The Theory of Implication

✍ Scribed by A. N. Prior

• Publisher: John Wiley and Sons
• Year: 1963
• Tongue: English
• Weight: 316 KB
• Volume: 9
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19630090102

✦ Synopsis

THE THEORY OF IMPLICATION by A. N. PRIOR in Manchester (England) It is shown in [7] that the formula CCCCpqrsCCqsCps, when combined with CpCqp , yields by substitution and detachment the complete classical system of pure material implication, and when combined with CqCpp yields the complete system of pure strict implication of S 5. I shall here (i) draw upon this result to axiomatise the full system S 5 with strict implication (denoted by 'Q'), material implication (denoted by 'C') and a constant impossible proposition (denoted by '0') as primitives; (ii) modify this to obtain an axiomatisation in F-C-0 of the system 54;

(iii) modify it in another way to obtain an axiomatisation of quantification theory with a single undefined constant ; and (iv) indicate some historical anticipations of these procedures.