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, for 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 ...