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  1. added 2017-12-12
    An Intrinsic Theory of Quantum Mechanics: Progress in Field's Nominalistic Program, Part I.Eddy Keming Chen - manuscript
    In this paper, I introduce an intrinsic account of the quantum state. This account contains three desirable features that the standard platonistic account lacks: (1) it does not refer to any abstract mathematical objects such as complex numbers, (2) it is independent of the usual arbitrary conventions in the wave function representation, and (3) it explains why the quantum state has its amplitude and phase degrees of freedom. -/- Consequently, this account extends Hartry Field’s program outlined in Science Without Numbers (...)
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  2. added 2017-11-01
    Can Mathematical Objects Be Causally Efficacious?Seungbae Park - 2018 - Inquiry: An Interdisciplinary Journal of Philosophy:00-00.
    Callard (2007) argues that it is metaphysically possible that a mathematical object, although abstract, causally affects the brain. I raise the following objections. First, a successful defence of mathematical realism requires not merely the metaphysical possibility but rather the actuality that a mathematical object affects the brain. Second, mathematical realists need to confront a set of three pertinent issues: why a mathematical object does not affect other concrete objects and other mathematical objects, what counts as a mathematical object, and how (...)
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  3. added 2017-08-13
    Hilbert's Program Then and Now.Richard Zach - 2007 - In Dale Jacquette (ed.), Philosophy of Logic. Amsterdam: North Holland. pp. 411–447.
    Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, “finitary” means, one should give proofs of the consistency of these axiomatic systems. Although Gödel’s incompleteness theorems show that the program as originally conceived cannot be carried out, it had many partial (...)
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  4. added 2017-08-13
    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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  5. added 2017-07-10
    Boarding Neurath's Boat: The Early Development of Quine's Naturalism.Sander Verhaegh - 2017 - Journal of the History of Philosophy 55 (2):317-342.
    W. V. Quine is arguably the intellectual father of contemporary naturalism, the idea that there is no distinctively philosophical perspective on reality. Yet, even though Quine has always been a science-minded philosopher, he did not adopt a fully naturalistic perspective until the early 1950s. In this paper, I reconstruct the genesis of Quine’s ideas on the relation between science and philosophy. Scrutinizing his unpublished papers and notebooks, I examine Quine’s development in the first decades of his career. After identifying three (...)
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  6. added 2017-06-17
    Optimal Representations and the Enhanced Indispensability Argument.Manuel Barrantes - 2017 - Synthese:1-17.
    The Enhanced Indispensability Argument (EIA) appeals to the existence of Mathematical Explanations of Physical Phenomena (MEPPs) to justify mathematical Platonism, following the principle of Inference to the Best Explanation. In this paper, I examine one example of a MEPP —the explanation of the 13-year and 17-year life cycle of magicicadas— and argue that this case cannot be used to justify mathematical Platonism. I then generalize my analysis of the cicada case to other MEPPs, and show that these explanations rely on (...)
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  7. added 2017-06-01
    Number Words as Number Names.Friederike Moltmann - 2017 - Linguistics and Philosophy 40 (4):331-345.
    This paper critically evaluates the view according to which number words in argument position retain the meaning they have when occurring as determiners or adjectives. In particular, it argues against syntactic evidence from German given by myself in support of that view.
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  8. added 2016-09-15
    Numerical Cognition and Mathematical Realism.Helen De Cruz - 2016 - Philosophers' Imprint 16.
    Humans and other animals have an evolved ability to detect discrete magnitudes in their environment. Does this observation support evolutionary debunking arguments against mathematical realism, as has been recently argued by Clarke-Doane, or does it bolster mathematical realism, as authors such as Joyce and Sinnott-Armstrong have assumed? To find out, we need to pay closer attention to the features of evolved numerical cognition. I provide a detailed examination of the functional properties of evolved numerical cognition, and propose that they prima (...)
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  9. added 2015-04-22
    Mathematics as Make-Believe: A Constructive Empiricist Account.Sarah Elizabeth Hoffman - 1999 - Dissertation, University of Alberta (Canada)
    Any philosophy of science ought to have something to say about the nature of mathematics, especially an account like constructive empiricism in which mathematical concepts like model and isomorphism play a central role. This thesis is a contribution to the larger project of formulating a constructive empiricist account of mathematics. The philosophy of mathematics developed is fictionalist, with an anti-realist metaphysics. In the thesis, van Fraassen's constructive empiricism is defended and various accounts of mathematics are considered and rejected. Constructive empiricism (...)
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  10. added 2014-09-06
    Tarski's Nominalism.Greg Frost-Arnold - 2008 - In Douglas Patterson (ed.), New Essays on Tarski and Philosophy. Oxford University Press.
    Alfred Tarski was a nominalist. But he published almost nothing on his nominalist views, and until recently the only sources scholars had for studying Tarski’s nominalism were conversational reports from his friends and colleagues. However, a recently-discovered archival resource provides the most detailed information yet about Tarski’s nominalism. Tarski spent the academic year 1940-41 at Harvard, along with many of the leading lights of scientific philosophy: Carnap, Quine, Hempel, Goodman, and (for the fall semester) Russell. This group met frequently to (...)
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  11. added 2014-06-07
    Numbers Versus Nominalists.Nathan Salmon - 2008 - Analysis 68 (3):177–182.
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  12. added 2014-04-02
    Abstract Expressionism and the Communication Problem.David Liggins - 2014 - British Journal for the Philosophy of Science 65 (3):599-620.
    Some philosophers have recently suggested that the reason mathematics is useful in science is that it expands our expressive capacities. Of these philosophers, only Stephen Yablo has put forward a detailed account of how mathematics brings this advantage. In this article, I set out Yablo’s view and argue that it is implausible. Then, I introduce a simpler account and show it is a serious rival to Yablo’s. 1 Introduction2 Yablo’s Expressionism3 Psychological Objections to Yablo’s Expressionism4 Introducing Belief Expressionism5 Objections and (...)
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  13. added 2014-03-07
    Of Numbers and Electrons.Cian Dorr - 2010 - Proceedings of the Aristotelian Society 110 (2pt2):133-181.
    According to a tradition stemming from Quine and Putnam, we have the same broadly inductive reason for believing in numbers as we have for believing in electrons: certain theories that entail that there are numbers are better, qua explanations of our evidence, than any theories that do not. This paper investigates how modal theories of the form ‘Possibly, the concrete world is just as it in fact is and T’ and ‘Necessarily, if standard mathematics is true and the concrete world (...)
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  14. added 2014-03-06
    Inference to the Best Explanation and Mathematical Realism.Sorin Ioan Bangu - 2008 - Synthese 160 (1):13-20.
    Arguing for mathematical realism on the basis of Field’s explanationist version of the Quine–Putnam Indispensability argument, Alan Baker has recently claimed to have found an instance of a genuine mathematical explanation of a physical phenomenon. While I agree that Baker presents a very interesting example in which mathematics plays an essential explanatory role, I show that this example, and the argument built upon it, begs the question against the mathematical nominalist.
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  15. added 2013-08-23
    Names and Objects.Dan Kurth - manuscript
    In this paper I try to fortify the nominalistic objectology (cf. Meinong's 'Gegenstandstheorie') with essentialist means. This also is intended as a preparation for introducing Information Monism.
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  16. added 2013-08-21
    A Sketch of a Sirenia: Meros Theory.Dan Kurth - manuscript
    This sketch of a perhaps future 'Elementary Theory of the Category of Mereological Sums (including Mereological Wholes and Parts)' relates to my previous papers "The Topos of Emergence" and "Intelligible Gunk". I assert that for successfully categorizing Mereology one has to start with a specific setting of gunk. In this paper we will give a sketch of a categorically version of particular mereological structures. I.e. we will follow the example of F.W.Lawvere’s “An elementary theory of the category of sets” -/- (...)
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  17. added 2011-12-06
    Reference to Numbers in Natural Language.Friederike Moltmann - 2013 - Philosophical Studies 162 (3):499 - 536.
    A common view is that natural language treats numbers as abstract objects, with expressions like the number of planets, eight, as well as the number eight acting as referential terms referring to numbers. In this paper I will argue that this view about reference to numbers in natural language is fundamentally mistaken. A more thorough look at natural language reveals a very different view of the ontological status of natural numbers. On this view, numbers are not primarily treated abstract objects, (...)
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  18. added 2011-08-25
    Weaseling and the Content of Science.David Liggins - 2012 - Mind 121 (484):997-1005.
    I defend Joseph Melia’s nominalist account of mathematics from an objection raised by Mark Colyvan.
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  19. added 2010-05-17
    Anti-Nominalism Reconsidered.David Liggins - 2007 - Philosophical Quarterly 57 (226):104–111.
    Many philosophers of mathematics are attracted by nominalism – the doctrine that there are no sets, numbers, functions, or other mathematical objects. John Burgess and Gideon Rosen have put forward an intriguing argument against nominalism, based on the thought that philosophy cannot overrule internal mathematical and scientific standards of acceptability. I argue that Burgess and Rosen’s argument fails because it relies on a mistaken view of what the standards of mathematics require.
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  20. added 2009-04-14
    REVIEW OF Alfred Tarski, Collected Papers, Vols. 1-4 (1986) Edited by Steven Givant and Ralph McKenzie. [REVIEW]John Corcoran - 1991 - MATHEMATICAL REVIEWS 91 (h):01101-4.
    Alfred Tarski (1901--1983) is widely regarded as one of the two giants of twentieth-century logic and also as one of the four greatest logicians of all time (Aristotle, Frege and Gödel being the other three). Of the four, Tarski was the most prolific as a logician. The four volumes of his collected papers, which exclude most of his 19 monographs, span over 2500 pages. Aristotle's writings are comparable in volume, but most of the Aristotelian corpus is not about logic, whereas (...)
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