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Profile: Jean-Pierre Marquis Marquis (Université de Montréal)
  1. Mathieu Bélanger & Jean-Pierre Marquis (2013). Menger and Nöbeling on Pointless Topology. Logic and Logical Philosophy 22 (2):145-165.
    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 First, Menger's geometrical perspective was superseded by (...)
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  2. Jean-Pierre Marquis (2013). Categorical Foundations of Mathematics or How to Provide Foundations for Abstract Mathematics. Review of Symbolic Logic 6 (1):51-75.
    Fefermans argument is indeed convincing in a certain context, it can be dissolved entirely by modifying the context appropriately.
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  3. Jean-Pierre Marquis (2013). Mathematical Forms and Forms of Mathematics: Leaving the Shores of Extensional Mathematics. Synthese 190 (12):2141-2164.
    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 mathematics, at least according (...)
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  4. Jean-Pierre Marquis (2012). Categorical Foundations of Mathematics. Review of Symbolic Logic.
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  5. Jean-Pierre Marquis (2011). Mario Bunge's Philosophy of Mathematics: An Appraisal. [REVIEW] Science and Education 21 (10):1567-1594.
    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.To Mario, with gratitude.
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  6. Jean-Pierre Marquis & Gonzalo Reyes (2011). The History of Categorical Logic: 1963-1977. In Dov Gabbay, Akihiro Kanamori & John Woods (eds.), Handbook of the history of logic. Elsevier.
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  7. Kenneth Easwaran, Philip Ehrlich, David Ross, Christopher Hitchcock, Peter Spirtes, Roy T. Cook, Jean-Pierre Marquis, Stewart Shapiro & Royt Cook (2010). The Palmer House Hilton Hotel, Chicago, Illinois February 18–20, 2010. Bulletin of Symbolic Logic 16 (3).
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  8. Jean-Pierre Marquis (2010). Albert Lautman, Philosophe des Mathématiques. Philosophiques 37 (1):3-7.
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  9. Jean-Pierre Marquis (2010). Mathematical Conceptware: Category Theory: R Alf K R Ö Mer . Tool and Object: A History and Philosophy of Category Theory. Philosophia Mathematica 18 (2):235-246.
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  10. Jean-Pierre Marquis (2009). From a Geometrical Point of View: A Study in the History and Philosophy of Category Theory. Springer.
    A 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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  11. Jean-Pierre Marquis, Category Theory. Stanford Encyclopedia of Philosophy.
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  12. Yiannis Moschovakis, Richmond H. Thomason, Steffen Lempp, Steve Awodey, Jean-Pierre Marquis & William Tait (2007). The Palmer House Hilton Hotel, Chicago, Illinois April 19–21, 2007. Bulletin of Symbolic Logic 13 (4).
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  13. Jean-Pierre Marquis (2006). A Path to the Epistemology of Mathematics: Homotopy Theory. In Jeremy Gray & Jose Ferreiros (eds.), Architecture of Modern Mathematics. Oxford University Press. 239--260.
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  14. Jean-Pierre Marquis (2006). Categories, Sets and the Nature of Mathematical Entities. In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics. Springer. 181--192.
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  15. Jean-Pierre Marquis (2006). John 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.
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  16. Jean-Pierre Marquis & Marie Martel (2006). Vie Et Logique d'Alfred Tarski. Dialogue 45 (2):367-374.
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  17. Elaine Landry & Jean-Pierre Marquis (2005). Categories in Context: Historical, Foundational, and Philosophical. Philosophia Mathematica 13 (1):1-43.
    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. In each context, what we aim to show (...)
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  18. Jean-Pierre Marquis (2000). A Subject with No Object. Canadian Journal of Philosophy 30 (1):161-178.
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  19. Jean-Pierre Marquis (2000). J. J. Katz, Realistic Rationalism. Erkenntnis 52 (3):419-423.
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  20. Jean-Pierre Marquis (1999). Mathematical Engineering and Mathematical Change. International Studies in the Philosophy of Science 13 (3):245 – 259.
    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 mathematics has important consequences on our conception (...)
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  21. Jean-Pierre Marquis (1998). Book Review: Colin McLarty. Elementary Categories, Elementary Toposes. [REVIEW] Notre Dame Journal of Formal Logic 39 (3):436-445.
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  22. Jean-pierre Marquis (1997). Abstract Mathematical Tools and Machines for Mathematics. Philosophia Mathematica 5 (3):250-272.
    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. We concentrate on one problem which immediately follows (...)
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  23. Jean-Pierre Marquis (1997). Category Theory and Structuralism in Mathematics: Syntactical Considerations. In. In Evandro Agazzi & György Darvas (eds.), Philosophy of Mathematics Today. Kluwer. 123--136.
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  24. Jean-Pierre Marquis (1996). Angèle Kremer-Marietti, La philosophie cognitive, Paris, PUF (coll. « Que sais-je ? » no 2817), 1994, 128 p.Angèle Kremer-Marietti, La philosophie cognitive, Paris, PUF (coll. « Que sais-je ? » no 2817), 1994, 128 p. [REVIEW] Philosophiques 23 (2):461-464.
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  25. Jean-pierre Marquis (1996). Special-Issue Book Review. Philosophia Mathematica 4 (2):202-205.
  26. Jean-Pierre Marquis (1995). Category Theory and the Foundations of Mathematics: Philosophical Excavations. Synthese 103 (3):421 - 447.
    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 (...)
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  27. Jean-Pierre Marquis (1992). Approximations and Logic. Notre Dame Journal of Formal Logic 33 (2):184-196.
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  28. Jean-Pierre Marquis (1991). Approximations and Truth Spaces. Journal of Philosophical Logic 20 (4):375 - 401.
    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, be they experimental or theoretical. Our goal is to lay down the conceptual and (...)
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  29. Jean-Pierre Marquis, On the Justification of Mathematical Intuitionism.
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