I propose that empirical procedures, like computational procedures, are justified in terms of truth-finding efficiency. I contrast the idea with more standard philosophies of science and illustrate it by deriving Ockham's razor from the aim of minimizing dramatic changes of opinion en route to the truth.

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)

Relativism is one of the most tenacious theories about truth, with a pedigree as old as philosophy itself. Nearly as ancient is the chief criticism of relativism, namely the charge that the theory is self-refuting. This paper develops a logic of relativism that (1) illuminates the classic self-refutation charge and shows how to escape it; (2) makes rigorous the ideas of truth as relative and truth as absolute, and shows the relations between them; (3) develops an intensional logic for relativism; (...) (4) provides a framework in which relativists can consistently promote ethical, mathematical, scientific, religious, and political truths (among others) as being relative; (5) argues that the notion of incommensurability is far less troubling than is commonly thought; and (6) argues that the concept of a perspective as needed by the theory is not prey to Davidson's well-known critique of conceptual schemes. The paper will not defend relativism as the correct theory of truth, nor will it provide a fully satisfying theory about the nature of a perspective. The logic of relativism is primarily meant to provide a formal framework in which relativists can consistently develop their theories. This alone is a considerable step forward, since the debate about relativism often founders upon the rock of self-refutation. It is argued that while 'everything is relative' is inconsistent, 'everything true is relatively true' is not. The latter is all a relativist really needs. (shrink)

In this paper we argue that Revision Rules, introduced by Anil Gupta and Nuel Belnap as a tool for the analysis of the concept of truth, also provide a useful tool for defining computable functions. This also makes good on Gupta's and Belnap's claim that Revision Rules provide a general theory of definition, a claim for which they supply only the example of truth. In particular we show how Revision Rules arise naturally from relaxing and generalizing a classical construction due (...) to Kleene, and indicate how they can be employed to reconstruct the class of the general recursive functions. We also point at how Revision Rules can be employed to access non-minimal fixed points of partially defined computing procedures. (shrink)