Posterior Analytics (Bouchier)/Book I/Chapter XXV

Chapter XXV: That Affirmative is superior to Negative Demonstration

 * Affirmative demonstration is superior to negative. It requires fewer propositions, is more persuasive and comprehensible, and also more immediate, for the negative is only proved through the medium of the affirmative.

That affirmative demonstration is superior to negative is plain from the following considerations. We may suppose that, other circumstances being similar, the demonstration which proceeds from fewer postulates, hypotheses, or premises is superior. If these fewer postulates are as well known as the more numerous, knowledge will be attained more quickly by their means: a desirable result. Now the reason for the assertion that the demonstration proceeding from fewer premises, so long as they are universal, is superior, is as follows. If the middle terms be equally well known, then the antecedent terms will likewise be better known. Firstly then let it be supposed that, by means of the middle terms B, C and D, the demonstration is arrived at that E is A, and then the same demonstration by means of the middle terms F and G. Here the fact that D is A is similar to the fact that E is A, but the fact that D is A is antecedent to and better known than the fact that E is A, for the latter is demonstrated by means of the former, and that by which a thing is demonstrated is more convincing than the thing demonstrated. Hence, other circumstances being similar, the demonstration proceeding by means of fewer propositions is superior. In both cases alike the proof is attained by means of three terms and two premises, but affirmative demonstration assumes that a certain thing exists, negative demonstration first that it does and then that it does not exist, so that the latter is inferior to the former. Further, since it has been proved that, when both premises are negative, no conclusion can be arrived at, a negative syllogism must have one negative and one affirmative premise. We should now add the following condition. When the demonstration is extended in application the number of affirmative premises must be increased, while the negative premises in each syllogism can never be more than one. Suppose that no B is A, but all C is B. If the premises are to be further enlarged a middle term must be interposed between each of these pairs. Let the middle between A and B be D, and that between BC be E. Now it is clear that the term E is affirmative, and D must be affirmative when joined to B, negative when joined to A, for all B must be D, and no D must be A. Thus one premise, DA, is negative.

The same method applies to other syllogisms. In affirmative syllogisms the middle term is always used affirmatively when joined with one of the other two terms, but in negative syllogisms the middle term must be negative in one premise. Thus one premise is negative but the others are affirmative. Also if that by which a thing is proved be more comprehensible and convincing than the thing itself, and the negative demonstration be proved by affirmative premises, but not vice versâ, the affirmative demonstration would seem to be prior to, and more comprehensible and convincing than the negative.

Moreover, since the first principle of syllogism is the universal immediate premise, and since in the affirmative syllogism the universal premise is affirmative, in the negative it is negative; since also the affirmative premise is prior to and more comprehensible than the negative (for the negation only becomes known by means of the affirmation, and affirmation is prior to negation, just as ‘being’ is prior to ‘not-being’); then the primary principle of the affirmative syllogism is superior to that of the negative, and that syllogism which uses superior principles must itself be superior. Moreover, the affirmative syllogism is more primary, because without it no negative syllogism can be formed.