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Jean-Pierre Marquis
Université de Montréal
  1. The History of Categorical Logic: 1963-1977.Jean-Pierre Marquis & Gonzalo Reyes - 2011 - In Dov Gabbay, Akihiro Kanamori & John Woods (eds.), Handbook of the history of logic. Elsevier.
  2. Mario Bunge’s Philosophy of Mathematics: An Appraisal.Jean-Pierre Marquis - 2012 - Science & 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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  3. Categories in Context: Historical, Foundational, and Philosophical.Elaine Landry & Jean-Pierre Marquis - 2005 - 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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  4. Stairway to Heaven: The Abstract Method and Levels of Abstraction in Mathematics.Jean Pierre Marquis & Jean-Pierre Marquis - 2016 - The Mathematical Intelligencer 38 (3):41-51.
    In this paper, following the claims made by various mathematicians, I try to construct a theory of levels of abstraction. I first try to clarify the basic components of the abstract method as it developed in the first quarter of the 20th century. I then submit an explication of the notion of levels of abstraction. In the final section, I briefly explore some of main philosophical consequences of the theory.
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  5.  31
    Canonical Maps.Jean-Pierre Marquis - 2018 - In Elaine Landry (ed.), Categories for the Working Philosophers. Oxford, UK: pp. 90-112.
    Categorical foundations and set-theoretical foundations are sometimes presented as alternative foundational schemes. So far, the literature has mostly focused on the weaknesses of the categorical foundations. We want here to concentrate on what we take to be one of its strengths: the explicit identification of so-called canonical maps and their role in mathematics. Canonical maps play a central role in contemporary mathematics and although some are easily defined by set-theoretical tools, they all appear systematically in a categorical framework. The key (...)
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  6.  5
    Categories in Context: Historical, Foundational, and Philosophical &Dagger.Elaine Landry & Jean-Pierre Marquis - 2005 - 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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  7.  94
    Mathematical Abstraction, Conceptual Variation and Identity.Jean-Pierre Marquis - 2014 - In Peter Schroeder-Heister, Gerhard Heinzmann, Wilfred Hodges & Pierre Edouard Bour (eds.), Logic, Methodology and Philosophy of Science, Proceedings of the 14th International Congress. London, UK: pp. 299-322.
    One of the key features of modern mathematics is the adoption of the abstract method. Our goal in this paper is to propose an explication of that method that is rooted in the history of the subject.
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  8.  34
    From a Geometrical Point of View: A Study in the History and Philosophy of Category Theory.Jean-Pierre Marquis - 2009 - 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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  9.  96
    Mathematical Forms and Forms of Mathematics: Leaving the Shores of Extensional Mathematics.Jean-Pierre Marquis - 2013 - 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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  10. Categorical Foundations of Mathematics or How to Provide Foundations for Abstract Mathematics.Jean-Pierre Marquis - 2013 - 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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  11. Category Theory and the Foundations of Mathematics: Philosophical Excavations.Jean-Pierre Marquis - 1995 - 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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  12.  50
    Mathematical Models of Abstract Systems: Knowing Abstract Geometric Forms.Jean-Pierre Marquis - 2013 - Annales de la Faculté des Sciences de Toulouse 22 (5):969-1016.
    Scientists use models to know the world. It i susually assumed that mathematicians doing pure mathematics do not. Mathematicians doing pure mathematics prove theorems about mathematical entities like sets, numbers, geometric figures, spaces, etc., they compute various functions and solve equations. In this paper, I want to exhibit models build by mathematicians to study the fundamental components of spaces and, more generally, of mathematical forms. I focus on one area of mathematics where models occupy a central role, namely homotopy theory. (...)
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  13.  35
    Abstract Mathematical Tools and Machines for Mathematics.Jean-pierre Marquis - 1997 - 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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  14.  44
    Categories, Sets and the Nature of Mathematical Entities.Jean-Pierre Marquis - 2006 - In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics. Springer. pp. 181--192.
  15.  76
    Category Theory.Jean-Pierre Marquis - 2008 - Stanford Encyclopedia of Philosophy.
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  16.  83
    Mathematical Conceptware: Category Theory: Critical Studies/Book Reviews.Jean-Pierre Marquis - 2010 - Philosophia Mathematica 18 (2):235-246.
    (No abstract is available for this citation).
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  17. A Path to the Epistemology of Mathematics: Homotopy Theory.Jean-Pierre Marquis - 2006 - In Jeremy Gray & Jose Ferreiros (eds.), Architecture of Modern Mathematics. Oxford University Press. pp. 239--260.
  18.  33
    Approximations and Truth Spaces.Jean-Pierre Marquis - 1991 - 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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  19. Special-Issue Book Review.Jean-pierre Marquis - 1996 - Philosophia Mathematica 4 (2):202-205.
  20.  39
    The Palmer House Hilton Hotel, Chicago, Illinois February 18–20, 2010.Kenneth Easwaran, Philip Ehrlich, David Ross, Christopher Hitchcock, Peter Spirtes, Roy T. Cook, Jean-Pierre Marquis, Stewart Shapiro & Royt Cook - 2010 - Bulletin of Symbolic Logic 16 (3).
  21.  53
    Categorical Foundations of Mathematics.Jean-Pierre Marquis - 2012 - Review of Symbolic Logic.
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  22.  73
    John L. BELL. The Continuous and the Infinitesimal in Mathematics and Philosophy. Monza: Polimetrica, 2005. Pp. 349. ISBN 88-7699-015-. [REVIEW]Jean-Pierre Marquis - 2006 - Philosophia Mathematica 14 (3):394-400.
    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 longer required, except (...)
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  23.  34
    A Subject with No Object. [REVIEW]Jean-Pierre Marquis - 2000 - Canadian Journal of Philosophy 30 (1):161-178.
  24.  36
    Book Review: Colin McLarty. Elementary Categories, Elementary Toposes. [REVIEW]Jean-Pierre Marquis - 1998 - Notre Dame Journal of Formal Logic 39 (3):436-445.
  25.  23
    Menger and Nöbeling on Pointless Topology.Mathieu Bélanger & Jean-Pierre Marquis - 2013 - 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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  26.  9
    Angèle Kremer-Marietti, La philosophie cognitive, Paris, PUF , 1994, 128 p.Jean-Pierre Marquis - 1996 - Philosophiques 23 (2):461-464.
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  27.  19
    The Palmer House Hilton Hotel, Chicago, Illinois April 19–21, 2007.Yiannis Moschovakis, Richmond H. Thomason, Steffen Lempp, Steve Awodey, Jean-Pierre Marquis & William Tait - 2007 - Bulletin of Symbolic Logic 13 (4).
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  28.  35
    J. J. Katz, Realistic Rationalism. [REVIEW]Jean-Pierre Marquis - 2000 - Erkenntnis 52 (3):419-423.
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  29.  22
    On the Justification of Mathematical Intuitionism.Jean-Pierre Marquis - 1985 - Dissertation, Université de Montréal
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  30.  13
    Albert Lautman, philosophe des mathématiques.Jean-Pierre Marquis - 2010 - Philosophiques 37 (1):3-7.
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  31.  5
    Review of 'Realistic Rationalism'. [REVIEW]Jean-Pierre Marquis - 2000 - Erkenntnis 52 (3):419-423.
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  32.  5
    Vie et logique d’Alfred Tarski.Jean-Pierre Marquis & Marie Martel - 2006 - Dialogue 45 (2):367-374.
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  33.  18
    Approximations and Logic.Jean-Pierre Marquis - 1992 - Notre Dame Journal of Formal Logic 33 (2):184-196.
  34.  7
    Category Theory and Structuralism in Mathematics: Syntactical Considerations.Jean-Pierre Marquis - 1997 - In Evandro Agazzi & György Darvas (eds.), Philosophy of Mathematics Today. Kluwer Academic Publishers. pp. 123--136.
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  35.  4
    Critical Notice.Jean-Pierre Marquis - 2000 - Canadian Journal of Philosophy 30 (1):161-178.
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  36.  3
    Tool and Object. [REVIEW]Jean-Pierre Marquis - 2009 - Bulletin of Symbolic Logic 15 (3):320-321.
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  37.  3
    A Note on Forrester’s Paradox.Clayton Peterson & Jean-Pierre Marquis - 2012 - Polish Journal of Philosophy 6 (2):53-70.
    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 , (...)
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  38. On Tobar-Arbulu's "Quarter Truths".Jean-Pierre Marquis - 1988 - Epistemologia 11 (1):139.
     
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  39. Towards a Theory of Partial Truth.Jean-Pierre Marquis - 1988 - Dissertation, Mcgill University (Canada)
    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 (...)
     
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