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1402Categorical foundations of mathematics or how to provide foundations for abstract mathematicsReview of Symbolic Logic 6 (1): 51-75. 2013.Fefermans argument is indeed convincing in a certain context, it can be dissolved entirely by modifying the context appropriately.
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64Book Review: Colin McLarty. Elementary Categories, Elementary Toposes (review)Notre Dame Journal of Formal Logic 39 (3): 436-445. 1998.
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1471The History of Categorical Logic: 1963-1977In Dov Gabbay, Akihiro Kanamori & John Woods (eds.), Handbook of the history of logic, Elsevier. 2011.
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240Categories in context: Historical, foundational, and philosophicalPhilosophia Mathematica 13 (1): 1-43. 2005.The aim of this paper is to put into context the historical, foundational and philosophical significance of category theory. We use our historical investigation to inform the various category-theoretic foundational debates and to point to some common elements found among those who advocate adopting a foundational stance. We then use these elements to argue for the philosophical position that category theory provides a framework for an algebraic in re interpretation of mathematical structuralism.…Read more
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238Categories, sets and the nature of mathematical entitiesIn Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics, Springer. pp. 181--192. 2006.
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15A Note on Forrester’s ParadoxPolish Journal of Philosophy 6 (2): 53-70. 2012.In this paper, we argue that Forrester’s paradox, as he presents it, is not a paradox of standard deontic logic. We show that the paradox fails since it is the result of a misuse of , a derived rule in the standard systems. Before presenting Forrester’s argument against standard deontic logic, we will briefly expose the principal characteristics of a standard system Δ. The modal system KD will be taken as a representative. We will then make some remarks regarding , pointing out that its use is r…Read more
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110John L. BELL. The continuous and the infinitesimal in mathematics and philosophy. Monza: Polimetrica, 2005. Pp. 349. ISBN 88-7699-015- (review)Philosophia Mathematica 14 (3): 394-400. 2006.Some concepts that are now part and parcel of mathematics used to be, at least until the beginning of the twentieth century, a central preoccupation of mathematicians and philosophers. The concept of continuity, or the continuous, is one of them. Nowadays, many philosophers of mathematics take it for granted that mathematicians of the last quarter of the nineteenth century found an adequate conceptual analysis of the continuous in terms of limits and that serious philosophical thinking is no lon…Read more
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398Abstract mathematical tools and machines for mathematicsPhilosophia Mathematica 5 (3): 250-272. 1997.In this paper, we try to establish that some mathematical theories, like K-theory, homology, cohomology, homotopy theories, spectral sequences, modern Galois theory (in its various applications), representation theory and character theory, etc., should be thought of as (abstract) machines in the same way that there are (concrete) machines in the natural sciences. If this is correct, then many epistemological and ontological issues in the philosophy of mathematics are seen in a different light. W…Read more
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61Menger and Nöbeling on Pointless TopologyLogic and Logical Philosophy 22 (2): 145-165. 2013.This paper looks at how the idea of pointless topology itself evolved during its pre-localic phase by analyzing the definitions of the concept of topological space of Menger and Nöbeling. Menger put forward a topology of lumps in order to generalize the definition of the real line. As to Nöbeling, he developed an abstract theory of posets so that a topological space becomes a particular case of topological poset. The analysis emphasizes two points. First, Menger's geometrical perspective was sup…Read more
Montreal, Quebec, Canada
Areas of Interest
Metaphysics |
Philosophy of Physical Science |
Science, Logic, and Mathematics |