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”.
