The study of truth is often seen as running on two separate paths: the nature path and the logic path. The former concerns metaphysical questions about the ‘nature’, if any, of truth. The latter concerns itself largely with logic, particularly logical issues arising from the truth-theoretic paradoxes. Where, if at all, do these two paths meet? It may seem, and it is all too often assumed, that they do not meet, or at best touch in only incidental ways. It is (...) often assumed that work on the metaphysics of truth need not pay much attention to issues of paradox and logic; and it is likewise assumed that work on paradox is independent of the larger issues of metaphysics. Philosophical work on truth often includes a footnote anticipating some resolution of the paradox, but otherwise tends to take no note of it. Likewise, logical work on truth tends to have little to say about metaphysical presuppositions, and simply articulates formal theories, whose strength may be measured, and whose properties may be discussed. In practice, the paths go their own ways. Our aim in this paper is somewhat modest. We seek to illustrate one point of intersection between the paths. Even so, our aim is not completely modest, as the point of intersection is a notable one that often goes unnoticed. We argue that the ‘nature’ path impacts the logic path in a fairly direct way. What one can and must say about the logic of truth is influenced, or even in some cases determined, by what one says about the metaphysical nature of truth. In particular, when it comes to saying what the well-known Liar paradox teaches us about truth, background conceptions — views on ‘nature’ — play a significant role in constraining what can be said. This paper, in rough outline, first sets out some representative ‘nature’ views, followed by the ‘logic’ issues (viz., paradox), and turns to responses to the Liar paradox. What we hope to illustrate is the fairly direct way in which the background ‘nature’ views constrain — if not dictate — responses to the main problem on the ‘logic’ path.. (shrink)

In this paper, we distinguish two versions of Curry's paradox: c-Curry, the standard conditional-Curry paradox, and v-Curry, a validity-involving version of Curry's paradox that isn’t automatically solved by solving c-curry. A unified treatment of curry paradox thus calls for a unified treatment of both c-Curry and v-Curry. If, as is often thought, c-Curry paradox is to be solved via non-classical logic, then v-Curry may require a lesson about the structure—indeed, the substructure—of the validity relation itself.

We shed light on an old problem by showing that the logic LP cannot define a binary connective $\odot$ obeying detachment in the sense that every valuation satisfying $\varphi$ and $(\varphi\odot\psi)$ also satisfies $\psi$ , except trivially. We derive this as a corollary of a more general result concerning variable sharing.

After indicating why this is needed, the paper proves a non-triviality result for paraconsistent theory containing arithmetic, naive truth and denotation predicates, and descriptions. The result is obtained by dualising a construction of Kroon. Its most notable feature is that there is a trivial object- one that has every property.

This is a philosophical and historical investigation of the role of inconsistent representations of the same scientific phenomenon. The logical difficulties associated with the simultaneous application of inconsistent models are discussed. Internally inconsistent scientific proposals are characterized as structures whose application is necessarily tied to the confirming evidence that each of its components enjoys and to a vision of the general form of the theory that will resolve the inconsistency. Einstein's derivation of the black body radiation law is used as (...) an example application of such a strategy and is contrasted with planck's derivation. (shrink)

The notion of a proposition is central to philosophy. But it is subject to paradoxes. A natural response is a hierarchical account and, ever since Russell proposed his theory of types in 1908, this has been the strategy of choice. But in this paper I raise a problem for such accounts. While this does not seem to have been recognized before, it would seem to render existing such accounts inadequate. The main purpose of the paper, however, is to provide a (...) new hierarchical account that solves the problem. (shrink)

In this paper I advance and defend a very simple position according to which logic is subclassical but is weaker than the leading subclassical-logic views have it.

We have seen that proofs of soundness of (Boolean) DS, EFQ and of ABS — and hence the legitimation of these inferences — can be achieved only be appealing to the very form of reasoning in question. But this by no means implies that we have to fall back on classical reasoning willy-nilly. Many logical theories can provide the relevant boot-strapping. Decision between them has, therefore, to be made on other grounds. The grounds include the many criteria familiar from the (...) philosophy of science: theoretical integrity (e.g., paucity of ad hoc hypotheses), adequacy to the data (explaining the data of inference —all inferences, not just those chosen from consistent domains!) and so on. This paper has not attempted to address these issues in general. All it demonstrates is that the charge that a dialetheist solution to the semantic paradoxes can be maintained only by making some intelligible notion ineffable cannot be made to stick. The dialetheist has a coherent position, endorsing the T-scheme, but rejecting DS, EFQ (even Boolean DS and EFQ) and ABS. And any argument to the effect that the relevant notions are both ineffable and intelligible begs the question. The case against consistent “solutions” to the semantic paradoxes therefore remains intact. (shrink)