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Award for foundations of mathematics study

 

The University of St Andrews’ School of Philosophical and Anthropological Studies has been awarded nearly half a million pounds to conduct research into the logical and metaphysical foundations of classical mathematics.

Professor Crispin Wright and Dr Fraser MacBride of the Department of Logic and Metaphysics have been awarded £450,000 from the Arts and Humanities Research Board to conduct the five-year study.

The grant, which will be administered under the aegis of the Philosophy Research Centre, Arché, of which Professor Wright and Dr MacBride are the directors, will be used to finance postdoctoral researchers and PhD students working on specific aspects of the project, and national and international conferences and workshops.

Professor Wright explained, “Most of us learn our basic mathematics as a network of accepted techniques and assumptions and never bother to inquire in what sense it constitutes a body of knowledge, or how it could be known in principle.

“Our study will revisit the answer of the great 19th century German philosopher and mathematician Gottlob Frege who attempted to show that the basic laws of classical arithmetic and analysis are in effect theorems of pure logic. If he had succeeded, he would have shown that our knowledge of these fundamental branches of pure mathematics is of a species with our knowledge of the laws of logic. His programme failed because the system into which he attempted to affect the necessary reduction proved irreparably inconsistent and the attempt was abandoned.

“But recent work has shown how important formal and epistemological insights can be salvaged from the wreckage. We now know that a modified but essentially Fregean programme for the foundations of arithmetic can be pushed through. Our project is to see whether a similar approach can be extended to the theory of real numbers and set theory, and to pursue the general metaphysical and epistemological issues it gives rise to, which have a bearing all over philosophy”.

In conjunction with the five-year Leverhulme Research Professorship awarded to Professor Wright in 1998 for his own work in the area, the AHRB award brings the external funding to St Andrews generated by this research to nearly three quarters of a million pounds and consolidates St Andrews’ reputation for excellence in philosophical research.

ENDS

Issued by Beattie Media on behalf of the University of St Andrews For more information please contact Claire Grainger on 01334 462530, 07730 415 015 or email cg24@st-andrews.ac.uk Ref: crispinwright/standrews/chg/29may2000

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