Authors
Paul Edward Oppenheimer
Stanford University
Edward Zalta
Stanford University
Abstract
Though Frege was interested primarily in reducing mathematics to logic, he succeeded in reducing an important part of logic to mathematics by defining relations in terms of functions. By contrast, Whitehead & Russell reduced an important part of mathematics to logic by defining functions in terms of relations (using the definite description operator). We argue that there is a reason to prefer Whitehead & Russell's reduction of functions to relations over Frege's reduction of relations to functions. There is an interesting system having a logic that can be properly characterized in relational but not in functional type theory. This shows that relational type theory is more general than functional type theory. The simplification offered by Church in his functional type theory is an over-simplification: one can't assimilate predication to functional application.<br>.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
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: 61,109
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

Mathematical Logic as Based on the Theory of Types.Bertrand Russell - 1908 - American Journal of Mathematics 30 (3):222-262.
A Formulation of the Simple Theory of Types.Alonzo Church - 1940 - Journal of Symbolic Logic 5 (2):56-68.
An Unsolvable Problem of Elementary Number Theory.Alonzo Church - 1936 - Journal of Symbolic Logic 1 (2):73-74.
A Formulation of the Simple Theory of Types.Alonzo Church - 1940 - Journal of Symbolic Logic 5 (3):114-115.

View all 17 references / Add more references

Citations of this work BETA

Guest Editor’s Introduction: JvH100. [REVIEW]Irving H. Anellis - 2012 - Logica Universalis 6 (3-4):249-267.

View all 7 citations / Add more citations

Similar books and articles

Analytics

Added to PP index
2009-01-28

Total views
93 ( #112,778 of 2,440,225 )

Recent downloads (6 months)
3 ( #208,874 of 2,440,225 )

How can I increase my downloads?

Downloads

My notes