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 2009 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. A Geneticist's Roadmap to Sanity.Gilbert B. Côté - manuscript
    World news can be discouraging these days. In order to counteract the effects of fake news and corruption, scientists have a duty to present the truth and propose ethical solutions acceptable to the world at large. -/- By starting from scratch, we can lay down the scientific principles underlying our very existence, and reach reasonable conclusions on all major topics including quantum physics, infinity, timelessness, free will, mathematical Platonism, happiness, ethics and religion, all the way to creation and a special (...)
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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. 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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  6. 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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  7. Abstracta and Possibilia: Modal Foundations of Mathematical Platonism.Hasen Khudairi - manuscript
    This paper aims to provide modal 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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  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. How Can Mathematical Objects Be Real but Mind-Dependent?Hazhir Roshangar - manuscript
    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, and it is mind-dependent in a specific sense. However, the bases of mathematics will characterize it as a real, non-fictional science of structures.
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  10. An Intrinsic Theory of Quantum Mechanics: Progress in Field's Nominalistic Program, Part I.Eddy Keming Chen - 2017
    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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  11. Unification and mathematical explanation in science.Sam Baron - forthcoming - Synthese:1-25.
    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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  12. How Does God Know That 2 + 2 = 4?Andrew Brenner - forthcoming - Religious Studies:1-16.
    Sometimes theists wonder how God's beliefs track particular portions of reality, e.g. contingent states of affairs, or facts regarding future free actions. In this article I sketch a general model for how God's beliefs track reality. God's beliefs track reality in much the same way that propositions track reality, namely via grounding. Just as the truth values of true propositions are generally or always grounded in their truthmakers, so too God's true beliefs are grounded in the subject matters of those (...)
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  13. The Uncanny Accuracy of God's Mathematical Beliefs.Robert Knowles - forthcoming - Religious Studies.
    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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  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.
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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. 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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  19. 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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  20. 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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  21. 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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  22. 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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  23. 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.
  24. 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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  25. The Metametaphysics of Neo-Fregeanism.Matti Eklund - 2020 - In Ricki Bliss & James Miller (eds.), The Routledge Handbook of Metametaphysics. Routledge.
  26. Representational Indispensability and Ontological Commitment.John Heron - 2020 - Thought: A Journal of Philosophy 9 (2):105-114.
    Thought: A Journal of Philosophy, EarlyView.
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  27. Mathematical and Moral Disagreement.Silvia Jonas - 2020 - Philosophical Quarterly 70 (279):302-327.
    The existence of fundamental moral disagreements is a central problem for moral realism and has often been contrasted with an alleged absence of disagreement in mathematics. However, mathematicians do in fact disagree on fundamental questions, for example on which set-theoretic axioms are true, and some philosophers have argued that this increases the plausibility of moral vis-à-vis mathematical realism. I argue that the analogy between mathematical and moral disagreement is not as straightforward as those arguments present it. In particular, I argue (...)
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  28. Epistemic Modality, Mind, and Mathematics.Hasen Khudairi - 2020 - Dissertation, University of St Andrews
    This book concerns the foundations of epistemic modality. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality relates to the computational theory of mind; metaphysical modality; the types of mathematical modality; to the epistemic status of undecidable propositions and abstraction principles in the philosophy of mathematics; to the modal profile of rational propositional intuition; and to the (...)
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  29. The adverbial theory of numbers: some clarifications.Joongol Kim - 2020 - Synthese 197 (9):3981-4000.
    In a forthcoming paper in this journal, entitled “Bad company objection to Joongol Kim’s adverbial theory of numbers”, Namjoong Kim presents an ingenious Russell-style paradox based on an analogue of Kim’s definition of the number 1, and argues that Kim’s theory needs to provide a criterion of demarcation between acceptable and unacceptable definitions of adverbial entities. This paper addresses this ‘bad company’ objection and some other related issues concerning Kim’s adverbial theory by clarifying the purposes and uses of the formal (...)
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  30. A Reductionist Reading of Husserl’s Phenomenology by Mach’s Descriptivism and Phenomenalism.Vasil Penchev - 2020 - Continental Philosophy eJournal 13 (9):1-4.
    Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. A comparison to Mach’s doctrine is used to be revealed the fundamental and philosophical reductionism of Husserl’s phenomenology leading to a kind of Pythagoreanism in the final (...)
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  31. Two Deductions: (1) From the Totality to Quantum Information Conservation; (2) From the Latter to Dark Matter and Dark Energy.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (28):1-47.
    The paper discusses the origin of dark matter and dark energy from the concepts of time and the totality in the final analysis. Though both seem to be rather philosophical, nonetheless they are postulated axiomatically and interpreted physically, and the corresponding philosophical transcendentalism serves heuristically. The exposition of the article means to outline the “forest for the trees”, however, in an absolutely rigorous mathematical way, which to be explicated in detail in a future paper. The “two deductions” are two successive (...)
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  32. Why Do Certain States of Affairs Call Out for Explanation? A Critique of Two Horwichian Accounts.Dan Baras - 2019 - Philosophia 47 (5):1405-1419.
    Motivated by examples, many philosophers believe that there is a significant distinction between states of affairs that are striking and therefore call for explanation and states of affairs that are not striking. This idea underlies several influential debates in metaphysics, philosophy of mathematics, normative theory, philosophy of modality, and philosophy of science but is not fully elaborated or explored. This paper aims to address this lack of clear explanation first by clarifying the epistemological issue at hand. Then it introduces an (...)
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  33. Mathematical Explanation by Law.Sam Baron - 2019 - British Journal for the Philosophy of Science 70 (3):683-717.
    Call an explanation in which a non-mathematical fact is explained—in part or in whole—by mathematical facts: an extra-mathematical explanation. Such explanations have attracted a great deal of interest recently in arguments over mathematical realism. In this article, a theory of extra-mathematical explanation is developed. The theory is modelled on a deductive-nomological theory of scientific explanation. A basic DN account of extra-mathematical explanation is proposed and then redeveloped in the light of two difficulties that the basic theory faces. The final view (...)
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  34. 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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  35. Towards a Theory of Singular Thought About Abstract Mathematical Objects.James E. Davies - 2019 - Synthese 196 (10):4113-4136.
    This essay uses a mental files theory of singular thought—a theory saying that singular thought about and reference to a particular object requires possession of a mental store of information taken to be about that object—to explain how we could have such thoughts about abstract mathematical objects. After showing why we should want an explanation of this I argue that none of three main contemporary mental files theories of singular thought—acquaintance theory, semantic instrumentalism, and semantic cognitivism—can give it. I argue (...)
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  36. Mathematical Creation in Frege's Grundgesetze.Philip A. Ebert & Marcus Rossberg - 2019 - In Philip A. Ebert & Marcus Rossberg (eds.), Essays on Frege's Basic Laws of Arithmetic. Oxford: Oxford University Press. pp. 325-342.
  37. The Enhanced Indispensability Argument, the Circularity Problem, and the Interpretability Strategy.Jan Heylen & Lars Arthur Tump - 2019 - Synthese 198 (4):3033-3045.
    Within the context of the Quine–Putnam indispensability argument, one discussion about the status of mathematics is concerned with the ‘Enhanced Indispensability Argument’, which makes explicit in what way mathematics is supposed to be indispensable in science, namely explanatory. If there are genuine mathematical explanations of empirical phenomena, an argument for mathematical platonism could be extracted by using inference to the best explanation. The best explanation of the primeness of the life cycles of Periodical Cicadas is genuinely mathematical, according to Baker (...)
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  38. The Problem of Fregean Equivalents.Joongol Kim - 2019 - Dialectica 73 (3):367-394.
    It would seem that some statements like ‘There are exactly four moons of Jupiter’ and ‘The number of moons of Jupiter is four’ have the same truth-conditions and yet differ in ontological commitment. One strategy to resolve this paradoxical phenomenon is to insist that the statements have not only the same truth-conditions but also the same ontological commitments; the other strategy is to reject the presumption that they have the same truth-conditions. This paper critically examines some popular versions of these (...)
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  39. Easy Ontology Without Deflationary Metaontology.Daniel Z. Korman - 2019 - Philosophy and Phenomenological Research 99 (1):236-243.
    This is a contribution to a symposium on Amie Thomasson’s Ontology Made Easy (2015). Thomasson defends two deflationary theses: that philosophical questions about the existence of numbers, tables, properties, and other disputed entities can all easily be answered, and that there is something wrong with prolonged debates about whether such objects exist. I argue that the first thesis (properly understood) does not by itself entail the second. Rather, the case for deflationary metaontology rests largely on a controversial doctrine about the (...)
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  40. 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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  41. Hitting a Moving Target: Gödel, Carnap, and Mathematics as Logical Syntax.Gregory Lavers - 2019 - Philosophia Mathematica 27 (2):219-243.
    From 1953 to 1959 Gödel worked on a response to Carnap’s philosophy of mathematics. The drafts display Gödel’s familiarity with Carnap’s position from The Logical Syntax of Language, but they received a dismissive reaction on their eventual, posthumous, publication. Gödel’s two principal points, however, will here be defended. Gödel, though, had wished simply to append a few paragraphs to show that the same arguments apply to Carnap’s later views. Carnap’s position, however, had changed significantly in the intervening years, and to (...)
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  42. Mathematical Descriptions.Bernard Linsky & Edward N. Zalta - 2019 - Philosophical Studies 176 (2):473-481.
    In this paper, the authors briefly summarize how object theory uses definite descriptions to identify the denotations of the individual terms of theoretical mathematics and then further develop their object-theoretic philosophy of mathematics by showing how it has the resources to address some objections recently raised against the theory. Certain ‘canonical’ descriptions of object theory, which are guaranteed to denote, correctly identify mathematical objects for each mathematical theory T, independently of how well someone understands the descriptive condition. And to have (...)
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  43. Einführung in die Philosophie der Mathematik.Jörg Neunhäuserer - 2019 - Wiesbaden, Deutschland: Springer Spektrum.
    Welche Art von Gegenständen untersucht die Mathematik und in welchem Sinne existieren diese Gegenstände? Warum dürfen wir die Aussagen der Mathematik zu unserem Wissen zählen und wie lassen sich diese Aussagen rechtfertigen? Eine Philosophie der Mathematik versucht solche Fragen zu beantworten. In dieser Einführung stellen wir maßgeblichen Positionen in der Philosophie der Mathematik vor und formulieren die Essenz dieser Positionen in möglichst einfachen Thesen. Der Leser erfährt, auf welche Philosophen eine Position zurückgeht und in welchem historischen Kontext diese entstand. Ausgehend (...)
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  44. Can Mathematical Objects Be Causally Efficacious?Seungbae Park - 2019 - Inquiry: An Interdisciplinary Journal of Philosophy 62 (3):247–255.
    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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  45. Gödel's Argument for Cantorian Cardinality.Matthew W. Parker - 2019 - Noûs 53 (2):375-393.
    On the first page of “What is Cantor's Continuum Problem?”, Gödel argues that Cantor's theory of cardinality, where a bijection implies equal number, is in some sense uniquely determined. The argument, involving a thought experiment with sets of physical objects, is initially persuasive, but recent authors have developed alternative theories of cardinality that are consistent with the standard set theory ZFC and have appealing algebraic features that Cantor's powers lack, as well as some promise for applications. Here we diagnose Gödel's (...)
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  46. Platonism in Lotze and Frege Between Psyschologism and Hypostasis.Nicholas Stang - 2019 - In Sandra Lapointe (ed.), Logic from Kant to Russell. Routledge. pp. 138–159.
    In the section “Validity and Existence in Logik, Book III,” I explain Lotze’s famous distinction between existence and validity in Book III of Logik. In the following section, “Lotze’s Platonism,” I put this famous distinction in the context of Lotze’s attempt to distinguish his own position from hypostatic Platonism and consider one way of drawing the distinction: the hypostatic Platonist accepts that there are propositions, whereas Lotze rejects this. In the section “Two Perspectives on Frege’s Platonism,” I argue that this (...)
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  47. Reseña de 'The Outer Limits of Reason' por Noson Yanofsky 403p (2013).Michael Richard Starks - 2019 - In Observaciones Sobre Imposibilidad, Incompleta, Paracoherencia,Indecisión,Aleatoriedad, Computabilidad, Paradoja E Incertidumbre En Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, Dacosta, Godel, Searle, Rodych, Berto,Floyd, Moyal-Sharrock Y Yanofsky. Las Vegas, NV USA: Reality Press. pp. 71-90.
    Doy una revisión detallada de ' los límites externos de la razón ' por Noson Yanofsky desde una perspectiva unificada de Wittgenstein y la psicología evolutiva. Yo indiqué que la dificultad con cuestiones como la paradoja en el lenguaje y las matemáticas, la incompletitud, la indeterminación, la computabilidad, el cerebro y el universo como ordenadores, etc., surgen de la falta de mirada cuidadosa a nuestro uso del lenguaje en el adecuado contexto y, por tanto, el Error al separar los problemas (...)
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  48. The Semantic Plights of the Ante-Rem Structuralist.Bahram Assadian - 2018 - Philosophical Studies 175 (12):1-20.
    A version of the permutation argument in the philosophy of mathematics leads to the thesis that mathematical terms, contrary to appearances, are not genuine singular terms referring to individual objects; they are purely schematic or variables. By postulating ‘ante-rem structures’, the ante-rem structuralist aims to defuse the permutation argument and retain the referentiality of mathematical terms. This paper presents two semantic problems for the ante- rem view: (1) ante-rem structures are themselves subject to the permutation argument; (2) the ante-rem structuralist (...)
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  49. Indispensability, Causation and Explanation.Sorin Bangu - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):219-232.
    When considering mathematical realism, some scientific realists reject it, and express sympathy for the opposite view, mathematical nominalism; moreover, many justify this option by invoking the causal inertness of mathematical objects. The main aim of this note is to show that the scientific realists’ endorsement of this causal mathematical nominalism is in tension with another position some of them also accept, the doctrine of methodological naturalism. By highlighting this conflict, I intend to tip the balance in favor of a rival (...)
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  50. Another Fine Footnote to Plato: Sam Cowling: Abstract Entities. Milton Park, UK and New York: Routledge, X+281pp, £31.99 PB.James Brown - 2018 - Metascience 27 (3):477-480.
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