Analyt. Pr.,' i. 23.) The demonstration which bests to an impossibility is thus :-If it were required to show that A does not belong (bncfpxst) to B, it must be assumed that it does, and that s belongs to c, so that it follows that A belongs to C. But let this (that A belongs to c) be known and agreed to be impossible. Then it is not possible .for A to belong to n. If then it is granted that B belongs to c, it is impossible for A to belong to n. And since the affirmative (scaTrryopuci) demonstrative is better than the negative, it is manifest that it is also better than the demon strative which leads to impossibility. Analyt. Post.,' i. 26.) (45.) The object of science and science differ from the object of opinion and opinion, inasmuch as science is universal and is of neces sity, and the necessary can not be otherwise, but opinion is unsettled. (‘ Analyt. Post.,' i. 33.) (46.) Induction is not possible when there is no sensuous perception ; for sensuous perception belongs to the particular. Nor yet through sense nor through perception is it possible to attain science. For though sensuous perception refers to a thing as being of a certain quality, and not to any definite thing, nevertheless it is necessary to have some one definite thing as the sensuous object, and the where and the when. But what is universal and in all things it is impossible to have sensuous perception of, for it is neither any particular thing nor now ; for, if it were, it would not be universal ; for we affirm that the always and the everywhere arc universal. Wherefore, also, if we were in the moon and saw the earth intercepting (the light of the sun), we should not know the cause of the eclipse ; for we should perceive that it is eclipsed now, but we should not know why at all, for there would be no sensuous perception of the universal. (‘ Analyt. Post.; i. 18, 3].) (47.) And I call universal whatever belongs to all both of itself and in itself. It is manifest, then, that whatever is universal of necessity belongs to the things. And the " of itself " and " in itself " are the same ; for example, of itself a point belongs to a line inasmuch as it is a line ; and to a triangle, inasmuch as it is a triangle, there belong two right angles ; for of itself the triangle (as to angles) is equal to two right angles. And the universal then is, when it can be demonstrated of any individual (of the class) and of no class prior to that. Analyt. Post,' i. 4.) (48.) To what thing anything of itself belongs, that very thing is its own cause (af-riov) ; and the universal is first, therefore the universal is the cause. Analyt. Post.,' i. 24.) (49.) Universally, of all things it is impossible for there to be demon stration ; for it would proceed indefinitely, so that thus there would be no demonstration at all. (' Metaph.; iv. 4.) And it is not possible for the thought to go through the infinite. (' Analyt. i. 22.) (50.) And those things aro true and first which not through other things, but through themselves receive assent ; for it is not necessary in scientific first principles for the " wherefore " to be inquired after, but each of the principles must itself of itself receive assent. (' Top.; 1.) And in two ways it is necessary first to know : for as to some things it is necessary first to admit that they are ; but as to others it is necessary to understand what the thing spoken of is; and as to others again both; for example, in the proposition that either to affirm or deny everything is true, we inuat assume the "is"; and in the triangle, that it signifies this particular thing ; and in the monad both, both what it means and that it Ls. (' Analyt. Post.; i. 1.) (51.) But we assert that all science is not demonstrative, but that that of the immediate (fiseera) is incapable of demonstration. And that this is a matter of necessity, is clear ; for if it is necessary to under stand the prior and those things from which the demonstration comes, and the immediate at any time enter into the demonstration, it is a matter of necessity that the immediate are not capable of demonstration. And this then we so affirm, and that there is not only science, but also some first principle (Itpx4) of science by which we know the terms (Epos). It is necessary not only to know first the first things, either all or some, but also to know them more : for always that through which each thing is, is more (in a higher degree); for example, that through which we love, is more love. So that if we know by the first things and believe, those things also we know and believe more, since by them we know also the things which come after. (' Analyt. Post.; i. 3. 2.) (52.) And an immediate proposition (weeSeasse tiatcros) is a beginning (lipx-h) of demonstration, and an immediate proposition is that to 'which there is no prior proposition. (' Analyt. Post.,' i. 2.) (53.) And of an immediate syllogistic beginning I call that the Thesis which need not be demonstrated, and which it is not necessary that ho who is going to learn anything should possess ; but what he who is going to learn anything must necessarily possess, is an axiom (41cona). (' Analyt. Post,' i. 2.)
(54.) The first things will be definitions (Spersoi) incapable of demonstration. For definition is of what the thing is and of essence ; but all demonstrations appear to go by hypothesis and to assume what a thing is; for example, mathematical demonstrations take for granted what a unit is and what odd is, and other kinds of demon stration in like manner.
The definition is a certain notification (ercepiesds) of essence. (` Analyt. Post.; ii. 3.) (55.) He who defines shows either what a thing is or what the name means. (` Analyt. Poet,' ii. 7.) All who in any way by a name give an account of a thing, mani festly do not give the definition of the thing, since every definition is speech (shot). (' i. 3.) What a triangle means, the geometer assumes ; but that it is, ho proves. (` Analyt. Post.,' ii. 7.) (56.) And it is necessary to investigate, when considering things which are alike and do not differ, in the first place what they all have in common, then again with respect to other things what things they have which are of the same genus as the former, and are the same as oue another in species, but different from the first narnecL And when in these things it has been found what they all have in common, and in the other things in like manner, we must consider again if there is anything in common in these things which have been taken, until you come to one notion (Sesser); for this will be a definition of the thing. But if a man does not come to one notion, but to two or more, it is manifest that what is sought cannot he ono, but more than one. For example, if we should inquire what magnanimity is, wo must consider in the case of some magnanimous persons whom we know, what one thing they all have by which they are such. For example, if Alcibiades is magnanimous, or Achilles, and Ajax, what one thing they have all in common I Non-endurance of insult ; for the first wade war, and the second was enraged, and the third killed himself.
Again in the case of others, such as Lysander or Socrates; if indiffer ence in prosperity and adversity are the things that they have in common, these two things I take and consider what same things aro contained in the absence of all feeling (araOs(a) as to fortune, and non endurance of insult. If they have nothing in common, there must be two species (ea le) of magnanimity. (' Analyt. Post.; ii. 13.) (57.) Of the things indeed which are in the definition, each will extend further, but all will not extend further. For of necessity there must be this essence (es(e) of the thing: for example, there is number in every Three (rpicii), odd (espeer4v), and the prime in both ways, both so as not to be measured by any number and not to be composed of numbers. This then is Three, number odd, and prime, and prime in this manner : for of each of these things some are in all odd numbers also, but the last is in Two also, but all are in none. (' Analyt. Poet.; 13.) (58.) And it is necessary, when a person is labouring at any whole thing, to divide the genus (76rol) into things indivisible in species, the first; fur example, to divide number into Three and Two. (` Aualyt. Poet,' ii. 13.) All genus is divided by differences which aro opposed to one another in division, as a living animal by the difference of quadruped and bird and fish. (' vi. 6.) That everything should fall under the division, if they be things opposed in which there is no middle, is not an assumption, for it cis necessary that everything should be in one of them, if there shall be a difference (8tacbood) in it (the genus). Analyt. Post,' ii. 13.) It is requisite, moreover, to divide by privation ((Trim:To), and those who cut into two parts divide by privation. And there is no dif ference in privation, so far as it is privation, for it is impossible that there should be species of a thing which does not exist; for example, of animals without feet or animals without wings, as there is in the case of winged animals and quadrupeds. (' Do Para. Animal.; i. 3.) (59.) Definition (Opforgas.) consists of germs and differences (Ificerpepae). (' Top.; i. 8.) It is requisite that ho who defines well define through genus and differences, and these belong to those things which are plainly clearer than and prior to the species (Mos).
And there are three ways in which the definition is not from prior things. Tho first is, if through what is opposed that which is opposed is defined; for example, if through evil good is defined; for the opposed exist by nature. But to some the knowledge of each of them appears to be also the same, so that neither is one better known than the other. But it should not escape notice that some things perhaps it is not possible to define otherwise ; for example, the double without the half, and all those things which of themselves are said iu relation to any thing (rp4s el) : for in all such things to be is the same thing as to be related to something in some manner, so that it is impossible without the one to know the other; wherefore it is necessary in the notion (Ad-yor) of the one that the other also be included.