Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Logic, Mathematics, Philosophy, Vintage EnthusiasmsOn Logicist Conceptions of Functions and Classes

Logic, Mathematics, Philosophy, Vintage Enthusiasms: On Logicist Conceptions of Functions and... [John Bell Bell, John L.Demopoulos, William arrived in “new” London in 1989, a refugee from the academy under Margaret Thatcher. We soon became good friends, and during the early years of our friendship we collaborated on two papers (Bell and Demopoulos, 1993, 1996). The first of these collaborations was a paper on the foundational significance of results based on second-order logic and Frege’s understanding of his Begriffsschrift; the second was on various notions of independence that arise in connection with elementary propositions in the philosophy of logical atomism. I retain fond memories of both collaborations; they proceeded quickly and almost effortlessly. In this contribution to John’s Festschrift, I propose to revisit our paper on Frege. That paper was occasioned by (Hintikka and Sandu, 1992), which questioned whether Frege’s understanding of second-order logic corresponded, in his framework of functions and concepts, to what we would now regard as the standard interpretation, the interpretation that takes the domain of the function variables to be the full power-set of the domain of individuals. Hintikka and Sandu Hintikka, JaakkoSandu, Gabriel maintained that it did not on the basis of a number of arguments, all of which they took to show that Frege Frege, Gottlob favored some variety of non-standard interpretation for which the domain of the function variables is something less than the characteristic functions of all subsets of the domain over which the individual variables range.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Logic, Mathematics, Philosophy, Vintage EnthusiasmsOn Logicist Conceptions of Functions and Classes

Part of the The Western Ontario Series in Philosophy of Science Book Series (volume 75)
Editors: DeVidi, David; Hallett, Michael; Clarke, Peter
Demopoulos, William
Logic, Mathematics, Philosophy, Vintage Enthusiasms — Jan 27, 2011
Download PDF
16 pages

Loading next page...
 
/lp/springer-journals/logic-mathematics-philosophy-vintage-enthusiasms-on-logicist-PboNRyr81r

References (16)

Publisher
Springer Netherlands
Copyright
© Springer Science+Business Media B.V. 2011
ISBN
978-94-007-0213-4
Pages
3 –18
DOI
10.1007/978-94-007-0214-1_1
Publisher site
See Chapter on Publisher Site

Abstract

[John Bell Bell, John L.Demopoulos, William arrived in “new” London in 1989, a refugee from the academy under Margaret Thatcher. We soon became good friends, and during the early years of our friendship we collaborated on two papers (Bell and Demopoulos, 1993, 1996). The first of these collaborations was a paper on the foundational significance of results based on second-order logic and Frege’s understanding of his Begriffsschrift; the second was on various notions of independence that arise in connection with elementary propositions in the philosophy of logical atomism. I retain fond memories of both collaborations; they proceeded quickly and almost effortlessly. In this contribution to John’s Festschrift, I propose to revisit our paper on Frege. That paper was occasioned by (Hintikka and Sandu, 1992), which questioned whether Frege’s understanding of second-order logic corresponded, in his framework of functions and concepts, to what we would now regard as the standard interpretation, the interpretation that takes the domain of the function variables to be the full power-set of the domain of individuals. Hintikka and Sandu Hintikka, JaakkoSandu, Gabriel maintained that it did not on the basis of a number of arguments, all of which they took to show that Frege Frege, Gottlob favored some variety of non-standard interpretation for which the domain of the function variables is something less than the characteristic functions of all subsets of the domain over which the individual variables range.]

Published: Jan 27, 2011

Keywords: Disjunctive Normal Form; Propositional Function; Transcendental Argument; Combinatorial Possibility; Logical Atomism

There are no references for this article.