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Logic and Mathematics
Published online by Cambridge University Press: 25 February 2009
Extract
It is often said to-day that mathematics is nothing but an extension or development of logic; indeed, the identity of logic and pure mathematics is alleged so confidently by persons whose mathematical attainments entitle them to consideration when they talk about the subject-matter of mathematics, as to be in danger of being ranked with the truths that an educated man should accept on the authority of the specialist. Yet a little reflection might at least make one hesitate. For whatever else may be said about logic, it is generally allowed to study thinking. Some would say merely that it studies inference; but inference is thinking. Now the mathematician thinks and infers, but he does not study the activity of thinking and inferring; and a study of that activity would never make the discoveries credited to the mathematicians.
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- Copyright © The Royal Institute of Philosophy 1928
References
page 4 note 1 Infra, p. 10.
page 5 note 1 In The Nature of Existence, by Mctaggart, J. E., p. 208Google Scholar, “M is N,” “ It is true that M is N,” “ It is true that it is true that M is N,” etc., is said to be an infinite series not vicious tor this sort of reason.
page 5 note 2 Was sind und was sollen die Zahlen, § 5.
page 7 note 1 Space, Time, and Deity, i, p. 43.Google Scholar