Axel Barceló

There has been considerable debate among scholars as to whether maps can play an inferential role. The debate has focused on whether maps possess the representational format required for logical transitions. This paper addresses a distinct challenge, namely whether maps can satisfy the taking condition, which has been proposed as a necessary condition for inference. In doing so, the focus of the discussion is slightly shifted by analyzing not only the representational structure of maps but also the rational transitions within them. Given that one of the main reasons for the use of maps is navigation, a dynamic notion of inference is proposed which takes into account practical reasoning. According to this view, logical theoretical inferences are just one type of many different kinds of inferential processes.

Contrary to what seems to be predicted by a Strawson-inspired view, in presupposition denials the presupposition triggered by, e.g., ‘the king of France’ seems to be cancelled. To explain this puzzling instance of the projection problem, defenders of a Strawson-inspired view have proposed various ad hoc ambiguities. I develop a version of Segmented Discourse Representation Theory that explains the puzzling presupposition-cancelling phenomenon relying only on independently motivated pragmatic processes. Appealing to Kripke’s “test” for the adequacy of ambiguity motivating counterexamples, I argue that my analysis is to be preferred over proposals that posit ad hoc ambiguities. Two key insights of my analysis are, first, that the “cancellation” of presuppositions in presupposition denials depends upon the illocutionary effects of rejection and correction, and, second, that the process of presupposition accommodation often involves the speaker performing an ancillary sort of speech act, viz. the speech act of presupposing.

Logic is an excellent tool for reasoning about most philosophical topics, including logical issues themselves. Discussions about the validity or otherwise of certain principles have been widespread throughout the history of logic. This chapter exemplifies that with the analysis of the debate surrounding connexive logics. In connexive logics, certain principles involving mainly negation and implication hold good, whereas they are not valid in most well-known logics. Despite their intuitiveness, the connexive principles quickly lead to contradictions and even to triviality, i.e. to the truth of every proposition. This chapter surveys the main arguments against the connexive principles and discusses some prospects for challenging those arguments and endorsing the connexive principles.

The aim of this article is to give students a small sense of what metamathematics is—that is, how one might use mathematics to study mathematics itself. School or college teachers could base a classroom exercise on the letter games I shall describe and use them as a springboard for further exploration. Since I shall presuppose no knowledge of formal logic, the games are less an introduction to Gödel's theorems than an introduction to an introduction to them. Nevertheless, they show, in an accessible way, how metamathematics can be mathematically interesting