Work on how to axiomatize the subtheories of a first-order theory in which only a proper subset of their extra-logical vocabulary is being used led to a theorem on recursive axiomatizability and to an interpolation theorem for first-order logic. There were some fortuitous events and several logicians played a helpful role.

This paper seeks to evaluate the potential of the Newman objection to function as an immanent critique of Carnap's use of the Ramsey method of regimenting scientific theories. Stress is laid on the distinctive way in which ramseyfications are used by Carnap to formulate the analytic/synthetic distinction for the theoretical language and on the difference between the ontological and the epistemic readings of the Newman objection. While the former reading of the Newman objection is rejected as trading on an assumption (...) that Carnap did not share, the latter is accepted as critical. It is argued to turn on overlooking that the Ramsey sentence constitutes an idealization concerning which our normal expectations of what theories are like are bound to be frustrated. This idealisation need not reflect Carnap's considered view but can be regarded as adopted solely for the project of semantic explication. The distinctions drawn in the course of the argument also help to motivate Carnap's abstention from the discourse of realism and its denial. (shrink)

Quine’s thesis of underdetermination is significantly weaker than it has been taken to be in the recent literature, for the following reasons: (i) it does not hold for all theories, but only for some global theories, (ii) it does not require the existence of empirically equivalent yet logically incompatible theories, (iii) it does not rule out the possibility that all perceived rivalry between empirically equivalent theories might be merely apparent and eliminable through translation, (iv) it is not a fundamental thesis (...) within Quine’s philosophy, and (v) it does not carry with it the anti-realistic consequences often associated with the thesis in recent debates. The paper analyzes Quine’s views on the matter and the changes they underwent over the years. A conjecture is put forth about why Quine’s thesis has been so widely misrepresented: Quine’s writings up to 1975 tackled primarily the formulation and justification of the thesis, but afterwards were concerned mostly with the question whether empirically equivalent rivals to the theory we hold are to be considered true also. When this latter discussion is read without bearing in mind Quine’s earlier formulation and justification of the thesis, his thesis seems to have stronger epistemic consequences than it actually does. A careful reading of his later writings shows, however, that the formulation of the thesis remained unchanged after 1975, and that his mature and considered views supported only a very mitigated version of the thesis. (shrink)

The logic of the weak law of excluded middleKC p is obtained by adding the formula A A as an axiom scheme to Heyting's intuitionistic logicH p . A cut-free sequent calculus for this logic is given. As the consequences of the cut-elimination theorem, we get the decidability of the propositional part of this calculus, its separability, equality of the negationless fragments ofKC p andH p , interpolation theorems and so on. From the proof-theoretical point of view, the formulation presented (...) in this paper makes clearer the relations betweenKC p ,H p , and the classical logic. In the end, an interpretation of classical propositional logic in the propositional part ofKC p is given. (shrink)