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On defining necessity in terms of entailment (1979)

Henry, Dennis ; Byrd, Michael

Springer

Studia logica 38 (1979), S. 95-104

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ISSN: 1572-8730

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Philosophy

Notes: Abstract In their book Entailment, Anderson and Belnap investigate the consequences of defining ‘Lp’ (it is necessary that p) in system E as (p→p)→p. Since not all theorems are equivalent in E, this raises the question of whether there are reasonable alternative definitions of necessity in E. In this paper, it is shown that a definition of necessity in E satisfies the conditions {⊢ E Lp→p, ⊢EL(p→q)→(Lp→Lq), ⊢E p→Lp} if and only if its has the form C 1→.C2→ ...→. Cn→p, where each C iis equivalent in E to either p→p or ((p→p)→p)→p.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00370435

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