Non-Classical Logics

Abstract

The construction of many-valued logical systems is commonly believed to have been one of the major achievements of the Warsaw School, and specifically of Łukasiewicz.1 The first mention of many-valued (three-valued) logic is to be found in Łukasiewicz’s farewell speech at Warsaw University on March 7,1918. He said: In 1910 I published a book on the principle of contradiction in Aristotle’s work, in which I strove to demonstrate that that principle is not so evident as it is believed to be. Even then I strove to construct non-Aristotelian logic, but in vain. Now I believe I have succeeded in this. ... Examination of that issue was the subject-matter of my last lectures. I have proved that in addition to true and false propositions there are possible propositions, to which objective possibility corresponds as a third value in addition to being and non-being. This gave rise to a system of three-valued logic, which I worked out in detail last summer. That system is as coherent and self-consistent as Aristotle’s logic, and is much richer in laws and formulae. That new logic, by introducing the concept of objective possibility, destroyed the former concept of science, based on necessity. Possible phenomena have no cause, although they themselves can be the beginning of a causal sequence. An act of a creative individual can be free and at the same time affect the course of the world (1918, p. 86).