Every affirmation and negation will consist either of a noun and a verb or of an indefinite noun and a verb. But without a verb there is neither affirmation nor negation. (` De Interpret.,' c. 2, 10.) (6.) Of things some are universal and some particular. I call that universal (oca86Aou) which can be said of more things (than one) ; and I call that particular (ra' reacerov) which cannot : thus, man belongs to the universal, and Callias to the particular. (` De Interpret.; c. 7.) A Proposition (rphans) then is speech either affirming or denying something about something. And this speech is either universal or particular (66 tape!), or indefinite (cialopereos). I call that universal which belongs either to all or to none; I call that particular which belongs either to some one, or not to some one, or not to all ; and I call that indefinite which either belongs or does not belong, without the universal or particular, as, for instance, of opposite things that there is the same science, or that pleasure is not a good. (' Analyt. Pr.,' i. 1.) It is very evident that the universal is more efficient, because, know ing the first of two propositions, we know in a manner the second also, and have it potentially ; for example, if a man knows that the angles of every triangle are together equal to two right angles, he knows in a way that the angles of an isosceles triangle also are together equal to two right angles potentially (Stnefeet), even if he does not know that the isosceles triangle is a triangle. But he who knows this proposition (the second) by no means knows the universal, either potentially or in reality (ivinef7). And the universal is an object of the intellect; but the particular terminates in the sensuous perception. ('Aualyt. Post,' i. 24.) (7.) Every proposition belongs either to what is, or to what must be, or to what can be. (' Analyt. Pr.' 1. 2.) (8.) Of all things indeed which exist there are some of such a kind that they can bo predicated with truth universally of nothing else, such as Cleon, Callias, and a single thing, and what is an object of sense; but of these things others can be predicated (for each of these persons is both man and animal); and some things are themselves predicated of other things, but of them there is no further predication by other things; and some are both themselves predicated of others, and others of them, for example, " man " is predicated of " Calling,' and "animal" of "man." Accordingly that there are some things which exist which cannot be predicated of anything is manifest. For of sensuous objects nearly every one is such that it can be predicated (Karrryopciaeat) of nothing. (` Anal. Pr.' i. 27.) The genera (71vn) are predicated of the species, but not the converse the species (63n) of the genera. (' Categ.' c. 5.) (9.) It is impossible for the same thing at the same time to belong (eircEpgetv) and not to belong to the same thing and in the same manner. This indeed of all principles is the most certain ; for it is impossible for any one to conceive that the same thing is and is not. Wherefore all who demonstrate, carry back (their demonstration) to this ultimato notion. (` Metaphys.' iv. 3.) Every thing which is true must agree with itself in every way : for with truth all which is true is in harmony, but with falsehood tho truth is soon at variance. ('Eth. Nic.' i. 8.) (10.) And limo it is possible for what belongs to be enunciated as not belonging, and what does not as belonging, and what belongs as belonging, and what does not belong as not belonging, and with respect to other times than the present in like manner, it is possible to deny both all that a man has affirmed, and to affirm what he has denied. So that it is manifest that to every affirmation a negation is opposed, and to every negation an affirmation; and let the contradiction (fteelsoaets) be this, affirmations and negations opposed.
And I call opposition (arructiaBai) the contradiction of the same thing about the same thing, but not 6eauelsicer. (Comp. Categ.; c. 1; De Interpret,' c. 6.) Contradiction is opposition (arrfeens) in which there is no mean in itself. And as parts of contradiction, there is on one side affirming something of something, and on the other side denying something from (ar6) something. (' Analyt. Post.; 1. 2.) In affirmation and negation always, whether it is a thing that exists or does not exist, the one will be false and the other true : for of the two that Socrates is sick and that Socrates is not sick, when Socrates exists, it is manifest that one of them is true and the other false, and if he does not exist in the rave manner : for that he is sick, when he does not exist, is false, and that he is not sick is true.
Accordingly, to those things alone, which are opposed as affirmation and negation, it will be peculiar for one of them always to be true or false. (' Categ.,' c. 10.) (11.) Things included in the same genus which differ most from one another, are defined to be contrary (1rdrna). (‘ Catog.; c. 6.) (12.) Therefore I say that affirmation is opposed to negation in the way of contradiction, when the one signifies that a thing is universal and the other signifies that the same is not universal : as for example, every man is white-not every man is white ; no man is white-a certain man is white. And I say that the universal affirmation and negation are opposed as contraries : as for example, every man is white -uo man is white ; every man is just-no man is just. Therefore it is not possible for these to be true at the same time. (' De Interpret.,' c. 7.) (IS.) And I say that propositions opposed are in common expression (Kara AI/Iv) four-namely, all and none, all and not all, some and none, some and not some ; but in truth three; for some is opposed to not some merely in expression. And of these three propositions the
universal, all and none, are contrary : for example, all knowledge is excellent, no knowledge is excellent ; but the other propositions are opposed (as contradictory). (' Annlyt. Pr.,' ii. 15.) (14.) And since every proposition is either of being or of necessarily being or of the possibility of being, and of these some are affirmative and some negative in every mode, and again of the affir mative and negative propositions some are universal and some particular and some indefinite, of necessity the proposition which is universally negative can be converted (arresspisici) in its terms (tpol) : for example, if no pleasure is a good thing, neither is any good thing pleasure ; but the affirmative proposition must be converted, not indeed universally but particularly ; thus if all pleasure is good, some good also is pleasure. And of particular propositions the affirmative proposition must be converted particularly, for if some pleasure is good, some good also is pleasure : but as to the negative, it is not of necessity, for, if " man " does not belong to (cannot be predicated of) some animal, it does not follow that "animal" cannot be predicated of "some man." Analyt. Pr.,' i. 2.) (15.) The things which are sought are equal in number to the things which we know. And we seek four things-the That, the Why, If it is, What it is. (ab errs, ab Was, El tart, Ti icrriv.) For when we seek whether this or that is, referring it to number, for example, whether the sun is eclipsed or not, we seek the That. And there is proof of this ; for when we have found out That it is eclipsed,we cease inquiring; and if from the beginning we know That it is eclipsed, we do not inquire whether it is. And when we know that it is, we inquire the Why for example, when we know that the sun is eclipsed, and that the earth moves, we inquire Why the sun is eclipsed, or Why the earth moves. These things accordingly we inquire after thus ; but some things we inquire after in another manner, as for example, Whether there is or is not Centaur or God. I simply mean if there is or is not, but not if he is white or not. And when we know that there is, we inquire What it is, for example, What is God or what is man. ('Analyt. Post.; ii. I.) (16.) To know That a thing is and to know Why it is are different; and the knowledge of the Why refers to the first cause. The chiefest of knowledge is to contemplate the Why. (' Analyt. Posts' i. 13, I4.) (17.) And we think that we know each thing simply when we think that we both know the cause by which the thing is, that it is its cause, and that it cannot be otherwise. eAnalyt. Post.,' i. 2.) (I8.) All instruction and all rational learning come from knowledge preceding. And this is manifest to them who contemplate all (sciences); for both those of the sciences which are mathematical by these means exist, and every one of the other arts. (' Analyt. Posts,' 1. I.) (19.) And things are prior and better known in two ways : for it is not the same thing to be prior by nature and prior as regards us, nor yet to be more known by nature and more known by us. And I call those things prior and more known as regards us which are nearer the sense, but I call simply prior and more known those things which are farther from the perception. And the farthest off are the most universal, and the nearest are the particular. (` Analyt. i. 2.) (20.) We get certainty in all things either bysyllogism (crulatryisids) or by induction (iirayors(j). Analyt. Pr.,' ii. 23.) W e learn either by induction or demonstration (Zir68(1/is); and demonstration proceeds from the general, but induction from the particular. (' Analyt. i. I8.) (21.) And syllogism is speech, in which when some things are laid down, something else different from what are laid down results by virtue of their being laid down ; and by virtue of their being laid down I mean that it results through them ; and I moan by resulting through them, that there is no need of any external term for the necessity to be. (' Analyt. Pr.,' 1. I.) (22.) And I call Term that into which the proposition is resolved, as the predicate and the thing of which it is predicated (subject). (' Analyt. Pr.,' L I.) (23.) Whatsoever is affirmed of the predicate (74 xaalryopouaivott), will be affirmed of the subject (soil 6roxstalvov) also. (' Categ., o. 5.) (24.) When three terms are so related to one another that the last is in the whole of the middle, and the middle is either in or not in the whole of the first, of necessity them is a perfect syllogism of the extremes. And I call middle (sicrov) that which is both itself in another and another in it, and which also by position becomes middle : And I call extremes (etxpa) both that which is in another, and in which another is. For if A can be predicated of all n, and n of all c, neces sarily A can be predicated of all c. And I call a figure (sx1ii.ta) of such description the first. (' Analyt. Pr.,' is 4.) (25.) And when the same thing belongs to all of one thing and to none of another, or to all or none of each, such a figure 1 call the second, and that which is predicated of both I call the middle term in it-And the middle term is placed without the extremes, but the first in position-And a syllogism will be possible both when the terms are universal and when they are not universal. When they are universal, there will be a syllogism, when the middle is in all of one, and in none of the other, if the negative be in one of the two terms : but other wise the syllogism cannot be.