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Science & Reason$
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Henry E. Kyburg

Print publication date: 1991

Print ISBN-13: 9780195062533

Published to Oxford Scholarship Online: October 2011

DOI: 10.1093/acprof:oso/9780195062533.001.0001

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Logic and Mathematics

Logic and Mathematics

Chapter:
(p.17) 2 Logic and Mathematics
Source:
Science & Reason
Author(s):

Jr. Henry E. Kyburg

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780195062533.003.0002

This chapter discusses the philosophy and logic behind the mathematical ideas of first-order logic, metalanguages, arithmetic, and geometry. It familiarizes the reader to these mathematical ideas, which will be used in succeeding chapters. The chapter also contrasts that mathematical or logical theories can utilize these mathematical ideas, while scientific theories will find them inapplicable. First-order logic involves conclusions based on premises which are given to be true with no room for imprecision or vagueness, both of which are crucial to the productive use of scientific language. Metalanguage is contrasted with object language, in which scientific laws are expressed. Both arithmetic and geometry are used with idealized, abstract objects and have a limited physical application.

Keywords:   mathematics, logic, first-order logic, metalanguages, arithmetic, geometry

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