Popper’s Correspondence with William Calvert Kneale

Abstract

AbstractWilliam Calvert Kneale (1906–1990) was a British logician and historian of logic, who is best known for his book The Development of Logic (Kneale and Kneale,.The Development of Logic, Oxford University Press, Clarendon Press, 1962) on the history of logic, jointly written with his wife Martha Kneale. (For further biographical details cf. Smiley,.Proceedings of the British Academy 87:385–397, 1995.) In his letter to Popper, Kneale suggests a generalization of Popper’s single-conclusion deducibility relation a1..... an.b to a multi-conclusion relation a1..... an.b1..... bm, where the formulas b1..... bm are understood conjunctively. This direction would later be pursued in ( Kneale, W. (1956). The Province of Logic. In: Contemporary British Philosophy, Third series. Ed. by H. D. Lewis. London: Allen & Unwin and New York: Humanities Press, pp. 235–261.) and in (Kneale and Kneale,.The Development of Logic, Oxford University Press, Clarendon Press, 1962), Ch. IX). Both of these texts refer to Popper, and Kneale develops Popper’s ideas of inferential definitions into a theory where logical constants are defined by double-line rules, that is, rules which can be read in both directions. This makes Kneale one of the few persons who further developed Popper’s ideas on the nature of logical constants.