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Set—Theoretical Representations of Ordered Pairs and Their Adequacy for the Logic of Relations

Published online by Cambridge University Press:  01 January 2020

Randall R. Dipert
Randall R. Dipert*
Affiliation:
S.U.N.Y. College at Fredonia
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Extract

One of the most significant discoveries of early twentieth century mathematical logic was a workable definition of ‘ordered pair’ totally within set theory. Norbert Wiener, and independently Casimir Kuratowski, are usually credited with this discovery. A definition of ‘ordered pair’ held the key to the precise formulation of the notions of ‘relation’ and ‘function’ — both of which are probably indispensable for an understanding of the foundations of mathematics. The set-theoretic definition of ‘ordered pair’ thus turned out to be a key victory for logicism, providing one admits set theory is logic. The definition also was instrumental in achieving the appearance of ontological economy — since it seemed only sets were needed — although this feature was emphasized only later.

Type
Research Article
Information
Canadian Journal of Philosophy , Volume 12 , Issue 2 , June 1982 , pp. 353 - 374
Copyright
Copyright © The Authors 1982

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