Work in Logic and Metaphysics
Sylvan was instrumental in the development and study of relevant logic. In 1972, Sylvan (in a paper co-authored with Plumwood) proposed a semantics for certain relevant logics that had been developed by American philosophers Nuel Belnap and Alan Ross Anderson. Together with Robert K. Meyer, Routley turned this into a semantics for a large number of logical systems. Their work in logic work helped make ANU a center for the study of non-classical logic in general. Routley's work had particular influence for Graham Priest, a well-known proponent of non-classical logic; Sylvan and Priest edited a well-regarded volume on the topic. Priest in turn influenced Sylvan; they met in 1976 at the Australasian Association of Logic conference in Canberra at a time when Sylvan was doing novel work on dialetheism — the view that some contradictions are true. Not long after meeting Priest, then investigating a logic capable of handling such true contradictions, Sylvan also endorsed the view.
Sylvan's studies ranged over a variety of topics in logic and the philosophy of logic. He wrote important papers on free logic, general modal logic, and natural deduction systems. However, much of his most important work in logic was dedicated to relevant logic, for which he authored numerous papers (both technical and expository).
From early in his career (and for many years after), Sylvan defended a sophisticated Meinong-inspired ontology (which he called "noneism"), first presented in his 1966 paper, "Some Things Do Not Exist." After several more papers in the 1970s, the theory was given a book-length treatment in 1980, Exploring Meinong's Jungle and Beyond. The view — also defended in recent years by Priest — utilizes a modal theory including "impossible worlds" to deal with supposed objects, like the "round square." Sylvan's formulation is logically consistent, and avoids certain paradoxes associated with Meinong's original ontology; although, like many Meinongian views, it faces criticism due to its presumed ontological implausibility.
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