Journal article
A NOTE ON PRINCIPIA'S 38 ON OPERATIONS
Russell, Vol.41(2), pp.131-153
12/01/2021
DOI: 10.1353/rss.2021.0012
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 female y" which lends itself to the misconception that female is itself an operation sign. The informal summary makes matters worse, writing "E! (x female y)" which is ungrammatical. This paper argues that with P, R and S as relation-e variables and alpha, beta, and mu as class variables, operations are comprehended by wffs such as "P =x female y", " mu = alpha female beta" and "P =R female S". Relying on triadic relations-e, I explain how the sign. can be entirely avoided using comprehension. Along the way, puzzling cases such as female and female are resolved.
Details
- Title: Subtitle
- A NOTE ON PRINCIPIA'S 38 ON OPERATIONS
- Creators
- Gregory Landini - Univ Iowa, Philosophy, Iowa City, IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Russell, Vol.41(2), pp.131-153
- Publisher
- Betrand Russell Research Centre
- DOI
- 10.1353/rss.2021.0012
- ISSN
- 0036-0163
- eISSN
- 1913-8032
- Number of pages
- 23
- Language
- English
- Date published
- 12/01/2021
- Academic Unit
- Philosophy
- Record Identifier
- 9984398409102771
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