Volume 2 · pp. 446–449
Chapter IV. How definition is destroyed by inspecting differences.
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CAPUT IV. Qualiter interimitur diffinitio inspiciendo ad differentias.
Rursum volenti interimere diffinitionem similiter sicut in genere in differentiis considerandum tripliciter, ut si simpliciter deficit differentia, sicut non est substantialis diffinitio, aut si non propria, aut specifica. Considerandum ergo si diffinitionem assignans per genus debitum, in diffinitione cum genere et differentias proximi generis dixit: nam si non rei ipsius diffinivit differentiis, proculdubio diffinitionem interimit.
Aut etiam considerandum si omnino sive generaliter ut differentiam aliquid tale accidentale dixit, quod nullius diffiniti substantialem esse differentiam contingit, ut animal aut substantiam quae genera sunt, et nullius differentiae sunt constitutivae, quamvis ab aliquo separent ut genera: palam enim quoniam sic diffinire volens non diffinivit, quia ei quod est quid, qualitatem substantialem, quae diffinit quale quid et facit, non adjunxit: ea enim quae dicta sunt, animal et substantia, nullius sunt differentia, sed sunt quid in subjectis differentiis formabile et determinabile.
Adhuc autem inspiciendo ad differentiam videndum est, si differentiae positae in diffinitione assignata est aliud quod e diverso per contrarium in eodem genere dividitur, id est, per divisionem generis accipitur, dictae in diffinitione differentiae: nam si non est opposita differentia, palam quod non erit quae dicta est generis differentia positi in diffinitione: cum omne genus his differentiis dividatur quae e diverso dividuntur, hoc est, per divisionem accipiuntur, velut animal genus dividitur gressibili, volatili et bipedi tanquam oppositis differentiis. Hujus causa est, quia nullum genus est quod sua communitate constituat speciem, et ideo oportet ipsum dividi. Cum autem sit forma, formae autem non dividuntur nisi per oppositionem quam habent ad invicem, et quemlibet dividentem oportet habere formam oppositam. Si igitur differentia posita in assignata diffinitione non habet differentiam etiam oppositam, interimitur et ipsa diffinitio in qua ponitur.
CHAPTER IV. How definition is destroyed by inspecting differences.
Again, for one wishing to destroy a definition, one must consider differences in three ways, just as in genus: either if difference is simply lacking, as then there is no substantial definition, or if it is not proper, or if it is not specific. Therefore one must consider whether one assigning a definition through the due genus has stated in the definition both with the genus and the differences of the proximate genus; for if he has not defined the thing itself by differences, he undoubtedly destroys the definition.
Or it must also be considered whether wholly or generally he has stated as difference some accidental thing of such a sort that it happens to be the substantial difference of no defined thing, as animal or substance, which are genera, and are constitutive of no difference, although they separate from something as genera. For it is plain that one wishing to define in this way has not defined, because to that which is what he has not joined the substantial quality which defines and makes a qualified what; for the things stated, animal and substance, are differences of nothing, but they are a what formable and determinable by differences in subjects.
Moreover, by inspecting difference, one must see whether, for the difference posited in the assigned definition, there is something else divided from diverse sides through contrariety in the same genus, that is, received through division of the genus, opposite to the difference stated in the definition. For if there is not an opposite difference, it is plain that what has been stated will not be a difference of the genus posited in the definition; since every genus is divided by those differences which are divided from diverse sides, that is, received through division, as the genus animal is divided by walking, flying, and biped as by opposed differences. The cause of this is that no genus constitutes a species by its own commonness, and therefore it must be divided. But since it is form, and forms are not divided except through opposition which they have to one another, every dividing thing must have an opposed form. Therefore, if the difference posited in the assigned definition does not also have an opposed difference, the very definition in which it is placed is destroyed.
Aut etiam si sit e diverso diversa differentia aliqua, considerandum si est vera de genere, hoc est, quod sit cum genere continens speciem: est enim differentia vera de genere, quando est essentialis qualitas diffiniens et determinans ad actum substantialem potentiam generis. Unde patet quod si opposita differentia non est vera de genere, palam est quoniam neutra neque proposita neque opposita generis assignati in diffinitione erit differentia: omnes enim quae e diverso dividuntur ex genere differentiae hoc modo, verae sunt de proprio genere ex cujus genere per divisionem accipiuntur.
Similiter autem considerandum est, quia si vera est quidem de genere, non facit autem opposita generi speciem, eo quod non est specifica, palam quod non erit haec quae assignata est, differentia specifica generis in diffinitione positi. Nam omnis specifica differentia cum genere conjuncta facit speciem. Si autem hoc oppositum non est differentia, nec quae dicta est, erit differentia: quia illa illi e diverso dividitur. Et sic interimitur diffinitio interempta vera differentia specifica per quam fieri debet diffinitio.
Amplius adhuc interimitur diffinitio respiciendo ad differentiam considerando si negatione, hoc est, differentia per negationem assignata, dividitur genus, quia negatio nullius speciei constitutiva est: velut contingit ipsi Euclidi etiam qui lineam diffinit, dicens lineam per diffinitionem esse longitudinem sine latitudine: quae tamen diffinitio primo a Platone posita est, et ab Euclide assumpta. Sine latitudine autem est negativa differentia, quia idem est sine latitudine quod non habens latitudinem: nihil enim aliud significat sine latitudine, quam talis longitudo non habens latitudinem. Accidit autem ex tali assignatione differentiae inconveniens. Primum quidem, quod genus participat speciem, et universaliter species praedicabitur de genere. Quod sic patet, quia quod est, vel est cum latitudine, aut sine latitudine: nam de omni eo quod est, affirmatio vel negatio vera est. Hae autem differentiae cum latitudine esse, vel sine latitudine, apponuntur per affirmationem et negationem. Propter quod sequitur, quod de genere lineae, quod est longitudo, alterum horum verum erit: longitudo ergo quae genus est lineae, aut est cum latitudine, aut sine latitudine: non cum latitudine: ergo longitudo quae est genus lineae, erit longitudo sine latitudine: sed de quo praedicatur diffinitio, praedicatur et diffinitum: longitudo autem sine latitudine, ut dicit adversarius, est diffinitio lineae: ergo linea praedicatur de longitudine quae est genus lineae. Ex quo sequitur quod genus participat speciem, quia ista praedicatio est essentialis. Hoc autem est inconveniens. Ergo inconveniens est hoc ex quo sequitur, quod etiam differentia per negationem assignetur. Sic etiam probatur quod differentia essentialis et universaliter praedicabitur de genere, quia longitudo est genus: latitudinem non habens, differentia: praedicabitur autem latitudinem non habens de longitudine, ut jam probatum est; et hoc est iterum inconveniens: ergo non debet assignari differentia per negationem.
Or also, if there is some diverse difference from a diverse side, one must consider whether it is true of the genus, that is, whether together with the genus it contains the species. For a difference is true of a genus when it is an essential quality defining and determining the potency of the genus to substantial act. Hence it is clear that if the opposed difference is not true of the genus, it is plain that neither the proposed nor the opposed difference will be a difference of the genus assigned in the definition; for all differences which are divided from diverse sides out of a genus are true in this way of their proper genus, from whose genus they are received through division.
Likewise one must consider that, if it is indeed true of the genus but does not make a species opposed to the genus, because it is not specific, it is plain that this which has been assigned will not be a specific difference of the genus posited in the definition. For every specific difference joined with genus makes species. But if this opposite is not a difference, neither will what has been stated be a difference, because that is divided from this from diverse sides. And thus the definition is destroyed when the true specific difference through which the definition ought to be made has been destroyed.
Furthermore, definition is still destroyed with respect to difference by considering whether the genus is divided by negation, that is, by a difference assigned through negation, because negation is constitutive of no species. This happens even to Euclid himself, who defines line, saying by definition that line is length without breadth; nevertheless this definition was first posited by Plato and assumed by Euclid. But without breadth is a negative difference, because without breadth is the same as not having breadth; for without breadth signifies nothing other than such a length not having breadth. But from such an assignment of difference an unsuitability follows. First, indeed, that genus participates in species, and universally species will be predicated of genus. This is clear thus, because whatever is, either is with breadth or without breadth; for concerning everything that is, affirmation or negation is true. But these differences, to be with breadth or without breadth, are appended through affirmation and negation. On account of this it follows that concerning the genus of line, which is length, one of these will be true: therefore length which is the genus of line either is with breadth or without breadth; not with breadth; therefore length which is the genus of line will be length without breadth. But of that of which the definition is predicated, the defined thing is also predicated. But length without breadth, as the adversary says, is the definition of line; therefore line is predicated of length which is the genus of line. From this it follows that genus participates in species, because that predication is essential. But this is unsuitable. Therefore that from which it follows, namely that difference is assigned through negation, is unsuitable. Thus it is also proved that essential difference will be predicated universally of genus, because length is the genus, and not having breadth is the difference; but not having breadth will be predicated of length, as has already been proved, and this again is unsuitable. Therefore difference ought not to be assigned through negation.
Similiter autem et simile inconveniens sequitur si genus quod est longitudo, cum latitudine esse dicatur tanquam cum opposita praedictae negationi differentia: nam sine latitudine et cum latitudine differentiae sunt oppositae ejusdem generis: ex genere autem et differentia est speciei ratio sive diffinitio: propter quod sequitur quod genus recipit in praedicando speciei rationem, et ideo per consequens etiam species praedicabitur de genere, quod est inconveniens. Et similiter suscipiet genus differentiae praedicationem, quod est inconveniens: eo quod altera dictarum differentiarum per affirmationem et negationem oppositarum de necessitate praedicabitur de genere per hanc maximam, de quolibet affirmatio vel negatio est vera.
Dictus autem hic locus utilis est contra eos qui ponunt genera esse formas separatas secundum se realiter consistentes: nam si est eadem numero separata longitudo quae est genus separatorum, quodammodo etiam separate praedicabitur de isto genere separatorum quod idem numero est, ut dicit Plato, quia latitudinem habet, aut sine latitudine est, per eamdem maximam, quod oportet de omni longitudine alterum eorum quae dicta sunt, verum esse, sive separata sit sive concepta cum materia: siquidem de genere sive generaliter de longitudine verum esse debeat, hoc quidem verum est etiam, quod omnis longitudo vel cum latitudine vel sine latitudine est: sed non accidit hoc quod genus participet speciem, et quod differentia universaliter praedicetur de genere; sunt enim longitudines latitudinem non habentes, ut lineae: et cum latitudine sunt quaedam, ut superficiei et corporis: propter quod ad illos solos qui formas ponunt, qui unum numero in his genus ponunt, utilis est hic locus. Qui vero non unum numero genus ponunt, sed diversum, et id potest esse, quia idem genere bene et non inconvenienter contraria in se habet: sed ad illos valet quicumque genus unum dicunt esse unum numero: hoc autem faciunt qui solas formas genera esse ponunt; nam illi eamdem numero longitudinem et idem numero animal genus esse dicunt, cujus sunt contrariae differentiae.
Likewise, a similar unsuitability follows if the genus which is length is said to be with breadth as with a difference opposite to the aforesaid negation; for without breadth and with breadth are opposed differences of the same genus. But from genus and difference comes the account or definition of the species; on account of this it follows that genus receives in predication the account of the species, and therefore consequently the species also will be predicated of genus, which is unsuitable. And likewise genus will receive the predication of difference, which is unsuitable, because one of the stated differences opposed through affirmation and negation will necessarily be predicated of the genus through this maxim: of anything whatever affirmation or negation is true.
But this stated place is useful against those who posit genera to be separated forms existing really according to themselves. For if the same separated length in number is the genus of separated things, in some way it will also be predicated separately of that genus of separated things which is the same in number, as Plato says, because it has breadth or is without breadth, through the same maxim, that one of the things which have been stated must be true of every length, whether it is separated or conceived with matter. Indeed, if this ought to be true of genus or of length generally, this too is true, that every length is either with breadth or without breadth; but it does not happen from this that genus participates in species and that difference is predicated universally of genus. For there are lengths not having breadth, as lines; and there are certain ones with breadth, as those of surface and body. On account of this, this place is useful only against those who posit forms, who posit one genus in number in these things. But those who do not posit one genus in number, but a diverse one, and this can be because what is the same in genus well and not unsuitably has contraries in itself; but it avails against all who say that one genus is one in number. This, however, is done by those who posit forms alone to be genera; for they say that the same length in number and the same animal in number are genus, whose differences are contrary.
Quamvis autem sic dictum sit, quod negativa non sit differentia, tamen hoc non generaliter verum est: quia fortasse in quibusdam quorumdam diffinitionibus necessarium est uti negatione in assignatione differentiae, ut in privationum diffinitionibus: nam caecum per diffinitionem est, quod non habet visum quando per naturam natum est habere. Et haec quidem de negativa differentia dicta sunt. In talibus autem nec affirmative accepta differentia valet ad diffinitionem, quia non habet differentiam etiam condivisam per affirmationem. Unde nihil differt negatione sive negativa differentia dividere genus, aut hujusmodi affirmatione quam negatione, hoc est, ad quam affirmationem necesse est e diverso dividi cum negatione. Ut si longitudinem quae est genus, habens latitudinem diffinivit: nam nihil e diverso dividitur nisi non habens latitudinem: propter quod sequitur quod necessario negatione dividatur genus, et sic relinquitur idem quod prius inconveniens.
But although it has thus been said that a negative thing is not a difference, nevertheless this is not universally true, because perhaps in certain definitions of certain things it is necessary to use negation in the assignment of difference, as in definitions of privations; for blind, through definition, is that which does not have sight when by nature it is apt to have it. And these things indeed have been said about negative difference. But in such things neither does a difference accepted affirmatively avail for definition, because it does not also have a difference co-divided through affirmation. Hence it makes no difference whether one divides a genus by negation or negative difference, or by an affirmation of this sort rather than by negation, that is, by an affirmation with which it must necessarily be divided from diverse sides together with negation. Thus, if one defined length, which is the genus, as having breadth, nothing is divided from diverse sides except not having breadth; on account of this it follows that the genus is necessarily divided by negation, and so the same unsuitability as before remains.
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