1 Introduction

Numerous solutions have been proposed to the semantic paradoxes. Two that are frequently singled out and compared are the following. The first is that according to which paradoxical sentences are neither true nor false — as it is sometimes put, they are semantic gaps. The second is that according to which paradoxical sentences are both true and false — as it is sometimes put, they are semantic gluts (dialetheias). Calling the first of these a solution is, in fact, somewhat misleading: it is rather like calling an opening gambit a game of chess. For the solution runs into severe problems almost immediately, and so can be only the first of a series of (often ad hoc) moves made to defend the original weak opening. Nonetheless, the symmetry involved in the gap and glut solutions is obvious enough to make the comparison a natural one.

Logical consequence is a notion that every person who reasons must possess, at least implicitly. To give a precise and accurate characterization of this notion is the fundamental task of logic. In a similar way, the notion of effectivity is a concept that anyone with a basic training in mathematics possesses, and the most fundamental task of a theory of computability is to give a precise characterization of this notion. The problem concerning effectivity was solved (at least to the satisfaction of most people) in the 1930s, almost as soon as it was raised, by the work of Turing, Church, and others. By contrast, the correct and precise characterization of logical consequence has been hotly contested through the two and a half thousand-year history of logic.

Buddhism and Marxism may seem unlikely bedfellows, since they come from such different times and places, and appear to address such different concerns. But the two have at least this much in common: both say that life, as we find it, is unsatisfactory; both have a diagnosis of why this is; and both offer the hope of making it better. In this paper, I argue that aspects of each complement aspects of the other. In particular, Buddhism provides a stable ethical base that Marxism always lacked; and Marxism provides a sophisticated political philosophy, which Buddhism never had. I will explain those aspects of each of the two on which I wish to draw, and then explain how they are complementary.

My topic concerns the martial arts – or at least the East Asian martial arts, such as karatedo, taekwondo, kendo, wushu. To what extent what I have to say applies to other martial arts, such as boxing, silat, capoeira, I leave as an open question. I will illustrate much of what I have to say with reference to karatedo, since that is the art with which I am most familiar; but I am sure that matters are much the same with other East Asian martial arts.

Towards Non-Being (Priest [2005]) develops an account of the semantics of intentional predicates and operators. The account appeals to objects, both existent and non-existent, and worlds, both possible and impossible. This paper formulates replies to a number of the more interesting objections to the semantics that have been proposed since the book was published.

Towards NonBeing (Priest, 2005) gives a noneist account of the semantics of intentional operators and predicates. The semantics for intentional operators are modelled on those for the □ in normal modal logics. In this paper an alternative semantics, modelled on neighborhood semantics for □, is given and assessed.

1.1 In standard modal logics, the worlds are 2-valued in the following sense: there are 2 values (true and false) that a sentence may take at a world. Technically, however, there is no reason why this has to be the case. The worlds could be many-valued. This paper presents one simple approach to a major family of many-valued modal logics, together with an illustration of why this family is philosophically interesting.

The paper argues that the view that the particular quantifier is ‘existentially loaded’ is a relatively new one historically and that it has become entrenched in modern philosophical logic for less than happy reasons.