David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
In Entailment, Anderson and Belnap motivated their modification E of Ackermann’s strenge Implikation Π Π’ as a logic of relevance and necessity. The kindred system R was seen as relevant but not as modal. Our systems of Peano arithmetic R# and omega arithmetic R## were based on R to avoid fallacies of relevance. But problems arose as to which arithmetic sentences were (relevantly) true. Here we base analogous systems on E to solve those problems. Central to motivating E is the rejection of fallacies of modality. Our slogan here for this is, “No diamonds entail any boxes.” Form the strenge Peano arithmetic E# like R#, adding appropriate forms of the Peano axioms to Ackermann’s E..
|Keywords||No keywords specified (fix it)|
|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
J. Michael Dunn (1979). Relevant Robinson's Arithmetic. Studia Logica 38 (4):407 - 418.
J. Michael Dunn (1980). Quantum Mathematics. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:512 - 531.
Robert K. Meyer (1998). ÂE is Admissible in ÂTrueâ Relevant Arithmetic. Journal of Philosophical Logic 27 (4):327-351.
C. Ward Henson, Matt Kaufmann & H. Jerome Keisler (1984). The Strength of Nonstandard Methods in Arithmetic. Journal of Symbolic Logic 49 (4):1039-1058.
Charles Sayward (2005). Why Axiomatize Arithmetic? Sorites 16:54-61.
Robert K. Meyer (1998). ⊃E is Admissible in “True” Relevant Arithmetic. Journal of Philosophical Logic 27 (4):327 - 351.
Fred G. Abramson & Leo A. Harrington (1978). Models Without Indiscernibles. Journal of Symbolic Logic 43 (3):572-600.
Harvey Friedman & Robert K. Meyer (1992). Whither Relevant Arithmetic? Journal of Symbolic Logic 57 (3):824-831.
Added to index2009-01-28
Total downloads50 ( #68,426 of 1,726,249 )
Recent downloads (6 months)32 ( #32,356 of 1,726,249 )
How can I increase my downloads?