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1653The History of Categorical Logic: 1963-1977In Dov M. Gabbay, John Woods & Akihiro Kanamori (eds.), Handbook of the history of logic, Elsevier. 2004.
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244Categories 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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268Categories, sets and the nature of mathematical entitiesIn Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics: Assessing Philosophy of Logic and Mathematics Today, Springer. pp. 181--192. 2006.
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18A 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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111John 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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413Abstract 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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63Menger 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
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828Category theory and the foundations of mathematics: Philosophical excavationsSynthese 103 (3). 1995.The aim of this paper is to clarify the role of category theory in the foundations of mathematics. There is a good deal of confusion surrounding this issue. A standard philosophical strategy in the face of a situation of this kind is to draw various distinctions and in this way show that the confusion rests on divergent conceptions of what the foundations of mathematics ought to be. This is the strategy adopted in the present paper. It is divided into 5 sections. We first show that already in th…Read more
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53Approximations and truth spacesJournal of Philosophical Logic 20 (4). 1991.Approximations form an essential part of scientific activity and they come in different forms: conceptual approximations (simplifications in models), mathematical approximations of various types (e.g. linear equations instead of non-linear ones, computational approximations), experimental approximations due to limitations of the instruments and so on and so forth. In this paper, we will consider one type of approximation, namely numerical approximations involved in the comparison of two results,…Read more
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95A Study of the History and Philosophy of Category Theory Jean-Pierre Marquis. to say that objects are dispensable in geometry. What is claimed is that the specific nature of the objects used is irrelevant. To use the terminology already ...
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37Mathematical Conceptware: Category Theory: Critical Studies/Book ReviewsPhilosophia Mathematica 18 (2): 235-246. 2010.(No abstract is available for this citation)
Montreal, Quebec, Canada
Areas of Interest
Metaphysics |
Philosophy of Physical Science |
Science, Logic, and Mathematics |