-
22Angèle Kremer-Marietti, La philosophie cognitive, Paris, PUF , 1994, 128 pPhilosophiques 23 (2): 461-464. 1996.
-
345Mathematical Forms and Forms of Mathematics: Leaving the Shores of Extensional MathematicsSynthese 190 (12): 2141-2164. 2013.In this paper, I introduce the idea that some important parts of contemporary pure mathematics are moving away from what I call the extensional point of view. More specifically, these fields are based on criteria of identity that are not extensional. After presenting a few cases, I concentrate on homotopy theory where the situation is particularly clear. Moreover, homotopy types are arguably fundamental entities of geometry, thus of a large portion of mathematics, and potentially to all mathemat…Read more
-
54Mathematical engineering and mathematical changeInternational Studies in the Philosophy of Science 13 (3). 1999.In this paper, I introduce and examine the notion of “mathematical engineering” and its impact on mathematical change. Mathematical engineering is an important part of contemporary mathematics and it roughly consists of the “construction” and development of various machines, probes and instruments used in numerous mathematical fields. As an example of such constructions, I briefly present the basic steps and properties of homology theory. I then try to show that this aspect of contemporary mathe…Read more
-
1381Categorical 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.
-
62Book Review: Colin McLarty. Elementary Categories, Elementary Toposes (review)Notre Dame Journal of Formal Logic 39 (3): 436-445. 1998.
-
1446The History of Categorical Logic: 1963-1977In Dov Gabbay, Akihiro Kanamori & John Woods (eds.), Handbook of the history of logic, Elsevier. 2011.
-
239Categories 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
-
229Categories, 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.
-
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
-
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
Montreal, Quebec, Canada
Areas of Interest
Metaphysics |
Philosophy of Physical Science |
Science, Logic, and Mathematics |