nly 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 e