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The philosophy of mathematics today
PART I: ONTOLOGY, MODELS, AND INDETERMINACY PART II: MATHEMATICS, SCIENCE, AND METHOD PART III: FINITISM AND INTUITIONISM PART IV: FREGE AND THE FOUNDATIONS OF ARITHMETIC PART V: SETS, STRUCTURE, ANDExpand
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Frege : importance and legacy
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Extensions of the Finitist Point of View
Hilbert developed his famous finitist point of view in several essays in the 1920s. In this paper, we discuss various extensions of it, with particular emphasis on those suggested by Hilbert andExpand
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WHAT FINITISM COULD NOT BE
SUMMARY: In his paper “Finitism” (1981), W.W. Tait maintains that the chief difficulty for everyone who wishes to understand Hilbert’s conception of finitist mathematics is this: to specify the senseExpand
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Hume’s Principle and Axiom V Reconsidered: Critical Reflections on Frege and His Interpreters
  • M. Schirn
  • Philosophy, Computer Science
  • Synthese
  • 2004
TLDR
In this paper, I shall discuss several topics related to Frege’s paradigms of second-order abstraction principles and his logicism. Expand
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Fregean Abstraction, Referential Indeterminacy and the Logical Foundations of Arithmetic
In Die Grundlagen der Arithmetik, Frege attempted to introduce cardinalnumbers as logical objects by means of a second-order abstraction principlewhich is now widely known as ``Hume's Principle''Expand
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Frege's Approach to the Foundations of Analysis (1874–1903)
The concept of quantity (Größe) plays a key role in Frege's theory of real numbers. Typically enough, he refers to this theory as ‘theory of quantity’ (‘Größenlehre’) in the second volume of his opusExpand
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