For let at be predicated of no part of N, but of all x. Since then the negative proposition can be converted, N will belong to no part of as : but se by the supposition was predicated of all x. Accordingly sr will be no part of x : for this has been shown before. Again, if m shall belong to all st, but to no part of x, neither will N belong to any part of x : for if m belongs to no part of x, neither will x belong to any part of m : but am by the supposition belongs to all N. Therefore x will belong to no part of N : for this also has become the first figure.
And since the negative proposition is convertible, (Ityrisrpicn) neither will N belong to any part of x, so that there will be the same syllogism. An affirmative syllogism is not produced by means of this figure, but they are all negative, both the universal syllogisms and the particular syllogisms. (' Analyt.' i. 5.) (26.) But if one thing belongs to the whole of the same thing and another belongs to no part of it, or both to the whole or to no part, such a figure I call the third; and I call that the middle in it of which both the predications are made, and I call the extremes the predicates : -And the middle is placed without the extremes, and last in position -And a syllogism will be possible both when the terms are universal and when not universal with reference to the middle.
Accordingly if they are universal, when both r and n belong to all s, r will belong to some part of n of necessity : for since the affirma tive is convertible, s will belong to some part of n, so that since r belongs to all of s, and s to some part of n, of necessity r belongs to some part of n : for the syllogism is produced by means of the first figure.
To form a syllogism universally by means of this figure is not possible, neither in the negative nor in the affirmative. e Analyt. Pr.,' i. 6.) (27.) And it is manifest that every demonstration will be by means of three terms and not more. And since this is clear, it is manifest that it consists of two propositions and not more : for the three terms are two propositions. (' Analyt. Pr.,' i. 25.) (28.) It is necessary in all the figures that the middle be in both the propositions. If then the middle tens both predicate and be the subject of predication, or itself predicates and anything is denied of it, it will be the first figure : but if it both predicates and is denied of something, it. will be the middle figure : and if other things are predicated of it, or one thing is denied and another predicated, it will be the Last figure. (' Analyt. Pr., i. 32.) (29.) Moreover in all syllogisms one of the terms must be affirmative and it must be universal : for without the universal there will either be no syllogism, or it will not relate to the thing proposed, or the very thing to be proved will be assumed. For let it be proposed to prove that music is an honourable pleasure; if then any one should assume that pleasure is honoumblo without adding the "all," it will not be a syllogism : and if he should assume that some pleasure is excellent, if he means other pleasure, it has nothing to do with the subject proposed, and if he means the very pleasure itself, he assumes tho very thing which is to bo proved. ('.Analyt. Pr.,' i. 24.) (30.) The science of what a thing is, it is possible to investigate by means of this figure alone (the first). For in the middle figure the syllogism is not affirmative, aud (the question)what science is, requires the affirmative : and in the last figure there is a syllogism, but not a universal syllogism, and the question what a thing is, belongs to the universal. Analyt. Post.; i. 14.) (31.) All who attempt to syllogise from things less credible than the conclusion, manifestly do not syllogiso rightly. (' Top.; viii. 6.)
(32.) From what is true it is not possible to form a false conclusion, but from what is false it is possible to form a true conclusion ; not however " why " but "that" the thing is. e Analyt. Pr.,' ii. 2.
Accordingly it is manifest that, if the conclusion be false, of necessity those things are false either wholly or partly from which the argumen tation (Aleyos) is derived ; but when the conclusion is true, it is not a matter of necessity for either anything or all to be true, but it is possible when none of the things in the syllogism are true, for the conclusion to be true notwithstanding, but not as a matter of necessity. And the reason is, that, when two things are so related to one another, that when one is, of necessity the other is, when this other is not, neither will the first be, but when it is, it is not a matter of necessity that the first be. (` Analyt. Pr.,' ii. 4.) (33.) And a Philosophema is a syllogism demonstrative, and an Epicheirema a syllogism dialectic, and a Sophisms a syllogism con tentious, and an Aporema a dialectic syllogism of contradiction. Top.; viii. 11.) Demonstration then is, when from true and first things the syllogism comes, or from things of such a kind which by means of some first and true things have received the beginning of the knowledge concerning them : and a Dialectic syllogism is that syllogism which is derived from common notions. ( Top.; i. 1.) And speech is called false in one manner, when it appears to be conclusive but is not conclusive,which is called a contentious syllogism (gpicr-rmis crulaoylcrids). (` Top.; viii. 12.) Contentious speech is the syllogising from notions that appear to be common notions, but are not; or it is merely apparent syllogising. (' Soph. Blench.; 2.) The equality of opposite arguments (Acrytanof) would appear to be productive of doubt. (‘ Top.; vi. 5.) (34.) Induction (is-wyaes-4) is the progress from the particular to the universal : thus if a pilot who is skilled is the best, and if a charioteer who is skilled is so, universally also the person who is skilled in eieh thing is the best. And induction is the more persuasive and more clear, and more intelligible to sense, and in Vogue among the many ; but the syllogism has more force and is more effective against opponents in argument. ( Top.; i. 12.) (35.) Induction then and the syllogism from induction, is through one extreme to syllogise the other with the middle term ; for example, if B is the middle term of A and c, by means of c to show that A may be predicated of is : for thus we make inductions.-But o must be considered as composed of all things individually : for induction is made through all. Analyt. Pr.; ii. 23.) (36.) In a manner induction is opposed to syllogism ; for the one (syllogism) by means of the middle term proves the first term to be predicated of the third, but the other (induction), by means of the third term, proves the first to be predicated of the middle term. Naturally then the syllogism through the middle term is prior and more familiar ; but to us the syllogism through induction is the clearer. Analyt. Pr. ' ii. 23.) (37.) Probable (EIKA) and Sign (croize7ov) are not the same, but Probable is a proposition conformable to opinion : for what for the most part men know to be produced in a particular way or not produced, or to be or not to lso, this is probable; for example, that men hate the envious, or like those who love. And Sign must he con sidered to be a proposition demonstrative either necessary or conformable to opinion : for if when anything is, the thing is, or when anything has happened, the thing happens before or after, this is a sign of the thing having happened or being.