Chapter

DEDUCTIVE CONSTRAINTS: PROBLEM CASES, POSSIBLE SOLUTIONS

David Christensen

in Putting Logic in its Place

Published in print November 2004 | ISBN: 9780199263257
Published online July 2005 | e-ISBN: 9780191602603 | DOI: http://dx.doi.org/10.1093/0199263256.003.0003
DEDUCTIVE CONSTRAINTS: PROBLEM CASES, POSSIBLE SOLUTIONS

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Develops an extended version of the Preface Paradox to show how the counter-intuitive binary beliefs mandated by deductive consistency and deductive closure can cascade into massive irrationality. This highlights the Preface Paradox's severity and illuminates what is absurd about the beliefs required by deductive cogency Then shows that situations with Preface Paradox structure occur commonly in ordinary life. Finally, examines and rejects attempts to defend deductive constraints by explaining away our troublesome intuitions in Preface cases and in related cases involving the Lottery Paradox.

Keywords: deductive closure; deductive cogency; deductive consistency; deductive constraints; Lottery Paradox; Preface Paradox; rationality

Chapter.  13745 words. 

Subjects: Philosophy of Mathematics and Logic

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