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  1. Woosuk Park.Philosophy’s Loss of Logic to Mathematics: An Inadequately Understood Take-Over. [REVIEW]James Franklin - forthcoming - Philosophia Mathematica:nkz018.
    ParkWoosuk.* * _ Philosophy’s Loss of Logic to Mathematics: An Inadequately Understood Take-Over _. Studies in Applied Philosophy, Epistemology, and Rational Ethics; 43. Springer, 2018. ISBN: 978-3-319-95146-1 ; 978-3-030-06984-1 978-3-319-95147-8. Pp. xii + 230. doi: 10.1007/978-3-319-95147-8.
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  • An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure, by Franklin, James: Hampshire: Routledge, 2014, Pp. X + 308, £63. [REVIEW]Catherine Legg - 2015 - Australasian Journal of Philosophy 93 (4):837-837.
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  • Discrete and Continuous: A Fundamental Dichotomy in Mathematics.James Franklin - 2017 - Journal of Humanistic Mathematics 7 (2):355-378.
    The distinction between the discrete and the continuous lies at the heart of mathematics. Discrete mathematics (arithmetic, algebra, combinatorics, graph theory, cryptography, logic) has a set of concepts, techniques, and application areas largely distinct from continuous mathematics (traditional geometry, calculus, most of functional analysis, differential equations, topology). The interaction between the two – for example in computer models of continuous systems such as fluid flow – is a central issue in the applicable mathematics of the last hundred years. This article (...)
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  • Philosophy’s Loss of Logic to Mathematics.Woosuk Park - 2018 - Springer Verlag.
    This book offers a historical explanation of important philosophical problems in logic and mathematics, which have been neglected by the official history of modern logic. It offers extensive information on Gottlob Frege’s logic, discussing which aspects of his logic can be considered truly innovative in its revolution against the Aristotelian logic. It presents the work of Hilbert and his associates and followers with the aim of understanding the revolutionary change in the axiomatic method. Moreover, it offers useful tools to understand (...)
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  • Uninstantiated Properties and Semi-Platonist Aristotelianism.James Franklin - 2015 - Review of Metaphysics 69 (1):25-45.
    Once the reality of properties is admitted, there are two fundamentally different realist theories of properties. Platonist or transcendent realism holds that properties are abstract objects in the classical sense, of being nonmental, nonspatial, and causally inefficacious. By contrast, Aristotelian or moderate realism takes properties to be literally instantiated in things. An apple’s color and shape are as real and physical as the apple itself. The most direct reason for taking an Aristotelian realist view of properties is that we perceive (...)
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  • Perceiving Necessity.Catherine Legg & James Franklin - 2017 - Pacific Philosophical Quarterly 98 (3).
    In many diagrams one seems to perceive necessity – one sees not only that something is so, but that it must be so. That conflicts with a certain empiricism largely taken for granted in contemporary philosophy, which believes perception is not capable of such feats. The reason for this belief is often thought well-summarized in Hume's maxim: ‘there are no necessary connections between distinct existences’. It is also thought that even if there were such necessities, perception is too passive or (...)
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  • Early Modern Mathematical Principles and Symmetry Arguments.James Franklin - 2017 - In The Idea of Principles in Early Modern Thought Interdisciplinary Perspectives. New York, USA: Routledge. pp. 16-44.
    The leaders of the Scientific Revolution were not Baconian in temperament, in trying to build up theories from data. Their project was that same as in Aristotle's Posterior Analytics: they hoped to find necessary principles that would show why the observations must be as they are. Their use of mathematics to do so expanded the Aristotelian project beyond the qualitative methods used by Aristotle and the scholastics. In many cases they succeeded.
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  • The Mereology of Structural Universals.Peter Forrest - 2016 - Logic and Logical Philosophy 25 (3):259-283.
    This paper explores the mereology of structural universals, using the structural richness of a non-classical mereology without unique fusions. The paper focuses on a problem posed by David Lewis, who using the example of methane, and assuming classical mereology, argues against any purely mereological theory of structural universals. The problem is that being a methane molecule would have to contain being a hydrogen atom four times over, but mereology does not have the concept of the same part occurring several times. (...)
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  • Aristoteles’in Matematik Felsefesi ve Matematik Soyut­lama.Murat Kelikli - 2017 - Beytulhikme An International Journal of Philosophy 7 (2):33-49.
    Although there are many questions to be asked about philosophy of mathematics, the fundamental questions to be asked will be questions about what the mathematical object is in view of being and what the mathematical reasoning is in view of knowledge. It is clear that other problems will develop in parallel within the framework of the answers to these questions. For this rea­ son, when we approach Aristotle's philosophy of mathematics over these two basic problems, we come up with the (...)
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  • 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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  • Philosophy of the Matrix.A. C. Paseau - 2017 - Philosophia Mathematica 25 (2):246-267.
    A mathematical matrix is usually defined as a two-dimensional array of scalars. And yet, as I explain, matrices are not in fact two-dimensional arrays. So are we to conclude that matrices do not exist? I show how to resolve the puzzle, for both contemporary and older mathematics. The solution generalises to the interpretation of all mathematical discourse. The paper as a whole attempts to reinforce mathematical structuralism by reflecting on how best to interpret mathematics.
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  • World Enough and Form: Why Cosmology Needs Hylomorphism.John G. Brungardt - 2019 - Synthese:1-33.
    This essay proposes a comprehensive blueprint for the hylomorphic foundations of cosmology. The key philosophical explananda in cosmology are those dealing with global processes and structures, the regularity of global regularities, and the existence of the global as such. The possibility of elucidating these using alternatives to hylomorphism is outlined and difficulties with these alternatives are raised. Hylomorphism, by contrast, provides a sound philosophical ground for cosmology insofar as it leads to notions of cosmic essence, the unity of complex essences, (...)
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  • Aristotle’s Philosophy of Mathematics and Mathematical Abstraction.Murat Kelikli - forthcoming - Beytulhikme An International Journal of Philosophy.
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  • The Epistemic Indispensability Argument.Cristian Soto - 2019 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 50 (1):145-161.
    This article elaborates the epistemic indispensability argument, which fully embraces the epistemic contribution of mathematics to science, but rejects the contention that such a contribution is a reason for granting reality to mathematicalia. Section 1 introduces the distinction between ontological and epistemic readings of the indispensability argument. Section 2 outlines some of the main flaws of the first premise of the ontological reading. Section 3 advances the epistemic indispensability argument in view of both applied and pure mathematics. And Sect. 4 (...)
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  • What If Haecceity is Not a Property?Woosuk Park - 2016 - Foundations of Science 21 (3):511-526.
    In some sense, both ontological and epistemological problems related to individuation have been the focal issues in the philosophy of mathematics ever since Frege. However, such an interest becomes manifest in the rise of structuralism as one of the most promising positions in recent philosophy of mathematics. The most recent controversy between Keränen and Shapiro seems to be the culmination of this phenomenon. Rather than taking sides, in this paper, I propose to critically examine some common assumptions shared by both (...)
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  • Review of An Aristotelian Realist Philosophy of Mathematics. [REVIEW]Max Jones - 2015 - Philosophia Mathematica 23 (2):281-288.
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  • Do We See Numbers?James Davies - 2015 - Metascience 24 (3):483-486.
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  • An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure by James Franklin. [REVIEW]Jude P. Dougherty - 2015 - Review of Metaphysics 68 (3):658-660.
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