Mathematical Platonism

Edited by Rafal Urbaniak (Uniwersytetu Gdanskiego, Uniwersytetu Gdanskiego)
Assistant editors: Sam Roberts, Pawel Pawlowski
About this topic
Summary Mathematical platonism is the view on which mathematical objects exist and are abstract (aspatial, atemporal and acausal) and independent of human minds and linguistic practices. According to mathematical platonism, mathematical theories are true in virtue of those objects possessing (or not) certain properties. One important challenge to platonism is explaining how biological organisms such as human beings could have knowledge of such objects. Another is to explain why mathematical theories about such objects should turn out to be applicable in sciences concerned with the physical world. 
Key works One of the most famous platonists was Frege (see e.g. Frege & Beaney 1997) and his line of thought is currently continued by neologicists (Wright 1983Wright & Hale 2001). Other famous platonists were Quine 2004 and Gödel 1947. Another group of platonists are structuralists, see the category summary for mathematical structuralism.
Introductions It's good to start with Linnebo 2014 and references therein. 
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  1. 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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  2. 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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  3. The philosophical implications of the loophole-free violation of Bell’s inequality: Quantum entanglement, timelessness, triple-aspect monism, mathematical Platonism and scientific morality.Gilbert B. Côté - manuscript
    The demonstration of a loophole-free violation of Bell's inequality by Hensen et al. (2015) leads to the inescapable conclusion that timelessness and abstractness exist alongside space-time. This finding is in full agreement with the triple-aspect monism of reality, with mathematical Platonism, free will and the eventual emergence of a scientific morality.
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  4. Platonism by the Numbers.Steven M. Duncan - manuscript
    In this paper, I defend traditional Platonic mathematical realism from its contemporary detractors, arguing that numbers, understood as abstract, non-physical objects of rational intuition, are indispensable for the act of counting.
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  5. Abstracta and Possibilia: Hyperintensional Foundations of Mathematical Platonism.David Elohim - manuscript
    This paper aims to provide hyperintensional 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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  6. The ontology of number.Jeremy Horne - manuscript
    What is a number? Answering this will answer questions about its philosophical foundations - rational numbers, the complex numbers, imaginary numbers. If we are to write or talk about something, it is helpful to know whether it exists, how it exists, and why it exists, just from a common-sense point of view [Quine, 1948, p. 6]. Generally, there does not seem to be any disagreement among mathematicians, scientists, and logicians about numbers existing in some way, but currently, in the mainstream (...)
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  7. A few historical-critical glances on mathematical ontology through the Hermann Weyl and Edmund Husserl works.Giuseppe Iurato - manuscript
    From the general history of culture, with a particular attention turned towards the personal and intellectual relationships between Hermann Weyl and Edmund Husserl, it will be possible to identify certain historical-critical moments from which a philosophical reflection concerning aspects of the ontology of mathematics may be carried out. In particular, a notable epistemological relevance of group theory methods will stand out.
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  8. Execution of the Universal Dream.Sergey Kljujkov - manuscript
    Even the ancient Greeks defined the Dream as a happy πόλις, Heraclitus - κόσμοπόλις, Socrates - ethical anthropology, Plato - Good, Hegel - absolute idea, Marx - communism... All of Humanity has made a lot of its survival experience for the realization of Dreams. Without any plan, to the touch to, only by the method of "trial and error" it aspired the Dream on unknown roads, which often stymied deadlocks. Among the many achieved results of Humanity by Plato's prompts, the (...)
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  9. Platonism and Intra-mathematical Explanation.Sam Baron - forthcoming - Philosophical Quarterly.
    I introduce an argument for Platonism based on intra-mathematical explanation: the explanation of one mathematical fact by another. The argument is important for two reasons. First, if the argument succeeds then it provides a basis for Platonism that does not proceed via standard indispensability considerations. Second, if the argument fails it can only do so for one of three reasons: either because there are no intra-mathematical explanations, or because not all explanations are backed by dependence relations, or because some form (...)
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  10. Why Can’t There Be Numbers?David Builes - forthcoming - The Philosophical Quarterly.
    Platonists affirm the existence of abstract mathematical objects, and Nominalists deny the existence of abstract mathematical objects. While there are standard arguments in favor of Nominalism, these arguments fail to account for the necessity of Nominalism. Furthermore, these arguments do nothing to explain why Nominalism is true. They only point to certain theoretical vices that might befall the Platonist. The goal of this paper is to formulate and defend a simple, valid argument for the necessity of Nominalism that seeks to (...)
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  11. Platonism, Nominalism, and Semantic Appearances.Justin Clarke-Doane - forthcoming - Logique Et Analyse.
    It is widely assumed that platonism with respect to a discourse of metaphysical interest, such as fictional or mathematical discourse, affords a better account of the semantic appearances than nominalism, other things being equal. Of course, other things may not be equal. For example, platonism is supposed to come at the cost of a plausible epistemology and ontology. But the hedged claim is often treated as a background assumption. It is motivated by the intuitively stronger one that the platonist can (...)
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  12. A Note on Consistency and Platonism.Alfredo Roque Freire & V. Alexis Peluce - forthcoming - In Alfredo Roque Freire & V. Alexis Peluce (eds.), 43rd International Wittgenstein Symposium proceedings.
    Is consistency the sort of thing that could provide a guide to mathematical ontology? If so, which notion of consistency suits this purpose? Mark Balaguer holds such a view in the context of platonism, the view that mathematical objects are non-causal, non-spatiotemporal, and non-mental. For the purposes of this paper, we will examine several notions of consistency with respect to how they can provide a platon-ist epistemology of mathematics. Only a Gödelian notion, we suggest, can provide a satisfactory guide to (...)
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  13. 43rd International Wittgenstein Symposium proceedings.Alfredo Roque Freire & V. Alexis Peluce (eds.) - forthcoming
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  14. Platonism in the Philosophy of Mathematics.Øystein Linnebo - forthcoming - Stanford Encyclopedia of Philosophy.
    Platonism about mathematics (or mathematical platonism) isthe metaphysical view that there are abstract mathematical objectswhose existence is independent of us and our language, thought, andpractices. Just as electrons and planets exist independently of us, sodo numbers and sets. And just as statements about electrons and planetsare made true or false by the objects with which they are concerned andthese objects' perfectly objective properties, so are statements aboutnumbers and sets. Mathematical truths are therefore discovered, notinvented., Existence. There are mathematical objects.
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  15. "On the platonism of more's" utopia".Harry Neumann - forthcoming - Social Research: An International Quarterly.
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  16. Some Versions of Platonism: Mathematics and Ontology According to Badiou.Christopher Norris - forthcoming - Philosophical Frontiers: Essays and Emerging Thoughts.
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  17. Ian Hacking, Why Is There Philosophy of Mathematics at All? [REVIEW]Max Harris Siegel - forthcoming - Mind 124.
  18. Neutrality and Force in Field's Epistemological Objection to Platonism.Ylwa Sjölin Wirling - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.
    Field’s challenge to platonists is the challenge to explain the reliable match between mathematical truth and belief. The challenge grounds an objection claiming that platonists cannot provide such an explanation. This objection is often taken to be both neutral with respect to controversial epistemological assumptions, and a comparatively forceful objection against platonists. I argue that these two characteristics are in tension: no construal of the objection in the current literature realises both, and there are strong reasons to think that no (...)
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  19. Who's afraid of mathematical platonism? An historical perspective.Dirk Schlimm - 2024 - In Karine Chemla, José Ferreiròs, Lizhen Ji, Erhard Scholz & Chang Wang (eds.), The Richness of the History of Mathematics. Springer. pp. 595-615.
    In "Plato's Ghost" Jeremy Gray presented many connections between mathematical practices in the nineteenth century and the rise of mathematical platonism in the context of more general developments, which he refers to as modernism. In this paper, I take up this theme and present a condensed discussion of some arguments put forward in favor of and against the view of mathematical platonism. In particular, I highlight some pressures that arose in the work of Frege, Cantor, and Gödel, which support adopting (...)
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  20. Elaine Landry.*Plato Was Not a Mathematical Platonist.Colin McLarty - 2023 - Philosophia Mathematica 31 (3):417-424.
    This book goes far beyond its title. Landry indeed surveys current definitions of “mathematical platonism” to show nothing like them applies to Socrates in Plat.
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  21. On What Ground Do Thin Objects Exist? In Search of the Cognitive Foundation of Number Concepts.Markus Pantsar - 2023 - Theoria 89 (3):298-313.
    Linnebo in 2018 argues that abstract objects like numbers are “thin” because they are only required to be referents of singular terms in abstraction principles, such as Hume's principle. As the specification of existence claims made by analytic truths (the abstraction principles), their existence does not make any substantial demands of the world; however, as Linnebo notes, there is a potential counter-argument concerning infinite regress against introducing objects this way. Against this, he argues that vicious regress is avoided in the (...)
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  22. Hilbert Mathematics versus Gödel Mathematics. III. Hilbert Mathematics by Itself, and Gödel Mathematics versus the Physical World within It: both as Its Particular Cases.Vasil Penchev - 2023 - Philosophy of Science eJournal (Elsevier: SSRN) 16 (47):1-46.
    The paper discusses Hilbert mathematics, a kind of Pythagorean mathematics, to which the physical world is a particular case. The parameter of the “distance between finiteness and infinity” is crucial. Any nonzero finite value of it features the particular case in the frameworks of Hilbert mathematics where the physical world appears “ex nihilo” by virtue of an only mathematical necessity or quantum information conservation physically. One does not need the mythical Big Bang which serves to concentrate all the violations of (...)
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  23. Mathematical Internal Realism.Tim Button - 2022 - In Sanjit Chakraborty & James Ferguson Conant (eds.), Engaging Putnam. Berlin, Germany: De Gruyter. pp. 157-182.
    In “Models and Reality” (1980), Putnam sketched a version of his internal realism as it might arise in the philosophy of mathematics. Here, I will develop that sketch. By combining Putnam’s model-theoretic arguments with Dummett’s reflections on Gödelian incompleteness, we arrive at (what I call) the Skolem-Gödel Antinomy. In brief: our mathematical concepts are perfectly precise; however, these perfectly precise mathematical concepts are manifested and acquired via a formal theory, which is understood in terms of a computable system of proof, (...)
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  24. The incubus of inter-translatability... a realist’s nightmare?: Penelope Rush: Ontology and the foundations of mathematics: talking past each other. New York: Cambridge University Press, 2022, 46 pp, $20 PB. [REVIEW]Nicholas Danne - 2022 - Metascience 32 (1):107-110.
  25. Platonism. Contributions of the 43rd International Wittgenstein Symposium.Herbert Hrachovec & Jakub Mácha (eds.) - 2022 - ALWS.
  26. The Price of Mathematical Scepticism.Paul Blain Levy - 2022 - Philosophia Mathematica 30 (3):283-305.
    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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  27. Embracing Scientific Realism.Seungbae Park - 2022 - Cham: Springer.
    This book provides philosophers of science with new theoretical resources for making their own contributions to the scientific realism debate. Readers will encounter old and new arguments for and against scientific realism. They will also be given useful tips for how to provide influential formulations of scientific realism and antirealism. Finally, they will see how scientific realism relates to scientific progress, scientific understanding, mathematical realism, and scientific practice.
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  28. Fermat’s last theorem proved in Hilbert arithmetic. II. Its proof in Hilbert arithmetic by the Kochen-Specker theorem with or without induction.Vasil Penchev - 2022 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (10):1-52.
    The paper is a continuation of another paper published as Part I. Now, the case of “n=3” is inferred as a corollary from the Kochen and Specker theorem (1967): the eventual solutions of Fermat’s equation for “n=3” would correspond to an admissible disjunctive division of qubit into two absolutely independent parts therefore versus the contextuality of any qubit, implied by the Kochen – Specker theorem. Incommensurability (implied by the absence of hidden variables) is considered as dual to quantum contextuality. The (...)
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  29. Fermat’s last theorem proved in Hilbert arithmetic. III. The quantum-information unification of Fermat’s last theorem and Gleason’s theorem.Vasil Penchev - 2022 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (12):1-30.
    The previous two parts of the paper demonstrate that the interpretation of Fermat’s last theorem (FLT) in Hilbert arithmetic meant both in a narrow sense and in a wide sense can suggest a proof by induction in Part I and by means of the Kochen - Specker theorem in Part II. The same interpretation can serve also for a proof FLT based on Gleason’s theorem and partly similar to that in Part II. The concept of (probabilistic) measure of a subspace (...)
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  30. How Can Mathematical Objects Be Real but Mind-Dependent?Hazhir Roshangar - 2022 - In Jakub Mácha & Herbert Hrachovec (eds.), PLATONISM: Contributions of the 43rd International Wittgenstein Symposium. Kirchberg am Wechsel: Austrian Ludwig Wittgenstein Society. pp. 159-161.
    Taking mathematics as a language based on empirical experience, I argue for an account of mathematics in which its objects are abstracta that describe and communicate the structure of reality based on some of our ancestral interactions with their environment. I argue that mathematics as a language is mostly invented. Nonetheless, in being a general description of reality it cannot be said that it is fictional; and as an intersubjective reality, mathematical objects can exist independent of any one person’s mind.
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  31. Înțelegerea lumii cu ajutorul matematicii.Gabriel Târziu - 2022 - Iași, Romania: Editura Universităţii „Alexandru Ioan Cuza”.
    Această carte face parte dintr-un curent recent din filosofia analitică de preocupare cu rolul matematicii în știință și se vrea a fi o contribuție la discuția filosofică recentă despre valoarea explicativă a matematicii în știință și despre contribuția acesteia la înțelegerea naturii. Obiectivul principal al cărții este prezentarea unei teorii filosofice cu privire la felul în care matematica poate contribui la înțelegerea fenomenelor naturii fără a juca un rol explicativ în raport cu acestea.
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  32. Are Euclid's Diagrams Representations? On an Argument by Ken Manders.David Waszek - 2022 - In Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics. The CSHPM 2019-2020 Volume. Birkhäuser. pp. 115-127.
    In his well-known paper on Euclid’s geometry, Ken Manders sketches an argument against conceiving the diagrams of the Elements in ‘semantic’ terms, that is, against treating them as representations—resting his case on Euclid’s striking use of ‘impossible’ diagrams in some proofs by contradiction. This paper spells out, clarifies and assesses Manders’s argument, showing that it only succeeds against a particular semantic view of diagrams and can be evaded by adopting others, but arguing that Manders nevertheless makes a compelling case that (...)
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  33. Unification and mathematical explanation in science.Sam Baron - 2021 - Synthese 199 (3-4):7339-7363.
    Mathematics clearly plays an important role in scientific explanation. Debate continues, however, over the kind of role that mathematics plays. I argue that if pure mathematical explananda and physical explananda are unified under a common explanation within science, then we have good reason to believe that mathematics is explanatory in its own right. The argument motivates the search for a new kind of scientific case study, a case in which pure mathematical facts and physical facts are explanatorily unified. I argue (...)
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  34. A Dilemma for Mathematical Constructivism.Samuel Kahn - 2021 - Axiomathes 31 (1):63-72.
    In this paper I argue that constructivism in mathematics faces a dilemma. In particular, I maintain that constructivism is unable to explain (i) the application of mathematics to nature and (ii) the intersubjectivity of mathematics unless (iii) it is conjoined with two theses that reduce it to a form of mathematical Platonism. The paper is divided into five sections. In the first section of the paper, I explain the difference between mathematical constructivism and mathematical Platonism and I outline my argument. (...)
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  35. The uncanny accuracy of God's mathematical beliefs.Robert Knowles - 2021 - Religious Studies 57 (2):333-352.
    I show how mathematical platonism combined with belief in the God of classical theism can respond to Field's epistemological objection. I defend an account of divine mathematical knowledge by showing that it falls out of an independently motivated general account of divine knowledge. I use this to explain the accuracy of God's mathematical beliefs, which in turn explains the accuracy of our own. My arguments provide good news for theistic platonists, while also shedding new light on Field's influential objection.
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  36. Models, structures, and the explanatory role of mathematics in empirical science.Mary Leng - 2021 - Synthese 199 (3-4):10415-10440.
    Are there genuine mathematical explanations of physical phenomena, and if so, how can mathematical theories, which are typically thought to concern abstract mathematical objects, explain contingent empirical matters? The answer, I argue, is in seeing an important range of mathematical explanations as structural explanations, where structural explanations explain a phenomenon by showing it to have been an inevitable consequence of the structural features instantiated in the physical system under consideration. Such explanations are best cast as deductive arguments which, by virtue (...)
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  37. Objectivity in Mathematics, Without Mathematical Objects†.Markus Pantsar - 2021 - Philosophia Mathematica 29 (3):318-352.
    I identify two reasons for believing in the objectivity of mathematical knowledge: apparent objectivity and applications in science. Focusing on arithmetic, I analyze platonism and cognitive nativism in terms of explaining these two reasons. After establishing that both theories run into difficulties, I present an alternative epistemological account that combines the theoretical frameworks of enculturation and cumulative cultural evolution. I show that this account can explain why arithmetical knowledge appears to be objective and has scientific applications. Finally, I will argue (...)
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  38. Quantum phenomenology as a “rigorous science”: the triad of epoché and the symmetries of information.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (48):1-18.
    Husserl (a mathematician by education) remained a few famous and notable philosophical “slogans” along with his innovative doctrine of phenomenology directed to transcend “reality” in a more general essence underlying both “body” and “mind” (after Descartes) and called sometimes “ontology” (terminologically following his notorious assistant Heidegger). Then, Husserl’s tradition can be tracked as an idea for philosophy to be reinterpreted in a way to be both generalized and mathenatizable in the final analysis. The paper offers a pattern borrowed from the (...)
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  39. Hilbert arithmetic as a Pythagorean arithmetic: arithmetic as transcendental.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (54):1-24.
    The paper considers a generalization of Peano arithmetic, Hilbert arithmetic as the basis of the world in a Pythagorean manner. Hilbert arithmetic unifies the foundations of mathematics (Peano arithmetic and set theory), foundations of physics (quantum mechanics and information), and philosophical transcendentalism (Husserl’s phenomenology) into a formal theory and mathematical structure literally following Husserl’s tracе of “philosophy as a rigorous science”. In the pathway to that objective, Hilbert arithmetic identifies by itself information related to finite sets and series and quantum (...)
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  40. New Foundations (Natural Language as a Complex System, or New Foundations for Philosophical Semantics, Epistemology and Metaphysics, Based on the Process-Socio-Environmental Conception of Linguistic Meaning and Knowledge).Gustavo Picazo - 2021 - Journal of Research in Humanities and Social Science 9 (6):33–44.
    In this article, I explore the consequences of two commonsensical premises in semantics and epistemology: (1) natural language is a complex system rooted in the communal life of human beings within a given environment; and (2) linguistic knowledge is essentially dependent on natural language. These premises lead me to emphasize the process-socio-environmental character of linguistic meaning and knowledge, from which I proceed to analyse a number of long-standing philosophical problems, attempting to throw new light upon them on these grounds. In (...)
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  41. Mr. Frege, The Platonist.Daniel Sierra - 2021 - Logiko-Filosofskie Studii 2 (Vol 19):136-144.
    Even though Frege is a major figure in the history of analytic philosophy, it is not surprising that there are still issues surrounding his views, interpreting them, and labeling them. Frege’s view on numbers is typically termed as ‘Platonistic’ or at least a type of Platonism (Reck 2005). Still, the term ‘Platonism’ has views and assumptions ascribed to it that may be misleading and leads to mischaracterizations of Frege’s outlook on numbers and ideas. So, clarification of the term ‘Platonism’ is (...)
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  42. Counterfactual Scheming.Sam Baron - 2020 - Mind 129 (514):535-562.
    Mathematics appears to play a genuine explanatory role in science. But how do mathematical explanations work? Recently, a counterfactual approach to mathematical explanation has been suggested. I argue that such a view fails to differentiate the explanatory uses of mathematics within science from the non-explanatory uses. I go on to offer a solution to this problem by combining elements of the counterfactual theory of explanation with elements of a unification theory of explanation. The result is a theory according to which (...)
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  43. A Sketch of Reality.Phillip Bricker - 2020 - In Modal Matters: Essays in Metaphysics. Oxford: Oxford University Press. pp. 3-39.
    In this introductory chapter to my collection of papers, Modal Matters, I present my tripartite account of reality. First, I endorse a plenitudinous Platonism: for every consistent mathematical theory, there is in reality a mathematical system in which the theory is true. Second, for any way of distributing fundamental qualitative properties over mathematical structures, there is a portion of reality that has that structure with fundamental properties distributed in that way; some of these portions of reality, when isolated, are the (...)
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  44. Realism without parochialism.Phillip Bricker - 2020 - In Modal Matters: Essays in Metaphysics. Oxford: Oxford University Press. pp. 40-76.
    I am a realist of a metaphysical stripe. I believe in an immense realm of "modal" and "abstract" entities, of entities that are neither part of, nor stand in any causal relation to, the actual, concrete world. For starters: I believe in possible worlds and individuals; in propositions, properties, and relations (both abundantly and sparsely conceived); in mathematical objects and structures; and in sets (or classes) of whatever I believe in. Call these sorts of entity, and the reality they comprise, (...)
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  45. Set-theoretic pluralism and the Benacerraf problem.Justin Clarke-Doane - 2020 - Philosophical Studies 177 (7):2013-2030.
    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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  46. Morality and Mathematics.Justin Clarke-Doane - 2020 - Oxford, England: Oxford University Press.
    To what extent are the subjects of our thoughts and talk real? This is the question of realism. In this book, Justin Clarke-Doane explores arguments for and against moral realism and mathematical realism, how they interact, and what they can tell us about areas of philosophical interest more generally. He argues that, contrary to widespread belief, our mathematical beliefs have no better claim to being self-evident or provable than our moral beliefs. Nor do our mathematical beliefs have better claim to (...)
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  47. How to make reflectance a surface property.Nicholas Danne - 2020 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 70:19-27.
    Reflectance physicalists define reflectance as the intrinsic disposition of a surface to reflect finite-duration light pulses at a given efficiency per wavelength. I criticize the received view of dispositional reflectance (David R. Hilbert’s) for failing to account for what I call “harmonic dispersion,” the inverse relationship of a light pulse's duration to its bandwidth. I argue that harmonic dispersion renders reflectance defined in terms of light pulses an extrinsic disposition. Reflectance defined as the per-wavelength efficiency to reflect the superimposed, infinite-duration, (...)
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  48. Ptolemy’s Philosophy: Mathematics as a Way of Life. By Jacqueline Feke. Princeton: Princeton University Press, 2018. Pp. xi + 234. [REVIEW]Nicholas Danne - 2020 - Metaphilosophy 51 (1):151-155.
  49. The Metametaphysics of Neo-Fregeanism.Matti Eklund - 2020 - In Ricki Bliss & James Miller (eds.), The Routledge Handbook of Metametaphysics. New York, NY: Routledge.
  50. Representational indispensability and ontological commitment.John Heron - 2020 - Thought: A Journal of Philosophy 9 (2):105-114.
    Recent debates about mathematical ontology are guided by the view that Platonism's prospects depend on mathematics' explanatory role in science. If mathematics plays an explanatory role, and in the right kind of way, this carries ontological commitment to mathematical objects. Conversely, the assumption goes, if mathematics merely plays a representational role then our world-oriented uses of mathematics fail to commit us to mathematical objects. I argue that it is a mistake to think that mathematical representation is necessarily ontologically innocent and (...)
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