But such objections imply that nothing short of absolute truth has any value; that all our discussions and investigations in science or social affairs are without logical criteria; that Logic must be confined to symbols, and considered entirely as mental gymnastics.  In this book prominence will be given to the character of Logic as a formal science, and it will also be shown that Induction itself may be treated formally; but it will be assumed that logical forms are valuable as representing the actual relations of natural and social phenomena.

Sec. 7.  Symbols are often used in Logic instead of concrete terms, not only in Symbolic Logic where the science is treated algebraically (as by Dr. Venn in his Symbolic Logic), but in ordinary manuals; so that it may be well to explain the use of them before going further.

It is a common and convenient practice to illustrate logical doctrines by examples:  to show what is meant by a Proposition we may give salt is soluble, or water rusts iron: the copulative exponible is exemplified by salt is savoury and wholesome; and so on.  But this procedure has some disadvantages:  it is often cumbrous; and it may distract the reader’s attention from the point to be explained by exciting his interest in the special fact of the illustration.  Clearly, too, so far as Logic is formal, no particular matter of fact can adequately illustrate any of its doctrines.  Accordingly, writers on Logic employ letters of the alphabet instead of concrete terms, (say) X instead of salt or instead of iron, and (say) Y instead of soluble or instead of rusted by water; and then a proposition may be represented by X is Y.  It is still more usual to represent a proposition by S is (or is not) P, S being the initial of Subject and P of Predicate; though this has the drawback that if we argue—­S is P, therefore P is S, the symbols in the latter proposition no longer have the same significance, since the former subject is now the predicate.

Again, negative terms frequently occur in Logic, such as not-water, or not-iron, and then if water or iron be expressed by X, the corresponding negative may be expressed by x; or, generally, if a capital letter stand for a positive term, the corresponding small letter represents the negative.  The same device may be adopted to express contradictory terms:  either of them being X, the other is x (see chap. iv., Sec.Sec. 7-8); or the contradictory terms may be expressed by x and [x], y and [y].

And as terms are often compounded, it may be convenient to express them by a combination of letters:  instead of illustrating such a case by boiling water or water that is boiling, we may write XY; or since positive and negative terms may be compounded, instead of illustrating this by water that is not boiling, we may write Xy.