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Platonism in the Philosophy of Mathematics

In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (2009)

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  1. "That's Not the Issue": Against a Lightweight Interpretation of Ontological Disputes.Manuel J. Sanchís Ferrer - manuscript
    In this paper I argue against what I label as "Lightweight interpretation of ontological disputes". This interpretation criteria sees ontological disputes as metalinguistic negotiations concerning the pursuing of practical objectives. I have developed an argument, called "That's not the issue", which shows that this interpretation criteria is inapplicable to most ontological disputes.
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  • How Not To Use the Church-Turing Thesis Against Platonism.R. Urbaniak - 2011 - Philosophia Mathematica 19 (1):74-89.
    Olszewski claims that the Church-Turing thesis can be used in an argument against platonism in philosophy of mathematics. The key step of his argument employs an example of a supposedly effectively computable but not Turing-computable function. I argue that the process he describes is not an effective computation, and that the argument relies on the illegitimate conflation of effective computability with there being a way to find out . ‘Ah, but,’ you say, ‘what’s the use of its being right twice (...)
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  • Sosein as Subject Matter.Matteo Plebani - 2018 - Australasian Journal of Logic 15 (2):77-94.
    Meinongians in general, and Routley in particular, subscribe to the principle of the independence of Sosein from Sein. In this paper, I put forward an interpretation of the independence principle that philosophers working outside the Meinongian tradition can accept. Drawing on recent work by Stephen Yablo and others on the notion of subject matter, I offer a new account of the notion of Sosein as a subject matter and argue that in some cases Sosein might be independent from Sein. The (...)
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  • Plato or Platonism. A Topic in Descending Dialectic.Eduardo Luft - 2017 - Veritas – Revista de Filosofia da Pucrs 62 (2):407.
    ***Platão ou Platonismo. Um tópico em dialética descendente***A ontologia dialética pode ser reconstruída percorrendo dois caminhos complementares. A via ascendente parte da influência da ontologia de Platão, mediada por Nicolau de Cusa, sobre Bertalanffy, o fundador da teoria de sistemas. Esta abordagem teórica, uma vez convergindo com o darwinismo, dará nascimento à teoria dos sistemas adaptativos complexos e logo se espalhará pelas diversas ciências, transmudando-se de uma ontologia regional em parte relevante de uma nova ontologia geral. O caminho descendente, a (...)
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  • 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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  • Proposed Solutions to the Questions "Why Does a Thing Exist?" and "Why is There Something Rather Than Nothing?".Roger Granet - manuscript
    A solution to the question "Why is there something rather than nothing?" is proposed that also entails a proposed solution to the question "Why does a thing exist?". In brief, I propose that a thing exists if it is a grouping. A grouping ties stuff together into a unit whole and, in so doing, defines what is contained within that new unit whole. The grouping is physically or mentally present and is visually seen as an edge, boundary, or enclosing surface (...)
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  • Non‐Factualism Versus Nominalism.Matteo Plebani - 2017 - Pacific Philosophical Quarterly 98 (3).
    The platonism/nominalism debate in the philosophy of mathematics concerns the question whether numbers and other mathematical objects exist. Platonists believe the answer to be in the positive, nominalists in the negative. According to non-factualists, the question is ‘moot’, in the sense that it lacks a correct answer. Elaborating on ideas from Stephen Yablo, this article articulates a non-factualist position in the philosophy of mathematics and shows how the case for non-factualism entails that standard arguments for rival positions fail. In particular, (...)
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  • Thomistic Foundations for Moderate Realism About Mathematical Objects.Ryan Miller - 2021 - In Proceedings of the Eleventh International Thomistic Congress.
    Contemporary philosophers of mathematics are deadlocked between two alternative ontologies for numbers: Platonism and nominalism. According to contemporary mathematical Platonism, numbers are real abstract objects, i.e. particulars which are nonetheless “wholly nonphysical, nonmental, nonspatial, nontemporal, and noncausal.” While this view does justice to intuitions about numbers and mathematical semantics, it leaves unclear how we could ever learn anything by mathematical inquiry. Mathematical nominalism, by contrast, holds that numbers do not exist extra-mentally, which raises difficulties about how mathematical statements could be (...)
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  • Social Constructivism in Mathematics? The Promise and Shortcomings of Julian Cole’s Institutional Account.Jenni Rytilä - 2021 - Synthese 199 (3-4):11517-11540.
    The core idea of social constructivism in mathematics is that mathematical entities are social constructs that exist in virtue of social practices, similar to more familiar social entities like institutions and money. Julian C. Cole has presented an institutional version of social constructivism about mathematics based on John Searle’s theory of the construction of the social reality. In this paper, I consider what merits social constructivism has and examine how well Cole’s institutional account meets the challenge of accounting for the (...)
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  • ‘Just is’-Statements as Generalized Identities.Øystein Linnebo - 2014 - Inquiry: An Interdisciplinary Journal of Philosophy 57 (4):466-482.
    Identity is ordinarily taken to be a relation defined on all and only objects. This consensus is challenged by Agustín Rayo, who seeks to develop an analogue of the identity sign that can be flanked by sentences. This paper is a critical exploration of the attempted generalization. First the desired generalization is clarified and analyzed. Then it is argued that there is no notion of content that does the desired philosophical job, namely ensure that necessarily equivalent sentences coincide in this (...)
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  • Problemas de Metafísica Analítica / Problems in Analytical Metaphysics.Guido Imaguire & Rodrigo Reis Lastra Cid (eds.) - 2020 - Pelotas: Editora da UFPel / UFPel Publisher.
    O desenvolvimento da filosofia acadêmica no Brasil é direcionada, entre vários fatores, pelas investigações dos diversos Grupos de Trabalho (GTs) da Associação Nacional de Pós-Graduação em Filosofia (ANPOF). Esses GTs se dividem de acordo com a temática investigada. O GT de Metafísica Analítica é relativamente novo e ainda tem poucos membros, mas os temas nele trabalhados são variados e todos centrais no debate metafísico contemporâneo internacional. A sua investigação se caracteriza pelo rigor lógico e conceitual com o qual aborda esses (...)
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  • Metaphor and the Philosophical Implications of Embodied Mathematics.Bodo Winter & Jeff Yoshimi - 2020 - Frontiers in Psychology 11.
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  • Mathematical Platonism Meets Ontological Pluralism?Matteo Plebani - 2020 - Inquiry: An Interdisciplinary Journal of Philosophy 63 (6):655-673.
    Mathematical platonism is the view that abstract mathematical objects exist. Ontological pluralism is the view that there are many modes of existence. This paper examines the prospects for plural platonism, the view that results from combining mathematical platonism and ontological pluralism. I will argue that some forms of platonism are in harmony with ontological pluralism, while other forms of platonism are in tension with it. This shows that there are some interesting connections between the platonism–antiplatonism dispute and recent debates over (...)
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  • Uninstantiated Properties and Semi-Platonist Aristotelianism.James Franklin - 2015 - Review of Metaphysics 69 (1):25-45.
    A problem for Aristotelian realist accounts of universals (neither Platonist nor nominalist) is the status of those universals that happen not to be realised in the physical (or any other) world. They perhaps include uninstantiated shades of blue and huge infinite cardinals. Should they be altogether excluded (as in D.M. Armstrong's theory of universals) or accorded some sort of reality? Surely truths about ratios are true even of ratios that are too big to be instantiated - what is the truthmaker (...)
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  • Two Criticisms Against Mathematical Realism.Seungbae Park - 2017 - Diametros 52:96-106.
    Mathematical realism asserts that mathematical objects exist in the abstract world, and that a mathematical sentence is true or false, depending on whether the abstract world is as the mathematical sentence says it is. I raise two objections against mathematical realism. First, the abstract world is queer in that it allows for contradictory states of affairs. Second, mathematical realism does not have a theoretical resource to explain why a sentence about a tricle is true or false. A tricle is an (...)
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  • The Philosophy of Computer Science.Raymond Turner - 2013 - Stanford Encyclopedia of Philosophy.
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