Representation of Functions and Total Antisymmetric Relations in Monadic Third Order Logic

Journal of Philosophical Logic 48 (2):263-278 (2019)
  Copy   BIBTEX

Abstract

We analyze the representation of binary relations in general, and in particular of functions and of total antisymmetric relations, in monadic third order logic, that is, the simple typed theory of sets with three types. We show that there is no general representation of functions or of total antisymmetric relations in this theory. We present partial representations of functions and of total antisymmetric relations which work for large classes of these relations, and show that there is an adequate representation of cardinality in this theory. The relation of our work to similar work by Henrard and Allen Hazen is discussed. This work can be understood as part of a program of assessing the capabilities of weak logical frameworks: our results are applicable for example, to the framework in David Lewis’s Parts of Classes.

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 103,486

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Analytics

Added to PP
2018-06-21

Downloads
23 (#997,657)

6 months
4 (#909,732)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

The philosophy of logical practice.Ben Martin - 2022 - Metaphilosophy 53 (2-3):267-283.

Add more citations

References found in this work

The Foundations of Mathematics and Other Logical Essays.Frank Plumpton Ramsey - 1925 - London, England: Routledge & Kegan Paul. Edited by R. B. Braithwaite.
Parts of Classes.David K. Lewis - 1991 - Mind 100 (3):394-397.
[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
Set Theory.T. Jech - 2005 - Bulletin of Symbolic Logic 11 (2):243-245.
Typical Ambiguity.Ernst P. Specker - 1962 - In Ernest Nagel, Logic, methodology, and philosophy of science. Stanford, Calif.,: Stanford University Press. pp. 116--23.

View all 8 references / Add more references