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  1. Everything, More or Less: A Defence of Generality Relativism, by J. P. Studd. [REVIEW]Luca Incurvati - 2021 - Mind 131 (524):1311-1321.
    The long-standing dispute between absolutists and relativists traditionally focuses on whether there are absolute truths, absolute epistemic norms, and absolute.
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  • Elaine Landry,* ed. Categories for the Working Philosopher. [REVIEW]Neil Barton - 2020 - Philosophia Mathematica 28 (1):95-108.
    LandryElaine, * ed. Categories for the Working Philosopher. Oxford University Press, 2017. ISBN 978-0-19-874899-1 ; 978-0-19-106582-8. Pp. xiv + 471.
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  • What is a Higher Level Set?Dimitris Tsementzis - 2016 - Philosophia Mathematica:nkw032.
    Structuralist foundations of mathematics aim for an ‘invariant’ conception of mathematics. But what should be their basic objects? Two leading answers emerge: higher groupoids or higher categories. I argue in favor of the former over the latter. First, I explain why to choose between them we need to ask the question of what is the correct ‘categorified’ version of a set. Second, I argue in favor of groupoids over categories as ‘categorified’ sets by introducing a pre-formal understanding of groupoids as (...)
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  • The Importance of Developing a Foundation for Naive Category Theory.Marcoen J. T. F. Cabbolet - 2015 - Thought: A Journal of Philosophy 4 (4):237-242.
    Recently Feferman has outlined a program for the development of a foundation for naive category theory. While Ernst has shown that the resulting axiomatic system is still inconsistent, the purpose of this note is to show that nevertheless some foundation has to be developed before naive category theory can replace axiomatic set theory as a foundational theory for mathematics. It is argued that in naive category theory currently a ‘cookbook recipe’ is used for constructing categories, and it is explicitly shown (...)
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  • The prospects of unlimited category theory: Doing what remains to be done.Michael Ernst - 2015 - Review of Symbolic Logic 8 (2):306-327.
    The big question at the end of Feferman is: Is it possible to find a foundation for unlimited category theory? I show that the answer is no by showing that unlimited category theory is inconsistent.
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  • On Bourbaki’s axiomatic system for set theory.Maribel Anacona, Luis Carlos Arboleda & F. Javier Pérez-Fernández - 2014 - Synthese 191 (17):4069-4098.
    In this paper we study the axiomatic system proposed by Bourbaki for the Theory of Sets in the Éléments de Mathématique. We begin by examining the role played by the sign \(\uptau \) in the framework of its formal logical theory and then we show that the system of axioms for set theory is equivalent to Zermelo–Fraenkel system with the axiom of choice but without the axiom of foundation. Moreover, we study Grothendieck’s proposal of adding to Bourbaki’s system the axiom (...)
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  • Categories for the Neologicist.Shay Allen Logan - 2017 - Philosophia Mathematica 25 (1):26-44.
    Abstraction principles provide implicit definitions of mathematical objects. In this paper, an abstraction principle defining categories is proposed. It is unsatisfiable and inconsistent in the expected ways. Two restricted versions of the principle which are consistent are presented.
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