History and Philosophy of Logic 26 (3):229-266 (2005)
|Abstract||Section 1 recalls a point noted by A. N. Prior forty years ago: that a certain formula in the language of a purely implicational intermediate logic investigated by R. A. Bull is unprovable in that logic but provable in the extension of the logic by the usual axioms for conjunction, once this connective is added to the language. Section 2 reminds us that every formula is interdeducible with (i.e. added to intuitionistic logic, yields the same intermediate logic as) some conjunction-free formula. Thus it would seem that any detour going via formulas with conjunction can be avoided, which raises a puzzle: how is this consistent with the point from Section 1? Sections 3 and 4 raise and discuss this puzzle. In fact, the puzzle turns out on closer inspection not to be so puzzling after all, but it does serve as a convenient centrepiece around which to organize a discussion of the phenomenon illustrated by the Bull?Prior example. Section 5 notes that Prior's observation can be extended to the case of the result of adding disjunction to Bull's logic, while Section 6 includes some further remarks aimed at diagnosing one source of possible residual puzzlement. A subtext of our discussion?spanning several of the notes?is that this work by Bull and Prior has been overlooked, their results having to be rediscovered, by many algebraists and logicians in more recent years|
|Keywords||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
Raymond M. Smullyan (1991). Some Unifying Fixed Point Principles. Studia Logica 50 (1):129 - 141.
A. D. Yashin (1999). Irreflexive Modality in the Intuitionistic Propositional Logic and Novikov Completeness. Journal of Philosophical Logic 28 (2):175-197.
Lloyd Humberstone (2013). Replacement in Logic. Journal of Philosophical Logic 42 (1):49-89.
Miklós Ferenczi (2009). On Conservative Extensions in Logics with Infinitary Predicates. Studia Logica 92 (1):121 - 135.
Michiro Kondo (1989). A1 is Not a Conservative Extension of S4 but of S. Journal of Philosophical Logic 18 (3):321 - 323.
Edwin D. Mares (2000). Ce is Not a Conservative Extension of E. Journal of Philosophical Logic 29 (3):263-275.
Gabriel Uzquiano (2010). How to Solve the Hardest Logic Puzzle Ever in Two Questions. Analysis 70 (1):39-44.
Brian Rabern & Landon Rabern (2008). A Simple Solution to the Hardest Logic Puzzle Ever. [REVIEW] Analysis 68 (2):105-112.
John Turri (2012). A Puzzle About Withholding. Philosophical Quarterly 62 (247):355-364.
Lloyd Humberstone (2001). The Pleasures of Anticipation: Enriching Intuitionistic Logic. Journal of Philosophical Logic 30 (5):395-438.
Added to index2010-08-10
Total downloads5 ( #160,483 of 549,511 )
Recent downloads (6 months)1 ( #63,397 of 549,511 )
How can I increase my downloads?