From logic to practice : Italian studies in the philosophy of mathematics
著者
書誌事項
From logic to practice : Italian studies in the philosophy of mathematics
(Boston studies in the philosophy of science, v. 308)
Springer, c2015
大学図書館所蔵 全9件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references
内容説明・目次
内容説明
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.
目次
- PART I: THE HISTORICAL DIMENSION OF MATHEMATICS.- Chapter 1: A Geometrical Constructive Approach to Infinitesimal Analysis: Epistemological Potential and Boundaries of Tractional Motion
- Pietro Milici.- Chapter 2: Plane and Solid Geometry: A Note on Purity of Methods
- Paolo Mancosu and Andrew Arana.- Chapter 3: Formalization and Intuition in Husserl's Raumbuch
- Edoardo Caracciolo.- PART II: LOOKING AT MATHEMATICS THROUGH LOGIC.- Chapter 4: Frege's Grundgesetze and a Reassessment of Predicativity
- Francesca Boccuni.- Chapter 5: A Deflationary Account of the Truth of the Goedel Sentence G
- Mario Piazza and Gabriele Pulcini.- Chapter 6: Rule-following and the Limits of Formalization: Wittgenstein's Considerations Through the Lens of Logic
- Paolo Pistone.- Chapter 7: Paradox and Inconsistency: Revising Tennant's Distinction Through Schroeder-Heister's Assumption Rules
- Luca Tranchini.- Chapter 8: Costructability and Geometry
- Alberto Naibo.- Chapter 9: A Cut-like Inference in a Framework of Explicit Composition for Various Calculi of Natural Deduction
- Michael Arndt and Laura Tesconi.- Chapter 10: On the Distinction Between Sets and Classes: A Categorical Perspective
- Samuele Maschio.- PART III: PHILOSOPHY AND MATHEMATICS.- Chapter 11: Structure and Applicability
- Michele Ginammi.- Chapter 12: Defending Maddy's Mathematical Naturalism from Roland's Criticism: The Role of Mathematical Depth
- Marina Imocrante.- Chapter 13: On the Indispensable Premises of the Indispensability Argument
- Marco Panza and Andrea Sereni.- Chapter 14: Naturalness in Mathematics: On the Statical-dynamical Opposition
- Luca San Mauro and Giorgio Venturi.- Chapter 15: An Inquiry Into the Practice of Proving in Low-dimensional Topology
- Silvia de Toffoli and Valeria Giardino.
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