From predication to programming
A free logic is one in which a singular term can fail to refer to an existent object, for example, 'Vulcan' or '5/0'. This essay demonstrates the fruitfulness of a version of this non-classical logic of terms (negative free logic) by showing (1) how it can be used not only to repair a looming inconsistency in Quine's theory of predication, the most influential semantical theory in contemporary philosophical logic, but also (2) how Beeson, Farmer and Feferman, among others, use it to provide a natural foundation for partial functions in programming languages. Vis a vis (2), the question is raised whether the Beeson-Farmer-Feferman approach is adequate to the treatment of partial functions in all programming languages. Gumb and the author say "No'', and suggest a way of handling the refractory cases by means of positive free logic. Finally, Antonelli's solution of a problem associated with the Gumb-Lambert proposal is mentioned.
predication programming negative free logic partial functions positive free logic extensional proto-semantics proof of unsoundness