Mosterin, Jesus (2004) How Set Theory Impinges on Logic. UNSPECIFIED.

Preview

PDF How_Set_Theory_Impinges_on_Logic.pdf Download (115kB)

Abstract

Standard (classical) logic is not independent of set theory. Which formulas are valid in logic depends on which sets we assume to exist in our set-theoretical universe. Second-order logic is just set theory in disguise. The typically logical notions of validity and consequence are not well defined in second-order logic, at least as long as there are open issues in set theory. Such contentious issues in set theory as the axiom of choice, the continuum hypothesis or the existence of inaccessible cardinals, can be equivalently transformed into question about the logical validity of pure sentences of second-order logic, where “pure” means that they only contain logical symbols and bound variables. Even standard first-order logic depends on the acceptance on infinite sets in our set-theoretical universe. Should we choose to admit only finite sets, the number of logically valid pure first-order formulas would increase dramatically and first-order logic would not be recursively enumerable any longer.

---

Export/Citation:

EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL

Social Networking:

Share |

---

Item Type:	Other
Creators:	Creators Email ORCID Mosterin, Jesus
Additional Information:	Published in Paul Weingartner (ed.), Alternative Logics: Do Sciences Need Them? Berlin-Heidelberg-New York, 2004, pp. 55-63.
Keywords:	Models, set-theoretical universe, infinite, first-order logic, second-order logic, set theory, continuum hypothesis
Subjects:	General Issues > Models and Idealization Specific Sciences > Mathematics
Depositing User:	Jesus Mosterin
Date Deposited:	16 Feb 2004
Last Modified:	07 Oct 2010 15:12
Item ID:	1620
Public Domain:	No
Subjects:	General Issues > Models and Idealization Specific Sciences > Mathematics
Date:	January 2004
URI:	https://philsci-archive.pitt.edu/id/eprint/1620

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item