Prior’s System Q and its Extensions

Recently, and as happens from time to time in New Zealand, a typescript of Prior’s turned up. This one was in the personal collection of Oliver Sutherland. Prior typed it in November 1957 and used copies in his senior logic group, an informal research group at Canterbury University. A terse and relentlessly compressed couple of pages, it concerns Prior’s system Q, which even towards the end of his life he was still describing as ‘the true modal logic’. We analyse Prior’s typescript and the issues underlying it, as well as providing an exposition of Q, and an examination of Łukasiewicz’s objections to Q. The article also includes an interview with Prior’s student Robert Bull concerning Q.