David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Logic and Computation 21:351-374 (2011)
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)|
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
No references found.
Citations of this work BETA
Anthony F. Beavers (2011). Recent Developments in Computing and Philosophy. Journal for General Philosophy of Science 42 (2):385-397.
Similar books and articles
Kevin C. Klement (2003). Russell's 1903 - 1905 Anticipation of the Lambda Calculus. History and Philosophy of Logic 24 (1):15-37.
Christopher Menzel (1986). A Complete, Type-Free "Second-Order" Logic and its Philosophical Foundations. Csli Publications.
Alfred North Whitehead & Bertrand Russell (1962/1997). Principia Mathematica, to *56. Cambridge University Press.
William M. Farmer & Joshua D. Guttman (2000). A Set Theory with Support for Partial Functions. Studia Logica 66 (1):59-78.
Kc Klement (2010). The Senses of Functions in the Logic of Sense and Denotation. Bulletin of Symbolic Logic 16 (2):153-188.
William M. Farmer (1995). Reasoning About Partial Functions with the Aid of a Computer. Erkenntnis 43 (3):279 - 294.
Added to index2009-01-28
Total downloads26 ( #78,066 of 1,679,474 )
Recent downloads (6 months)6 ( #39,577 of 1,679,474 )
How can I increase my downloads?