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Single Idea 10832

[from 'On Second-Order Logic' by George Boolos, in 5. Theory of Logic / G. Quantification / 2. Domain of Quantification ]

Full Idea

One may say that '∀x x=x' means 'everything is identical to itself', but one must realise that one's answer has a determinate sense only if the reference (range) of 'everything' is fixed.

Gist of Idea

'∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed

Source

George Boolos (On Second-Order Logic [1975], p.46)

Book Reference

Boolos,George: 'Logic, Logic and Logic' [Harvard 1999], p.519


A Reaction

This is the problem now discussed in the recent book 'Absolute Generality', of whether one can quantify without specifying a fixed or limited domain.