Charles Sayward

The standard response is illustrated by E, J. Lemmon's claim that if all objects in a given universe had names and there were only finitely many of them, then we could always replace a universal proposition about that universe by a complex proposition. It is because these two requirements are not always met that we need universal quantification. This paper is partly in agreement with Lemmon and partly in disagreement. From the point of view of syntax and semantics we can replace a universal proposition about any universe (finite or infinite, countable or uncountable) by a complex proposition (= sentence built up from atomic sentences and the connectives). But from the point of view of communication such a replacement is not possible if the universe is infinite.

The fundamental thought of moral relativism is set out as follows: moral criteria, derived from overall moral points of view, are used to derive particular moral judgments. Thus such a judgment might be correct relative to one overall moral point of view and incorrect relative to another. The evaluation of an overall moral point of view does not involve the application of moral criteria. Rather, the evaluation of a morality takes us outside the province of morality. The result of sharpening this view is a doctrine called system relativism. System relativism is contrasted with other conceptions of moral relativism that have recently been propounded. It is argued that system relativism is the most defensible version.

Four views of arithmetical truth are distinguished: the classical view, the provability view, the extended provability view, the criterial view. The main problem with the first is the ontology it requires one to accept. Two anti-realist views are the two provability views. The first of these is judged to be preferable. However, it requires a non-trivial account of the provability of axioms. The criterial view is gotten from remarks Wittgenstein makes in Tractatus 6.2-6.22 . It is judged to be the best of four views. It is also defended against objections.

In this book a non-realist philosophy of mathematics is presented. Two ideas are essential to its conception. These ideas are (i) that pure mathematics--taken in isolation from the use of mathematical signs in empirical judgement--is an activity for which a formalist account is roughly correct, and (ii) that mathematical signs nonetheless have a sense, but only in and through belonging to a system of signs with empirical application. This conception is argued by the two authors and is critically discussed by three philosophers of mathematics.

The morality of an economic system characterized as an Adam Smith type system is compared with one characterized by central planning. A prima facie case is made that, while the latter has attributes that satisfy a necessary condition for having moral attributes, the former does not and, as a result, has no moral attributes. But then a deeper look at the situation reveals that the directed systems really do not satisfy the necessary condition either. Both the directed and undirected systems end up in the same boat. Neither have any moral attributes

Let C1 and C2 be distinct moral codes formulated in English. Let C1 contain a norm N and C2 its negation. The paper construes the moral relativist as saying that if both codes are consistent, then, in the strongest sense of correctness applicable to moral norms, they are also both correct in the sense that they contain only correct moral norms. If we believe that the physical statements of English are true (false) in English, we will reject an analogous statement made of physical theories. We will hold that the strongest sense of correctness applicable to physical statements is not system-relative. The moral relativist denies that there is any corresponding sense of correctness applicable to moral norms. That is, there is no notion of moral correctness that is not system-dependent. It is argued that, while the position may not be true, there is not a strictly logical basis for refuting it.

Suppose there is a domain of discourse of English, then everything of which any predicate is true is a member of that domain. If English has a domain of discourse, then, since ‘is a domain of discourse of English’ is itself a predicate of English and true of that domain, that domain is a member of itself. But nothing is a member of itself. Thus English has no domain of discourse. We defend this argument and go on to argue to the same conclusion without relying on the supposition that English is a language which contains the predicate ‘is a domain of discourse of English’.