Philip Hugly

In this paper the authors recapitulate, justify, and defend against criticism the extension of the redundancy theory of truth to cover a wide range of uses of ‘true’ and ‘false’. In this they are guided by the work of A. N. Prior. They argue Prior was right about the scope and limits of the redundancy theory and that the line he drew between those uses of ‘true’ which are and are not susceptible to treatment via redundancy serves to distinguish two important and mutually irreducible types of truth: redundancy truth and predicative truth. Only the latter serves for semantic theorizing.

Robert cummins has recently attacked this line of argument: if p is a semantically primitive predicate of a first order language l, then p requires its own clause in the definition of satisfaction integral to a definition of truth of l. thus if l has infinitely many such p, the satisfaction clause cannot be completed and truth for l will remain undefined. against this cummins argues that a single clause in a general base theory for l can specify satisfaction conditions for even infinitely many semantically primitive predicates of l. against cummins we argue that a general base theory contains a primitive expression 'applies to' and that to make his case cummins would need to prove this expression stands for a semantical relation sufficient to a truth definition for l. not only is such a proof lacking but we show the claim to be altogether dubious

The significance of the semantical paradoxes for natural languages is examined. If Tarski’s reflections on the issue are correct, English is inconsistent. Paul Ziff responds to Tarskian reflections by arguing to the conclusion that no natural language is or can be inconsistent. The authors reject Ziff’s argument, but they defend something similar to its conclusion: no language, natural or otherwise, is or can be inconsistent in the way that Tarski holds languages capable of formulating the Epimenides are inconsistent.

In this book a non-realist philosophy of mathematics is presented. Two ideas are essential to its conception. These ideas are (i) that pure mathematics--taken in isolation from the use of mathematical signs in empirical judgement--is an activity for which a formalist account is roughly correct, and (ii) that mathematical signs nonetheless have a sense, but only in and through belonging to a system of signs with empirical application. This conception is argued by the two authors and is critically discussed by three philosophers of mathematics.

A case against Prior’s theory of propositions goes thus: (1) everyday propositional generalizations are not substitutional; (2) Priorean quantifications are not objectual; (3) quantifications are substitutional if not objectual; (4) thus, Priorean quantifications are substitutional; (5) thus that Priorean quantifications are not ontologically committed to propositions provides no basis for a similar claim about our everyday propositional generalizations. Prior agrees with (1) and (2). He rejects (3), but fails to support that rejection with an account of quantification on which there could be quantifications that are neither substitutional nor objectual. The paper draws from the work of Lorenzen an alternative conception of quantification in terms of which that needed account can be given.