ABSTRACT
In ‘Many-valued Logics’, a lecture broadcast over New Zealand's public radio in 1957, Arthur N. Prior (1914–1969) complained that conjunctions are put ‘to something like forced labour’ in Łukasiewicz's three-valued semantics, Ł3. In this paper, we discuss what Prior might have meant by this.
Acknowledgments
We thank Hazel T. Biana, Ben Blumson, Brian Garrett, and the editor and referees of this journal for the useful suggestions that greatly improved this paper.
Notes
1 A portion of Prior's lecture can be accessed through http://www.ngataonga.org.nz/collections/catalogue/catalogue-item?record_id=168375. The lecture starts at the 15:17 mark.
2 Prior Citation1957, p. 717.
3 Prior Citation1957, p. 718.
4 Prior Citation1957, p. 718.
5 Prior Citation1957, p. 718.
6 Prior Citation1957, p. 718.
7 Compare the discussion here with Priest Citation2008, pp. 122–124, and Sider Citation2010, pp. 75–77.
8 The designated values are the only values preserved in valid arguments, see Priest Citation2008, p. 121.
9 A corresponding definition of logical truths in Ł3 can be derived from this.
10 The idea of truth-functionality employed here follows the standard textbook definition as seen, for example, in Beall and Logan Citation2017, p. 27, and Sider Citation2010, p. 84.
11 Prior Citation1960.
12 For purposes of an interpretation of this logic, we do not need to distinguish those atomic sentences that are necessarily true or necessarily false.
13 Prior Citation1962, p. 5.
14 We follow Prior's practice of using Polish (prefix) notation here. As such, ‘Kpq’ is the prefix notation for ‘’. For a discussion of Prior's preference for Polish notation, see Joaquin Citation2022.
15 Prior Citation1967, p. 136.