David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Philosophical Logic 37 (2):169 - 181 (2008)
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).
|Keywords||Abelian logic Allen Hazen C. I. Lewis Funny Logic Scroggs property|
|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
No citations found.
Similar books and articles
Roberto Cignoli (1999). Algebraic Foundations of Many-Valued Reasoning. Kluwer Academic Publishers.
Francis Oger (1984). The Model Theory of Finitely Generated Finite-by-Abelian Groups. Journal of Symbolic Logic 49 (4):1115-1124.
Francis Oger (2001). Elementary Equivalence for Abelian-by-Finite and Nilpotent Groups. Journal of Symbolic Logic 66 (3):1471-1480.
Francesco Paoli, Matthew Spinks & Robert Veroff (2008). Abelian Logic and the Logics of Pointed Lattice-Ordered Varieties. Logica Universalis 2 (2):209-233.
Gregory L. Cherlin & Peter H. Schmitt (1981). Undecidable Lt Theories of Topological Abelian Groups. Journal of Symbolic Logic 46 (4):761 - 772.
Longyun Ding & Su Gao (2006). Diagonal Actions and Borel Equivalence Relations. Journal of Symbolic Logic 71 (4):1081 - 1096.
Frank O. Wagner (1993). Quasi-Endomorphisms in Small Stable Groups. Journal of Symbolic Logic 58 (3):1044-1051.
Andrzej Pelc (1984). Idempotent Ideals on Abelian Groups. Journal of Symbolic Logic 49 (3):813-817.
H. Kushida & M. Okada (2007). A Proof–Theoretic Study of the Correspondence of Hybrid Logic and Classical Logic. Journal of Logic, Language and Information 16 (1):35-61.
Added to index2009-01-28
Total downloads13 ( #136,783 of 1,410,179 )
Recent downloads (6 months)3 ( #75,846 of 1,410,179 )
How can I increase my downloads?