• Mario Bunge's Philosophy of Mathematics: An Appraisal
    Science & 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.
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    Categories
    In 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.
  •  842
    The Structuralist Mathematical Style: Bourbaki as a case study
    In Stefano Boscolo Claudio Ternullo Gianluigi Oliveri (ed.), Boston Studies in the Philosophy and the History of Science. pp. 199-231. 2022.
    In this paper, we look at Bourbaki’s work as a case study for the notion of mathematical style. We argue that indeed Bourbaki exemplifies a mathematical style, namely the structuralist style.
  •  436
    Abstract logical structuralism
    Philosophical Problems in Science 69 67-110. 2020.
    Structuralism has recently moved center stage in philosophy of mathematics. One of the issues discussed is the underlying logic of mathematical structuralism. In this paper, I want to look at the dual question, namely the underlying structures of logic. Indeed, from a mathematical structuralist standpoint, it makes perfect sense to try to identify the abstract structures underlying logic. We claim that one answer to this question is provided by categorical logic. In fact, we claim that the latte…Read more
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    Forms of Structuralism: Bourbaki and the Philosophers
    Structures Meres, Semantics, Mathematics, and Cognitive Science. 2020.
    In this paper, we argue that, contrary to the view held by most philosophers of mathematics, Bourbaki’s technical conception of mathematical structuralism is relevant to philosophy of mathematics. In fact, we believe that Bourbaki has captured the core of any mathematical structuralism.
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    Erich Reck* and Georg Schiemer.** The Prehistory of Mathematical Structuralism
    Philosophia 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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    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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    Vérité partielle et réalisme scientifique: une approche bungéenne
    Mεtascience: Discours Général Scientifique 1 293-314. 2020.
    Le réalisme scientifique occupe une place centrale dans le système philosophique de Mario Bunge. Au cœur de cette thèse, on trouve l’affirmation selon laquelle nous pouvons connaître le monde partiellement. Il s’ensuit que les théories scientifiques ne sont pas totalement vraies ou totalement fausses, mais plutôt partiellement vraies et partiellement fausses. Ces énoncés sur la connaissance scientifique, à première vue plausible pour quiconque est familier avec la pratique scientifique, demanden…Read more
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    Mario Bunge: A Centenary Festschrift (edited book)
    with Mario Augusto Bunge, Michael R. Matthews, Guillermo M. Denegri, Eduardo L. Ortiz, Heinz W. Droste, Alberto Cordero, Pierre Deleporte, María Manzano, Manuel Crescencio Moreno, Dominique Raynaud, Íñigo Ongay de Felipe, Nicholas Rescher, Richard T. W. Arthur, Rögnvaldur D. Ingthorsson, Evandro Agazzi, Ingvar Johansson, Joseph Agassi, Nimrod Bar-Am, Alberto Cupani, Gustavo E. Romero, Andrés Rivadulla, Art Hobson, Olival Freire Junior, Peter Slezak, Ignacio Morgado-Bernal, Marta Crivos, Leonardo Ivarola, Andreas Pickel, Russell Blackford, Michael Kary, A. Z. Obiedat, Carolina I. García Curilaf, Rafael González del Solar, Luis Marone, Javier Lopez de Casenave, Francisco Yannarella, Mauro A. E. Chaparro, José Geiser Villavicencio- Pulido, Martín Orensanz, Reinhard Kahle, Ibrahim A. Halloun, José María Gil, Omar Ahmad, Byron Kaldis, Marc Silberstein, Carolina I. García Curilaf, Rafael González del Solar, Javier Lopez de Casenave, Íñigo Ongay de Felipe, and Villavicencio-Pulid
    Springer Verlag. 2019.
    This volume has 41 chapters written to honor the 100th birthday of Mario Bunge. It celebrates the work of this influential Argentine/Canadian physicist and philosopher. Contributions show the value of Bunge’s science-informed philosophy and his systematic approach to philosophical problems. The chapters explore the exceptionally wide spectrum of Bunge’s contributions to: metaphysics, methodology and philosophy of science, philosophy of mathematics, philosophy of physics, philosophy of psychology…Read more
  •  548
    Bunge’s Mathematical Structuralism Is Not a Fiction
    In Michael Robert Matthews (ed.), Mario Bunge: A Centenary Festschrift, Springer Verlag. pp. 587-608. 2019.
    In this paper, I explore Bunge’s fictionism in philosophy of mathematics. After an overview of Bunge’s views, in particular his mathematical structuralism, I argue that the comparison between mathematical objects and fictions ultimately fails. I then sketch a different ontology for mathematics, based on Thomasson’s metaphysical work. I conclude that mathematics deserves its own ontology, and that, in the end, much work remains to be done to clarify the various forms of dependence that are involv…Read more
  •  893
    Canonical Maps
    In Elaine Landry (ed.), Categories for the Working Philosophers, . pp. 90-112. 2018.
    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 a…Read more
  •  346
    Mathematical Models of Abstract Systems: Knowing abstract geometric forms
    Annales de la Faculté des Sciences de Toulouse 22 (5): 969-1016. 2013.
    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 model…Read more
  •  711
    Mathematical Abstraction, Conceptual Variation and Identity
    In Peter Schroeder-Heister, Gerhard Heinzmann, Wilfred Hodges & Pierre Edouard Bour (eds.), Logic, Methodology and Philosophy of Science, Proceedings of the 14th International Congress, . pp. 299-322. 2014.
    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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    Review of 'Realistic Rationalism' (review)
    Erkenntnis 52 (3): 419-423. 2000.
  •  654
    Stairway to Heaven: the abstract method and levels of abstraction in mathematics
    with Jean-Pierre Marquis
    The Mathematical Intelligencer 38 (3): 41-51. 2016.
    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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    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
  •  691
    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 sections. We first show that already in th…Read more
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    Approximations and truth spaces
    Journal of Philosophical Logic 20 (4). 1991.
    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,…Read more
  •  89
    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 ...
  •  101
    Mathematical Conceptware: Category Theory: Critical Studies/Book Reviews
    Philosophia Mathematica 18 (2): 235-246. 2010.
    (No abstract is available for this citation)
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    Critical Notice (review)
    Canadian Journal of Philosophy 30 (1): 161-178. 2000.
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    Towards a Theory of Partial Truth
    Dissertation, 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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    Category Theory and Structuralism in Mathematics: Syntactical Considerations
    In Evandro Agazzi & György Darvas (eds.), Philosophy of Mathematics Today, Kluwer Academic Publishers. pp. 123--136. 1997.
  •  322
    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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    Mathematical engineering and mathematical change
    International 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