David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Philosophical Logic 27 (4):327 - 351 (1998)
The system R## of "true" relevant arithmetic is got by adding the ω-rule "Infer VxAx from AO, A1, A2, ...." to the system R# of "relevant Peano arithmetic". The rule ⊃E (or "gamma") is admissible for R##. This contrasts with the counterexample to ⊃E for R# (Friedman & Meyer, "Whither Relevant Arithmetic"). There is a Way Up part of the proof, which selects an arbitrary non-theorem C of R## and which builds by generalizing Henkin and Belnap arguments a prime theory T which still lacks C. (The key to the Way Up is a Witness Protection Program, using the ω-rule.) But T may be TOO BIG, whence there is a Way Down argument that produces a better theory TR, such that R## ⊆ TR ⊆ T. (The key to the Way Down is a Metavaluation, on which membership in T is combined with ordinary truth-functional conditions to determine TR.) The result is a theory that is Just Right, whence it never happens that A ⊃ C and A are theorems of R## but C is a non-theorem
|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
Edwin Mares (2012). Relevant Logic and the Philosophy of Mathematics. Philosophy Compass 7 (7):481-494.
Similar books and articles
Alistair H. Lachlan & Robert I. Soare (1994). Models of Arithmetic and Upper Bounds for Arithmetic Sets. Journal of Symbolic Logic 59 (3):977-983.
Robert Goldblatt & Michael Kane (2010). An Admissible Semantics for Propositionally Quantified Relevant Logics. Journal of Philosophical Logic 39 (1):73 - 100.
J. Michael Dunn (1979). Relevant Robinson's Arithmetic. Studia Logica 38 (4):407 - 418.
Harvey Friedman & Robert K. Meyer (1992). Whither Relevant Arithmetic? Journal of Symbolic Logic 57 (3):824-831.
Robert K. Meyer (1998). ÂE is Admissible in ÂTrueâ Relevant Arithmetic. Journal of Philosophical Logic 27 (4):327-351.
Added to index2009-01-28
Total downloads9 ( #154,897 of 1,098,129 )
Recent downloads (6 months)1 ( #283,807 of 1,098,129 )
How can I increase my downloads?