Frege
A fusion of horizontals
Bibliographic Data
| ID | 20142754 |
|---|---|
| Authors | Francesco Bellucci (0000-0002-0435-5453, Department of the Arts (DAR) University of Bologna Bologna Italy, corresponding author), Daniele Chiffi (0000-0002-5487-8244, DAStU Politecnico di Milano Milan Italy), Luca Zanetti (0000-0002-3733-9193, Linguistics & Philosophy IUSS Center (L&PIC) Scuola Universitaria Superiore IUSS Pavia Italy) |
| Year | 2023 |
| Volume | 89 |
| Issue | 5 |
| Pages | 690-709 |
| Publication date | 2023-10-01 |
| Peer Reviewed | Yes |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Theoria (JOURNAL) |
| Journal identifiers | ISSN: 0040-5825 • E-ISSN: 1755-2567 |
| Publisher | Wiley (PUBLISHER • GB) |
| DOI | 10.1111/theo.12488 |
| OpenAlex | W4387856665 |
| Language | EN |
| References cited | 24 |
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
Epistemology · Geometry · Horizontal and vertical · Mathematical analysis · Sign (mathematics) · Classical Philosophy and Thought · Computer Science · Logic, Reasoning, and Knowledge · Mathematics · Philosophy · Philosophy and Theoretical Science
Frege
Sameness of Fregean sense
Speech acts in mathematics
Inference versus consequence” revisited
Assertion
The Interpretation of Frege's Philosophy
Frege's Theory of Judgment
Frege's Judgment-Stroke
Frege on Definitions
Frege's Judgement Stroke and the Conception of Logic as the Study of Inference not Consequence
| Citation velocity | historical |
|---|---|
| Highly cited | No |