Charles Sayward

The significance of the semantical paradoxes for natural languages is examined. If Tarski’s reflections on the issue are correct, English is inconsistent. Paul Ziff responds to Tarskian reflections by arguing to the conclusion that no natural language is or can be inconsistent. The authors reject Ziff’s argument, but they defend something similar to its conclusion: no language, natural or otherwise, is or can be inconsistent in the way that Tarski holds languages capable of formulating the Epimenides are inconsistent.

Conversational implicatures are easy to grasp for the most part. But it is another matter to give a rational reconstruction of how they are grasped. We argue that Grice's attempt to do this fails. We distinguish two sorts of cases: (1) those in which we grasp the implicature by asking ourselves what would the speaker have to believe given that what he said is such as is required by the talk exchange; (2) those in which we grasp the implicature by asking ourselves why it is that what the speaker said is so obviously not such as is required by the talk exchange. We argue that Grice's account does not fit those cases falling under (2).

Quine argues that if sentences that are set theoretically equivalent are interchangeable salva veritate, then all transparent operators are truth-functional. Criticisms of this argument fail to take into account the conditional character of the conclusion. Quine also argues that, for any person P with minimal logical acuity, if ‘belief’ has a sense in which it is a transparent operator, then, in that sense of the word, P believes everything if P believes anything. The suggestion is made that he intends that result to show us that ‘believes’ has no transparent sense. Criticisms of this argument are either based on unwarranted assertions or on definitions of key terms that depart from Quine’s usage of those terms.

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.