Some Axiom-Pairs for Material and Strict Implication

✍ Scribed by A. N. Prior

• Publisher: John Wiley and Sons
• Year: 1961
• Tongue: English
• Weight: 194 KB
• Volume: 7
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19610070111

✦ Synopsis

Of the four formulac L1. c p c q p M1. CqCpp L2. CCCCpqrsCCqsCps M2. CCCCpqrqCCqsCps, the pair ( L l , L2) were given by LUKASIEWICZ as sufficient (with substitution and detachment) for tho classical implicational propositional calculus, while thc pair (&Ill M2) were givcn by C. A. MEREDITH in 1956 as sufficicnt (with substitution and detachment) for C5, i.e., that portion of the LEWIS systcm 8 5 which can be cxprcsscd with strict implication as the soh constant. L1, with C for material implication, expresses the principlc that a true proposition is materially implied by any proposition, while 311, with C for strict implication, cxcniplifics the principlc that a necessary proposition (in this case Cpp) is strictly implied by any proposition.