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.
Chapter 12 Chapter 12 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.
Chapter 13 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.
Chapter 14 Chapter 14 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.
Chapter 15 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.
Chapter 16 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.
Chapter 17 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.
Chapter 18 Chapter 18 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.
Chapter 19 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.