In Die Grundgesetze der Arithmetik (I, §48), Frege introduces his rule of the fusion of horizontals, according to which if an occurrence of the horizontal stroke is followed by another occurrence of the same stroke, either in isolation or “contained” in a propositional connective, the two occurrences can be fused with each other. However, the role of this rule, and of the horizontal sign more generally, is controversial; Michael Dummett notoriously claimed, for instance, that the horizontal is “wholly superfluous” in (...) Frege's logical system. In this paper, we challenge Dummett's view by providing a comprehensive analysis of the significance of the horizontal stroke. After some preliminary remarks, we argue that even if Frege's connectives in some sense “contain” the horizontal, yet they are total functions. Then, we take up the question of the sense expressed by the horizontal, and we claim that, unlike other sentential operators, the horizontal is not sense‐compositional. Finally, we consider the semantic and pragmatic aspects of Frege's horizontal in connection to his judgment stroke and the double judgment stroke. Contra Dummett, we argue that the horizontal is a special and indispensable element of Frege's logic. (shrink)

This programmatic paper is an attempt to connect some worries in the philosophy of language with some traditional views in artificial intelligence. After a short introduction to the notion of context in philosophy (§1), starting from the inventor of mathematical logic, Gottlob Frege, I list three debates in the philosophy of language where the solution is strongly undecided: §2 treats the debate between holism and molecularism; §3 describes the debate on the boundaries between semantics and pragmatics; §4 hints at a (...) solution of the debate between explicit and implicit view of incomplete descriptions. These debates may be considered case studies on what is happening to the notion of context in philosophy in the first two decades of XXI century; they push us to look for a unifying framework in which to frame those worries: I propose to shift the attention towards a representation of the basic abilities required to navigate across contexts (§5). In the conclusion, I use some suggestions from computer sciences as a contribution towards a better definition of what is meant by “pragmatic competence”, strictly connected to the philosophical enterprise (§6). (shrink)

In this paper I shall deal with the role of "understanding a thought" in the debate on the definition of the content of an assertion. I shall present a well known tension in Frege's writings, between a cognitive and semantic notion of sense. This tension is at the source of some of the major contemporary discussions, mainly because of the negative influence of Wittgenstein's Tractatus, which did not give in-depth consideration to the tension found in Frege. However many contemporary authors, (...) after the first attempt by Carnap himself, have tried to make room both for a cognitive and semantic aspect of meaning. I claim that at least some of these attempts (Dummett, Perry and Chalmers) are seriously flawed, mainly due to the difficulty in making a proper connection between the two different conceptions of sense. I shall outline an alternative project, which takes into consideration Frege's requirements on antipsychologism and of the objectivity of thought, while maintaining a close connection between the two aspects of sense. (shrink)

In this paper we give some formal examples of ideas developed by Penco in two papers on the tension inside Frege's notion of sense (see Penco 2003). The paper attempts to compose the tension between semantic and cognitive aspects of sense, through the idea of sense as proof or procedure – not as an alternative to the idea of sense as truth condition, but as complementary to it (as it happens sometimes in the old tradition of procedural semantics).