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94A 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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113Mathematical Conceptware: Category Theory: Critical Studies/Book ReviewsPhilosophia Mathematica 18 (2): 235-246. 2010.(No abstract is available for this citation)
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842A path to the epistemology of mathematics: homotopy theoryIn Jeremy Gray & Jose Ferreiros (eds.), The Architecture of Modern Mathematics: Essays in History and Philosophy, Oxford University Press. pp. 239--260. 2006.
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1Towards a Theory of Partial TruthDissertation, Mcgill University (Canada). 1988.The nature of truth has occupied philosophers since the very beginning of the field. Our goal is to clarify the notion of scientific truth, in particular the notion of partial truth of facts. Our strategy consists to brake the problem into smaller, more manageable, questions. Thus, we distinguish the truth of a scientific theory, what we call the "global" truth value of a theory, from the truth of a particular scientific proposition, what we call the "local" truth values of a theory. We will pre…Read more
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24Category Theory and Structuralism in Mathematics: Syntactical ConsiderationsIn Evandro Agazzi & György Darvas (eds.), Philosophy of Mathematics Today, Kluwer Academic Publishers. pp. 123--136. 1997.
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22Angèle Kremer-Marietti, La philosophie cognitive, Paris, PUF , 1994, 128 pPhilosophiques 23 (2): 461-464. 1996.
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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
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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
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1379Categorical 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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62Book Review: Colin McLarty. Elementary Categories, Elementary Toposes (review)Notre Dame Journal of Formal Logic 39 (3): 436-445. 1998.
Montreal, Quebec, Canada
Areas of Interest
Metaphysics |
Philosophy of Physical Science |
Science, Logic, and Mathematics |