Book II, lectio XVDUO ERRORES EXCLUDUNTUR. - QUAE SECUNDUM REI VERITATEM REQUIRANTUR AD CONSTITUENDAM DEFINITIONEM PER VIAM DIVISIONIS

Nihil autem oportet definientem et dividentem omnia scire quae sunt. Et tamen impossibile quidam dicunt esse differentias cognoscere, quae sunt ad unumquodque, non cognoscentem unumquodque; sine autem differentiis non esse unumquodque scire: a quo enim non differt, idem esse huic, a quo autem differt, alterum ab hoc. Primum quidem igitur hoc falsum est: non enim secundum omnem differentiam alterum est. Multae enim sunt differentiae in eadem specie, sed non secundum substantiam, neque per se. Postea cum accipiat opposita et differentiam, et quod omne incidit hinc aut inde, et accipiat in altero quod quaeritur esse, et hoc cognoscat, nihil differt scire aut nescire de quibuscunque praedicantur aliis differentiae. Manifestum enim quoniam si sic vadens veniat in haec, quorum non amplius est differentia, habebit rationem substantiae. Omne autem incidere in divisionem, si sint opposita quibus nihil interest, non est petitio. Necesse enim est omne in altero ipsorum esse, si quidem illius differentia est.

Ad construendum autem terminum per divisiones tria oportet coniecturare; ut accipiantur praedicata in eo quod quid est, et haec ordinare quid primum aut secundum, et quoniam haec omnia sint. Est autem horum unum primum per id, quod possumus sicut ad accidens syllogizare quoniam est, et per genus probare. Ordinare autem sicut oportet erit, si primum accipiat. Hoc autem erit, si primum accipiatur quod omnibus sequitur, illi autem non omnia. Necesse est enim aliquod esse huiusmodi. Accepto autem hoc, iam erit idem in omnibus inferioribus modus. Secundum enim aliorum primum erit, et tertium habitorum. Remoto enim quod est sursum, habitum aliorum primum erit. Similiter autem est et in aliis. Quod autem haec omnia sint, manifestum est ex hoc quod recipimus primum quidem secundum divisionem, quoniam omne animal est aut hoc aut illud, est autem hoc; et iterum huius totius differentiam; extremi autem non amplius esse differentiam, vel etiam statim cum ultima differentia a toto nil differre specie hoc. Manifestum enim est quoniam neque plus hoc apponitur: omnia enim in eo quod quid est accipiuntur horum. Neque deficit nihil. Aut genus, aut differentia utique esset. Genus quidem igitur est primum, et cum differentiis hoc acceptum est. Differentiae autem omnes continentur: non enim amplius est posterior; specie enim differret et ultimum; hoc autem est dictum non differre.

The Latin version St Thomas commented, as the Leonine edition prints it.

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 investigate¹ 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 which² is of 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.³ 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.⁴ 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,⁵ 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,⁶ and of a right angle; afterwards assuming what the genus is,⁷ for instance, whether it is quantity or quality, he should investigate the peculiar passions⁸ through common first (principles.)⁹ For those which happen to the composites from individuals will be evident from the definitions,¹⁰ because definition and that which is simple¹¹ 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 differences¹² 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,¹³ 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,¹⁴ 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,¹⁵ 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,¹⁶ but the first difference of animal is that into which every animal falls. Likewise in regard to each of the rest, both of those genera¹⁷ 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, 1 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 whole¹⁸ but that of the last¹⁹ there is no longer any difference, or immediately with the last difference²⁰ this|| does not differ in species from the whole:²¹ 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 last²² 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 magnanimity²³ 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.

The whole chapters, in the translation of Octavius Freire Owen (London: George Bell & Sons, 1889 (Bohn's Classical Library), vol. I, from the plates of the first edition (London: H. G. Bohn, 1853), same pagination).