In Bernard Linsky & Nicholas Griffin (eds.), The Palgrave Centenary Companion to Principia Mathematica. Palgrave-Macmillan. pp. 218-246 (2013)

Authors
Kevin Klement
University of Massachusetts, Amherst
Abstract
Along with offering an historically-oriented interpretive reconstruction of the syntax of PM ( rst ed.), I argue for a certain understanding of its use of propositional function abstracts formed by placing a circum ex on a variable. I argue that this notation is used in PM only when de nitions are stated schematically in the metalanguage, and in argument-position when higher-type variables are involved. My aim throughout is to explain how the usage of function abstracts as “terms” (loosely speaking) is not inconsistent with a philosophy of types that does not think of propositional functions as mind- and language-independent objects, and adopts a nominalist/substitutional semantics instead. I contrast PM’s approach here both to function abstraction found in the typed λ-calculus, and also to Frege’s notation for functions of various levels that forgoes abstracts altogether, between which it is a kind of intermediary.
Keywords type theory  abstraction  propositional functions
Categories (categorize this paper)
Buy the book Find it on Amazon.com
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 58,348
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Logic and Knowledge.BERTRAND RUSSELL - 1957 - Philosophical Quarterly 7 (29):374.
Mathematical Logic as Based on the Theory of Types.Bertrand Russell - 1908 - American Journal of Mathematics 30 (3):222-262.
On Concept and Object.Gottlob Frege - 1951 - Mind 60 (238):168-180.

View all 22 references / Add more references

Citations of this work BETA

The Functions of Russell’s No Class Theory.Kevin C. Klement - 2010 - Review of Symbolic Logic 3 (4):633-664.

Add more citations

Similar books and articles

Analytics

Added to PP index
2010-07-02

Total views
47 ( #216,360 of 2,420,320 )

Recent downloads (6 months)
1 ( #542,912 of 2,420,320 )

How can I increase my downloads?

Downloads

My notes