Formalism and Beyond
On the Nature of Mathematical Discourse

Ed. by Link, Godehard



The essays collected in this volume focus on the role of formalist aspects in mathematical theorizing and practice, examining issues such as infinity, finiteness, and proof procedures, as well as central historical figures in the field, including Frege, Russell, Hilbert and Wittgenstein. Using modern logico-philosophical tools and systematic conceptual and logical analyses, the volume provides a thorough, up-to-date account of the subject.

Table of Contents

Frontmatter
Pages i-iv

Contents
Pages v-viii

Preface
Pages ix-x

Duality, Epistemic Efficiency & Consistency
Pages 1-24

Frege on Quantities and Real Numbers in Consideration of the Theories of Cantor, Russell and Others
Pages 25-96

Frege on Formality and the 1906 Independence-Test
Pages 97-118

Formal Discourse in Russell: From Metaphysics to Philosophical Logic
Pages 119-182

On Live and Dead Signs in Mathematics
Pages 183-208

Generalization and the Impossible: Issues in the search for generalized mathematics around 1900
Pages 209-228

Assumptions of Infinity
Pages 229-274

The Interpretation of Classes in Axiomatic Set Theory
Pages 275-314

Purity in Arithmetic: some Formal and Informal Issues
Pages 315-336

Domain Extensions and Higher-Order Syntactical Interpretations
Pages 337-350

Finite Methods in Mathematical Practice
Pages 351-410

List of Contributors
Pages 411-412

Name Index
Pages 413-420

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