Truth and the next section presents a way (...)
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  23. added 2012-12-16
    Ontology, Modality, and Mathematics: Remarks on Chihara's Constructibility Theory.Stephen Puryear - 2000 - Dissertation, Texas A&M University
    Chihara seeks to avoid commitment to mathematical objects by replacing traditional assertions of the existence of mathematical objects with assertions about possibilities of constructing certain open-sentence tokens. I argue that Chihara's project can be defended against several important objections, but that it is no less epistemologically problematic than its platonistic competitors.
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  24. added 2011-06-18
    What Mathematical Knowledge Could Not Be.Philip A. Ebert - 2007 - Aporia 1 (1):46-70.
    This is an introductory survey article to the philosophy of mathematics. I provide a detailed account of what Benacerraf’s problem is and then discuss in general terms four different approaches to ….
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  25. added 2011-06-18
    Testing the Philosophy of Mathematics in the History of Mathematics.Eduard Glas - 1989 - Studies in History and Philosophy of Science Part A 20 (1):115-131.
    Recent philosophical accounts of mathematics increasingly focus on the quasi-Empirical rather than the formal aspects of the field, The praxis of how mathematics is done rather than the idealized logical structure and foundations of the theory. The ultimate test of any philosophy of mathematics, However idealized, Is its ability to account adequately for the factual development of the subject in real time. As a text case, The works and views of felix klein (1849-1925) were studied. Major advances in mathematics turn (...)
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  26. added 2011-06-18
    Realism, Mathematics & Modality.Hartry Field - 1989 - Blackwell.
  27. added 2011-06-18
    Realism, Mathematics and Modality.Hartry Field - 1988 - Philosophical Topics 16 (1):57-107.
  28. added 2011-06-06
    Morality and Mathematics: The Evolutionary Challenge.Justin Clarke-Doane - 2012 - Ethics 122 (2):313-340.
    It is commonly suggested that evolutionary considerations generate an epistemological challenge for moral realism. At first approximation, the challenge for the moral realist is to explain our having many true moral beliefs, given that those beliefs are the products of evolutionary forces that would be indifferent to the moral truth. An important question surrounding this challenge is the extent to which it generalizes. In particular, it is of interest whether the Evolutionary Challenge for moral realism is equally a challenge for (...)
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  29. added 2011-05-26
    Benacerraf and Mathematical Truth.Richard Creath - 1980 - Philosophical Studies 37 (4):335 - 340.
  30. added 2010-11-03
    What is the Problem of Mathematical Knowledge?Michael Potter - 2007 - In Michael Potter, Mary Leng & Alexander Paseau (eds.), Mathematical Knowledge.
    Suggests that the recent emphasis on Benacerraf's access problem locates the peculiarity of mathematical knowledge in the wrong place. Instead we should focus on the sense in which mathematical concepts are or might be "armchair concepts" – concepts about which non-trivial knowledge is obtainable a priori.
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  31. added 2010-05-07
    The Epistemology of Geometry I: The Problem of Exactness.Anne Newstead & Franklin James - 2010 - Proceedings of the Australasian Society for Cognitive Science 2009.
    We show how an epistemology informed by cognitive science promises to shed light on an ancient problem in the philosophy of mathematics: the problem of exactness. The problem of exactness arises because geometrical knowledge is thought to concern perfect geometrical forms, whereas the embodiment of such forms in the natural world may be imperfect. There thus arises an apparent mismatch between mathematical concepts and physical reality. We propose that the problem can be solved by emphasizing the ways in which the (...)
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  32. added 2010-03-27
    Reliabilism, Intuition, and Mathematical Knowledge.Jennifer Wilson Mulnix - 2008 - Filozofia 62 (8):715-723.
    It is alleged that the causal inertness of abstract objects and the causal conditions of certain naturalized epistemologies precludes the possibility of mathematical know- ledge. This paper rejects this alleged incompatibility, while also maintaining that the objects of mathematical beliefs are abstract objects, by incorporating a naturalistically acceptable account of ‘rational intuition.’ On this view, rational intuition consists in a non-inferential belief-forming process where the entertaining of propositions or certain contemplations results in true beliefs. This view is free of any (...)
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  33. added 2009-08-04
    Some Recent Appeals to Mathematical Experience.Michael J. Shaffer - 2006 - Principia 10 (2):143-170.
    ome recent work by philosophers of mathematics has been aimed at showing that our knowledge of the existence of at least some mathematical objects and/or sets can be epistemically grounded by appealing to perceptual experience. The sensory capacity that they refer to in doing so is the ability to perceive numbers, mathematical properties and/or sets. The chief defense of this view as it applies to the perception of sets is found in Penelope Maddy’s Realism in Mathematics, but a number of (...)
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  34. added 2009-04-13
    Halfway Up To the Mathematical Infinity I: On the Ontological & Epistemic Sustainability of Georg Cantor’s Transfinite Design.Edward G. Belaga - manuscript
    Georg Cantor was the genuine discoverer of the Mathematical Infinity, and whatever he claimed, suggested, or even surmised should be taken seriously -- albeit not necessary at its face value. Because alongside his exquisite in beauty ordinal construction and his fundamental powerset description of the continuum, Cantor has also left to us his obsessive presumption that the universe of sets should be subjected to laws similar to those governing the set of natural numbers, including the universal principles of cardinal comparability (...)
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  35. added 2008-12-31
    Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.