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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 Ref
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.
| 18073 | Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability [Dummett, by Kitcher] |
| 19054 | Meaning as use puts use beyond criticism, and needs a holistic view of language [Dummett] |
| 19055 | Stating a sentence's truth-conditions is just paraphrasing the sentence [Dummett] |
| 19056 | If a sentence is effectively undecidable, we can never know its truth conditions [Dummett] |
| 19057 | Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances [Dummett] |