THE LOGIC OF THE CATUSKOTI

In early Buddhist logic, it was standard to assume that for any state of affairs there were four possibilities: that it held, that it did not, both, or neither. This is the catuskoti (or tetralemma). Classical logicians have had a hard time making sense of this, but it makes perfectly good sense in the semantics of various paraconsistent logics, such as First Degree Entailment. Matters are more complicated for later Buddhist thinkers, such as Nagarjuna, who appear to suggest that none of these options, or more than one, may hold. The point of this paper is to examine the matter, including the formal logical machinery that may be appropriate

On An Error In Grove's Proof

Nearly a decade has past since Grove gave a semantics for the AGM postulates. The semantics, called sphere semantics, provided a new perspective of the area of study, and has been widely used in the context of theory or belief change. However, the soundness proof that Grove gives in his paper contains an error. In this note, we will point this out and give two ways of repairing it

The nature of philosophy and its place in the university

Inaugural lecture delivered at the University of Queensland 18 October 1989

Logical Theory Choice: The Case of Vacuous Counterfactuals

There is at present a certain dispute about counterfactuals taking place. What is at issue is whether counterfactuals with necessarily false antecedents are all true. Some hold that such counterfactuals are vacuously true, appearances notwithstanding. Let us call such people vacuists. Others hold that some counterfactuals with necessarily false antecedents are true; some are false: it just depends on their contents. Let us call such people non-vacuists. As a notable representative of the vacuists, I will take Tim Williamson. On the other side, I will take the position defended by Berto, French, Priest, and Ripley. I will argue (unsurprisingly) that the better choice is Non-Vacuism. That, however, is a subsidiary aim of this paper. The main point is to illustrate the method of theory-choice

Berry's Paradox... Again

The paper is a discussion of whether Berry's Pardox presupposes the Principle of Excluded Middle, with particular reference to the work of Ross Brady

Evans' Argument and Vague Objects

In 1978, Gareth Evans published a short and somewhat cryptic article purporting to establish that there are no vague objects. This paper is a commentary on this. Prima facie, the claim that there are no vague objects is clearly false. Mt Everest, for example, has no precise boundaries. And if this is so, there must be something wrong with Evans' argument. In the paper, I discuss what this is, giving a model of vague objects in the process

Much Ado About Nothing

The point of this paper is to bring together three topics: non-existent objects, mereology, and nothing(ness). There are important inter-connections, which it is my aim to spell out, in the service of an account of the last of these

Plurivalent Logics

In this paper, I will describe a technique for generating a novel kind of semantics for a logic, and explore some of its consequences. It would be natural to call the semantics produced by the technique in question ‘many-valued'; but that name is, of course, already taken. I call them, instead, ‘plurivalent'. In standard logical semantics, formulas take exactly one of a bunch of semantic values. I call such semantics ‘univalent'. In a plurivalent semantics, by contrast, formulas may take one or more such values (maybe even less than one). The construction I shall describe can be applied to any univalent semantics to produce a corresponding plurivalent one. In the paper I will be concerned with the application of the technique to propositional many-valued (including two-valued) logics. Sometimes going plurivalent does not change the consequence relation; sometimes it does. I investigate the possibilities in detail with respect to small family of many-valued logics

Don’t be so Fast with the Knife: A Reply to Kapsner

The is a brief reply to the central objection against the construction of my The Fifth Corner of Four by Andi Kapsner in his “Cutting Corners: A Critical Note on Priest’s Five-Valued Catuṣkoṭi. This concerns the desirability of adding a fifth corner (ineffability) to the four of the catuṣkoṭi