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Set Theory and Structures

In Deniz Sarikaya, Deborah Kant & Stefania Centrone (eds.), Reflections on the Foundations of Mathematics. Springer Verlag. pp. 223-253 (2019)

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  1. Exploring Categorical Structuralism.C. Mclarty - 2004 - Philosophia Mathematica 12 (1):37-53.
    Hellman [2003] raises interesting challenges to categorical structuralism. He starts citing Awodey [1996] which, as Hellman sees, is not intended as a foundation for mathematics. It offers a structuralist framework which could denned in any of many different foundations. But Hellman says Awodey's work is 'naturally viewed in the context of Mac Lane's repeated claim that category theory provides an autonomous foundation for mathematics as an alternative to set theory' (p. 129). Most of Hellman's paper 'scrutinizes the formulation of category (...)
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  • Categories for the Working Philosopher.Elaine M. Landry (ed.) - 2017 - Oxford, England: Oxford University Press.
    This is the first volume on category theory for a broad philosophical readership. It is designed to show the interest and significance of category theory for a range of philosophical interests: mathematics, proof theory, computation, cognition, scientific modelling, physics, ontology, the structure of the world.
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  • Numbers can be just what they have to.Colin McLarty - 1993 - Noûs 27 (4):487-498.
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  • How we learn mathematical language.Vann McGee - 1997 - Philosophical Review 106 (1):35-68.
    Mathematical realism is the doctrine that mathematical objects really exist, that mathematical statements are either determinately true or determinately false, and that the accepted mathematical axioms are predominantly true. A realist understanding of set theory has it that when the sentences of the language of set theory are understood in their standard meaning, each sentence has a determinate truth value, so that there is a fact of the matter whether the cardinality of the continuum is א2 or whether there are (...)
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  • From Kant to Hilbert: A Source Book in the Foundations of Mathematics. [REVIEW]Antoni Kosinski - 2003 - Isis 94:345-347.
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