Meaning and proofs: on the conflict between classical and intuitionistic logic

it is claimed that nothing less than the total use of the language determines the meaning of an individual sentence. This is to give up the possibility of finding any other fundamental principle of meaning. A second common kind of meaning thoery modifies such a drastically holistic view by singling out a class of sentences that are given individual contents independent of the use of the rest of the language. Typically, there are sentences that are decidable, e.g., by observation, or in matematics, by calculation, and their meaning can thus be understood as determined by their truth-conditions in the classical sense. This is of course a common view in the philosophy of science where the meaning of theoretical sentences is reduced in this way to that of observational sentences. In the case of mathematics, this view was held by Hilbert. A view of this kind immediately makes criticism of use possible because the total use of the sentences cannot be allowed to be used to infer privileged sentences that are false according to the meaning given to them. What may make revisions necessary here is that there are two situations in which privileged sentences can be asserted: whan they are found to be true according to their individual meaning, and when they can be inferred from other sentences. When there is a conflict between these two frounds for asserting a sentence, the first on has the priority; i.e., the first kind of use is the central one that determines meaning.