ON EDGINGTON’S FORMALIZATION OF THE PRINCIPLE OF KNOWABILITY

The formalization of the principle of knowability suggested by Dorothy Edgington is examined. This formalization has been suggested as a solution to the Fitch problem. It is interesting in that it blocks the Fitch argument and, in informal reading, makes a clear and intuitively appealing sense. On the other hand, as is shown in the paper, the semantic theory behind this formalization has two significant gaps: 1) it does not define the interpretation of actuality operator, and 2) it does not define the semantic way of representing the agent’s knowledge. The main outcome of the papers is critical. It is to the effect that unless those gaps are filled, Edgington’s theory cannot count as a solution to the Fitch problem.

Knowability Without Rigidity

The most straightforward interpretation of the principle of knowability is that every true proposition may be known. This, taken together with some intuitively appealing ideas, raises a problem known as the Church–Fitch paradox. There is a wide variety of alternative interpretations of the principle of knowability that have been offered to avoid the paradox. Some of them are based on rigidification of certain aspects of what is knowable. I examine three proposals representing this strategy, those by Edgington, Rückert and Jenkins. Edgington defines what is knowable as a proposition prefixed by the actuality operator. Rückert and Jenkins maintain that what makes a proposition knowable is the possibility of knowing de re (Rückert) or recognizing (Jenkins) the state of affairs that renders the proposition actually true. In both cases, the link to the actual world (or situation) rigidifies what is knowable in some aspect or other. I argue that all three theories have strongly counterintuitive consequences, and I offer an interpretation of the principle of knowability that is both free from rigidity and immune to the Church–Fitch argument.

Epistemicism and modality

What kind of semantics should someone who accepts the epistemicist theory of vagueness defended in Timothy Williamson's Vagueness (1994) give a definiteness operator? To impose some interesting constraints on acceptable answers to this question, I will assume that the object language also contains a metaphysical necessity operator and a metaphysical actuality operator. I will suggest that the answer is to be found by working within a three-dimensional model theory. I will provide sketches of two ways of extracting an epistemicist semantics from that model theory, one of which I will find to be more plausible than the other.

Representing Counterparts

This paper presents a counterpart theoretic semantics for quantified modal logic based on a fleshed out account of Lewis's notion of a 'possibility'. According to the account a possibility consists of a world and some haecceitistic information about how each possible individual gets represented de re. Following Hazen, a semantics for quantified model logic based on evaluating formulae at possibilities is developed. It is shown that this framework naturally accommodates an actuality operator, addressing recent objections to counterpart theory, and is equivalent to the more familiar Kripke semantics for quantied modal logic with an actuality operator.

WHAT IS THE CORRECT LOGIC OF NECESSITY, ACTUALITY AND APRIORITY?

This paper is concerned with a propositional modal logic with operators for necessity, actuality and apriority. The logic is characterized by a class of relational structures defined according to ideas of epistemic two-dimensional semantics, and can therefore be seen as formalizing the relations between necessity, actuality and apriority according to epistemic two-dimensional semantics. We can ask whether this logic is correct, in the sense that its theorems are all and only the informally valid formulas. This paper gives outlines of two arguments that jointly show that this is the case. The first is intended to show that the logic is informally sound, in the sense that all of its theorems are informally valid. The second is intended to show that it is informally complete, in the sense that all informal validities are among its theorems. In order to give these arguments, a number of independently interesting results concerning the logic are proven. In particular, the soundness and completeness of two proof systems with respect to the semantics is proven (Theorems 2.11 and 2.15), as well as a normal form theorem (Theorem 3.2), an elimination theorem for the actuality operator (Corollary 3.6), and the decidability of the logic (Corollary 3.7). It turns out that the logic invalidates a plausible principle concerning the interaction of apriority and necessity; consequently, a variant semantics is briefly explored on which this principle is valid. The paper concludes by assessing the implications of these results for epistemic two-dimensional semantics.