Projects per year
Abstract
Recent years have seen a wealth of discussion on the topic of the foundations of mathematics, and the extent to which category theory, set theory, or some other framework serves, or can serve, as a foundation, or the foundation of some, most, or all of mathematics. Of course, adjudications of these matters depend on what, exactly, a foundation is, and what it is for, and it depends on what mathematics is. It is like a game of Jeopardy. We are given some answers: set theory, category theory, abstraction principles, etc., and we have to figure out what the questions are. Most of the participants in this debate are at least fairly clear about what their questions are, but it seems that the participants do not have the same questions in mind. And some of the questions have disputable presuppositions concerning the nature of mathematics. My purpose here is to survey some of the terrain. The goal is to clarify the discussion, and perhaps to advance parts of it, without plumping for one or the other view.
Original language  English 

Title of host publication  Foundational theories of classical and constructive mathematics 
Editors  Giovanni Sommaruga 
Place of Publication  Dordrecht 
Publisher  Springer 
Pages  97110 
ISBN (Electronic)  9789400704312 
ISBN (Print)  9789400704305 
DOIs  
Publication status  Published  2011 
Publication series
Name  Western Ontario Series in the Philosophy of Science 

Publisher  Springer 
Volume  76 
ISSN (Print)  1566659X 
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Dive into the research topics of 'Foundations: structures, sets, and categories'. Together they form a unique fingerprint.Projects
 1 Finished

FOUNDATIONS OF LOGICAL CONSEQUENCE: Foundations of Logical Consequence
Read, S., Priest, G. G., Shapiro, S. & Celani, L.
Arts and Humanities Research Council
1/01/09 → 30/06/12
Project: Standard