Ai, Me and Lewis (Abelian Implication, Material Equivalence and C I Lewis 1920)

Journal of Philosophical Logic 37 (2):169-181 (2008)
  Copy   BIBTEX

Abstract

C I Lewis showed up Down Under in 2005, in e-mails initiated by Allen Hazen of Melbourne. Their topic was the system Hazen called FL (a Funny Logic), axiomatized in passing in Lewis 1921. I show that FL is the system MEN of material equivalence with negation. But negation plays no special role in MEN. Symbolizing equivalence with → and defining ∼A inferentially as A→f, the theorems of MEN are just those of the underlying theory ME of pure material equivalence. This accords with the treatment of negation in the Abelian l-group logic A of Meyer and Slaney (Abelian logic. Abstract, Journal of Symbolic Logic 46, 425–426, 1981), which also defines ∼A inferentially with no special conditions on f. The paper then concentrates on the pure implicational part AI of A, the simple logic of Abelian groups. The integers Z were known to be characteristic for AI, with every non-theorem B refutable mod some Zn for finite n. Noted here is that AI is pre-tabular, having the Scroggs property that every proper extension SI of AI, closed under substitution and detachment, has some finite Zn as its characteristic matrix. In particular FL is the extension for which n = 2 (Lewis, The structure of logic and its relation to other systems. The Journal of Philosophy 18, 505–516, 1921; Meyer and Slaney, Abelian logic. Abstract. Journal of Symbolic Logic 46, 425–426, 1981; This is an abstract of the much longer paper finally published in 1989 in G. G. Priest, R. Routley and J. Norman, eds., Paraconsistent logic: essays on the inconsistent, Philosophica Verlag, Munich, pp. 245–288, 1989).

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

Similar books and articles

Definable groups in models of Presburger Arithmetic.Alf Onshuus & Mariana Vicaría - 2020 - Annals of Pure and Applied Logic 171 (6):102795.
Elementary Equivalence for Abelian-by-Finite and Nilpotent Groups.Francis Oger - 2001 - Journal of Symbolic Logic 66 (3):1471-1480.
On non-abelian C-minimal groups.Patrick Simonetta - 2003 - Annals of Pure and Applied Logic 122 (1-3):263-287.

Analytics

Added to PP
2009-01-28

Downloads
141 (#163,647)

6 months
4 (#909,732)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations