Omniscience in Łukasiewicz's, Kleene's and Blau's Three-Valued Logics

Polish Journal of Philosophy 5 (1):59-78 (2011)
Abstract
In this paper several assumptions concerning omniscience and future contingents on the one side, and omniscience and self-reference on the other, areexamined with respect to a classical and a three-valued semantic setting (the latter pertains especially to Łukasiewicz’s, Kleene’s and Blau’s three-valued logics).Interesting features of both settings are highlighted and their basic assumptions concerning omniscience are explored. To generate a context in which the notion of omniscience does not deviate from some basic intuitions, two special futurity operators are introduced in this article: one for what will definitely take place and another one for what is indeterminate as to whether it will take place. Once these operators are introduced, some puzzles about omniscience in combination with future contingents are removed. An analogous solution to some puzzles concerning omniscience and selfreferentiality is also provided
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