Single Idea 19057

[catalogued under 5. Theory of Logic / G. Quantification / 1. Quantification]

Full Idea

Classical quantification represents an infinite conjunction or disjunction, and the truth-value is determined by the infinite sum or product of the instances ....but this presupposes that all the instances already possess determinate truth-values.

Gist of Idea

Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances

Source

Michael Dummett (The philosophical basis of intuitionist logic [1973], p.246)

Book Reference

Dummett,Michael: 'Truth and Other Enigmas' [Duckworth 1978], p.246


A Reaction

In the case of the universal quantifier, Dummett is doing no more than citing the classic empiricism objection to induction - that you can't make the universal claim if you don't know all the instances. The claim is still meaningful, though.