Exploring topics in the history and philosophy of logic (Q2345169)

This book presents a number of topics -- negative terms, the liar paradox, predication and identity, the square of opposition, ontology, etc. -- from the point of view of the term logic developed by Fred Sommers and the author. Indeed, two chapters, on the liar and on ratiocination, are by Sommers himself, who sadly died soon after the book was completed. Term logic contrasts with the familiar function-argument logic due to Frege, but here is shown to manage such matters as identity, relations, and multiple generality, which were beyond the capacity of both the traditional formal logic of the middle ages and the nineteenth-century algebraic logics over which Frege's logic triumphed. The treatment of the liar paradox is cassationist, following Ryle and (ultimately) Chrysippus: it denies that the sentence ``This sentence is false'' expresses a proposition. Term logic's claims to be ``natural'' may be clear if the contrast is against classical predicate logic, but not against such claimants as \textit{C. L. Hamblin}'s ``Felicitous fragment of the predicate calculus'' [Notre Dame J. Formal Logic 14, 433--447 (1973; Zbl 0214.00801)], which is similarly variable-free and (almost) follows English word order.