Ideas from 'The philosophical basis of intuitionist logic' by Michael Dummett [1973], by Theme Structure

[found in 'Truth and Other Enigmas' by Dummett,Michael [Duckworth 1978,0-7156-1650-1]].

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4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability
                        Full Idea: Dummett argues that classical logic depends on the choice of the concept of truth as central to the theory of meaning, while for the intuitionist the concept of assertability occupies this position.
                        From: report of Michael Dummett (The philosophical basis of intuitionist logic [1973]) by Philip Kitcher - The Nature of Mathematical Knowledge 06.5
                        A reaction: Since I can assert any nonsense I choose, this presumably means 'warranted' assertability, which is tied to the concept of proof in mathematics. You can reason about falsehoods, or about uninterpreted variables. Can you 'assert' 'Fx'?
5. Theory of Logic / G. Quantification / 1. Quantification
Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances
                        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.
                        From: Michael Dummett (The philosophical basis of intuitionist logic [1973], 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.
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
Stating a sentence's truth-conditions is just paraphrasing the sentence
                        Full Idea: An ability to state the condition for the truth of a sentence is, in effect, no more than an ability to express the content of the sentence in other words.
                        From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.224)
                        A reaction: Alternatively, if you give something other than a paraphrase of the sentence as its meaning (such as a proof of its truth), then you seem to have departed from your target sentence. Can we reduce and eliminate our sentences in this way?
If a sentence is effectively undecidable, we can never know its truth conditions
                        Full Idea: If a sentence is effectively undecidable, the condition which must obtain for it to be true is not one which we are capable of recognising whenever it obtains, or of getting ourselves in a position to do so.
                        From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.225)
                        A reaction: The instances of 'undecidable' sentences are most clearly seen in mathematics, such as the Continuum Hypothesis or Goldbach's Conjecture, or anything involving vast infinite cardinals. But do you need precise truth-conditions for meaning?
19. Language / A. Nature of Meaning / 6. Meaning as Use
Meaning as use puts use beyond criticism, and needs a holistic view of language
                        Full Idea: If use constitutes meaning, it might seem that use is beyond criticism. ....But such an attitude can, ultimately, be supported onlly by the adoption of a holistic view of language.
                        From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.218)
                        A reaction: Dummett goes on to say that the rejection of the holistic view of mathematical meaning leads to his preference for intuitionistic logic.