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Leibniz and Russell on Existence and Quantification Theory

Published online by Cambridge University Press:  01 January 2020

Jeffrey Skosnik*
Affiliation:
Simon Fraser University

Extract

Never shall this be proved, that things that are not are. Parmenides

To say that something does not exist, or that there is something which is not, is clearly a contradiction in terms; hence “(∀x) (x exists)” must be true. Moreover, we should certainly expect leave to put any primitive name of our language for the “x” of any matrix “ … x … ”, and to infer the resulting singular statement from “(∀x) ( … x … )”; it is difficult to contemplate any alternative logical rule for reasoning with names.

Type
Research Article
Copyright
Copyright © The Authors 1980

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