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Leibniz and Russell on Existence and Quantification Theory
Published online by Cambridge University Press: 01 January 2020
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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.
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References
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