^{page 221 note 1} I use the technical terms ‘valid’ and ‘validity’ in their wider sense, in which they attach to the same kinds of argument as do the non-technical terms ‘good,’ ‘cogent’ and ‘conclusive’. ‘Valid’ is technical in my use only because it disregards the truth of the premisses. The non-technical terms do not, so that one must distinguish arguments that are cogent from those that would be (if the premisses were true). The intention is not to prejudge what belongs to logic, which is the very question I raise, but to avoid distinguishing kinds of argument by means of terms for the appraisal of any particular argument.

^{page 222 note 1} Formal logic then has to do with any principles of this kind which are formal, in the sense of principles whose statement requires only expressions like ‘not’, ‘and’, ‘if’, ‘is’, ‘belongs to’, ‘any’, ‘something’, ‘of a certain kind’. Arguments having formal principles can mention almost anything, and so formal principles could also be called topic-neutral principles.

There is a tendency to confuse formal principles and analytic principles (in a wide sense). No doubt the boundaries of the class of formal principles are usually drawn so narrowly that the only interesting formal principles will be analytically true. But the converse does not hold. For many analytically true principles are material (i.e. non-formal), nor are these confined to principles which are special cases of analytically true formal principles. That an uncle has either a nephew or a niece is a principle of a class of arguments, whose form is given by this principle; and unlike the principle that a great-great- uncle is older than his great-great-nephew or -niece, it is analytic; yet it is material, since its statement uses ‘uncle’, ‘nephew’, and ‘niece’, and further its analytic truth arises from the definitions of these words. So material principles of argument may be either analytic or synthetic. The former might be said to exhibit the meanings of the terms in which they are expressed, but not the latter.

In any case, of course, the boundaries of the formal must be drawn by decree, and most logicians simply set down a list of the concepts they will allow in their formal principles. Topic-neutrality has degrees, and for some purposes it might be tempting to make Euclid’s second axiom a formal principle, in spite of the word ‘equal’, or to speak of more and less formal principles. A more careful account of what makes logic formal, and of the special motives, spirit and procedures of the formal logician, is given in Ryle’s Dilemmas, in “Formal and informal logic”.

^{page 226 note 1} There axe two distinct interpretations for the title of Hare’s book The Language of Morals. One shows his method, the other his philosophical position. On the one hand he examines the concepts occurring in morals, and in the contemporary manner does so by explicit study of the uses of words. On the other hand, in seeking to exhibit whatever rationality moral thinking possesses (p. 45), he identifies this rationality with, successively: moral judgments being governed by logical rules (p. 16), there being inference of one prescription from another, there being entailments between prescriptions, and there being connections of meaning between the words used in prescriptions (Ch. 3), including first-person imperatives, introduced for the purpose of being entailed (Cf. p. 187 ff.). Thus he grounds the rationality of morals in the language of morals.