Journal article
Note on Principia's 38 on Operations
Russell, Vol.41(2), pp.131-153
Winter 2021
DOI: 10.15173/russell.v41i2.5046
Abstract
Principia Mathematica *38 introduces what it calls “Relations and Classes Derived from a Double Descriptive Function”. The notion of a relation-e (relation in extension) so derived is called an operation, and of course all dyadic relation-e theorems rely ultimately on the comprehension axiom schema for relations in intension given at *12.11. But in attempting to give a general pattern of definition, *38 uses the odd-looking “x?y ” which lends itself to the misconception that is itself an operation sign. The informal summary makes matters worse, writing “E!(x?y)” which is ungrammatical. This paper argues that with P, R and S as relation-e variables and ?, ?, and ? as class variables, operations are comprehended by wffs such as “ P=x?y”, “?=???” and “P=R?S”. Relying on triadic relations-e, I explain how the sign ? can be entirely avoided using comprehension. Along the way, puzzling cases such as ? and ? are resolved. [Greek and other symbols do not repoduce here. See the first page of the paper for the correct abstract.--Ed.]
Details
- Title: Subtitle
- Note on Principia's 38 on Operations
- Creators
- Gregory Landini
- Resource Type
- Journal article
- Publication Details
- Russell, Vol.41(2), pp.131-153
- DOI
- 10.15173/russell.v41i2.5046
- ISSN
- 0036-0163
- eISSN
- 1913-8032
- Language
- English
- Date published season
- Winter 2021
- Date published
- 2021
- Academic Unit
- Philosophy
- Record Identifier
- 9984397185202771
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