Foundational Adventures

by Neil Tennant (Editor)

This volume is a tribute by his peers, and by younger scholars of the next generation, to Harvey M. Friedman, perhaps the most profound foundationalist since Kurt Godel. Friedman's researches, beginning precociously in his mid-teens, have fundamentally shaped our contemporary understanding of set theory, recursion theory, model theory, proof theory and metamathematics. His achievements in concept formation and theory formulation have also renewed the standard set by Godel and Alfred Tarski for the general intellectual interest and importance of technical work in foundations. Friedman pioneered the now well-established and flourishing field of Reverse Mathematics, whose aim is to calibrate the intrinsic logico-mathematical consistency-strength of all the important theorems of mathematics. He has relentlessly pursued the full extent of the incompleteness phenomena into which Godel provided the first revealing glimpse. The Godel--Friedman program, as it is now deservingly called, seeks to find simple, natural and elegant mathematical statements of a combinatorial nature, that can be proved to be independent of set theory even when extended by powerful large-cardinal existence axioms.

314 pages, Paperback

First published January 8, 2014

About the author

Neil Tennant is an American philosopher. He is Arts & Humanities Distinguished Professor of Philosophy at the Ohio State University; and, before taking up his appointment at the Ohio State University he held positions at the University of Edinburgh, the University of Stirling, and the Australian National University.

Along with Michael Dummett, Crispin Wright, Tennant is one of the most notable figures who have attempted to extend the project of providing anti-realist semantics for empirical language. He has also written extensively on intuitionistic logic and other non-classical logics. [wikipedia]