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Free Will and Modern Science$
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Richard Swinburne

Print publication date: 2011

Print ISBN-13: 9780197264898

Published to British Academy Scholarship Online: January 2013

DOI: 10.5871/bacad/9780197264898.001.0001

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Gödel’s incompleteness theorems, free will and mathematical thought

Gödel’s incompleteness theorems, free will and mathematical thought

Chapter:
(p.102) 6 Gödel’s incompleteness theorems, free will and mathematical thought
Source:
Free Will and Modern Science
Author(s):

SOLOMON FEFERMAN

Publisher:
British Academy
DOI:10.5871/bacad/9780197264898.003.0007

The determinism-free will debate is perhaps as old as philosophy itself and has been engaged in from a great variety of points of view including those of scientific, theological, and logical character. This chapter focuses on two arguments from logic. First, there is an argument in support of determinism that dates back to Aristotle, if not farther. It rests on acceptance of the Law of Excluded Middle, according to which every proposition is either true or false, no matter whether the proposition is about the past, present or future. In particular, the argument goes, whatever one does or does not do in the future is determined in the present by the truth or falsity of the corresponding proposition. The second argument coming from logic is much more modern and appeals to Gödel's incompleteness theorems to make the case against determinism and in favour of free will, insofar as that applies to the mathematical potentialities of human beings. The claim more precisely is that as a consequence of the incompleteness theorems, those potentialities cannot be exactly circumscribed by the output of any computing machine even allowing unlimited time and space for its work. The chapter concludes with some new considerations that may be in favour of a partial mechanist account of the mathematical mind.

Keywords:   determinism, free will, Law of Excluded Middle, mathematical mind, Gödel, incompleteness theorems, logic

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