Boston Studies in the Philosophy and History of Science

From Logic to Practice

Italian Studies in the Philosophy of Mathematics

Editors: Lolli, Gabriele, Panza, Marco, Venturi, Giorgio (Eds.)

  • Allows young (untenured) scholars meet philosophy in their (non philosophical) work
  • Revisits traditional questions and explores new realities
  • Demonstrates the limits of formalization
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  • ISBN 978-3-319-10434-8
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Hardcover $129.00
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  • ISBN 978-3-319-10433-1
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  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
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  • ISBN 978-3-319-34845-2
  • Free shipping for individuals worldwide
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About this book

This book brings together young researchers from a variety of fields within mathematics, philosophy and logic. It discusses questions that arise in their work, as well as themes and reactions that appear to be similar in different contexts. The book shows that a fairly intensive activity in the philosophy of mathematics is underway, due on the one hand to the disillusionment with respect to traditional answers, on the other to exciting new features of present day mathematics. The book explains how the problem of applicability once again plays a central role in the development of mathematics. It examines how new languages different from the logical ones (mostly figural), are recognized as valid and experimented with and how unifying concepts (structure, category, set) are in competition for those who look at this form of unification. It further shows that traditional philosophies, such as constructivism, while still lively, are no longer only philosophies, but guidelines for research. Finally, the book demonstrates that the search for and validation of new axioms is analyzed with a blend of mathematical historical, philosophical, psychological considerations.

About the authors

Gabriele Lolli is Professor of Philosophy of Mathematics at the Scuola Normale Superiore of Pisa, after a career in Mathematical Logic. His main present interests concern the origin of set theory, mathematical proof and the relations between mathematics and literature. Among his recent publications are QED. Fenomenologia della dimostrazione, Bollati Boringhieri, Turin, 2005; “Experimental methods in proofs", in R. Lupacchini, G. Corsi (eds.), Deduction, Computation, Experiment, Springer, 2008; Nascita di un'idea matematica, Edizioni della Normale, Pisa, 2013; “Mathematics according to Calvino", in M. Emmer (ed.), Imagine Math2, Springer, 2013.

Marco Panza is Research Director at the CNRS and member of the IHPST (CNRS and Univ. of Paris 1 Panthéon Sorbonne). He is the author of several books and papers and the editor of several collective volumes in the domains of history and philosophy of mathematics. For the Boston Studies in the Philosophy of Sciences, he edited, with M. Otte, Analysis and sinthesis in Mathematics. History and Philosophy (1997). His books include: Newton et les origines de l'analyse, 1664-1666, Blanchard, Paris, 2005, and Plato's Problem. Introduction to Mathematical Platoinism, Palgrave Mac Millan, Bsingstoke (UK), 2013 (co-authored with Andrea Sereni).

Giorgio Venturi is currently a post-doc at CLE (Campinas) and former PhD student both in philosophy at Scuola Normale Superiore of Pisa, under the supervision of Gabriele Lolli, and in mathematics at the Université Paris Diderot, under the supervision of Boban Velickovic. His main research field is set theory, both from a purely mathematical perspective - he co-authored Velickovic Proper forcing remastered appeared in Appalachian set theory (Cambridge University Press) - and from a philosophical point of view, as in Foundation of mathematics between theory and practice appeared in Philosophia scientae 18(1), 2014.

Table of contents (15 chapters)

  • A Geometrical Constructive Approach to Infinitesimal Analysis: Epistemological Potential and Boundaries of Tractional Motion

    Milici, Pietro

    Pages 3-21

  • Plane and Solid Geometry: A Note on Purity of Methods

    Mancosu, Paolo (et al.)

    Pages 23-31

  • Formalization and Intuition in Husserl’s Raumbuch

    Caracciolo, Edoardo

    Pages 33-50

  • Frege’s Grundgesetze and a Reassessment of Predicativity

    Boccuni, Francesca

    Pages 53-70

  • A Deflationary Account of the Truth of the Gödel Sentence $$\mathcal{G}$$

    Piazza, Mario (et al.)

    Pages 71-90

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-319-10434-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-319-10433-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-3-319-34845-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
From Logic to Practice
Book Subtitle
Italian Studies in the Philosophy of Mathematics
Editors
  • Gabriele Lolli
  • Marco Panza
  • Giorgio Venturi
Series Title
Boston Studies in the Philosophy and History of Science
Series Volume
308
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-10434-8
DOI
10.1007/978-3-319-10434-8
Hardcover ISBN
978-3-319-10433-1
Softcover ISBN
978-3-319-34845-2
Series ISSN
0068-0346
Edition Number
1
Number of Pages
XIX, 336
Number of Illustrations and Tables
17 b/w illustrations, 10 illustrations in colour
Topics