Fitch's argument purports to show that if all truths are knowable then all truths are known. The argument exploits the fact that the knowledge predicate or operator is untyped and may thus apply to sentences containing itself. This article outlines a response to Fitch's argument based on the idea that knowledge is typed. The first part of the article outlines the philosophical motivation for the view, comparing it to the motivation behind typing truth. The second, formal part presents a logic (...) in which knowledge is typed and demonstrates that it allows nonlogical truths to be knowable yet unknown. (shrink)

This reissue of his collection of early essays, Logico-Linguistic Papers, is published with a brand new introduction by Professor Strawson but, apart from minor ...

The „Paradox of the Concept Horse" arises on the assumption of the Reference Principle: that co-referential expressions should be cross-substitutable salva veritate in extensional contexts and salva congruitate in all. Accordingly no singular term can co-refer with an unsaturated expression. The paper outlines a number of desiderata for a satisfactory response to the problem and argues that recent treatments by Dummett and Wiggins fall short by their lights. It is then pointed out that a more consistent perception of the requirements (...) of the Reference Principle leads not to the Paradox but to the result that Frege had no business extending the notion of Bedeutung to unsaturated expressions in the first place. Rather the relation between, e.g., predicates and the entities that comprise the range of higher-order logical variables must be logically unlike that between singular terms and their referents; the way is therefore opened for singular terms to refer to entities of the former kind after all. The Concept Horse is a concept (and a Fregean object too.). (shrink)

If □ is conceived as an operator, i.e., an expression that gives applied to a formula another formula, the expressive power of the language is severely restricted when compared to a language where □ is conceived as a predicate, i.e., an expression that yields a formula if it is applied to a term. This consideration favours the predicate approach. The predicate view, however, is threatened mainly by two problems: Some obvious predicate systems are inconsistent, and possible-worlds semantics for predicates of (...) sentences has not been developed very far. By introducing possible-worlds semantics for the language of arithmetic plus the unary predicate □, we tackle both problems. Given a frame (W, R) consisting of a set W of worlds and a binary relation R on W, we investigate whether we can interpret □ at every world in such a way that □ $\ulcorner A \ulcorner$ holds at a world ᵆ ∊ W if and only if A holds at every world $\upsilon$ ∊ W such that ᵆR $\upsilon$ . The arithmetical vocabulary is interpreted by the standard model at every world. Several 'paradoxes' (like Montague's Theorem, Gödel's Second Incompleteness Theorem, McGee's Theorem on the ω-inconsistency of certain truth theories, etc.) show that many frames, e.g., reflexive frames, do not allow for such an interpretation. We present sufficient and necessary conditions for the existence of a suitable interpretation of □ at any world. Sound and complete semi-formal systems, corresponding to the modal systems K and K4, for the class of all possible-worlds models for predicates and all transitive possible-worlds models are presented. We apply our account also to nonstandard models of arithmetic and other languages than the language of arithmetic. (shrink)