John Lemmon - Modal Logic

Modal Logic

John Lemmon became interested in modal logic when Arthur Prior visited Oxford University in 1956 to give the John Locke lectures, later published as his Time and Modality (Prior 1957). Prior returned for twelve months soon after, to lead a small group including Lemmon, Peter Geach and Ivo Thomas (Copeland 2004). John Lemmon became one of the early champions of Prior's distinctive approach to tense logic, and Lemmon's later work on alethic modality and applications of modal logic to ethics bear the mark of Prior's influence. At this time, Lemmon published a treatment of alethic and epistemic modalities which introduced some systems of non-normal modal logics that have proven to have had lasting interest, the alethic system S0.5 and the epistemic systems E1–E5 linked to the systems S0.5 and Lewis's system S2–S5, but which lack the law of necessitation (Lemmon 1957).

Lemmon was a pioneer of the modern approach to the semantics of modal logic, particularly through his collaboration with Dana Scott, but also became interested in the rival algebraic semantics of modal logic that follows more closely the kind of semantics found in the work of Tarski and Jònson.