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The Philosophy of Mathematical Practice
TLDR
This chapter discusses the philosophical relevance of the interaction between mathematical physics and pure mathematics, and the role of computers in mathematics in this interaction. Expand
From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920s
Section 1 L.E.J. BROUWER Section 2 H. WEYL Section 3 P. BERNAYS AND D. HILBERT Section 4 INTUITIONISTIC LOGIC Index
Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century
TLDR
Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period with a sophisticated picture of the subtle dependencies between technical development and philosophical reflection. Expand
MEASURING THE SIZE OF INFINITE COLLECTIONS OF NATURAL NUMBERS: WAS CANTOR’S THEORY OF INFINITE NUMBER INEVITABLE?
  • P. Mancosu
  • Computer Science, Mathematics
  • The Review of Symbolic Logic
  • 1 December 2009
TLDR
This article reviewing the contributions of some thinkers who argued in favor of the assignment of different sizes to infinite collections of natural numbers and some recent mathematical developments that generalize the part–whole principle to infinite sets in a coherent fashion show how these new developments are important for a proper evaluation of a number of positions in philosophy of mathematics. Expand
Mathematical Explanation: Why it Matters
This chapter offers a broad survey of the literature on mathematical explanation, and shows the importance of this area of work for a philosophical understanding of mathematical practice and forExpand
The Varieties of Mathematical Explanation
Nous vous presentons ici le colloque "Fondements et Justification des Pratiques en Mathematiques" qui s'est deroule a l'issu du groupe : Les fondations des mathematiques au XIXe siecle : entreExpand
Visualization in Logic and Mathematics
TLDR
The article describes and explains the way in whichVisual thinking fell into desrepute, the renaissance of visual thinking in mathematics over recent decades, and the ways in which visual thinking has been rehabilitated in epistemology of mathematics and logic. Expand
Torricelli's Infinitely Long Solid and Its Philosophical Reception in the Seventeenth Century
IN 1641 EVANGELISTA TORRICELLI discovered that a certain solid of infinite length, which he called the "acute hyperbolic solid," has a finite volume. This paradoxical result created considerableExpand
Visualization, Explanation and Reasoning Styles in Mathematics
This book contains groundbreaking contributions to the philosophical analysis of mathematical practice. Several philosophers of mathematics have recently called for an approach to philosophy ofExpand
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