These principles, which were necessarily to some extent anticipated in chap. iv.  Sec. 7, the next chapter will further illustrate.

Sec. 6.  But first we must draw attention to a maxim (also already mentioned), which is strictly applicable to Immediate Inferences, though (as we shall see) in other kinds of proof it may be only a formal condition:  this is the general caution not to go beyond the evidence.  An immediate inference ought to contain nothing that is not contained (or formally implied) in the proposition by which it is proved.  With respect to quantity in denotation, this caution is embodied in the rule ‘not to distribute any term that is not given distributed.’  Thus, if there is a predication concerning ‘Some S,’ or ‘Some men,’ as in the forms I. and O., we cannot infer anything concerning ‘All S.’ or ’All men’; and, as we have seen, if a term is given us preindesignate, we are generally to take it as of particular quantity.  Similarly, in the case of affirmative propositions, we saw that this rule requires us to assume that their predicates are undistributed.

As to the grounds of this maxim, not to go beyond the evidence, not to distribute a term that is given as undistributed, it is one of the things so plain that to try to justify is only to obscure them.  Still, we must here state explicitly what Formal Logic assumes to be contained or implied in the evidence afforded by any proposition, such as ’All S is P.’  If we remember that in chap. iv.  Sec. 7, it was assumed that every term may have a contradictory; and if we bear in mind the principles of Contradiction and Excluded Middle, it will appear that such a proposition as ‘All S is P’ tells us something not only about the relations of ‘S’ and ‘P,’ but also of their relations to ‘not-S’ and ‘not-P’; as, for example, that ‘S is not not-P,’ and that ’not-P is not-S.’  It will be shown in the next chapter how Logicians have developed these implications in series of Immediate Inferences.

If it be asked whether it is true that every term, itself significant, has a significant contradictory, and not merely a formal contradictory, generated by force of the word ‘not,’ it is difficult to give any better answer than was indicated in Sec.Sec. 3-5, without venturing further into Metaphysics.  I shall merely say, therefore, that, granting that some such term as ‘Universe’ or ‘Being’ may have no significant contradictory, if it stand for ’whatever can be perceived or thought of’; yet every term that stands for less than ‘Universe’ or ‘Being’ has, of course, a contradictory which denotes the rest of the universe.  And since every argument or train of thought is carried on within a special ‘universe of discourse,’ or under a certain suppositio, we may say that within the given suppositio every term has a contradictory, and that every predication concerning a term implies some predication concerning its contradictory.  But the name of the suppositio itself has no contradictory, except with reference to a wider and inclusive suppositio.