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, AND… Expand

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 and… Expand

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 sense… Expand

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

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 opus… Expand