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38Categories in Context: Historical, Foundational, and Philosophical &daggerPhilosophia 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 structuralis…Read more
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36Erich Reck* and Georg Schiemer.** The Prehistory of Mathematical StructuralismPhilosophia Mathematica 28 (3): 416-420. 2020._Erich Reck* * and Georg Schiemer.** ** The Prehistory of Mathematical Structuralism. _Oxford University Press, 2020. Pp. 454. ISBN: 978-0-19-064122-1 ; 978-0-19-064123-8. doi: 10.1093/oso/9780190641221.001.0001.
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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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20A View from Space: The Foundations of MathematicsIn Wuppuluri Shyam & Francisco Antonio Dorio (eds.), The Map and the Territory: Exploring the Foundations of Science, Thought and Reality, Springer. pp. 357-375. 2018.Suppose we were to meet with extraterrestrials and that we were able to have a discussion about our respective cultures. At some point, they start asking questions about that something which we call “mathematics”. “What is it?”, they ask. Tough question. How should we answer them?
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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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10Ralf Krömer. Tool and object: A history and philosophy of category theory. Science Networks. Historical Studies, vol. 32. Birkhäuser, Basel, 2007, xxxvi + 367 pp (review)Bulletin of Symbolic Logic 15 (3): 320-322. 2009.
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7CategoriesIn Sven Ove Hansson & Vincent F. Hendricks (eds.), Introduction to Formal Philosophy, Springer. pp. 251-271. 2012.Mathematical categories provide an abstract and general framework for logic and mathematics. As such, they could be used by philosophers in all the basic fields of the discipline: semantics, epistemology and ontology. In this paper, we present the basic definitions and notions and suggest some of the ways categories are starting to infiltrate formal philosophy.
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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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Mario Bunge's Philosophy of Mathematics: An AppraisalScience & Education 21 1567-1594. 2012.In this paper, I present and discuss critically the main elements of Mario Bunge’s philosophy of mathematics. In particular, I explore how mathematical knowledge is accounted for in Bunge’s systemic emergent materialism.
Montreal, Quebec, Canada
Areas of Interest
Metaphysics |
Philosophy of Physical Science |
Science, Logic, and Mathematics |