It is known that evidential support, on the Bayesian definition of this notion, is intransitive. According to some, however, the Bayesian definition is too weak to be materially adequate. This paper investigates whether evidential support is transitive on some plausible probabilistic strengthening of that definition. It is shown that the answer is negative. In fact, it will appear that even under conditions under which the Bayesian notion of evidential support is transitive, the most plausible candidate strengthenings are not.

The concept of truth arguably plays a central role in many areas of philosophical theorizing. Yet, what seems to be one of the most fundamental principles governing that concept, i.e. the equivalence between ‘ ‘P’ is true’ and ‘P’, is inconsistent in full classical logic, as shown by the semantic paradoxes. I propose a new solution to those paradoxes, based on a principled revision of classical logic. Technically, the key idea consists in the rejection of the unrestricted validity of the structural principle of contraction. I first motivate philosophically this idea with the metaphysical picture of the states-of-affairs expressed by paradoxical sentences as being distinctively “unstable”. I then proceed to demonstrate that the theory of truth resulting from this metaphysical picture is, in many philosophically interesting respects, surprisingly stronger than most other theories of truth endorsing the equivalence between ‘ ‘P’ is true’ and ‘P’ (for example, the theory vindicates the validity of the traditional laws of excluded middle and of non-contradiction, and also vindicates the traditional constraint of truth preservation on logical consequence). I conclude by proving a cutelimination theorem that shows the consistency of the theory.

We present Arrow Update Logic, a theory of epistemic access elimination that can be used to reason about multi-agent belief change. While the belief-changing “arrow updates” of Arrow Update Logic can be transformed into equivalent belief-changing “action models” from the popular Dynamic Epistemic Logic approach, we prove that arrow updates are sometimes exponentially more succinct than action models. Further, since many examples of belief change are naturally thought of from Arrow Update Logic’s perspective of eliminating access to epistemic possibilities, Arrow Update Logic is a valuable addition to the repertoire of logics of information change. In addition to proving basic results about Arrow Update Logic, we introduce a new notion of common knowledge that generalizes both ordinary common knowledge and the “relativized” common knowledge familiar from the Dynamic Epistemic Logic literature.

This paper develops a new framework for combining propositional logics, called “juxtaposition.” Several general metalogical theorems are proved concerning the combination of logics by juxtaposition. In particular, it is shown that under reasonable conditions, juxtaposition preserves strong soundness. Under reasonable conditions, the juxtaposition of two consequence relations is a conservative extension of each of them. A general strong completeness result is proved. The paper then examines the philosophically important case of the combination of classical and intuitionist logics. Particular attention is paid to the phenomenon of collapse. It is shown that there are logics with two stocks of classical or intuitionist connectives that do not collapse. Finally, the paper briefly investigates the question of which rules, when added to these logics, lead to collapse.

There are well-known quasi-formal arguments that identity is a “strict” relation in at least the following three senses: (1) There is a single identity relation and a single distinctness relation; (2) There are no contingent cases of identity or distinctness; and (3) There are no vague or indeterminate cases of identity or distinctness. However, the situation is less clear cut than it at first may appear. There is a natural formal theory of identity that is very close to the standard classical theory but which does not validate the formal analogues of (1)–(3). The core idea is simple: We weaken the Principle of the Indiscernibility of Identicals from a conditional to an entailment and we adopt a weakly classical logic. This paper investigates this weakly classical theory of identity (and related theories) and discusses its philosophical ramifications. It argues that we can accept a reasonable theory of identity without committing ourselves to the uniqueness, necessity, or determinacy of identity.

We offer an interpretation of the words and works of Richard Dedekind and the David Hilbert of around 1900 on which they are held to entertain diverging views on the structure of a deductive science. Firstly, it is argued that Dedekind sees the beginnings of a science in concepts, whereas Hilbert sees such beginnings in axioms. Secondly, it is argued that for Dedekind, the primitive terms of a science are substantive terms whose sense is to be conveyed by elucidation, whereas Hilbert dismisses elucidation and consequently treats the primitives as schematic.