Chapter 1 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.
Chapter 2 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, for it is of things inherent, as that there are two right angles or that it is greater or less.
Chapter 3 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.
Chapter 4 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."
Chapter 5 Chapter 5 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.
Chapter 6 Chapter 6 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.
Chapter 7 Chapter 7 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.
Chapter 8 Chapter 8 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.
Chapter 9 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.
Chapter 10 Chapter 10 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.
Chapter 11 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.