From Sets and Types to Topology and Analysis

Towards practicable foundations for constructive mathematics

Author: Laura Crosilla

Publisher: Clarendon Press

ISBN:

Category: Mathematics

Page: 372

View: 135

This edited collection bridges the foundations and practice of constructive mathematics. Aimed at academic logicians, mathematicians, philosophers and computer scientists. Including, with contributions from leading researchers, it is up-to-date, highly topical and broad in scope.

Computer Science Logic

23rd International Workshop, CSL 2009, 18th Annual Conference of the EACSL, Coimbra, Portugal, September 7-11, 2009, Proceedings

Author: European Association for Computer Science Logic

Publisher: Springer Science & Business Media

ISBN:

Category: Computers

Page: 567

View: 342

This book constitutes the proceedings of the 23rd International Workshop on Computer Science Logic, CSL 2009, held in Coimbra, Portugal, in September 2009. The 34 papers presented together with 5 invited talks were carefully reviewed and selected from 89 full paper submissions. All current aspects of logic in computer science are addressed, ranging from foundational and methodological issues to application issues of practical relevance. The book concludes with a presentation of this year's Ackermann award, the EACSL Outstanding Dissertation Award for Logic in Computer Science.

Logicism, Intuitionism, and Formalism

What Has Become of Them?

Author: Sten Lindström

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 512

View: 412

This anthology reviews the programmes in the foundations of mathematics from the classical period and assesses their possible relevance for contemporary philosophy of mathematics. A special section is concerned with constructive mathematics.

Logic, Mathematics, Philosophy, Vintage Enthusiasms

Essays in Honour of John L. Bell

Author: David DeVidi

Publisher: Springer Science & Business Media

ISBN:

Category: Philosophy

Page: 486

View: 398

The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic (William Lawvere, Peter Aczel, Graham Priest, Giovanni Sambin); analytical philosophy (Michael Dummett, William Demopoulos), philosophy of science (Michael Redhead, Frank Arntzenius), philosophy of mathematics (Michael Hallett, John Mayberry, Daniel Isaacson) and decision theory and foundations of economics (Ken Bimore). Most articles are contributions to current philosophical debates, but contributions also include some new mathematical results, important historical surveys, and a translation by Wilfrid Hodges of a key work of arabic logic.

Epistemology versus Ontology

Essays on the Philosophy and Foundations of Mathematics in Honour of Per Martin-Löf

Author: P. Dybjer

Publisher: Springer Science & Business Media

ISBN:

Category: Philosophy

Page: 388

View: 956

This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice (ZFC). This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics?