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311 results on '"Panza, Marco"'

1. Platonism, De Re, and (Philosophy of) Mathematical Practice

Author

Panza, Marco

Subjects
Mathematics - History and Overview
Abstract

The chapter advances a reformulation of the classical problem of the nature of mathematical objects (if any), here called "Plato's problem," in line with the program of a philosophy of mathematical practice. It then provides a sketch of a platonist solution, following the same perspective. This solution disregards as nonsensical the question of the existence of abstract, and specifically mathematical, objects, by rather focusing on the modalities of our access to them: objects (in general, both concrete and abstract) are regarded as individual contents that we have (or can have) a de re epistemic access to. The question of the existence of mathematical objects is then replaced by that of the modalities of our de re epistemic access to individual mathematical contents.

Published
2023

2. Gastronomical Platonism

Author

Panza, Marco, Rahman, Shahid, Series Editor, Redmond, Juan, Managing Editor, Symons, John, Founding Editor, van Bendegem, Jean Paul, Editorial Board Member, Benis Sinaceur, Hourya, Editorial Board Member, van Benthem, Johan, Editorial Board Member, Chemla, Karine, Editorial Board Member, Dubucs, Jacques, Editorial Board Member, Fagot-Largeault, Anne, Editorial Board Member, Van Fraassen, Bas C., Editorial Board Member, Gabbay, Dov M., Editorial Board Member, McNamara, Paul, Editorial Board Member, Priest, Graham, Editorial Board Member, Sandu, Gabriel, Editorial Board Member, Smets, Sonja, Editorial Board Member, Street, Tony, Editorial Board Member, Sundholm, Göran, Editorial Board Member, Wansing, Heinrich, Editorial Board Member, Williamson, Timothy, Editorial Board Member, Zarepour, Mohammad Saleh, Editorial Board Member, and Klev, Ansten, editor

Published
2024
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4. The Agnostic Structure of Data Science Methods

Author

Napoletani, Domenico, Panza, Marco, and Struppa, Daniele

Subjects
Statistics - Other Statistics, 68T01
Abstract

In this paper we argue that data science is a coherent and novel approach to empirical problems that, in its most general form, does not build understanding about phenomena. Within the new type of mathematization at work in data science, mathematical methods are not selected because of any relevance for a problem at hand; mathematical methods are applied to a specific problem only by 'forcing', i.e. on the basis of their ability to reorganize the data for further analysis and the intrinsic richness of their mathematical structure. In particular, we argue that deep learning neural networks are best understood within the context of forcing optimization methods. We finally explore the broader question of the appropriateness of data science methods in solving problems. We argue that this question should not be interpreted as a search for a correspondence between phenomena and specific solutions found by data science methods; rather, it is the internal structure of data science methods that is open to precise forms of understanding., Comment: 24 pp., no figures, a new abstract and new key-words added

Published
2021

5. Frege's Theory of Real Numbers: A consistent Rendering

Author

Boccuni, Francesca and Panza, Marco

Subjects
Mathematics - Logic
Abstract

Frege's definition of the real numbers, as envisaged in the second volume of \textit{Grundgesetze der Arithmetik}, is fatally flawed by the inconsistency of Frege's ill-fated \textit{Basic Law V}. We restate Frege's definition in a consistent logical framework and investigate whether it can provide a logical foundation of real analysis. Our conclusion will deem it doubtful that such a foundation along the lines of Frege's own indications is possible at all.

Published
2021

12. Asymptotic Quasi-completeness and ZFC

Author

Džamonja, Mirna, Panza, Marco, Wansing, Heinrich, Editor-in-Chief, Avron, Arnon, Editorial Board Member, Bimbó, Katalin, Editorial Board Member, Corsi, Giovanna, Editorial Board Member, Czelakowski, Janusz, Editorial Board Member, Giuntini, Roberto, Editorial Board Member, Goré, Rajeev, Editorial Board Member, Herzig, Andreas, Editorial Board Member, Holliday, Wesley, Editorial Board Member, Indrzejczak, Andrzej, Editorial Board Member, Mundici, Daniele, Editorial Board Member, Odintsov, Sergei, Editorial Board Member, Orlowska, Ewa, Editorial Board Member, Schroeder-Heister, Peter, Editorial Board Member, Venema, Yde, Editorial Board Member, Weiermann, Andreas, Editorial Board Member, Wolter, Frank, Editorial Board Member, Xu, Ming, Editorial Board Member, Malinowski, Jacek, Editorial Board Member, Skurt, Daniel, Assistant Editor, Wojcicki, Ryszard, Founding Editor, and Carnielli, Walter, editor

Published
2018
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18. Forcing Optimality and Brandt’s Principle

Author

Napoletani, Domenico, Panza, Marco, Struppa, Daniele C., Bokulich, Alisa, Series editor, Cohen, Robert S., Series editor, Renn, Jürgen, Series editor, Gavroglu, Kostas, Series editor, Lenhard, Johannes, editor, and Carrier, Martin, editor

Published
2017
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32. Newton on Indivisibles

Author

Malet, Antoni, Panza, Marco, Knobloch, Eberhard, Series editor, Kragh, Helge, Series editor, Remmert, Volker, Series editor, and Jullien, Vincent, editor

Published
2015
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33. Wallis on Indivisibles

Author

Malet, Antoni, Panza, Marco, Knobloch, Eberhard, Series editor, Kragh, Helge, Series editor, Remmert, Volker, Series editor, and Jullien, Vincent, editor

Published
2015
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34. Platonismo, De Re e (Filosofia da) Prática Matemática

Author

Panza, Marco

Subjects
Objetos Matemáticos, (Filosofia da) Prática Matemática, De Re, Materials Chemistry, Platonismo
Abstract

No presente artigo, expõe-se uma versão acerca do platonismo voltada para uma filosofia da prática matemática, qual seja (tal versão) a de que a matemática pode ser adequadamente explicada como uma atividade intelectual que trata de conteúdos abstratos individuais sui generis, fixados de modo a serem capazes de nos permitir um acesso epistêmico de re a eles. Busca-se deixar claro que essa versão não tem estritamente nada a ver com a existência de tais conteúdos (nem com a veracidade de algumas afirmações sobre eles). Ou melhor, o autor do texto não só não afirma a existência de objetos matemáticos, mas também não a nega.

Published
2022
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36. Many infinities, or only one?

Author

Struppa, D. C., Panza, Marco, and Giardina, Giovanna

Subjects
Aristotle, Projective Geometry, Potential and actual infinity, Set Theory, Aristotle, Potential and actual infinity, Projective Geometry, Infinitesimal Calculus, Set Theory, Measure Theory, Infinitesimal Calculus, Measure Theory
Published
2023

45. A Question of Fundamental Methodology:Reply to Mikhail Katz and His Coauthors

Author

Archibald, Tom, Arthur, Richard T. W., Ferraro, Giovanni, Gray, Jeremy, Jesseph, Douglas, Lützen, Jesper, Panza, Marco, Rabouin, David, Schubring, Gert, Archibald, Tom, Arthur, Richard T. W., Ferraro, Giovanni, Gray, Jeremy, Jesseph, Douglas, Lützen, Jesper, Panza, Marco, Rabouin, David, and Schubring, Gert

Published
2022

47. La géométrie de Descartes est-elle une extension de celle d’Euclide ?

Author

Panza, Marco

Subjects
Mathématiques, Exactitude, Ontologie, Démonstration, Construction
Abstract

Dans cet article nous cherchons à montrer comment la géométrie de Descartes s’enracine dans une vision de la nature de la géométrie dérivant directement de la manière classique de faire et concevoir celle-ci, se retrouvant dans les Éléments d’Euclide. En particulier, nous insistons sur la structure de l’ontologie de la géométrie et sur le rôle crucial joué par la solution des problèmes dans la constitution de celle-ci.

Published
2022
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48. L'applicabilité des mathématiques

Author

Molinini, Daniele, Panza, Marco, Universidade de Lisboa (ULISBOA), Institut d'Histoire et de Philosophie des Sciences et des Techniques (IHPST), Université Paris 1 Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS), and Chapman University

Subjects
[SHS.HISPHILSO]Humanities and Social Sciences/History, Philosophy and Sociology of Sciences, ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2022

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