Habent autem sic sein operibus.Si facIa est domus, necesse est decisos esse lapides,etfacturn esse hec propter quid est,quoniam necesse est fundamentum factum esse, si quidem et domus facta est, si vero fundamentum est,prius lapides esse factos necesse ist; iterum si erit domus, similiter prius erunl parietes (demonstratur autem per medium similiter), erit enim fundamentum prius.
CAPUT XIII.
in iis quæ circularem.circulo gignuntur demonstratiollem esse
Quoniam autem videmus in iis quæ fiunt,circulo quamdam generationem ease.et contingit boc esse, si quidem consequanturad invicem medium et termini, in his enim converti est, optensum autem es hoc impriæis quod convertuntur conclusiones circulo autem hoc est.In operibus autem videtur sic,depluta terra, necesse est vaporem fieri, boc autem facto, nubem, bac autem facta,aquarn, hac vero facta,necesse est terram deplutam esse. Hoc autem erat ex principio, quare circulo circuivit, cum enim unum borum quodlibet est alterum est,et cum illud alterum et cum hoc prirnurn.Sunt autem quædam quæ fiunt universaliter,semper enim et in omni aut sic se ha.
For in works things stand thus. If a house has been made, it is necessary that the stones have been cut, and that this has come to be; and the reason why is that it is necessary that the foundation has been made, if indeed the house too has been made; but if the foundation is, it is necessary that the stones have been made first; again, if there will be a house, similarly there will first be walls (and this is demonstrated similarly through the middle term), for the foundation will be first.
CHAPTER XIII.
That in things which are generated in a circle there is demonstration
Since we see in things that come to be a certain circular generation, and it is possible for this to be so, if indeed the middle term and the extremes follow one another; for in these there is conversion, and it has been shown above all that the conclusions are converted in a circle, and this is [the circle]. But in works it appears thus: the earth having been moistened, it is necessary that vapor come to be; this having been made, cloud; this having been made, water; this having been made, it is necessary that the earth have been moistened. But this was from the beginning; therefore it has gone around in a circle, for when any one of these is, the other is, and when that other is, the first. But there are certain things that come to be universally, for always and in every case either thus they stand.
bent, aut fiunt; alia vero quidem semper non, sed sicut frequenter 5unt,ut non omnis homo masculus habet barbam,sed est sicut frequenter.Talium igitur necesse est et medium sicutfrequenteresse.Si enim a de prædicatur universaliter,et hoc de universaliter necesse est, et a de sernper,et de omn prædicari,hoc enim est universaliter,et de omni,et semper,sed suppositum est sicut frequenter esse;necesse est ergo medium sicut frequenter esse quod est in quo b. Erunt ergo et eorum principia frequenter sine medio, quæcunque ut plurimum sic sunt, aut fiunt.
CAPUT XIV.
Quo pacto definilio vesliganda sit..
Quomodo quidem sit quod quid est in terminos assignandum,et qualiter demonstratio,aut definitio sit ipsius, aut non, dictum est prius.Quomodo autem oportet venari in eo quod quid est prædicantia, nunc dicemus.Eorumigiturquæinsuntsemper unicuique, quaedam sc: extendunt in plus, non tamen extra genus.
...or come to be; but others not always, yet as it happens for the most part, as not every man has a beard, but it is so for the most part. Of such things, therefore, it is necessary that the middle term also be as it happens for the most part. For if A is predicated universally of B, and this universally of C, it is necessary that A be predicated always and of every one; for this is what is universal, and of every one, and always. But it has been supposed that it is as it happens for the most part; it is necessary, therefore, that the middle term, which is that in which B is, be as it happens for the most part. Therefore the principles of these things will also be for the most part without a middle term, whatever things are or come to be thus for the most part.
CHAPTER XIV.
How a definition is to be sought out.
In what way that which a thing is should be assigned in terms, and how demonstration or definition of it exists or does not, has been said earlier. But in what way one ought to hunt for the predicates in that which a thing is, we shall now say. Of those things, then, which are always present in each thing, some extend more widely, yet not outside the genus.
Dico autem in plus esse quæcunque insuntquidem unicuique universaIiter,at non vero et alii, ut est aliquid quod omni trinitati inest,sed et non trinitati;sicut quod est, inest trinitati,sed et non numero, sed impar inest omni trinitati, et in plus est, et namque ipsi quinario inest,sed non extra genus, quinarius quidem numerus est, nullum autem extra numerum, impar est.Hujusmodi igitur accipiendasunt usque ad hoc, quousque tot accipiantur primum quorum unumquodque in plus sit,omniu autem non in plus,banc enim necesse est subslantiam rei esse. Ut trinitati inest omni, numerus imparprimus utrobique,et sicut quod est non mensurari numero,et sicut non componi ex numeris.Hoc itaque jam trinitas eat, numerus impar primus,et sic prirnus.Horum enim unumquodque illa quidem imparibus omnibus insunt,ultimum autem et duaIitati,omnia autem nulli.Quoniam autem osten sum a nobis in superioribus, quod necessaria quidem sunt in eo quod quid est prædicantia,universalia autem necessaria sunt, trinitati autem,et cuilibet alii sic accipiuntur in eo quod quid est accepta, sic ex necessitate quidem erit trinitas haec.
I say that "in more" are whatever things belong to each thing universally, but not truly also to others, as there is something that belongs to every trinity, but also to what is not a trinity; such as that which is, belongs to trinity, but also to what is not number; but odd belongs to every trinity, and is in more, for it also belongs to the five itself, but not outside the genus—the five is indeed a number, and nothing outside number is odd. Things of this sort, therefore, are to be taken up to this point, until as many are taken first of which each one is in more, but all together are not in more; for this must be the substance of the thing. As to trinity belongs every number that is odd and primary in both respects, and as that which is not measured by number, and as not composed of numbers. This, then, is already trinity: a number odd, primary, and in this way primary. For each of these belongs to all odd numbers, but the last also to duality, but all together to nothing. Since, however, it has been shown by us in the earlier passages that the things predicated in the what-it-is are necessary, and universals are necessary, but for trinity and for anything else such things are taken as are accepted in the what-it-is, thus from necessity trinity will be this.
Quod autem substantia sit, ex his manifestum est, necesse est enim nisi hoc sit trinitatis esse, ut genus aliquod esse;boc autem nominatum est,aut non nominatum erit igitur in plus quam trinitati inexistens.Concessum enim hujusmodi sit esse genus, ut quod insit quidem secundum potentiamin plus,si igitur nulli inest alii quam atomis trinitatibus,hac utique erit trinitatis esse;supponaturenim hoc substantia unius cujusque esse, quae in atomis ultimum praedicatum, quare similiter et alii cuilibet,sic demonstratorum quidem, illi esse erit. Congruum autem est cum totum aliquod negotietur aliquis departiri genus in atoma specie prima,ut numerum in trinitatem, et dualitatem, postea sic illorum definitiones accipere tentare, ut rectae lineæ, et circuli, et recti anguli. Post hæc autem accipientemquod genus sit, ututrum quantitatum,autqualitatum,proprias passiones speculari per communia prima, compositis enim exatomis convenientia,ex definitionibus erunt rnanifesta,propterea quod principium est omnium definitio,et quod simplex est, et simplicibus per se inesse convenientia soIis,aliis autem secundum ilia.
That it is a substance is clear from these considerations; for unless this were so, it would be necessary either that being a trinity be some genus, or that this be named, or else it will be unnamed and thus present in more things than the trinity. For let it be granted that such a thing be a genus, so that it is present indeed in potentiality in more things. If, therefore, it is present in no other things than the atomic trinities, this will surely be the being of the trinity; for let this be supposed to be the substance of each thing, which is the last predicate in atoms. Wherefore similarly also for any other thing, of things demonstrated in this way, that will be its being. It is fitting, moreover, when someone treats of some whole, to divide the genus into first atomic species, as number into trinity and duality, and afterwards thus to attempt to receive their definitions, as of the straight line, the circle, and the right angle. After this, however, one who has grasped what the genus is—whether of quantities or of qualities—should contemplate the proper affections through the common first principles; for the things fitting things composed of atoms will be manifest from the definitions, because definition is the principle of all things, and what is simple, and things fitting simples per se belong to simples alone, but to others according to those.
Sed divisiones quæ sunt secundum differentias,utiles sunt ad hoc adeundum, ut tamen monstrant, dictum est prius.Utiles autem erunt sic utique solum ad colligendum quod quid est,et videbitur utique nibil monstrare, sed mox decipere omnia,tanquam si ex princi pio acceperit aliquis sine divisione. Differt autem aliquid primum et posterius prædicamentorum prædicari, ut. est dicere animal mansuetum bipes, vel bipes animal mansuetum; si enim omne ex duobus est,et unum quid sit animal mansuetum,iterurn ex hoc et diiferentiahomo aut quodlibet unum sit, necesse est dividentem petere.AmpIius, nihil relinquendum in eo quod quid est,sic solummodo contingit,cum enim primum accipiatur genus,si quidemalicujus inferiorum aliquam divisionum accipiat,non incidet omne in hoc,ut non omne animal, aut totum pennatum est,aut divisum pennis, sed pennatum,animal omne.Hujusenirn differentia haec est. Prima autem differentia est animalis, in quam omne animal incidit. Similiter autem et in unoquoque aliorum, et in iis quae extra genera, et quae sub ipsis sunt, utinave,in quaest omnis avis, et in pisce, in quo omnis est piscis. Sic igitur vadenti promptum estscirequoniam nihil relictum est, aliter autem relinquere necesse est, et non scire.
But divisions that are made according to differences are useful for this approach, as has been said before, provided that they show it. They will, however, be useful in this way only for collecting what a thing is, and it will seem to show nothing but rather to deceive everything at once, as if someone had taken a starting point without division. But it makes a difference whether the first or the later of the predicaments is predicated, as for example to say "tame two-footed animal" or "two-footed tame animal"; for if everything is composed of two, and "tame animal" is one thing, and again from this and a difference "man" or some single thing, then one who divides must necessarily beg the question. Moreover, nothing must be left out in what a thing is, and this is possible only in this way: for when the genus is first taken, if one takes any one of the lower divisions, not everything will fall under it, so that not every animal is either wholly feathered or divided by feathers, but every animal is feathered. For this is the difference of it. But the first difference of animal is that into which every animal falls. Similarly also in each of the others, both in those outside the genera and in those under them, as in the case of bird, in which every bird is, and in fish, in which every fish is. So for one proceeding in this way it is easy to know that nothing has been left out; otherwise one must leave something out and not know.
Nibil autem oportet definientem et dividentem omnia scire quæ 5unt,et tamen impopsibiie dicunt esse quidam,differentias cognoscere,quæ sunt ad unumquodque non cognoscentem un umquodque,sine autem differentiis non esseunumquodqusscire,a quo enim non differt,idem esse huic,a quo autem differt, alterum ab hoc. Primum quidem hoc falsum est, non enim secundum omnem differentiam alterum est; multæ enim sunt differentiæ in eisdem specie, sed nonn secundum substantiarn,neque per se.Postea cum accipiantur oppositaetdifferentia,etquod omne incidit hinc aut inde, et accipiat in altero quod quaeritur esse, et hoc cognoscat, nihil differt scire aut non scire de quibuscunque prædicantur aliis differentiæ. Manifestum enim est quod si sic vadens veniat in hæc quorum non est amplius differentia,habebit rationem substantiæ,omne autem incidere in divisionem, sisint opposita quibus aihil interest, non est petitio; necesse est enim omne in altero ipsorum esse, si quidem illius differentia est.Ad probandum autemterminum per divisiones, tria oportet conjecturare, ut accipiantur praedicata in eo quod quid est, et haec ordinate quid primum est, aut secundum,et quoniam haec omnia sint.Est autem unum horum et primum per id quod possumus sicut ad accidens syllogizare, quoniam est et per genus probare.
But the one who defines and divides ought not to know all things that exist, and yet some say it is impossible to know the differences that pertain to each thing without knowing each thing, and that without differences it is not possible to know each thing; for that from which a thing does not differ is the same as it, but that from which it differs is other than it. First, indeed, this is false, for it is not according to every difference that a thing is other; for there are many differences in things of the same species, but not according to substance, nor per se. Next, when opposites and differences are assumed, and that everything falls under one or the other, and one assumes in the one alternative that which is sought to be, and knows this, it makes no difference whether one knows or does not know the other things of which the differences are predicated. For it is evident that if one proceeding in this way arrives at those things of which there is no further difference, he will have the account of the substance; but that everything falls under the division, if the things between which there is no difference are opposites, is not a begging of the question; for it is necessary that everything be in one of them, if indeed it is a difference of that thing. But for proving a term through divisions, three things must be conjectured: that the predicates in the what-it-is be assumed, and these in order—which is first, or second—and that all these exist. And one of these, and the first, is through what we can syllogize as to an accident, that it is, and prove through the genus.
Ordinare autem sicut oportet, erit, si primum accipiat, hoc autem erit si accipiatur quod omnibus sequitur,ilIi autem non omnia, necesse est enim aliquod esse hujusmodi, accepto autem hoc,jamidem inferioribus modus,secundum enim,aliorum primum erit, et tertium continuorum remoto enim quod est sursum, continuum aliorum primum erit,simiIiterautem et in aliis.Quod autem omnia bæc sint,manifestum ex hoc quod recipimus, primum quidem secundum divisionem, quoniam omne aut hoc,aut illud est,esl au tem hoc, et iterum hujus totius differentiam,extremi autem non amplius esse differentiam,vel etiam statim cum ultimadiSerentia a toto non differre specie. Hoc manifestum enim est, quoniam neque plus hoc opponitur.
But to arrange them as is fitting will be possible if one takes the first, and this will be if that which follows all is taken; but those do not [follow] all, for it is necessary that there be some such thing. Once this is taken, there is already a limit for the lower ones; for the second will be the first of the others, and the third of those that follow in order. For when that which is above is removed, the first of the others will be continuous, and similarly also in other cases. But that all these are so is manifest from what we have received: first, indeed, with respect to division, since everything is either this or that, and this is so; and again, the difference of this whole; but of the last there is no longer a difference, or even immediately, since the last difference does not differ in species from the whole. For this is manifest, since not even more is this opposed.
Omnia enim in eoquod'quid estaccipiunturhornm,neque deficit nihil,aut enim genus,aut differentia utique erit, genus quidem igitur est primum, et cum differentiis hoc acceptum est, differentiæ autem omnes habentur,non enim amplius est posterior.Specie enim utique differret,et uItimum,hocautem dictum est non difl'erre.Quærere autem oportet mtendentem in similia,et indifl'erentia,primum quid omnia idem habeant, postea iterum in altera, quas in eodem quidem genere sunt cum illis, sunt autem ipsis quidem idem specie,ab illis autem altera,cum autem in his accipiatur quid omnino idem, et in aliis simililer,in acceptis iterum intendendum est si idem sit, quousque in unam conveniant rationem. Haec enim erit definitio.Si vero non vadit in unam, sed in duas, aut plures, manifestum est quod utique non est unum aliquod quod prædicatur, sed plura, Ut dico,si quid est magnanimitas quærimus, intendendum est in quosdam rnagnanimos,quosscimus quid habeant unum omnes inquantum sunt huj usmodL Ut si Alcibiades magnanimus,aut Achilles, et Ajax, quid unum omnes habent?
For all things are taken in the what-it-is of these, and nothing is lacking: for it will be either genus or difference. The genus, then, is first, and with the differences this is taken; and all the differences are had, for there is no further posterior one. For it would differ in species, and be last; but this has been said not to differ. But one must inquire, directing attention to things that are similar and undifferentiated: first, what it is that all have the same, then again in another group, those which are in the same genus with those, but are the same in species with them, while others are different from them; and when in these the wholly same thing is taken, and similarly in others, one must again direct attention among the things taken, whether the same thing is present, until they come together into one account. For this will be the definition. But if it does not proceed into one, but into two or more, it is clear that there is not some one thing that is predicated, but several. As I say, if we seek what magnanimity is, one must direct attention to certain magnanimous men, whom we know to have one thing in common insofar as they are of this sort. For example, if Alcibiades is magnanimous, or Achilles, and Ajax, what one thing do all have?
non tolerare injuriati.Hic enim dimicavit,ille insanivit, hic autem interfecitseipsum.Iterum idem est in alteris ut Lysandroj et Socrate,si jam indifferentes esse,et fortunati, etinfortunati; haec duo accipiens intendas quid idem habent, aut impassibilitas quæ est circa fortunas, aut non tolerantia cum injuriantur; si vero nullum sit commune,duæ species erunt utique magnanimitatis. Semperenim estomnis defiaitio universaIis,non enim in quodam oculo dicit sanabile medicus, sed aut in omni, aut in specie determinans.
CAPUT XV.
Species facilius quam genera definiri.
Facile autem est magis singulare definire, quam universale,unde oportet a singularibus in universalia ascendere. Et namque aequivocationes magis latent in universalibus quam in indifferentibus.Sicut autem in demonstrationibus oportetsyllogizari inesse sic et in terminis clarum: hoc autem erit, si per ea quae secundum unumquodque dicuntu!',sit in unoquoque genere definiri separatim, ut simile non omne, sed in coloribus et figuris, et acutum,quod est in voce,et sic in commune erit ire,timentem ne æquivocatio contingat.Si autem nou oportet disputare in methaphoris,manifestum est neque definire rnetaphoris,neque quæcunquedicuntur in metaphoris, disputare enim erit necesse in metaphoris.
For to not tolerate being wronged. For this one fought, that one raged, and this one killed himself. Again the same holds in other cases, as with Lysander and Socrates, if they are now alike in being indifferent and fortunate and unfortunate; taking these two, you should consider what they have in common, either insensibility regarding fortunes, or non-tolerance when wronged; but if there is nothing common, they will surely be two species of magnanimity. For every definition is always universal, for the doctor does not say "curable" of some particular eye, but either of every eye or of a species determining it.
CHAPTER XV.
Species are defined more easily than genera.
It is easy to define the more particular rather than the universal, and hence one must ascend from particulars to universals. For equivocations lie more hidden in universals than in things not differing. But just as in demonstrations one must syllogize that something belongs, so also in terms it must be clear: and this will be the case if, through the things said according to each one, one defines separately in each genus, as not every similar thing, but in colors and figures, and sharp, which is in the voice, and so one must go to the common, fearing lest equivocation occur. But if one must not dispute in metaphors, it is manifest that neither must one define by metaphors, nor whatever things are said in metaphors; for it will be necessary to dispute in metaphors.
CAPUT XVI.
Anatomen el analogiam terminandis problematis momenlum habere.
Ut habeamus proposita,eligere oportet decisiones et divisiones,sic autem eligere secundum subjectum genus commune omnium. Ut si animalia sint quae considerantur, qualia omni animaIi insunt.Acceptis autem his, reliquorum primo qualia omni sequantur, ut si hoc est avis,qualia omni sequantur avi et sic sem-. per illiproxima.Manifestum enim est quoniam habebimusjam dicere propter quid insunt sequentia iis quæ sunt sub communi,ut propter quid homini aut equo insunt.Sit autem animal in quo a, autem sequentia omni animali,in quibus autem sunt e e,sicut quaedam ani malia, manifesturn igitur est propter quod est in d, propter a enim, similiter autem et ill aliis, et semper in aliis eadem est ratio. Nunc quidem secundum ea quae assignantur communia nomina, dicimus. Oportet autem non solum in his considerare,sed et si aliud aliquidvidetur commune existens accipientern,posteaquibus boc inhæreat,et qualia huic sequantur,ut cornua hahentibus habere ventres, et non utrobique dentes esse, item habere cornua quibus sequitur, manifestum enim propter quid in illis est quod dicitur, propter id enim quod cornua habent, inest.
CHAPTER XVI.
That anatomy and analogy have weight for settling problems.
In order to have our propositions set out, we must select definitions and divisions, and we must select them in this way: according to the common genus of all the subjects under consideration. For example, if the things considered are animals, [we ask] what belongs to every animal. Having accepted these, [we ask] next what belongs to all the rest, first what follows upon every [member], for example if this is a bird, what follows upon every bird, and so always with the things next in order. For it is clear that we shall then be able to state why the things that follow belong to the things that fall under the common [genus], for example why they belong to man or to horse. Let A be animal, and let the things that follow upon every animal be [the attributes]; and let the things in which they are be C, as certain animals. It is clear, then, why [the attribute] is in D: it is because of A. And similarly in the other cases, and always the same account holds in the others. Now we speak according to the common names that are assigned. But one must consider not only these things, but also, if something else seems to be common, [one must] take it, and afterwards [consider] what things it inheres in, and what things follow upon it—for example, that horned animals have bellies, and that they are not to have teeth on both jaws; and likewise, [consider] what things follow upon having horns. For it is clear why what is stated is present in those things: it is present because of their having horns.
AmpIius,alius modus est se,cundum anaIogum eIigere,unum enim accipere non est idem, quod oportet vocare seipsum, et spinam, et os,sunt autem quæ sequuntur,et his,tanquam natura una hujusmodiexistente.Eadem autem proposita sunt,quæ quidem idem medium habent,llt quoniam omniacontrarii status,horum autem quædam genere eadem sunt,quæ cunque habent ditferentias, ex quo aliorum aut aliter sunt, ut propter quid resonat, aut propter quid apparet, et propter quod iris; omnia enim hæc quidem unum propositum sunt genere, omnia enim repercussio sunt,sed specie altera. Alia autem ex eo qUlod medium quidem subalternum medium est,differunt propositorurn,ut propter quid Nilus finiente mense nJagisfluit? propter id quod hibernior est finiens mensis. Propter quid autem hibernior est finiens mensis? propterid quod luna deficit. Hæc enim sic se habent ad invicem.
Further, there is another mode of selecting according to analogy; for to take one thing is not the same as what one ought to call itself, and a spine, and a bone; and the following things are so, these being as it were one nature of this kind. The same propositions are also those which have the same middle term, for example, why every contrary has a state; of these, however, some are the same in kind, whatever have differences, from which they are either otherwise or in another way, as why it resounds, or why it appears, and why the rainbow; for all these are one proposition in kind, for all are a reflection, but differ in species. Others differ in their propositions because the middle term is a subordinate middle term, as why does the Nile flow more at the end of the month? Because the end of the month is more wintry. But why is the end of the month more wintry? Because the moon fails. For these are related to one another in this way.
CAPUT XVII.
De causis et etfeciis, et an unius plures sivit causæ.
De causa autem,et cujuscausa est dubitabit aliquis, nunquid cum causatum est,et causa est,ut si folia fluunt, aut deficit luna, et causa deficiendi,vel folia cadendi erit,ut si hujus est lata habere folia, deficiendi autem terram in medio esse.Si enim non, aliqua alia erit causa ipsorum, si vero causa sit,et causatum simuI,ut si in medio est terra,deficit,aut, si latum est folium, folia flunnt; si autem sic est, simul utique erunt,et demonstrabuntur per invicem. Sit enim folium fluere in quo a,latum autem folium in quo b,vitis vero in quo::,si igitur in est a,omne enim latum folium habens folio fluit, autem inest b,omnis enim vitis habet lata folia,et ain est, omnis vitis folio fluit: causa est medium. Sed et quoniam latis foliis vitis sit,est propter id quod folio fluit demonstrare. Sit enim latum quidem folium, e autem folio fluere, vitis vero in quo f. In / igitur est e,etenim folio Unit omnis vitis,in e autem est,omne enim fluens folio,latum est folium babens; omnis itaque vitis latum est folium habens, causa autem est folio fluere.Si autem non contingit casus esse ad invicem, causa enim prius est eo cujus est causa,et deficiendi quidem est causa,terram esse in medio,ejus autem quod est in medio terram esse, non est causa deficere.
CHAPTER XVII.
On causes and effects, and whether one thing has several causes.
Concerning cause, and that of which it is the cause, someone will raise the question whether, when the effect exists, the cause also exists: for example, if leaves fall or the moon wanes, will there be a cause of the waning or of the falling of the leaves—as, if this [tree] has broad leaves, [the cause] of falling is that the earth is in the middle. For if not, there will be some other cause of these things; but if the cause exists, the effect exists at the same time: as, if the earth is in the middle, [the moon] wanes; or, if the leaf is broad, the leaves fall. But if it is so, they will surely exist at the same time and will be demonstrated through one another. For let "leaves fall" be that in which A [is present], "broad leaf" that in which B [is present], "vine" that in which C [is present]. If then A is present in B—for every broad-leaved [plant] sheds its leaves—and B is present in C—for every vine has broad leaves—then A is present in C: every vine sheds its leaves. The cause is the middle term. But also, because the vine has broad leaves, one may demonstrate that it sheds its leaves on account of this. For let "broad leaf" be [that in which] E [is present], "shedding leaves" [that in which] F [is present], and "vine" that in which G [is present]. In G, then, F is present—for every vine sheds its leaves; and in F, E is present—for everything that sheds its leaves has broad leaves; therefore every vine has broad leaves. The cause is the shedding of leaves. But if one cannot have reciprocal predication—for the cause is prior to that of which it is the cause—then the cause of waning is that the earth is in the middle; but of the earth's being in the middle, the waning is not the cause.
Si igit,ur per causam demonstratio est, propter quid est, si vero non per causam ipsius,quia,quoniam quidemterrain medio est cognovit, propter qu:d autem non. Quod autem non, deficere causa sit in medio esse, sed hoc, deficiendi manifestum est; in ratione enim deficiendi, inest quod est in medio,quare manifestum est quod per hoc illud cognoscetur, sed, non boc per illud. Į An contingit unius pluresesse causas?et namquE si est idem de pluribus primis prædicari primo,sit a in primo existens, et in alio primo, et hoc sit in d, hoc vero sit in e, erit itaque a in et in e, causa autem quod a sit in dquidcm b,in e autem c;quaro cum causa sit,necesse est rem omnem esse, sed res cum sit, non necesse est esse omne quodcunque sit causa, sed causam quidem necesse est esse, non tamen omnem.An si semper universale propositum, et causa totum quiddam est,et cujus est causa universalo?ut foliofluere intoto quodam determinatum est, et species ipsius sint. Universaliter igitur aut pIantis,aut hujusmodi plantis,quare et medium aequale oportet esse in his et cujus est causa,et converti, ut propter quid arbores folio fluunt, si ergo propterdensitatem humidi,sive folio fluit arbor,opor. tet esse densitatem, sive densitas est non in qualibet, sed in arbore, est folio Quere. Utrum autem contingat non eamdem essecausam ejusdem in omnibus, sed alteram, an non?
If, then, demonstration through the cause is demonstration of the reason why, but if not through the cause itself, it is demonstration of the fact—for instance, one knows that the earth is in the middle, but not why. That the cause of not being in the middle is lacking, however, is evident; for in the account of lacking, that which is in the middle is present, so it is clear that through this that will be known, but not this through that. Whether it is possible for one thing to have several causes? For if the same thing is predicated primarily of several primary things, let A be present in a primary thing, and in another primary thing, and let this be in D, but that in E; then A will be in both D and E, and the cause of A's being in D is B, but of its being in E is C. Therefore, since the cause exists, the thing must also exist; but when the thing exists, it is not necessary that everything whatsoever that is a cause exist—rather, the cause must exist, but not every cause. Or, if the proposition is always universal, is the cause also a whole, and is that of which it is the cause universal? For instance, shedding leaves is determined within a certain whole, and its species exist. Universally, therefore, either of a plant, or of plants of this sort; hence the middle term must also be equal in these, both in respect of that of which it is the cause, and it must convert—as, for example, why do trees shed leaves? If, then, because of the density of moisture, either the tree sheds leaves, the density must exist; or if density is not in any chance thing, but in a tree, then it sheds leaves. But whether it is possible that the same cause is not the cause of the same thing in all cases, but a different one, or not?
an siquidem per se demonstretur,aut non secundum signum aut accidens? non potest esse. Ratio enim extremi, medium; si vero non sic contingit, est autem et cujus causa et cui, considerare secundunn accidens, non tamen videntur proposita esse.Si autem non,similiter se habebit rnedium,siquidem sunt æquivoca,æquivocum medium est,si vero sicut in genere,similiter se habebit, ut propter quid commutabiliter, anaIogurn, alia enim est causa in numeris,et in Iineis,et eadem quidem inquantum lineæ, alia,inquantum autem ha. bens augmentum hujusmodi,eadem,sic in omnibus. Similem autem esse colorem coIori,etfiguram figuræ, aliam esse causam alii,æquivocum enim est simile in bis,hic quidemest fortassissecundum analogiam habere latera et aequales anguIos,in coloribus autem unumsensumesse,autaHquid aliud hujusmodi,quæ autem secundum analogiam sunt eadem,et medium habent secundum analogiam.Habet autem sic consequi causa ad invicem, et cujus est causa,et cui est causa unum quodque quidem accipienti,et cujus est causa in plus est, ut quatuor æquales qui sunt ext.ra,in plus sunt quam triangulus,aut quadrangulus,in omnibus autem ut in aequalibus est, quaecunque pnim,quator aequales qui sunt extra,et medium similiter est.
For if it is demonstrated through itself, is it not according to sign or accident? It cannot be. For the definition of the extreme is the middle term; but if this does not hold in that way, yet there is both that of which it is the cause and that for which it is the cause, to consider according to accident—nevertheless the things proposed do not seem to be so. But if not, the middle term will be related in like manner; if indeed they are equivocal, the middle term is equivocal; but if as in a genus, it will be related in like manner, as the reason why convertibly, by analogy—for the cause is different in numbers and in lines, and the same insofar as they are lines, but different insofar as they have increase of this sort, the same—so in all cases. But for color to be similar to color, and figure to figure, the cause is different for each; for "similar" is equivocal in these cases—here perhaps it is to have sides and equal angles according to analogy, but in colors it is for there to be one sensation, or something else of this sort; and those things which are the same according to analogy also have a middle term according to analogy. But the cause is related in this way to one another, both that of which it is the cause and that for which it is the cause: for each one, when taken, that of which it is the cause is more extensive, as the four equal [angles] that are outside are more extensive than a triangle or a quadrilateral; but in all cases as in equals, whatever they are—for the four equal [angles] that are outside, and the middle term is similarly.
Estautem medium ratio primi extremi,ex quo omnes scientiæ per definitionem fiunt; ut folio fluere si militer sequitur viti, et excellit,et ficui pt excelJit,eed non omnia,sed æqual ia sunt;si vero acci[1ias primum medium, ratio fluendi foliisest, erit enim primum quidem in altera, medium, quoniam hujusmodi suntomnia,deinde hujus medium,quoniam succus densatur,autiquiddam aliud hujusmodi. Quid autem est folio fluere? densari in contactu seminis succum.In figuris autem sicassignabit quærentibus consecutionem causæ,et cujus est causa,sit a quidem in omni, autem in unoquoque eorum qua? sunt d,in plus autem, igituruniversale utique ipsis inerit j hoc autem dico universale, quod non convertitur, primum autem universale, cui unumquoque quidem non convertitur, omnia autem convertuntur, et non excedunt, ipsis igitur causa ipsius a est b. Oportet itaque a in plna quam extendi; si vero non, quid magis causa erit boc illius? Si igitur in omnibus e est a, erunt aliquid illa unum omnia aliud quam b.Si enim non, quomodo erit dicere quoniam in quo est e sit a, omni? in quo autem a non omni sit? 6? propter quid enim non eritcausa aliqua ut a sit in omnibus d? sed nunquid et quae sunt e erunt aliquod unum? considerare oportet hoc,et sit e,contingil igitur ej usdem plures causas esse, sed non eisdem specie.
But the middle term is the definition of the first extreme, from which all sciences come about through definition; for example, if the flowing of leaves follows similarly for the vine, and it excels, and for the fig it excels, but not all things, but they are equal; but if you take the first middle term, the definition of the flowing of leaves is the reason, for there will be first, in one, the middle term, that all such things are so, then the middle term of this, that the moisture thickens, or something else of this sort. But what is it for a leaf to flow? For the moisture to thicken at the contact of the seed. In figures, however, he will assign to those seeking the sequence of the cause and that of which it is the cause: let A be in every one, and in each of the things that are D, but in more; therefore the universal will surely be in them. But I call that universal which is not convertible; but the first universal is that to which each one indeed is not convertible, but all are convertible and do not exceed. Therefore the cause of A itself is B. It is necessary, then, that A extend more widely; but if not, what will be the cause of this rather than that? If, therefore, E is A in all things, those things will be some one thing other than B. For if not, how will it be possible to say that in whatever E is, A is in every one? But in whatever A is, it is not in every one? For why will there not be some cause that A is in all D? But will the things that are E also be some one thing? It is necessary to consider this, and let it be E. It happens, therefore, that there are several causes of the same thing, but not the same in species.
Ut longæ vitae quadrupedia,non habere cboleram causa est, volatilia autem, sicca esse aut altera aliqua, si autem nalomum non statim veniunt,et non solum unum medium, sed plura, et causæ plures sunt. Utrum autem causa mediorum,quod ad universale primum est, aut quod ad singulare singularibus? Manifestum igitur est ea esse, quae proxima unicuiquecuicausaept,primumenimsub universaIi esse,hæc est causa,ut in d,sit quod est a,causa est c, in quidem igitur essea,causa est c,in autem b, in hoc autem, eadem est. De syllogismo igitur, et de demonstratione, quidque unumquoque est, et quomodo fit,manifestum est,simul autem et de scientia demonstrativa, idem enim est.
CAPUT XVIII.
Quomodo principia cognoscantur,et sit habitus.quis principio rum
De principiis autem qualiter fiunt cognita,etquis gst cognoscens habitus, hinc est manifestumjdubitantibus prirnum.Quod quidem igiturnon contingit sci re per demonstrationem,non cognoscentem prima principia imrnediata, dictum est prius, immediatorum autem cognitionem utrum eadem est, an non eadem,dubitabit utique aliqnis. Et utrum scientia in utroque est, an nOn,an hujus quidem scientia,ilJius auterr, alterum aliquod genus sit.
That long-lived quadrupeds are without choler is the cause; but that birds are dry, or some other such thing. But if the causes do not come about at once, and there is not only one middle term but several, and the causes are several. But whether the cause of the middle terms is that which is first with respect to the universal, or that which is with respect to the singular for singulars? It is evident, then, that they are those which are nearest to each thing and to each cause; for the first is to be under the universal; this is the cause, as in the case of d, that which is a is the cause, and c is the cause; in respect of essence, then, c is the cause, but in respect of b, and in this, it is the same. Concerning syllogism, then, and demonstration, what each one is and how it comes about, is evident; and at the same time concerning demonstrative science, for it is the same.
CHAPTER XVIII.
How principles are known, and what habit is. Which of the principles
Concerning principles, however, how they become known, and what the knowing habit is, is evident from this, for those who first raise the question. That it does not happen that one knows through demonstration without knowing the first immediate principles has been said before; but whether the cognition of immediates is the same or not the same, someone will indeed doubt. And whether science is in both, or not, or whether of this one there is science, but of that one some other genus.
Et utrum cum non insint habitus, fiant, an cum insint, JateanL Siquidern igitur habemus ipsos,inconveniens est,contingit enim certiores habere cognitiones demonstratione, et Jatere,si autem accipiamus non habentes prius,qualiter utique cognoscamus,et addiscamus ex non praeexistenti cognitione? impossibile enim est, sicntin demonstratione diximus. Manifestum igitur estquoniamnequc; habere possi bile est(neque ignorantibus)etnequo non habentibus habitum fieri.Necesse ast itaque habere quamdam quid em potentiam, non h:Jjusmodi autem habere quae est his honor.bilior secundum certitudinem. Videtur autem hæe omnibusinesseanimalibus,babent Anim connaturalem potentiam judicativam,quam vocant sensum. Cum insit autem sensus,in iis quidem animalium fit mansio sensibil is,in alii" autern non fit, in qmbuscunque igitur non fit"aut omnino,aut circa quæ non fit, nec estin his cognitio extra qnod sentiunl;in quibus autem iuest sentientibus habere unum quiddam in anima multis quidem factis hujusmodijamdifFerentia quædam fit, ut in his quamdam sit fieri rationern ex lalium memoria,in aliis vero non. Ex sensu igitur fit memoria, sicut dicimus. Ex memoria autem multoties ejusdem t'acta, experimentum.
And whether they come to be when the habits are not present, or when they are present, is unclear. For if we have them, it is strange—for it follows that we have more certain cognitions than demonstration—and to be unaware, if we do not have them; but if we receive them without having them beforehand, how shall we know and learn from a cognition that did not pre-exist? For it is impossible, as we said in the demonstration. It is clear, therefore, that neither is it possible to have them (nor for those who are ignorant), nor for those who do not have the habit to come to be. It is necessary, then, to have a certain power, but not to have it of such a kind as is more honorable than these in respect of certainty. But this seems to be present in all animals: for they have a connatural power of judgment, which they call sense. But when sense is present, in some animals a persistence of the sensible comes about, but in others it does not; in those, then, in which it does not come about, either altogether or concerning those things about which it does not come about, there is no cognition in them beyond what they sense; but in those in which it does come about, when they have sensed, there is a certain one thing in the soul, and when many such things have been made, a certain difference already comes about, so that in some there is a certain principle of reason from the memory of such things, but in others not. From sense, therefore, memory comes about, as we say. But from memory, when the same thing has been made many times, experience.
Multæ enim memoria' numero experimentum est unum, ex experimento aut ex omni quiescente universali in anim;, uno pra'ter multa (quod cum in omnibus unum sit illud idem) artis principium, et scientiæ,si quidem igitur circa generationem artis est,si vero circa ens, scientiæ. Neque igitur insunt determinati habitus, neque abaliis babitibus fiunt notioribus,sed a sensu. Ut in pugna eversione f'acta, uno stanle,alter stetit, postea aller,quousque in principium veniaat,anima autem hujusmodi. cum sit qualis possit pati hoc. Quod autem dictua est, ante, sed non clare dictum est,iterum dicamus;stante enim uno indiSerentium, primum quidem in anima universale est,et namque sentire quidem singulare, sensusautem universalis est, ut bominis non Callia; hominis. Ilerum in his statur,quousque uti im partibilia stentet universalia, ut hujusmodi animal, quousque anima!, et in hoc similiter.Manifestum igiturest quoniam nobis pri nia inductione cognoscere necessarium est, et namque et sensus sic universale facit Quoniam autem circa intelligentiam habituum quibus verum dicimus,alii quidem semper veri sunt, alii recipiunt falsitatem, ut opinio: et ratio, vera antem semper sunt scientia ct.inteIlectus,et nihil est scientia certil1s aliud genus quam intellect liS, principia autem dcmonstralionibus notiora sunt, scientia autem omnis cum ratione est, principiorum scientia quidem non utique erit.
For many memories numerically make one experience, and from experience—or from the universal wholly at rest in the soul, the one beside the many (whichever, being one and the same in all of them, is the principle of art and of science)—if indeed it concerns coming to be, it is of art; but if it concerns being, it is of science. Therefore neither are determinate habits present, nor do they come from other, more known habits, but from sense. As in a battle when a rout has occurred, one man stands fast, then another, and afterwards another, until they come back to the beginning; and the soul is of such a nature as to be able to undergo this. But what was said before, though not clearly said, let us say again: for when one of the indiscernibles has stood fast, first indeed a universal is in the soul—for one perceives the singular, but sense is of the universal, as of man, not of Callias; of man. Again one comes to rest in these, until the indivisible universals stand fast, as of such-and-such an animal, until of animal, and in this likewise. It is evident, therefore, that we must know the first principles by induction; for indeed sense in this way makes the universal. But since concerning understanding—of the habits by which we speak the truth, some are always true, others admit falsehood, as opinion and reasoning; but science and intellect are always true, and no other genus is more certain than science than intellect; and the principles are more known than demonstrations, while all science is with reason—there will surely not be science of the principles.
Quoniam autem nihil verius contingit esse scientia quam intellectum, inteI!eclus utique erit principioru Ex his considerantibus et quomam demonstrationis principium non demonstratio, quare neque scientiæ scientia, si igitur nullum aliud praeter scientiam habemus genus verum,intellectus utique eritscientiae principium, et principium quidem principii erit utique: omne autem similiter se habet ad rem omnem.
Since nothing truer than knowledge can be, namely understanding, understanding will assuredly be the principle of principles. From these considerations, and because the principle of demonstration is not demonstration, neither therefore is there knowledge of knowledge. If, then, we have no other true genus besides knowledge, understanding will assuredly be the principle of knowledge, and it will indeed be the principle of principle; but everything is related in like manner to every thing.