This book proposes a novel theory of truth and falsity. It argues that truth is a form of reference and falsity is a form of reference failure. -/- Most of the philosophical literature on truth concentrates on certain ontological and epistemic problems. This book focuses instead on language. By utilizing the Fregean idea that sentences are singular referring expressions, the author develops novel connections between the philosophical study of truth and falsity and the huge literature in in the philosophy of (...) language on the notion of reference. The first part of the book constructs the author’s theory and argues for it in length. Part II addresses the ways in which the theory relates to, and is different from, some of the basic theories of truth. Part III takes up how to account for the truth of sentences with logical operators and quantifiers. Finally, Part IV discusses the applications and implications of the theory for longstanding problems in philosophy of language, metaphysics, and epistemology. -/- A Referential Theory of Truth and Falsity will appeal to researchers and advanced students working in philosophy of language, epistemology, metaphysics, and linguistics. -/- . (shrink)

The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, (...) a trilattice of truth values – a specific algebraic structure with information ordering and two distinct logical orderings, one for truth and another for falsity. Each logical order not only induces its own logical vocabulary, but determines also its own entailment relation. We consider both semantic and syntactic ways of formalizing these relations and construct various logical calculi. (shrink)

The famous “slingshot argument” developed by Church, Gödel, Quine and Davidson is often considered to be a formally strict proof of the Fregean conception that all true sentences, as well as all false ones, have one and the same denotation, namely their corresponding truth value: the true or the false . In this paper we examine the analysis of the slingshot argument by means of a non-Fregean logic undertaken recently by A.Wóitowicz and put to the test her claim that the (...) slingshot argument is in fact circular and presupposes what it intends to prove. We show that this claim is untenable. Nevertheless, the language of non-Fregean logic can serve as a useful tool for representing the slingshot argument, and several versions of the slingshot argument in non-Fregean logics are presented. In particular, a new version of the slingshot argument is presented, which can be circumvented neither by an appeal to a Russellian theory of definite descriptions nor by resorting to an analogous “Russellian” theory of λ–terms. (shrink)

Over the course of the nineteenth century mathematicians became vividly aware that great advances in intuitive “understanding” could be obtained if novel definitions were devised for old notions such as “conic section”, for one thereby often gained a deeper appreciation for why old theorems in the subject had to be true. From a naïve philosophical standpoint, such definitional alterations look as if they must properly displace the “propositional contents” of the very theorems they seek to illuminate. Haven’t our reformers merely (...) “changed the subject”, rather than truly provided. The conceptual enlightenment they claim? Many practitioners of the time claimed that “Science” enjoys a special prerogative to ignore “surface content” in its search for truth, a sentiment with which Frege often concurs, at least in his early writings. Yet it is hard to render these opinions consistent with his official views on sense andreference, as this essay details. It also surveys Russell’s views on such topics, although he was generally less aware than Frege of the revolutionary mathematical work pursued within the “search for fruitful definitions” program. (shrink)