Frege on Definitions
Bibliographic Data
| ID | 4079498 |
|---|---|
| Authors | Sanford Shieh (0000-0002-0307-5310, Wesleyan University, corresponding author) |
| Year | 2008 |
| Volume | 3 |
| Issue | 5 |
| Pages | 992-1012 |
| Publication date | 2008-09-01 |
| Peer Reviewed | Yes |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Philosophy Compass (JOURNAL) |
| Journal identifiers | ISSN: 1747-9991 • E-ISSN: 1747-9991 |
| Publisher | Wiley (PUBLISHER • GB) |
| DOI | 10.1111/j.1747-9991.2008.00167.x |
| OpenAlex | W2090913390 |
| Language | EN |
| Citations received | 4 |
| References cited | 14 |
This article treats three aspects of Frege's discussions of definitions. First, I survey Frege's main criticisms of definitions in mathematics. Second, I consider Frege's apparent change of mind on the legitimacy of contextual definitions and its significance for recent neo-Fregean logicism. In the remainder of the article I discuss a critical question about the definitions on which Frege's proofs of the laws of arithmetic depend: do the logical structures of the definientia reflect the understanding of arithmetical terms prevailing prior to Frege's analyses? Unless they do, it is unclear how Frege's proofs demonstrate the analyticity of the arithmetic in use before logicism. Yet, especially in late writings, Frege characterizes definitions as arbitrary stipulations of the senses or references of expressions unrelated to pre-definitional understanding. I conclude by examining some options for conceiving of the status of Frege's logicism in light of this apparent tension, and outline a suggestion for a philosophically fruitful way of resolving this tension
Arithmetic function · Discrete mathematics · Epistemology · Legitimacy · Mathematical proof · Principle of compositionality · History and Theory of Mathematics · Law · Mathematics · Philosophy · Philosophy and Theoretical Science · Philosophy, Science, and History
| Unique citing works | 4 |
|---|---|
| Citations per year | 0,36 |
| Citation span | 2015 - 2023 (9) |
| Citation velocity | historical |
| Highly cited | No |
| Citation types | Neutral: 3 |