"... an excellent collection... " —Journal of Language & Social Psychology An important collection of original essays by well-known scholars debating the questions of logical versus psychologically-based interpretations of language.

This paper presents completeness and conservative extension results for the boolean extensions of the relevant logic T of Ticket Entailment, and for the contractionless relevant logics TW and RW. Some surprising results are shown for adding the sentential constant t to these boolean relevant logics; specifically, the boolean extensions with t are conservative of the boolean extensions without t, but not of the original logics with t. The special treatment required for the semantic normality of T is also shown along (...) the way. (shrink)

The prepositional calculiC n , 1 n introduced by N.C.A. da Costa constitute special kinds of paraconsistent logics. A question which remained open for some time concerned whether it was possible to obtain a Lindenbaum''s algebra forC n . C. Mortensen settled the problem, proving that no equivalence relation forC n . determines a non-trivial quotient algebra.The concept of da Costa algebra, which reflects most of the logical properties ofC n , as well as the concept of paraconsistent closure system, (...) are introduced in this paper. (shrink)

The propositional calculi $C_{n}$ , $1\leq n\leq \omega $ introduced by N.C.A. da Costa consitute special kinds of paraconsistent logics. A question which remained open for some time concerned whether it was possible to obtain a Lindenbaum's algebra for $C_{n}$ . C. Mortensen settled the problem, proving that no equivalence relation for $C_{n}$ determines a non-trivial quotient algebra. The concept of da Costa algebra, which reflects most of the logical properties of $C_{n}$ , as well as the concept of paraconsistent (...) closure system, are introduced in this paper. We show that every da Costa algebra is isomorphic with a paraconsistent algebra of sets, and that the closure system of all filters of a da Costa algebra is paraconsistent. (shrink)

In this paper I propose a fundamental modification of standard type theory, produce a new kind of type theoretic language, and couch in this language a comprehensive theory of abstract individuals and abstract properties and relations of every type. I then suggest how to employ the theory to solve the four following philosophical problems: the identification and ontological status of Frege's Senses; the deviant behavior of terms in propositional attitude contexts; the non-identity of necessarily equivalent propositions, and the paradox of (...) analysis. We can roughly describe these solutions as follows: the senses of English names and descriptions which denote individuals will be modelled as abstract individuals; the senses of English relation denoting expressions of a given type will be modelled as abstract relations of that type. Inside de dicto attitude contexts, these English expressions denote their senses. Relations and propositions will not be identified with their extensions, nor with functions or sets of any kind. They will be taken as primitive, and precise being and identity conditions will be proposed consistent with the view that necessarily equivalent relations and propositions may be distinct. With the modelling described in, the expressions being a brother and being a male sibling may both denote the same property, though their senses may differ. Just as Frege predicts, being a brother just is being a male sibling is an informative identity statement because the terms flanking the identity sign have the same denotation, though distinct senses. (shrink)