Organon (Owen)/The Posterior Analytics/Book 2
Chap. 1. That the subjects of Scientific Investigation are four.
- 1.1. Subjects of investigation: the that; the why; the if; and the what. A thing is το ότι τὸ, διοτι, εἰ ἔστιν, τί ἐστιν. Instances.
Chap. 2. That all Investigation has reference to the Discovery of the Middle Term.
- 2.1. The former four investigations may be reduced to two, concerning the middle term, if there be one, and what it is.
- 2.2. The middle is that which expresses the cause why the major is predicated of the minor.
- 2.3. We do not investigate the middle, if the thing itself, and its cause, fall within the cognizance of our senses.
Chap. 3. Upon the Difference between Demonstration and Definition.
- 3.1. We cannot know by definition every subject capable of demonstration.
- 3.2. Nor by demonstration all those which are capable of definition.
- 3.3. In fact, nothing capable of definition admits demonstration.
- 3.4. One part of a definition is not predicated of another.
- 3.5. Recapitulation.
Chap. 4. That the Definition of a thing cannot be demonstrated.
- 4.1. In order to collect by a syllogism what a thing is, the middle term ought to express the definition.
- 4.2. A twofold consideration.
- 4.3. He who proves the definition by a syllogism begs the question.
Chap. 5. That there is no Conclusion by Divisions proved.
- 5.1. That the method by division is inconclusive.
- 5.2. The same reasoning good in long or short definition.
- 5.3. A rule applied for divisional definition.
- 5.4. By constant division, when a perfect definition is arrived at, we are said to arrive at the individual.
Chap. 6. Case of one Proposition defining the Definition itself.
- 6.1. It is proved that there is no demonstration of the definition, neither if one proposition defines the definition itself.
- 6.2. Nor by any other hypothetical syllogism.
Chap. 7. That what a thung us can neither be known by Demonstration nor by Definition.
- 7.1. An inquiry into the method of concluding definition. Objections.
- 7.3. "Esse" is not the substance to any thing.
- 7.4. Error of present modes.
- 7.6. Recapitulation. It is proved that we can know "Quid res sit" neither by definition nor by demonstration.
Chap. 8. Of the logical Syllogism of what a thing is.
- 8.1. Questions propounded for consideration.
- 8.2. The logical syllogism "de eo, quid sit." The "why" and the "that" sometimes simultaneously known. The "if" sometimes known. κατὰ συμβεβηκὸς.
- 8.3. Of what a thing is, there is neither a syllogism nor demonstration, but it is manifested by both. Cf. ch. 3.
Chap. 9. Of certain Natures or Principles incapable of Demonstration.
- 9.1. A two-fold division of things—the method used in each.
Chap. 10. Upon Definition and its kinds.
- 10.1. Definition either explains the name of a thing;
- 10.2. Or shows its cause. A distinction drawn.
- 10.3. Brief summary—three forms of definition.
Chap. 11. Of Causes and their Demonstration.
- 11.1. Causes of things are four which are all expressed by the middle term.
- 11.2. The same thing may sometimes possess two causes.
- 11.3. Necessity is two-fold; instances. Cf. Rhet. i. 11.
Chap. 12. Upon the causes of the Present, Past, and Future.
- 12.1. Identity of cause.
- 12.2. Causes and effects properly simultaneous—an inquiry into causes of things not simultaneous.
- 12.3. The posterior not collected from the prior.
- 12.4. Medium must be simultaneous with those of which it is the medium.
- 12.5. In the cases of past and futures, some principle or first must be taken.
- 12.6. Things generated in a circle must have a similar demonstration.
- 12.7. Of things which are not universally, but usually, the principles should be non-necessary, but for the most part true.
Chap. 13. Upon the Method of investigating Definition.
- 13.1. Division of things quoad extension.
- 13.2. For the attainment of definition those to be taken, each of which is of wider extension than, but all together equal to, the thing to be defined.
- 13.3. Method of dividing the genus.
- 13.4. Differential division useful in the investigation of definition.
- 13.5. It is not requisite that he who defines should know all other subjects from which he distinguishes the thing defined.
- 13.6. A division into opposite members, as of animal into rational and irrational.
- 13.7. Three things to be attended to, in divisional definition—how to effect these.
- 13.8. The summum genus assumed in the definition.
- 13.9. Method to be applied in the case of several species with something common.
- 13.10. The especially universal most difficult to be defined.
Chap. 14. Rules for Problems.
- 14.1. Need of division for rightly appropriating problems to each science.
- 14.2. Also of investigating that which is inherent in the singulars as something common.
- 14.3. Selection κατὰ τὸ ἀνάλογον.
Chap. 15. Of Identical Problems.
- 15.1. Problems are identical which have either the same middle term, or of which the one is subjected to the other.
Chap. 16. Of Causes and Effects.
- 16.1. Solution of a difficulty—the middle term should always express the cause of the inference.
- 16.2. There is only one cause of one and the same thing, from which it is inferred.
Chap. 17. Extension of the same subject.
- 17.1. If the same thing is predicated of many, except there is an accidental demonstration, it must be shown from the same cause. If the conclusion is equivocal, the middle term will be so. Cf. An. Post. i. 13.
- 17.2. The major term ought to equal the minor in extent, although it ought to exceed the individuals comprehended.
- 17.3. If the same is predicated of things differing in species, it can be demonstrated by diverse middle terms.
Chap. 18. Observation upon Cause to Singulars.
- 18.1. The middle term ought to be the nearest to the singular to which it is cause.
Chap. 19. Upon the Method and Habit necessary to the ascertainment of Principles.
- 19.1. Of the necessity and method of obtaining principles of science—certain questions relative to habits solved.
- 19.2. Animals possess sensible perception.
- 19.3. In what way we arrive at certain art or science from singulars subjected to the senses.
- 19.4. Intellect alone conversant with, and itself the principle of science. All science through demonstration knows the objects of science.
The subjects of investigation are equal in number to the things which we scientifically know; but we investigate four things; that a thing is, why it is, if it is, what it is. For when we inquire whether it is this, or that, having reference to a number (as whether the sun is eclipsed or not) we investigate the that, and a sign of this is that when we have found that it is eclipsed we desist from our inquiries, and if we knew from the first that it is eclipsed, we do not inquire whether it is so. But when we know the that, we investigate the why, for instance, when we know that there is an eclipse, and there is an earthquake, we inquire why there is an eclipse, and an earthquake. These things indeed we investigate thus, but some after another manner, for instance, if there is, or is not, a centaur or a God. I say if there is or is not, simply, and not if it is white or not. When however we know that a thing is, we inquire what it is, for instance, what God, or what man is.
The things then which we investigate, and which having discovered we know, are such and so many, but when we inquire the that or if a thing is simply, then we inquire whether there is a medium of it or not, but when knowing, either that it is, or if is, either in part or simply, we again investigate why it is, or what it is, then we inquire what the middle is. But I mean by the that if it is in a part and simply, in a part indeed (as) is the moon eclipsed or increased? for in such things we inquire if a thing is or is not; but simply (as) if there is a moon or not, or if night is or not. In all these inquiries it occurs that we investigate either if there is a middle or what the middle is, for the cause is the middle, and this is investigated in all things. Is there then an eclipse? is there a certain cause or not? after this, when we know that there is, we inquire what this is. For the cause of a thing not being this or that, but simply substance, or not simply, but something of those which subsist per se, or accidentally, is the middle. I mean by what is simply (substance) the subject, as the moon, or the earth, or the sun, or a triangle, but by a certain thing, (as) an eclipse, equality, inequality if it is in the middle or not. For in all these it is evident that what a thing is and why it is are the same; what is an eclipse? a privation of light from the moon through the interposition of the earth. Why is there an eclipse, or why is the moon eclipsed? because its light fails through the interposition of the earth. What is symphony? a ratio of numbers in sharp and flat. Why does the sharp accord with the flat? because the sharp and flat have the ratio of numbers. Do then the sharp and flat accord? is there then a ratio of them in numbers? assuming that there is, what then is the ratio?
That the inquiry is of the middle those things prove whose middle falls within the cognizance of the senses, since we inquire when we have not a sensible perception, as of an eclipse, whether it is or not. But if we were above the moon we should not inquire neither if, nor why, but it would be immediately evident, as from sensible perception we should also obtain knowledge of the universal; for sense (would show us) that the earth is now opposed, for it would be evident that there is now an eclipse, and from this there would arise the universal.
As therefore we say, the knowledge of the what is the same as the knowledge of the why, and this is either simply, and not somewhat of things inherent,it is of things inherent, as that there are two right angles or that it is greater or less.
That all investigations then are an inquiry of the middle is evident, but let us show how what a thing is, is demonstrated, and what is the method of training up a thing to its principles, also what a definition is, and of what subjects doubting first about these. But let the commencement of the future (doubts) be that which is most appropriate to the following discussion, since perhaps a man might doubt whether it is possible to know the same thing, and according to the same by definition and demonstration, or whether it is impossible? For definition seems to be of what a thing is, but every thing (which signifies) what a thing is, is universal and affirmative, but some syllogisms are negative, others not universal; for instance, all those in the second figure are negative, but those in the third not universal. Next, neither is there definition of all affirmatives in the first figure, as that every triangle has angles equal to two right angles; the reason of this is, because to know scientifically that which is demonstrable, is to possess demonstration, so that if there is demonstration in regard to things of this kind, there can evidently not be also definition of them, for a person might know by definition without demonstration, since nothing prevents the possession of it at one and the same time. A sufficient evidence of this is also derived from induction, for we have never known by definition, any of those which are inherent per se nor which are accidents; besides, if definition be a certain indication of substance, it is evident that such things are not substances.
Clearly then, there is not definition of every thing of which there is also demonstration, but what, is there then demonstration of every thing of which there is definition or not? there is one reason and the same also of this. For of one thing, so far as it is one, there is one science, so that if to know that which is demonstrable be to possess demonstration, an impossibility would happen, for he who possesses definition would know scientifically without demonstration. Besides, the principles of demonstration are definitions, of which it has been shown before, there will not be demonstrations, since either principles will be demonstrable, and principles of principles, and this would proceed to infinity, or the first (principles) will be indemonstrable definitions.
Yet if there are not of every thing and the same, may there not be definition and demonstration of a certain thing and the same? or is it impossible? since there is not demonstration of what there is definition. For definition is of what a thing is, and of substance, but all demonstrations appear to suppose and assume what a thing is, as mathematics, what is unity and what an odd number, and the rest in like manner. Moreover every demonstration shows something of somewhat, as that it is, or that it is not, but in definition one thing is not predicated of another, as neither animal of biped, nor this of animal, nor figure of superficies, for superficies is not figure, nor figure superficies. Again, it is one thing to show what a thing is, but another to show that it is, definition then shows what a thing is, but demonstration that this thing, either is or is not of this. Of a different thing indeed there is a different demonstration, unless it should be as a certain part of the whole. I say this because the isosceles has been shown (to have angles equal) to two right, if every triangle has been shown (to have them), for that is a part, but this a whole: these however, that a thing is, and what it is, do not thus subsist in reference to each other, since the one is not a part of the other.
Evidently then there is neither entirely demonstration of what there is definition, nor entirely definition of what there is demonstration; hence in short it is impossible to have both of the same thing, so that it is also evident that definition and demonstration will neither be the same, nor the one contained in the other, otherwise their subjects would subsist similarly.
Let then so far these things be matters of doubt, but as to what a thing is whether is there, or is there not, a syllogism and a demonstration of it, as the present discussion supposed? for a syllogism shows something in respect of somewhat through a medium, but the (definition) what a thing is, is both peculiar and is predicated in respect of what it is. Now it is necessary that these should reciprocate: for if A is the property of C, it is evidently also that of B, and that of C, so that all reciprocate with each other. Nevertheless, if A is present with every B in respect of what it is, and universally B is predicated of every C in respect of what it is, it is also necessary that A should be predicated of C in the question what it is. Still if some one should assume without this reduplication, it will not be necessary that A should be predicated of C in the question what a thing is, though A should be predicated of B in the same question, but not of those of which B is predicated in this question. Now both these will signify what a thing (C) is, wherefore B will also be the definition of C, hence if both signify what a thing is, and what the very nature of it is, there will be the very nature of a thing prior in the middle term. Universally also, if it is possible to show what man is, let C be man, but A what he is, whether biped animal, or any thing else; in order then that a conclusion should be drawn, A must necessarily be predicated of every B, and of this there will be another middle definition, so that this also will be a definition of a man, wherefore a person assumes what he ought to show, for B also is the definition of a man.
We must however consider it in two propositions, and in first and immediate (principles), for what is stated becomes thus especially evident: they therefore who show what the soul is, or what man or any thing else is, by conversion, beg the question, as if a man should assume the soul to be that which is the cause to itself of life, and that this is number moving itself, he must necessarily so assume as a postulate that the soul is number moving itself, as that it is the same thing. For it does not follow if A is consequent to B, and this to C, that A will therefore be the definition of the essence of C, but it will be only possible to say that this is true, nor if A is that which is predicated essentially of every B. For the very nature of animal is predicated of the very nature of man, since it is true that whatever exists as man, exists as animal, (just as every man is animal,) yet not so, as for both to be one thing. If then a person does not assume this, he will not conclude that A is the very nature and substance of C, but if he thus assume it, he will assume prior to the conclusion that B is the definition of the essence of C. Therefore there has been no demonstration, for he has made a "petitio principii."
Nevertheless, neither does the method through divisions infer a conclusion, as we observed in the analysis about figures, since it is never necessary that when these things exist, that should exist, as neither does he demonstrate who forms an induction. For the conclusion ought not to inquire nor to exist from being granted, but it necessarily is, when they exist, although the respondent does not acknowledge it. Is man (for instance) animal or inanimate, if he has assumed him to be an animal, it has not been syllogistically concluded. Again, every animal is either pedestrian or aquatic, he assumes it pedestrian, and that man is that whole animal pedestrian, is not necessary from what is said, but he assumes also this. It signifies nothing however, whether he does this in respect of many things or few, since it is the same thing; to those therefore who thus proceed, and in what is capable of syllogistic conclusion, this use is unsyllogistic. For what prevents the whole of this being true of man, yet without enunciating what a thing is, or the very nature of it? Again, what prevents something being added to, or taken away from, or exceeding the essence?
Negligence then happens about these things, but we may avoid it by assuming all things (as granted) in respect of what a thing is, and the first being made a postulate by arranging the order in division, omitting nothing. This however is requisite for it is necessary that there should be an individual, yet nevertheless there is not a syllogism, but if so it indicates after another manner. And this is not at all absurd, since neither perhaps does he who makes an induction demonstrate, though at the same time he renders something manifest, but he who selects definition from division does not state a syllogism. For as in conclusions without media, if a man state that from such things being granted, this particular thing necessarily exists, it is possible to inquire why, thus also is it definitions by division. What is man? A mortal animal, pedestrian, biped, without wings. Why? according to each addition, for he will state and show by division as he thinks that every one is either mortal or immortal. The whole however of such a sentence is not definition, wherefore though it should be demonstrated by division, yet the definition does not become a syllogism.
Is it however possible to demonstrate what a thing is according to substance, but from hypothesis assuming that the very nature of a thing in the question what it is, is something of its peculiar principles, and that these alone indicate its substance, and that the whole is its peculiarity? for this is its essence. Or again, has a person assumed the very nature of a thing in this also? for we must necessarily demonstrate through a middle term. Moreover, as in a syllogism, we do not assume what is to have been syllogisticaliy concluded, (for the proposition is either a whole or a part, from which the syllogism consists,) thus neither ought the very nature of a thing to be in a syllogism, but this should be separate from the things which are laid down, and in reply to him who questions whether this has been syllogistically concluded or not, we must answer that it is, for this was the syllogism. And to him who asserts that the very nature of the thing was not concluded, we must reply that it was, for the very nature of the thing was laid down by us, so that it is necessary that without the definition of syllogism, or of the definition itself, something should be syllogistically inferred.
Also, if a person should demonstrate from hypothesis, for instance, if to be divisible is the essence of evil; but of a contrary, the essence is contrary of as many things as possess a contrary; but good is contrary to evil, and the indivisible to the divisible, then the essence of good is to be indivisible. For here he proves assuming the very nature of a thing, and he assumes it in order to demonstrate what is its very nature: let however something be different, since in demonstrations is assumed that this is predicated of that, yet not that very thing, nor that of which there is the same definition, and which reciprocates. To both however there is the same doubt against him who demonstrates by division, and against the syllogism thus formed, why man will be an animal biped pedestrian, but not an animal and pedestrian, for from the things assumed, there is no necessity that there should be one predicate, but just as the same man may be both a musician and a grammarian.
How then will he who defines show the essence of a thing, or what it is? for neither as demonstrating from things which are granted will he render it evident that when they exist, it is necessary that something else should be, for demonstration is this, nor as forming an induction by singulars which are manifest, that every thing thus subsists, from nothing subsisting otherwise; since he does not show what a thing is, but that it is, or is not. What remaining method is there? for he will not indicate by sense nor by the finger.
Moreover how will he show what it is? for it is necessary that he also who knows what man is, or any thing else, should also know that he is, for no one knows with respect to non-being that it is, but what the definition or the name signifies, as when I say "tragelaphos," it is impossible to know what tragelaphos is. Moreover, if he should show what a thing is, and that it is, how will he show this in the same sentence? for both definition and also demonstration manifest one certain thing, but what man is is one thing, and the essence of man is another.
We next say that it is necessary to show by demonstration every thing, that it is, except it be substance, but to be, is not substance to any thing, for being is not the genus. There will then be demonstration that it is, and this the sciences now effect. For what a triangle means, the geometrician assumes, but that it is, he demonstrates. What then will he who defines what it is, prove? that it is a triangle? he then who knows what it is by definition, will not know if it is, but this is impossible.
Evidently then those who define according to the present methods of definition, do not demonstrate that a thing is, for although those lines be equal which are drawn from the middle, yet why is it the thing defined? and why is this a circle? for we might say that there is the same definition of brass. For neither do definitions demonstrate that it is possible for that to be which is asserted, nor that that thing is, of which they say there are definitions, but it is always possible to say why.
If then he who defines shows either what a thing is or what the name signifies, except there is, by no means (an explanation) of what a thing is, definition will be a sentence signifying the same thing as a name, but this is absurd. For in the first place there would be a definition of non-essences and of non-entities, since it is possible even for non-entities to have a signification. Again, all sentences will be definitions, for we might give a name to any sentence, so that we might all discuss in definitions, and the Iliad would be a definition. Besides, no science would demonstrate that this name signifies this thing, neither therefore do definitions manifest this.
From these things therefore it appears that neither definition nor syllogism are the same thing, nor are syllogism and definition of the same thing, moreover that definition neither demonstrates nor shows any thing, and that we can know what a thing is neither by definition nor by demonstration.
Moreover we must consider which of these things is well, and which is not well asserted, also what definition is, and whether there is in a certain way or by no means a demonstration and definition of what a thing is. Now since it is the same thing as we have said to know what a thing is, and to know the cause wherefore it is, and the reason of this is, that there is a certain cause, and this is either the same or another, and if it is another, it is either demonstrable or indemonstrable; if then it is another, and is capable of demonstration, it is necessary that the cause should be a medium, and should be demonstrated in the first figure, for that which is demonstrated is both universal and affirmative. Now one method will be that which has been now investigated, viz. to demonstrate what a thing is through something else, for of those things which are predicated in respect of what a thing is, it is necessary that the medium should be what it is, and a property in respect of properties, wherefore of two essential natures of the same thing, it will demonstrate the one, but not the other.
That this method then is not demonstration, has been shown before, but it is a logical syllogism of what a thing is, still let us show in what method this is possible, discussing it again from the beginning. For as we investigate why a thing is, when we know that it is, but sometimes those become evident at the same time, but it is not possible to know why it is, prior to knowing that it is, it is clear that in like manner the very nature of a thing or what it is, cannot be known, without knowing that it is, since it is impossible to know what a thing is, when ignorant if it is. We sometimes indeed know if it is, accidentally, knowing sometimes something belonging to the thing, as thunder we know, because it is a certain sound of the clouds, and an eclipse, because it is a certain privation of light, and a man, because it is a certain animal, and soul, because it moves itself. As regards then whatever we know accidentally that they are, it is by no means necessary that we should possess any thing by which to know what they are, for neither do we (really) know that they are, and to inquire what a thing is, when we do not know that it is, is to inquire about nothing. In those things however of which we know something, it is easy (to inquire) what they are; hence as we know that a thing is, so also are we disposed to know what it is, now of those things, of whose essential nature we know something, let this be first an example, an eclipse A, the moon C, the opposition of the earth B. To inquire then whether there is an eclipse or not, is to inquire whether B is or not, but this does not at all differ from the inquiry if there is a reason of it, and if this is, we say that that also is. Or we (inquire) of which contradiction there is a reason, whether of possessing, or of not possessing, two right angles, but when we have discovered, we know at the same time, that it is, and why it is, if it is inferred through media; but if it is not so inferred, we know the that, but not the why. Let C be the moon, A an eclipse, not to be able to produce a shadow when the moon is full and nothing is seen interposed between us, B, if then B, that is, not to be able to produce a shadow when there is nothing between us, be present with C, and A, to be eclipsed, present with this, that there is an eclipse, is indeed evident, but why is not yet so, and that there is an eclipse, we indeed know, but what it is we do not know. Yet as it is clear that A is with C, (to inquire) why it is, is to investigate what B is, whether it is the opposition (of the earth), or the turn of the moon, or the extinction of light, but this is the definition of the other extreme, as in those (examples) of A, since an eclipse is the interposition of the earth. What is thunder? the extinction of fire in a cloud: why does it thunder? because fire is extinguished in a cloud. Let C be a cloud, A thunder, B the extinction of fire, hence B is present with C, that is, with the cloud, for fire is extinguished in it, but A, sound, is present with this, and B is the definition of A, the first extreme; if there be again another medium of this it will be from the remaining definitions.
We have shown therefore thus, how what a thing is, is assumed, and becomes known, wherefore there is neither syllogism nor demonstration of what a thing is, still it will become evident through syllogism, and through demonstration; and hence without demonstration it is neither possible to know what a thing is, of which there is another cause, nor is there demonstration of it, as we have already observed in the doubts.
Of some things indeed there is a certain other cause, but of others there is not, so that it is plain that some of them are immediate, and principles, whose existence and what they are, we must suppose, or make manifest after another manner, which indeed the arithmetician does, for he both supposes what unity is, and that it is. Of those however which have a medium, and of whose essence there is another cause, it is possible, as we have said, to produce a manifestation through demonstration, yet not by demonstrating what they are.
Since definition is said to be a sentence (explanatory) of what a thing is, it is evident that one definition will be of what a name signifies, or another nominal sentence, as what a thing signifies, which is so far as it is a triangle, which when we know that it is, we inquire why it is. Still it is difficult thus to assume things, the existence of which we do not know, and the cause of this difficulty has been explained before, because neither do we know whether it is or is not, except accidentally. One sentence is indeed in two ways, the one by conjunction, as the Iliad, but the other from signifying one thing of one, not accidentally.
The above-named then is one definition of a definition, but the other definition is a sentence showing why a thing is, so that the former signifies, but does not demonstrate, but the latter will evidently be, as it were, a demonstration of what a thing is, differing from demonstration in the position (of the terms). For there is a difference between saying, why does it thunder? and what is thunder? for thus a person will answer, because fire is extinguished in the clouds; but what is thunder? the sound of fire extinguished in the clouds; hence there is the same sentence spoken in another manner, and in the one way there is a continued demonstration, but in the other there is a finition. Moreover the definition of thunder is, a sound in the clouds, but this is the conclusion of the demonstration of what it is; now the definition of things immediate is, the indemonstrable thesis of essence.
One definition then is, an indemonstrable sentence (significative) of essence, but another is a syllogism of essence, differing from demonstration in case, and a third is the conclusion of the demonstration of what a thing is. Wherefore, from what we have said, it is evident how there is, and how there is not, a demonstration of what a thing is, also of what things there is, and of what there is not; moreover in how many ways definition is enunciated, and how it demonstrates the essence of a thing, and how it does not; also of what things there is, and of what there is not, definition; yet more, how it subsists with respect to demonstration, and how it may, and how it may not be, of the same thing.
Since we think that we scientifically know, when we are cognizant of the cause, but causes are four, one indeed as to the essence of a thing, another that which from certain things existing, this necessarily exists, a third that which first moves something, and a fourth on account of which a thing (exists); all these are demonstrated through a medium. For the one that this existing it is necessary that that should be, is not from one proposition being assumed, but from two at the least, but this is, when they have one medium; this one therefore being assumed, there is necessarily a conclusion, which is evidently thus: Why is the angle a right one in a semicircle, or from the existence of what, is it right? Let then A be a right angle, B the half of two right angles, and the angle in the semicircle C. Hence B is the cause why A the right angle is inherent in C, i. e. in the angle of a semicircle; for this angle is equal to A, but C is equal to B, for it is the half of two right angles; B then being the half of two right angles, A is inherent in C, and this was for the angle in a semicircle to be a right angle. This however is the same as the explanation of the essence of a thing, because definition signifies this, but the cause of the essence of a thing has been shown to be the middle. Why was there a Median war with the Athenians? What was the cause of waging war with the Athenians? Because the latter with the Eretrians attacked Sardis; this was the first cause of the movement. Let war then be A, first made the attack B, the Athenians C, B then is present with C, i.e. to have first made the attack is present with the Athenians, but A is also with B, for they make war with the aggressors, A then is present with B, i. e. to wage war is present with the aggressors, but this, B, is present with the Athenians, for they were the aggressors. Wherefore the middle is the cause here, and that which first moves; but of those things, whose cause is for the sake of something, as, why does he walk? that he may be well; why is a house built? that furniture may be preserved; the one is for the sake of health, but the other for the sake of preservation. Still there is no difference between why is it necessary to walk after supper, and for the sake of what is it necessary? but let walking after supper be C, the food not to rise B, to be well A. Let then walking after supper be the cause why the food does not rise to the mouth of the stomach, and let this be healthy; for B, that is, for the food not to rise, appears to be present with walking, C, and with this A, salubrious. What then is the cause that A, which is that for the sake of which (the final cause), is present with C? B (is the cause), that is, the food not rising, this however is as it were, the definition of it, for A will be thus explained. Why is B present with C? because to be thus affected is to be well: we must nevertheless change the sentences, and thus the several points will be more clear. The generations here indeed, and in causes respecting motion, subsist vice versâ, for there it is necessary that the middle should be first generated, but here C, which is the last, and that for the sake of which is generated the last.
Possibly indeed the same thing; may be for the sake of something, and from necessity; for instance, why does light pass through a lantern? for necessarily that which consists of smaller particles passes through larger pores, if light is produced by transit, also (it does so) on account of something, that we may not fall. If then it possibly may be, is it also possible to be generated? as if it thunders, fire being extinguished, it is necessary that it should crash and rumble, and, as the Pythagoreans say, for the sake of threatening, that those in Tartarus may be terrified. Now there are many things of this kind, especially in those which are constituted and consist from nature, for nature produces one thing for the sake of something, and another from necessity; but necessity is two-fold, one according to nature and impulse, another with violence, contrary to impulse; thus a stone is borne from necessity both upward and downward, yet not from the same necessity. In things however which are from reason, some never subsist from chance, as a house, or a statue, nor from necessity, but for the sake of something, whilst others are also from fortune, as health and safety. Especially in those which are capable of a various subsistence, as when the generation of them is not from fortune, so that there is a good end, on account of which it takes place, and either by nature or by art: from fortune however nothing is produced for the sake of something.
The cause of things which are, is the same also as that of things which are generated, which have been generated, and which will be, for the middle is the cause, except that being is the cause to be, what is generated, to those which are generated, what has been, to those which have been, and what will be to those that will be. Thus why was there an eclipse? because the earth was interposed, but an eclipse is generated, because an interposition of the earth is generated, but there will be, because the earth will be, and there is, because it is interposed. What is ice? Let it be assumed to be congealed water; let water be C, congealed A, the middle cause B, a perfect defect of heat; B then is present with C, but with this A, viz. to be congealed, but ice is generated, when B is generated, it was so, when the latter was so, and it will be, when the latter will be.
Hence that which is thus a cause, and that of which it is the cause, are generated at one and the same time, when they are generated; are simultaneously when they are; and in like manner, in respect to the having been, and the will be, generated. In the case of things which are not simultaneous, are there in a continued time, as it seems to us, different causes of different things? for instance, is another thing having been generated the cause of this thing having been generated, and another thing which will be, the cause that this will be, and of this being, something which was generated before? the syllogism however is from what was afterwards generated. And the principle of these are those things which have been generated, wherefore the case is the same as to things which are generated. From the prior indeed there is no (syllogism), as that this thing was afterwards generated, because that thing was generated, it is the same also in regard to the future. For whether the time be indefinite or definite, it will not result that because that thing was truly said to have been generated, this which is posterior is truly said to have been generated, since in the interval it will be false to say this, when already another thing has been produced. The same reasoning also happens to what will be, nor because that was produced, will this be, as the middle must be generated at the same time; of things that have been that which has been, of the future the future, of what are produced that which is produced, of things which are that which is, but of what was generated, and of that which will be, the middle cannot possibly be produced at one and the same time. Moreover neither can the interval be indefinite, nor definite, since it will be false to assert it in the interval; but we must consider what is connected with it, so that after the having been generated, to be generated may exist in things. Or is it evident that what is generated is not connected with what was generated? for the past does not cohere with what was generated, since they are terms and individuals. As then neither points are mutually connected, those things which have been produced are not so, for both are indivisible; nor for the same reason does that which is, cohere with that which has been generated, for that which is generated is divisible, but that which has been is indivisible. As a line then is to a point, so is that which is to that which was generated, for infinite things which have been, are inherent in that which is; we must however enunciate these matters more clearly in the universal discussions about motion.
Concerning then the manner in which, when there is a successive generation, the middle cause subsists, let so much be assumed, for in these also it is necessary that the middle and the first should be immediate, thus A was generated because C was so, but C was after, A before. The principle indeed is C, because it is nearer to the now, which is the principle of time, but C was generated if D was, hence from D having been, it is necessary that A should have been. The cause however is C, for from D having been, it is necessary that C should have been generated, but C having been, A must of necessity have been produced before. When however we thus assume the middle, will (the process) at any time stop at the immediate, or on account of the infinity will a medium always intervene? for, as we have stated, what has been generated is not connected with what has been; nevertheless we must commence at least from the immediate and from the first now. Likewise with regard to the "will be," for if it is true to say that D will be, it is necessary that, prior to this, it should be true to say that A will be, the cause however of this is C, for if D will be, prior to it C will be, but if C will be, prior to it A will be. Likewise also in these the division is infinite, for things which will be, are not mutually coherent, but an immediate principle must also be assumed in these. It is thus in the case of works, if a house has been built, stones must necessarily have been cut, and formed; and why this? because the foundation must of necessity have been laid, if the house was built, but if the foundation was laid, stones must necessarily have been prepared before. Again, if there shall be a house, in like manner there will be stones prior to this, still the demonstration is in like manner through a medium, for the foundation will have a prior subsistence.
Notwithstanding, since we see in things which are, that there is a certain generation in a circle, this happens when the middle and the extremes follow each other, for in these there is a reciprocation; this however was shown in the first treatise, viz. that the conclusions are converted; but the case of being in a circle is thus. In works it appears after this manner, when the earth has been moistened, vapour is necessarily produced, from the production of this, there is a cloud, from this last, water, and from the presence of this, the earth is necessarily moistened, this however was the (cause) at first, so that it has come round in a circle, for any one of these existing, another is, and if that is, another, and from this, the first.
There are some things which are generated universally, (for always, and in every thing, they either thus subsist, or are generated,) but others not always, but for the most part; thus not every vigorous man has a beard, but this is generally the case, now or such things it is necessary that the medium also should be for the most part; for if A is universally predicated of B, and this of C universally, it is necessary that A also should be predicated always, and of every C, (for the universal is that which is present with every individual and always,) but it was supposed to be for the most part, wherefore it is necessary that the medium also, B, should be for the most part: hence of those which are for the most part, the principles are immediate, as many as thus subsist for the most part, or are generated.
We have before shown how what a thing is, is attributed to definitions, and in what way there is or is not a demonstration or definition of it, how therefore it is necessary to investigate things which are predicated in respect to what a thing is, let us now discuss.
Of those then, which are always present with each individual, some have a wider extension, yet are not beyond the genus. I mean those have a wider extension, as many as are present with each individual universally, yet also with another thing, thus there is something which is present with every triad, and also with that which is not a triad, as being is present with a triad, but also to that which is not number. Nevertheless the odd is present with every triad, and is of wider extension, for it is with five, but it is not beyond the genus, for the five is number, and nothing out of number is odd. Now such things we must take so far until so many are first assumed, each of which is or wider extension, but all of them together are not of greater extent, for it is necessary that this should be the substance of a thing. For example, number, the odd is present with every triad, the first in both ways, both as not being measured by number and as not being composed of numbers. Now therefore the triad is this, viz. the first odd number, and the first in this way, for each of these is present, the one with all odd numbers, but the last also with the dual, yet all of them (together) with none (but the triad). Since however we have shown above, that those things which are predicated in respect of what a thing is are necessary, but universals are necessary, but what are thus assumed of a triangle, or any other thing, are assumed in respect to what a thing is, thus from necessity the triad will be these things. That this however is its essence appears from this, since it is necessary, unless the very nature of a triad were not this, that this should be a certain genus, either denominated or anonymous. It will be therefore of wider extension than to be with a triad alone, for let the genus be supposed of that kind as to be more widely extended according to power, if then it is present with nothing else than individual triads, this will be the essence of the triad. Let this also be supposed, that an ultimate predication like this of individuals is the essence of each thing, wherefore in like manner, when any thing is thus demonstrated, it will be the essence of that thing.
Nevertheless it is right when any one is conversant with a certain whole, to divide the genus into the individuals which are first in species, for instance, number into triad and dual, then to endeavour thus to assume the definitions of these, as of a straight line, of a circle, and of a right angle; afterwards assuming what the genus is, for instance, whether it is quantity or quality, he should investigate the peculiar passions through common first (principles.) For those which happen to the composites from individuals will be evident from the definitions, because definition and that which is simple are the principles of all things, and accidents are essentially present with simple things alone, but with others according to them. The divisions indeed by differences are useful for our progression in this way, but how indeed they demonstrate we have shown before, but they would thus be useful only for syllogizing what a thing is, and indeed they may appear to do nothing, but to assume every thing immediately, just as if any one assumed from the beginning without division. It makes some difference, however, whether what is predicated be so, prior or posterior, as for instance, whether we call animal, mild biped, or biped, animal mild, for if every thing consists of two, and one certain thing is animal mild, and again from this, and the difference, man or any thing else which is one, consists, we must necessarily make a postulate by division. Besides, thus only is it possible to leave out nothing in the definition, since when the first genus is assumed, if a person takes a certain inferior division, every thing will not fall into this; for instance, not every animal has entire or divided wings, but every animal which is winged, for this is the difference of it, but the first difference of animal is that into which every animal falls. Likewise in regard to each of the rest, both of those genera which are external to animal, and of those which are contained under it, as of bird, is that into which every bird falls, and of fish that into which every fish falls. Thus proceeding we may know that nothing is omitted, but otherwise we must omit something, and not know it. It is not at all necessary that he who defines and divides, should know all things that subsist, though some say it is impossible to know the differences of each thing without knowing each; but it is impossible to know each thing without differences, for that from which this does not differ, is the same with this, but that from which it differs is something else than this. In the first place then this is false, for it is not something else according to every difference, since there are many differences in things which are the same in species, yet not according to substance, nor per se. Next, when any one assumes opposites, and difference, and that every thing falls into this or that, and assumes also that the question is in one part of the two, and knows this, it is of no consequence whether he knows or does not those other things of which the differences are predicated. For it is evident that thus proceeding, if he should arrive at those of which there is no longer a difference, he will obtain the definition of the substance; but that every thing will fall into division, if there should be opposites of which there is no medium, is not a postulate, since every thing must necessarily be in one of them, if indeed it will be the difference of it.
In order to frame definition by divisions, we must attend to three things, viz. to assume the things predicated in respect of what a thing is; to arrange these, which shall be first or second; and that these are all. Now the first of these arises from our being able as syllogistically to collect accident, that it is inherent, so to construct through genus. There will however be a proper arrangement if what is first be assumed, and this will be if that be taken which is consequent to all, but all not consequent to it; for there must be something of this kind. This then being taken, there must now be the same method in the things inferior, since the second will be that which is first of the rest, and the third that which is first of the following, for what is superior being taken away, whatever succeeds will be the first of the others; there is also similar reasoning in the other cases. Still that all these should be, is clear from assuming what is first in the division, that every animal is either this or that, but this is inherent; and again the difference of this whole but that of the last there is no longer any difference, or immediately with the last difference this does not differ in species from the whole: for it is clear that neither more (than is necessary) is added, for every thing has been assumed in reference to what a thing is, nor is any thing deficient, for it would be either genus or difference. Both the first then is genus, and this assumed together with differences, but all the differences are contained, for there is no longer any posterior difference. Otherwise the last would differ in species, this however has been shown not to differ.
Still we must investigate, looking to those which are similar and do not differ, first (considering) what that is which is the same in all these, then again in other things which are in the same genus with them, and which are among themselves the same in species, but different from those. Yet when in these that is assumed which all have the same, and in others similarly, we must consider in the things assumed whether it is the same, until we arrive at one reason, for this will be the definition of the thing. Yet if we do not arrive at one, but at two or more, it is evident that the question will not be one, but many for instance, I mean if we should inquire what magnanimity is, we must consider in the cases of certain magnanimous persons, whom we know what one thing they all possess, so far as they are such. Thus if Alcibiades is magnanimous, or Achilles, or Ajax, what one thing have they all? intolerance of insult, for one of them fought, another sulked, another slew himself. Again, in other instances, as in that of Lysander or Socrates. If then (it is common to these) to behave in the same manner, in prosperity and adversity, taking these two, I consider what indifference with regard to fortune, and what impatience under insult possess in common; if they have nothing there will be two species of magnanimity.
Every definition is nevertheless universal, for the physician does not prescribe what is wholesome for a certain eye, but defines what is fit for every eye, or for the species. The singular however is easier to define than the universal, wherefore we must pass from singulars to universals, for equivocations lie more concealed in universals, than in things without a difference. But as in demonstrations the power of syllogizing must necessarily be inherent, so also perspicuity must be in definitions, and there will be this, if through things which are singularly enunciated, what is in each genus be separately defined; as with the similar, not every similar, but that which is in colours and in figures, and the sharp that which is in voice, and so to proceed to what is common, taking care that equivocation does not occur. But if it is not right to use metaphors in disputation, we must clearly not define by metaphors, nor by those things which are spoken by metaphor, otherwise it will be necessary to use metaphors in disputation.
Now that we may have problems, we must select sections and divisions, and thus select, the common genus of all being supposed, as for example, if animals were the subjects of consideration, (we must first consider,) what kind of things are present with every animal. When these have been taken, we must again see what kind of things are consequent to every first individual of the rest, thus if this is a bird, what things follow every bird, and so always that which is nearest, for we shall evidently now be able to say why things are present, which are consequent to those under what is common, as why they are present with man or horse. Let then animal be A, B things consequent to every animal, C D E certain animals, why then B is present with D is evident, for it is present through A: in a similar manner with the rest, and in others there is always the same reasoning.
Now then we speak according to presented common names, but we must not only consider in these, but also assume if any thing else should be seen to be common, afterwards consider to what things this is consequent, and the quality of the things consequent to this, as those consequent to having horns are the possession of a rough muscular lining to the stomach, and the not having teeth in both jaws. Moreover to what things the possession of horns is consequent, for it will be evident why what has been mentioned is present with them, for it will be so in consequence of their possessing horns.
There is yet another mode of selection by analogy, since it is impossible to assume one and the same thing, which it is necessary to call sepium, spine, and bone, there are also things consequent to these, as if there were one certain nature of this kind.
Some problems are the same from having the same medium, for instance, because all things are an antiperistasis, but of these some are the same in genus, which have differences from belonging to other things, or from subsisting differently, e. g. why is there an echo, or why is there a reflection, and why a rainbow? for all these are the same problem in genus, (for all are reflection,) but they differ in species. Other problems differ from the medium being contained under another medium, as why does the Nile have a greater flow during the fall of the month? because the fall of the month is more winterly: but why is the fall more winterly? because the moon fails, for thus do these subsist towards each other.
Some one may perhaps doubt concerning cause and that of which it is the cause, whether when the effect is inherent, the cause also is inherent, as if the leaves fall from a tree, or there is an eclipse, will there also be the cause of the eclipse, or of the fall of the leaves? As if the cause of this, is the having broad leaves, but of an eclipse the interposition of the earth, for if this be not so, something else will be the cause of these, and if the cause is present, at the same time the effect will be, thus if the earth be interposed, there is an eclipse, or if a tree have broad leaves, it sheds them. But if this be so, they would be simultaneous, and demonstrated through each other, for let the leaves to fall be A, the having broad leaves B, and a vine C, if then A is present with B, (for whatever has broad leaves sheds them,) but B is present with C, for every vine has broad leaves, A is present with C, and every vine sheds its leaves, but the cause is B, the middle. We may also show that the vine has broad leaves, from its shedding them, for if D be what has broad leaves, E to shed the leaf, F a vine, E then is present with F, (for every vine sheds its leaf,) but D with E, (for every thing which sheds its leaf, has broad leaves,) every vine then has broad leaves, the cause is, its shedding them. Nevertheless if they cannot be the cause of each other, (since cause is prior to that of which it is the cause,) the cause of an eclipse indeed is the interposition of the earth, but an eclipse is not the cause of the earth interposing. If then the demonstration by cause (shows) why a thing is, but that which is not through cause, that it is, one knows indeed that the earth is interposed, but why it is, he does not know. Yet that an eclipse is not the cause of the interposition, but this of an eclipse, is plain, since in the definition of an eclipse, the interposition of the earth is inherent, so that evidently that is known through this, but not this through that.
Or may there be many causes of one thing? for if the same thing may be predicated of many primary, let A be present with B a first, and with C another first, and these with D E, A then will be present with D E, but the cause why it is with D will be B, and C the cause why it is with E, hence from the existence of the cause there is necessarily the existence of the thing, but when the thing exists, it is not necessary that every cause should exist, still some cause indeed, yet not every cause. Or if the problem is always universal, is the cause also a certain whole, and that of which it is the cause universal? as to shed the leaf is present definitely with a certain whole, though there should be species of it, and with these universally, i. e. either with plants or with such plants. Hence in these, the medium and that of which it is the cause must be equal, and reciprocate, for instance, why do the trees shed their leaves? if indeed through the concretion of moisture, whether the tree casts its leaf, there must of necessity be concretion, or whether there is concretion not in any thing indiscriminately, but in a tree, the latter must necessarily shed its leaf.
Whether however may there not be possibly the same cause of the same thing in all things, but a different one, or is this impossible? or shall we say it cannot happen, if it is demonstrated per se and not by a sign or accident? for the middle is the definition of the extreme, but if it is not thus, (shall we say that) it is possible? We may however consider that of which and to which it is the cause by accident still they do not appear to be problems, but if not, the medium will subsist similarly, if indeed they are equivocal, the medium will be equivocal, if however as in genus the medium will be similar. For instance, why is there alternate proportion? for there is a different cause in lines, and in numbers, and the same (medium) so far as they are lines, is different, but so far as it has an increase of the same kind, it is the same, the like also occurs in all things. There is indeed a different cause in a different subject, why colour is similar to colour, and figure to figure, for the similar in these is equivocal, for here perhaps it is to have the sides analogous, and the angles equal, but in colours it consists in there being one sense (of their perception) or something else of the kind. Things however analogically the same, will have also the same medium by analogy, and this is so from cause, and that of which, and to which it is the cause following each other; but by assuming each singly, that of which it is the cause is more widely extended, as for the external angles to be equal to four, is or wider extension than triangle or square, but equal in all, for whatever have external angles equal to four right, will also have the medium similarly. The medium however is the definition of the first extreme, wherefore all sciences are produced by definition, thus to shed the leaf, is at the same time consequent to the vine, and exceeds, and to the fig tree, and exceeds, yet does not exceed all (plants), but is equal to them. If then you take the first middle it is the definition of shedding the leaf, for the first will be the middle of one of them, because all are such, next the middle of this is, that sap is congealed, or something else of the sort, but what is it to shed the leaf? it is for the sap to be congealed, at the junction of the seed.
In figures, to those who investigate the consequence of the cause, and of what it is the cause, we may explain the matter thus: let A be present with every B, and B with every D, but more extensively, B then will be universal to D, I call that universal which does not reciprocate, but that the first universal, with which each singular does not reciprocate, but all together reciprocate, and are of similar extension. B then is the cause why A is present with D, wherefore it is necessary that A should be more widely extended than B, for if not, why will this be rather the cause than that? If then A is present with all those of E, all those will be some one thing different from B, for if not, how will it be possible to say that A is present with every thing with which E is, but E not with every thing with which A is? for why will there not be a certain cause as there is why A is present with all D? wherefore will all those of E be one thing? We must consider this, and let there be C, hence there may be many causes of the same of the same thing, but not to the same in species, for instance, the cause why quadrupeds are long-lived, is their not having bile, but why birds live long, their being of a dry complexion, or something else: if however they do not arrive immediately at an individual, and there is not one medium only, but many, the causes also are many.
Which of the media is the cause to singulars, whether that which belongs to the first universal, or that to the singular? Evidently the nearest to the singular to which it is cause. For this is the cause why the first, under the universal, is inherent, C is the cause that B is inherent in D, hence C is the cause why A is inherent in D, but B is the cause why it is in C, yet to this itself is the cause.
Concerning syllogism then and demonstration, what either of them is, and how it is produced, is clear, and at the same time about demonstrative science, for it is the same: but about principles, how they become known, and what is the habit which recognises them, is manifest hence to those who have previously doubted it.
That it is then impossible to have scientific knowledge through demonstration, without a knowledge of first immediate principles, has been elucidated before, still some one may doubt the knowledge of immediate principles, both whether it is the same or not the same, also whether there is a science of each or not, or a science of one, but a different kind (of science) of another, and whether non-inherent habits are ingenerated, or when inherent are latent. If then, indeed, we possess them, it is absurd, for it happens that it (the principle) escapes those who have a more accurate knowledge than demonstration, but if, not having them before, we acquire them, how can we know and learn without pre-existent knowledge? for this is impossible, as we said also in the case of demonstration. It is evident then, that they can neither be possessed, nor ingenerated in the ignorant, and in those who have no habit, wherefore it is necessary to possess a certain power, yet not such an one as shall be more excellent according to accuracy than these. Now this appears inherent in all animals, for they have an innate power, which they call sensible perception, but sense being inherent in some animals, a permanency of the sensible object is engendered, but in others it is not engendered. Those, therefore, wherein the sensible object does not remain, either altogether or about those things which do not remain, such have no knowledge without sensible perception, but others when they perceive, retain one certain thing in the soul. Now since there are many of this kind, a certain difference exists, so that with some, reason is produced from the permanency of such things, but in others it is not. From sense, therefore, as we say, memory is produced, but from repeated remembrance of the same thing, we get experience, for many remembrances in number constitute one experience. From experience, however, or from every universal being at rest in the soul, that one besides the many, which in all of them is one and the same, the principle of art and science arises, if indeed it is conversant with generation, of art, but if with being, of science. Neither, therefore, are definite habits inherent, nor are they produced from other habits more known, but from sensible perception, as when a flight occurs in battle, if one soldier makes a stand, another stands, and then another, until the fight is restored. But the soul has such a state of being, as enables it to suffer this, what, however, we have before said, but not clearly, let us again explain. When one thing without difference abides, there is (then) first, universal in the soul, (for the singular indeed is perceived by sense, but sense is of the universal, as of man, but not of the man Callias,) again, in these it stops, till individuals and universals stop, as such a kind of animal, until animal, and in this again (it stops) after a similar manner. It is manifest then that primary things become necessarily known to us by induction, for thus sensible perception produces the universal. But since, of those habits which are about intellect, by which we ascertain truth, some are always true, but others admit the false, as opinion, and reasoning, but science, and intellect, are always true, and no other kind of knowledge, except intellect, is more accurate than science, but the principles of demonstrations are more known, and all science is connected with reason, there could not be a science of principles: but since nothing can be more true than science except intellect, intellect will belong to principles, and to those who consider from these it is evident also, that as demonstration is not the principle of demonstration, so neither is science the principle of science. If then we have no other true genus (of habit) besides science, intellect will be the principle of science: it will also be the principle (of the knowledge of the principle, but all this subsists similarly with respect to every thing.