The existence of non-standard numbers in first-order arithmetics is a semantic obstacle for modelling our arithmetical skills. This article argues that so far there is no adequate approach to overcome such a semantic obstacle, because we can also find out, and deal with, non-standard elements in Turing machines.

Gödel always claimed that he did not know Skolem's Helsinki lecture when writing his dissertation. Some questions and doubts have been raised about this claim, in particular on the basis of a library slip showing that he had requested Skolem's paper in 1928. It is shown that this library slip does not constitute evidence against Gödel's claim, and that, on the contrary, the library slip and other archive material actually corroborate what Gödel said.

In his famous paper Der Wahrheitsbegriff in den formalisierten Sprachen (Polish edition: Nakładem/Prace Towarzystwa Naukowego Warszawskiego, wydzial, III, 1933), Alfred Tarski constructs a materially adequate and formally correct definition of the term “true sentence” for certain kinds of formalised languages. In the case of other formalised languages, he shows that such a construction is impossible but that the term “true sentence” can nevertheless be consistently postulated. In the Postscript that Tarski added to a later version of this paper (Studia Philosophica, (...) 1, 1935), he does not explicitly include limits for the kinds of language for which such a construction is possible. This absence of such limits has been interpreted as an implied claim that such a definition of the term “true sentence” can be constructed for every language. This has far-reaching consequences, not least for the widely held belief that Tarski changed from an universalistic to an anti-universalistic standpoint. We will claim that the consequence of anti-universalism is unwarranted, given that it can be argued that the Postscript is not in conflict with the existence of limits outside of which a definition of “true sentence” cannot be constructed. Moreover, by a discussion of transfinite type theory, we will also be able to accommodate other of the changes made in Tarski’s Postscript within a type-theoretical framework. The awareness of transfinite type theory afforded by this discussion will lead, in turn, to an account of Tarski’s Postscript that shows a gradual change in his logical work, rather than any of the more radical transitions which the Postscript has been claimed to reflect. (shrink)

In this paper an attempt is made to present Skolem's argument, for the relativity of some set-theoretical notions as a sensible one. Skolem's critique of set theory is seen as part of a larger argument to the effect that no conclusive evidence has been given for the existence of uncountable sets. Some replies to Skolem are discussed and are shown not to affect Skolem's position, since they all presuppose the existence of uncountable sets. The paper ends with an assessment of (...) the assumptions on which Skolem's argument rests from a present-day perspective. (shrink)

Using hitherto unpublished manuscripts from the Zermelo Nachlass, I describe the development of the notion of definiteness and the discussion about it, giving a conclusive picture of Zermelo's thoughts up to the late thirties. As it turns out, Zermelo's considerations about definiteness are intimately related to his concept of a Cantorian universe of categorically definable sets that may be considered an inner model of set theory in an ideationally given universe of classes.

Many contributors of the debate about knowledge by testimony concentrate on the problem of justification. In my paper I will stress a different point – the concept of testimony itself. As a starting point I will use the definitional proposal of Jennifer Lackey. She holds that the concept of testimony should be regarded as entailing two aspects – one corresponding to the speaker, the other one to the hearer. I will adopt the assumption that we need to deal with both (...) aspects. Nevertheless, I will show that her concept – which suggests regarding testimony as an act of communication conveying information – is too broad and, therefore, I will end up with a different twofold definition. (shrink)

This paper is divided in five sections. Section 11.1 sketches the history of the distinction between speech act with negative content and negated speech act, and gives a general dynamic interpretation for negated speech act. “Downdate semantics” for AGM contraction is introduced in Section 11.2. Relying on semantically interpreted contraction, Section 11.3 develops the dynamic semantics for constative and directive speech acts, and their external negations. The expressive completeness for the formal variants of natural language utterances, none of which is (...) a retraction, has been proved in Section 11.4. The last section gives a laconic answer to the question posed in the title of the paper. (shrink)