Alex Oliver

A Modest Logic of Plurals

We present a plural logic that is as expressively strong as it can be without sacrificing axiomatisability, axiomatise it, and use it to chart the expressive limits set by axiomatisability. To the standard apparatus of quantification using singular variables our object-language adds plural variables, a predicate expressing inclusion (is/are/is one of/are among), and a plural definite description operator. Axiomatisability demands that plural variables only occur free, but they have a surprisingly important role. Plural description is not eliminable in favour of quantification; on the contrary, quantification is definable in terms of it. Predicates and functors (function signs) can take plural as well as singular terms as arguments, and both many-valued and single-valued functions are expressible. The system accommodates collective as well as distributive predicates, and the condition for a predicate to be distributive is definable within it; similarly for functors. An essential part of the project is to demonstrate the soundness and completeness of the calculus with respect to a semantics that does without set-theoretic domains and in which the use of set-theoretic extensions of predicates and functors is replaced by the sui generis relations and functions for which the extensions were at best artificial surrogates. Our metalanguage is designed to solve the difficulties involved in talking plurally about individuals and about the semantic values of plural items.

Trade Marks as Property: A Philosophical Perspective

In this chapter, we investigate the idea of trade marks as property. Three questions need to be answered. The first is a conceptual matter: are trade marks capable of being property or are they ruled out as a matter of conceptual necessity? The second is conceptual- cum -descriptive: is the current laws treatment of trade marks treatment of them as property? The third is normative: if the current law does in fact treat them as property, is it right to do so? The questions need to be tackled in turn. Are trade marks capable of being property? When we ask whether trade marks are capable of being property, we are of course assuming that it makes sense to speak of things (resources, assets) being property. In other words, we assume with the layman and the practising lawyer that it makes sense to speak of an owner of a thing, where the thing owned is the property. Admittedly, among legal theorists there is a long tradition going back to Bentham that ridicules this way of speaking. It insists that property is best characterized not as the thing itself but as a bundle of normative relationships between people concerning the use of the thing. But, as Harris has rightly argued, this is a false opposition. In particular, scepticism about the very idea of ownership of a thing is generally based on the thesis that ownership involves the right to use a thing in any way one pleases.