Philosophia Mathematica

ISSNs: 0031-8019, 1744-6406

8 found

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  1.  21
    Joel D. Hamkins. Lectures on the Philosophy of Mathematics.José Ferreirós - 2024 - Philosophia Mathematica 32 (1):124-127.
  2.  22
    The Interest of Philosophy of Mathematics (Education).Karen François - 2024 - Philosophia Mathematica 32 (1):137-142.
  3.  23
    Dominique Pradelle.*Être et genèse des idéalités. Un ciel sans éternité.Bruno Leclercq - 2024 - Philosophia Mathematica 32 (1):128-136.
    In Intuition et idéalités: Phénoménologie des objets mathématiques (2020), Dominique Pradelle questioned the nature of mathematical knowledge–the status of math.
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  4.  55
    No Easy Road to Impredicative Definabilism.Øystein Linnebo & Sam Roberts - 2024 - Philosophia Mathematica 32 (1):21-33.
    Bob Hale has defended a new conception of properties that is broadly Fregean in two key respects. First, like Frege, Hale insists that every property can be defined by an open formula. Second, like Frege, but unlike later definabilists, Hale seeks to justify full impredicative property comprehension. The most innovative part of his defense, we think, is a “definability constraint” that can serve as an implicit definition of the domain of properties. We make this constraint formally precise and prove that (...)
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  5.  41
    Identity and Extensionality in Boffa Set Theory.Nuno Maia & Matteo Nizzardo - 2024 - Philosophia Mathematica 32 (1):115-123.
    Boffa non-well-founded set theory allows for several distinct sets equal to their respective singletons, the so-called ‘Quine atoms’. Rieger contends that this theory cannot be a faithful description of set-theoretic reality. He argues that, even after granting that there are non-well-founded sets, ‘the extensional nature of sets’ precludes numerically distinct Quine atoms. In this paper we uncover important similarities between Rieger’s argument and how non-rigid structures are conceived within mathematical structuralism. This opens the way for an objection against Rieger, whilst (...)
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  6.  18
    Internal Applications and Puzzles of the Applicability of Mathematics.Douglas Bertrand Marshall - 2024 - Philosophia Mathematica 32 (1):1-20.
    Just as mathematics helps us to represent and reason about the natural world, in its internal applications one branch of mathematics helps us to represent and reason about the subject matter of another. Recognition of the close analogy between internal and external applications of mathematics can help resolve two persistent philosophical puzzles concerning its applicability: a platonist puzzle arising from the abstractness of mathematical objects; and an empiricist puzzle arising from mathematical propositions’ lack of empirical factual content. In order to (...)
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  7.  33
    Sizes of Countable Sets.Kateřina Trlifajová - 2024 - Philosophia Mathematica 32 (1):82-114.
    The paper introduces the notion of size of countable sets, which preserves the Part-Whole Principle. The sizes of the natural and the rational numbers, their subsets, unions, and Cartesian products are algorithmically enumerable as sequences of natural numbers. The method is similar to that of Numerosity Theory, but in comparison it is motivated by Bolzano’s concept of infinite series, it is constructive because it does not use ultrafilters, and set sizes are uniquely determined. The results mostly agree, but some differ, (...)
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  8.  72
    Intuition, Iteration, Induction.Mark van Atten - 2024 - Philosophia Mathematica 32 (1):34-81.
    Brouwer’s view on induction has relatively recently been characterised as one on which it is not only intuitive (as expected) but functional, by van Dalen. He claims that Brouwer’s ‘Ur-intuition’ also yields the recursor. Appealing to Husserl’s phenomenology, I offer an analysis of Brouwer’s view that supports this characterisation and claim, even if assigning the primary role to the iterator instead. Contrasts are drawn to accounts of induction by Poincaré, Heyting, and Kreisel. On the phenomenological side, the analysis provides an (...)
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