Works › Posterior Analytics, Books I–II
Volume 2 · pp. 37–48
Treatise II, Chapter VII Continuation. On Necessary Things and On Every
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autem id scibile, quod est secundum demonstrativam scientiam scitum et scibile: demonstrativa autem scientia est, quam habemus in habendo demonstrationem: conclusionis enim habitae per demonstrationem est demonstrativa scientia: igitur syllogismus ex necessariis propositionibus simpliciter est demonstratio. Accipiendum igitur est ex quibus et qualibus necessariis sit demonstratio vel demonstrationes secundum omnem diversitatem conditionum earum quae sunt verae et necessariae: et hoc est quod est de omni, et per se, et universale. Et primo accipiamus hanc, quod sit necessarium, et de omni.
Dicamus igitur primo quod in demonstrativis necessariis est dici de omni. Dico igitur quod de omni dicit comparationem praedicati ad subjectum, quod cum insit, inest secundum quamlibet sui partem, non ita quod sit in aliquo quodam, et in quodam non: et secundum omne tempus, non ita quod insit aliquando, et aliquando non. Hoc enim sufficit in his quae sunt de omni ut nunc: sed non sufficit in his quae sunt de omni simpliciter. In illis enim quae necessaria sunt, quae supra tempus sunt et aeterna, ut dicit Aristoteles in sexto Ethicorum, oportet quod semper insit, et non insit aliquando, et aliquando non, sed semper. Et quia hoc dupliciter contingit, ideo de hoc duo dabimus exempla: et de hoc quod omni subjecto et semper insit, exemplum est, sicut animal dicitur de omni homine, non de aliquo dicitur, et de aliquo non: et non aliquando dicitur, et aliquando non: et ideo sive homo sit actu in natura, sive non, semper haec est vera, homo est animal: et quia cum animal sit principium intelligendi hominem, necesse est quod et actu et intellectu semper sit in homine: et ideo semper est praedicatum de ipso: et ideo si verum est dicere hominem, verum est dicere animal. Sicut enim diximus, necessaria sunt supra tempus et semper vera et nunc et semper. Contingentia vero ut nunc vera sunt et non semper.
Exemplum ejus quod est principium et non praedicatur ut de subjecto, sed sicut principium existens in omni et semper, est punctum in linea: si tamen in omni linea punctum est formale principium ut terminans et continuans qui est actus formae. Et hoc dico: quia quidam dixerunt punctum in linea esse materiale principium, et punctum componere substantialiter lineam, ita quod linea sit ex punctis, sicut in libro de indivisibilibus lineis determinatum est. Hoc igitur dicimus in demonstrativis et necessariis.
Quod autem verum sit quod dicitur, probatur per signum quod ab usu Philosophorum disputantium accipitur. Sic enim contra de omni instantias proferimus, sicut est videre: de omni enim interrogati, hoc est, si interrogamus in demonstrativis an probatio sit de omni demonstrativo, volentes ostendere quod non est de omni, instamus dicentes quod in quodam non est: aut instamus per hoc si aliquando non est, et sic probamus quod non est de omni in necessariis et demonstrativis. Per hoc enim quod dicitur quod non est aliquando, et aliquando non, significatur quod nulla parte temporis mensuratur necessarium, quod simpliciter necessitate rei necessarium est, et non necessarium per accidens, sicut quod positione vel conditione est necessarium.
but I mean that knowable thing which is known and knowable according to demonstrative science. But demonstrative science is what we have in having demonstration; for of a conclusion had through demonstration there is demonstrative science. Therefore a syllogism from necessary propositions simply is demonstration. Therefore it must be received from which necessary things and of what sort demonstration is, or demonstrations are, according to every diversity of the conditions of those things which are true and necessary; and this is what is of every, and per se, and universal. And first let us receive this condition, that it be necessary, and of every.
Therefore let us first say that in necessary demonstrative matters there is a saying of every. Therefore I say that of every says a comparison of the predicate to the subject, namely that when it is present, it is present according to any part whatever of it, not so that it is in some one thing and not in some other; and according to every time, not so that it is present at some time and not at some time. For this suffices in those things which are of every as now, but it does not suffice in those things which are of every simply. For in those things which are necessary, which are above time and eternal, as Aristotle says in the sixth book of the Ethics, it must always be present, and not be present at some time and not at some time, but always. And because this happens in two ways, therefore we shall give two examples of this: and of this, that it is present to every subject and always, an example is as animal is said of every man; it is not said of one and not of another, and it is not said at one time and not at another. And therefore whether man exists actually in nature or not, this is always true: man is animal; and because, since animal is the principle of understanding man, it is necessary that both in act and in intellect it always be in man, therefore it is always predicated of him; and therefore if it is true to say man, it is true to say animal. For as we have said, necessary things are above time and are always true both now and always. But contingent things as now are true now and not always.
An example of that which is a principle and is not predicated as of a subject, but as a principle existing in every and always, is a point in a line, if nevertheless in every line a point is a formal principle as terminating and continuing, which is the act of form. And I say this because certain persons said that a point in a line is a material principle, and that a point substantially composes a line, so that a line is from points, as has been determined in the book On Indivisible Lines. Therefore we say this in demonstrative and necessary matters.
But that what is said is true is proved through a sign which is received from the usage of philosophers disputing. For thus we bring forward instances against of every, as may be seen. For when we are asked concerning of every, that is, if we ask in demonstrative matters whether a proof is of every demonstrative thing, wishing to show that it is not of every, we make an instance by saying that it is not in some one thing; or we make an instance through this, if it is not at some time, and thus we prove that it is not of every in necessary and demonstrative matters. For by this which is said, that it is not at some time and not at another time, it is signified that the necessary is measured by no part of time, namely that which is necessary simply by necessity of the thing, and is not necessary by accident, as what is necessary by position or by condition.
Scias etiam quod in aliquibus est dici de omni demonstrative, in quibus non est actualis multitudo contentorum, sicut in sole et similibus aliis: et ideo de omni non potest diffiniri per hoc, quod sit universaliter de omnibus: sed cum additur negatio, quod non est de quodam et de quodam non, hoc de omnibus convenit scire, sive habeant actualem multitudinem, sive non habeant. Propter quod etiam per negationem oportuit determinare id quod est de omni, et per affirmationem determinari non potuit.
Et hoc quidem principium quod est dici de omni, et quod est dici de nullo, determinata sunt in libro Priorum secundum quod sunt communia principia syllogismum in communi praecedentia, et significant communem subjectorum universalitatem, qua propositiones syllogismi universales dicuntur quantum ad continentiam subjectorum: hic autem determinatur de omni prout consequitur propositionem universalem et demonstrativam. Quae universalitas duplici conditione determinanda est, scilicet universalitate subjectorum et universalitate temporum, propter duo quae sunt in syllogismo demonstrativo, in quo necesse est universalitatem subjectorum esse propter decretum syllogisticae argumentationis: et necesse est esse universalitatem temporum propter necessitatem conclusionis et propositionum in syllogismo in quantum demonstrativus est syllogismus.
Advertendum autem est, quod ex necessitate inesse dicitur duobus modis. Uno quidem modo quando id quod inesse dicitur, non potest non inesse: propter hoc quod id quod inest, substantiale dat ei cui inest: ita etiam id cui inest, egreditur essentialiter ab essentia ejus quod inesse dicitur: et hoc modo quidquid ex necessitate inest, per se inest. Alio modo dicitur ex necessitate inesse quod semper inest ei cui inest, sed non dat ei esse per hoc quod inest ipsi: quinimo id cui inest, non obstante natura ejus cui inest, posset esse sine ipso, sicut multis subjectis multa insunt accidentia inseparabilia. Et sic patet, quod omne quod est de omni prout hic determinatur, est de necessitate: non tamen omne tale est per se. Et sic patet quod hoc principium quod est per se, addit super id principium quod est de omni.
You should also know that in some things there is a demonstrative saying of every in which there is not an actual multitude of contained things, as in the sun and in other similar things; and therefore of every cannot be defined through this, that it is universally about all things. But when the negation is added, that it is not of one thing and not of another, this befits knowing about all things, whether they have an actual multitude or do not have one. On account of this also it was necessary to determine that which is of every through negation, and it could not be determined through affirmation.
And this principle, namely what it is to be said of every, and what it is to be said of none, were determined in the book of the Priors according as they are common principles preceding syllogism in common, and signify the common universality of subjects, by which the propositions of a syllogism are called universal with respect to the containment of subjects. But here of every is determined insofar as it follows upon a universal and demonstrative proposition. This universality must be determined by a double condition, namely by the universality of subjects and the universality of times, on account of the two things that are in a demonstrative syllogism, in which it is necessary that there be universality of subjects on account of the decree of syllogistic argumentation, and it is necessary that there be universality of times on account of the necessity of the conclusion and of the propositions in the syllogism insofar as it is a demonstrative syllogism.
But it must be observed that to be present from necessity is said in two ways. In one way, indeed, when that which is said to be present cannot not be present, on account of the fact that that which is present gives substantial being to that in which it is present; thus also that in which it is present proceeds essentially from the essence of that which is said to be present. And in this mode whatever is present from necessity is present per se. In another mode something is said to be present from necessity because it is always present in that in which it is present, but it does not give being to it through the fact that it is present in it. Rather, that in which it is present, notwithstanding the nature of that in which it is present, could exist without it, as many inseparable accidents are present in many subjects. And thus it is evident that everything which is of every as it is determined here is of necessity; nevertheless not every such thing is per se. And thus it is evident that this principle which is per se adds something over that principle which is of every.
Caput VIII. De modis dicendi per se qui sunt quatuor, et de primo et per se.
Conditionem demonstrationis quae est per se, non oportet diffinire: quia hoc commune, quod est per se, de suis modis dicitur multipliciter secundum analogiam et non univoce, ut dicit Aristoteles in quinto primae philosophiae 1 in capitulo de diffinitione modorum per se. Et quia hoc quod est per se, maxime necessarium est demonstrationi, ideo diligentius hic tractandum est: et, ut hoc fiat, distinguendi sunt modi ejus omnes, et singuli sunt tractandi: et secundo videamus qualiter se habent ad demonstrationem.
In modis autem dicendi per se duae sunt diversitates. Dicuntur enim duo modi primi, hoc est, primus et secundus modi per se inhaerendi, vel praedicatum subjecto, vel subjectum praedicato: et illi cadunt in simpliciter scibilibus. Alii autem duo differunt in hoc, quod tertius modus dicit modum per se existendi, et quartus dicit modum non per se existendi, sed per se causandi praedicatum in subjecto in essendo: et illi duo non cadunt in simpliciter scibilibus, licet cadant in demonstratione. In simpliciter enim scibilibus cadunt quae sunt principium et existendi et sciendi hoc esse in hoc vel de hoc per suam substantiam propriam, qua scibile constituunt secundum quod in suis substantiis cadere et esse considerantur: quae autem non dicunt hujusmodi causam et principium, non dicuntur cadere in vere scibilibus.
Hoc autem sic probatur. Cum per se dicatur quatuor modis, per se primo modo sunt, quaecumque in communi substantialiter et formaliter sunt in eo quod quid est, hoc est, in diffinitione substantiali et formali sive directe sive indirecte secundum obliquum praedicetur de ipso, hoc est, quaecumque substantialiter praedicantur sive secundum rectum, sive secundum obliquum: et iste est modus primus: sicut inest animal homini et secundum rectum praedicatur de ipso: et sicut linea inest triangulo secundum obliquum praedicata de ipso: est enim triangulus figura tribus rectis lineis seu angulis contenta, habens tres angulos aequales duobus rectis. Et sic lineae finitae et rectae inest punctum oblique cadens in ejus diffinitione. Est enim linea recta finita longitudo sine latitudine, cujus extrema vel termini sunt duo puncta, sicut dicitur in primo Euclidis. Hoc autem modo non est punctum in linea infinita, nec in circulari linea. In linea quidem infinita non est: quia illa non est nisi in potentia, et non in actu: omne enim terminatum per punctum, actu est finitum: et ideo proprie loquendo infinitum non habet essentialem diffinitionem. Circulari autem non convenit: quia circulus non habet suae existentiae terminum in seipso, ita quod sit in ipsa circumferentia, sed extra se in centro: quod patet per diffinitionem circuli in primo Euclidis, quae sic dicit, circulus est figura plana, una linea contenta, in cujus medio est punctum a quo omnes lineae productae ad circumferentiam, sunt aequales: propter quod punctum illud undique a circumferentia aequaliter distat: et patet ex hoc, quod punctum non cadit ut terminans essentialiter lineam circularem.
Chapter VIII. On the modes of speaking per se, which are four, and on the first and per se.
It is not necessary to define the condition of demonstration which is per se, because this common thing, which is per se, is said of its modes in many ways according to analogy and not univocally, as Aristotle says in the fifth book of first philosophy 1, in the chapter on the definition of the modes of per se. And because that which is per se is especially necessary to demonstration, therefore it must be treated more diligently here. And so that this may be done, all its modes must be distinguished, and each one must be treated; and secondly let us see how they are related to demonstration.
But in the modes of speaking per se there are two diversities. For two modes are called first, that is, the first and second modes of inhering per se, either the predicate in the subject or the subject in the predicate; and those fall within things knowable simply. But the other two differ in this, that the third mode says the mode of existing per se, and the fourth says the mode not of existing per se, but of causing per se the predicate in the subject in being. And those two do not fall within things knowable simply, although they do fall within demonstration. For in things knowable simply fall those things which are a principle both of existing and of knowing that this is in this or about this through their own proper substance, by which they constitute the knowable according as they are considered to fall and to be in their substances. But things which do not state a cause and principle of this kind are not said to fall within things truly knowable.
But this is proved as follows. Since per se is said in four modes, things are per se in the first mode whenever, in common, they are substantially and formally in what a thing is, that is, in the substantial and formal definition, whether something is predicated of it directly or indirectly according to an oblique case; that is, whenever things are predicated substantially, whether according to a direct case or according to an oblique case. And this is the first mode, as animal is present in man and is predicated of him according to a direct case, and as line is present in triangle when predicated of it according to an oblique case. For a triangle is a figure contained by three straight lines or angles, having three angles equal to two right angles. And thus a point is present in a finite and straight line, falling obliquely in its definition. For a straight finite line is length without breadth, whose extremes or terms are two points, as is said in the first book of Euclid. But in this mode there is not a point in an infinite line, nor in a circular line. Indeed, there is not one in an infinite line, because that line exists only in potency and not in act; for everything terminated by a point is actually finite, and therefore, properly speaking, the infinite does not have an essential definition. But it does not belong to a circular line, because a circle does not have the term of its existence in itself, so that it would be in the circumference itself, but outside itself in the center. This is evident through the definition of a circle in the first book of Euclid, which speaks thus: a circle is a plane figure contained by one line, in the middle of which there is a point from which all lines drawn to the circumference are equal. On account of this, that point is equally distant from every side of the circumference; and from this it is evident that the point does not fall as essentially terminating the circular line.
Iste ergo est unus primus modus dicendi per se, quoniam substantia formalis diffinitorum ex his est quae cadunt in diffinitione eorum, et substantia quae diffinitur, formaliter constituitur ex illis: et hoc est quando praedicatum velut formale principium cadit in diffinitione subjecti, sicut substantia hominis est ex animali rationali, et substantia lineae ex punctis in actu formae acceptis et secundum materiam: et hoc modo cadit in linea in diffinitione figurae ut terminans et finiens esse ipsius.
Quod autem quidam dicunt, quod punctum ut materialiter et substantialiter lineam constituens, cadit in diffinitione lineae, et linea in diffinitione figurae, est contra Aristotelem et est dictum Platonis, quod quidam affirmant distinguentes duplicem esse lineam, finitam scilicet, et infinitam: et dicunt quod lineae quidem infinitae punctum non est substantia nec principium, sed finitae. Adhuc autem dicunt quod punctum substantialiter constituens lineam, aut sumitur infinities in linea et secundum nullum numerum finitum, aut sumitur finities et ad aliquem numerum determinatum. Si sumitur finities, dicunt quod non constituit lineam: quia sic in linea punctum esset consequens ad punctum, et punctum contingeret punctum, et punctum consequeretur ad punctum: quae omnia probata sunt esse impossibilia in principio sexti Physicorum 2. Si autem infinities sumitur, dicunt quod punctum substantialiter constituit lineam finitam.
Si autem quaeritur ab his quare punctum infinities sumptum, non est consequens vel contingens vel continuum cum puncto in linea infinita, non possunt dicere, nisi quia in infinito non est primum nec medium nec ultimum. Sed tamen talis finita linea est continua, et in tali continuo, si ita est ut dicunt, necessario punctum continuatur ad punctum, si linea est ex punctis etiam infinities sumptis. Adhuc secundum Aristotelem, diffinitio consequentis et diffinitio contingentis et diffinitio continui faciunt, quod indivisibile in continuo non sequitur indivisibile, nec contingit ipsum, nec continuatur ad ipsum. Quia consequentia sunt, quorum non est medium sui generis: inter quaelibet autem duo puncta in continuo cadit linea quae est sui generis. Et contingentia sunt, quorum ultima sunt simul: indivisibile autem non habet ultimum. Continua etiam sunt, quorum est terminus unus, et ideo continuum terminatum est. Punctum autem non habet terminum. Non ergo est ex linea, quod punctum non sequitur nec contingit nec continuatur ad punctum, sed ex puncto: et ideo sive infinities sive finities sumatur, semper quamdiu est punctum, nec consequi nec contingere nec continuari potest in continuo: propter quod dictum illud Platonis nullum est, et probatum ab Aristotele quod falsum est et impossibile: et ideo primo modo est dicendum.
Therefore this is one first mode of speaking per se, since the formal substance of defined things is from those things which fall in their definition, and the substance which is defined is formally constituted from them. And this is when the predicate falls in the definition of the subject as a formal principle, as the substance of man is from rational animal, and the substance of a line is from points received in the act of form and according to matter; and in this mode it falls in line in the definition of figure as terminating and finishing its being.
But what certain persons say, that a point, as constituting a line materially and substantially, falls in the definition of line, and line in the definition of figure, is against Aristotle and is a saying of Plato, which certain persons affirm while distinguishing that line is twofold, namely finite and infinite. And they say that of an infinite line a point is not the substance nor the principle, but it is of a finite line. Furthermore they say that a point substantially constituting a line is either taken infinitely many times in the line and according to no finite number, or it is taken finitely and according to some determinate number. If it is taken finitely, they say that it does not constitute a line, because thus in a line point would be consequent upon point, and point would touch point, and point would follow upon point; all of which have been proved to be impossible at the beginning of the sixth book of the Physics 2. But if it is taken infinitely many times, they say that a point substantially constitutes a finite line.
But if it is asked of these men why a point taken infinitely many times is not consequent or contiguous or continuous with a point in an infinite line, they cannot say anything except that in the infinite there is no first, nor middle, nor last. But nevertheless such a finite line is continuous, and in such a continuum, if it is as they say, necessarily point is continued to point, if the line is from points even taken infinitely many times. Furthermore, according to Aristotle, the definition of the consequent and the definition of the contiguous and the definition of the continuous bring it about that an indivisible in a continuum does not follow upon an indivisible, nor touch it, nor is continued to it. For consequents are those things of which there is no middle of their genus; but between any two points whatever in a continuum there falls a line which is of their genus. And contiguous things are those whose extremes are together; but an indivisible does not have an extreme. Continuous things also are those of which there is one term, and therefore the continuous is terminated. But a point does not have a term. Therefore it is not from line that point does not follow upon, touch, or become continuous with point, but it is from point; and therefore, whether it is taken infinitely many times or finitely, always so long as it is a point, it cannot follow, touch, or be continued in the continuum. On account of this, that saying of Plato is nothing, and it has been proved by Aristotle that it is false and impossible; and therefore one must speak according to the first mode.
Adhuc si linea sic substantialiter esset ex punctis, quid esset quod lineae dat formam continuitatis, et quid ponit eam in genere continuitatis? hoc enim non potest facere infinities sumptum punctum, sicut patet ex ratione inducta: et ideo dictum illud impossibile est, et non dictum secundum philosophiam. Et Plato quando hoc dixit, non sicut isti dicunt intellexit: sed dixit quod motus imaginativus puncti in continuum, facit lineam: et quia illud quod imaginatur moveri est indivisibile, ideo substantia ejus est ab eo quod imaginatur moveri, et continuitas est a motu continuo imaginativo: sicut a motu ejus quod movetur in ubi, continuitas significatur in ubi per quod movetur. Tale igitur dictum est erroneum. Sed dicendum est quod punctum est principium lineae sine quo non est linea, et linea principium figurae sine quo non est figura, et ex quo sicut terminante substantialis est diffinitio ipsius. Iste igitur primus modus est dicendi per se.
Furthermore, if a line were substantially from points in this way, what would it be that gives the line the form of continuity, and what places it in the genus of continuity? For a point taken infinitely many times cannot do this, as is evident from the reason introduced; and therefore that saying is impossible and is not said according to philosophy. And when Plato said this, he did not understand it as these men say, but he said that the imaginative motion of a point into a continuum makes a line; and because that which is imagined to be moved is indivisible, therefore its substance is from that which is imagined to be moved, and continuity is from continuous imaginative motion, just as from the motion of that which is moved in place, continuity is signified in the place through which it is moved. Therefore such a saying is erroneous. But it must be said that a point is a principle of line without which there is no line, and line is a principle of figure without which there is no figure, and that from which, as from something terminating, its substantial definition comes. Therefore this is the first mode of speaking per se.
Caput IX. De secundo modo dicendi per se, et de tertio.
Est autem secundus modus dicendi per se, quando subjectum inest in diffinitione praedicati, hoc est, quibuscumque subjectis eorum praedicatorum quae insunt ipsis subjectis ipsa substantia sunt in ratione diffinitiva et ratione quid est demonstranti. Et dico demonstranti: quia per talem diffinitionem passio demonstratur inesse subjecto: et talis diffinitio ex subjecto secundum quod est causa talis passionis, dicit quid est passio per causam et essentiam: ut hoc rectum inest lineae, et linea cadit in diffinitione recti. Quod patet in primo Euclidis in diffinitione recti: dicit enim Euclides quod rectum est brevissima linea inter duo puncta. Plato autem, quod rectum est linea cujus prima pars vel primum punctum totam operit lineam: vel cujus medium non exit ab extremis: et ideo primum punctum totam lineam operit. Et hoc modo circulare sive etiam curvum insunt lineae: quia curvum est, cujus medium exit ab extremis: et ideo principium lineae totum medium lineae non operit. Hoc etiam modo par et impar insunt numero: quia par est numerus in duo aequa divisibilis: impar autem, quia in duo media numerus non potest dividi, unitate indivisibili intercidente. Hoc modo etiam se habent ad numerum primum et compositum: est enim primum in numeris, qui ex sola componitur unitate, ut binarius: et ideo binarius primus est numerus. Compositum autem est in numeris numerus, qui ex unitate et numero vel numeris componitur. Et sicut iterum in numero et in continuo sunt aequilaterum, et altera parte longius: in horum enim diffinitionibus cadit subjectum: quia sive in numeris sive in continuis aequilaterum est, cujus in seipsum ductus aequalis est radici, ut linea ducta in seipsam vel numerus ductus in seipsum: et utrumque facit quadratum numerum, sicut dicitur in secundo Arithmeticae, quod numeri cujuslibet ductus in seipsum facit quadratum numerum: vel de continuo quadrato quod sic fiat, dicitur in quarto Euclidis.
Quod autem numerus quadratus ductus in seipsum facit quadratum in numeris, dicitur secundo Arithmeticae quod fecit Pythagoras. Et generaliter loquendo, dicimus quod omnibus his praedicatis subjecta insunt in ratione dicente quid est passio: sicut hinc quidem, hoc est in diffinitione recti et curvi inest linea: et inde vero, hoc est, in diffinitione paris et imparis, vel primi vel compositi, vel quadrati et altera parte longioris quadranguli inest in una parte linea, in alia parte numerus: est enim quadrangulum altera parte longius numerus vel linea cujus ductus longior est radice: sicut quando numerus minor ducitur in majorem, vel e converso, ut ter in quatuor: vel cum linea bicubita ducitur in circulatam. Similiter autem est in omnibus aliis hujusmodi. Dico esse per se quaecumque vel primo modo quo praedicatum inest subjecto, vel secundo modo cum subjectum est in ratione praedicati omnia talia per se esse dico.
Quaecumque vero praedicata vel subjecta neutraliter insunt praedicatis vel subjectis, accidentia sunt et accidentaliter insunt, sicut musicum et album insunt animali: ita quod nec praedicatum est de ratione subjecti, nec subjectum in ratione praedicati: et ideo praedicatum tale accidit subjecto, et est commune non proprium et subjectum accidit praedicato 3. Est autem attendendum quod in hoc secundo modo subjectum intrans in diffinitionem praedicati, loco est differentiae contrahentis et specificantis: et id quod est genus passionis, est respectu ejus in potentia, sicut patet in diffinitione simi et aquili circa nasum: concavitas enim in medio nasi facit simum, gibbositas autem facit aquilum: in quibus curvitas et gibbositas loco generis sunt: nasus autem determinat ad speciem passionis sicut ultima differentia: et ideo subjectum est causa propria passionis, et diffinitio subjecti dicit quare et quia passio est in subjecto.
Chapter IX. On the second mode of speaking per se, and on the third.
But the second mode of speaking per se is when the subject is present in the definition of the predicate, that is, when for any subjects whatever of those predicates which are present in those subjects, the very substance is in the definitive account and in the account demonstrating what it is. And I say demonstrating, because through such a definition the property is demonstrated to be present in the subject; and such a definition from the subject, insofar as it is the cause of such a property, says what the property is through cause and essence. For example, this straight belongs to line, and line falls in the definition of straight. This is evident in the first book of Euclid in the definition of straight; for Euclid says that the straight is the shortest line between two points. But Plato says that the straight is a line whose first part or first point covers the whole line, or whose middle does not go outside the extremes; and therefore the first point covers the whole line. And in this mode circular or also curved things are present in line, because curved is that whose middle goes outside the extremes; and therefore the principle of the line does not cover the whole middle of the line. In this mode also even and odd are present in number, because even is a number divisible into two equal parts; but odd is so because number cannot be divided into two middles, with an indivisible unit falling between. In this mode also prime and composite are related to number. For prime in numbers is what is composed from unity alone, as two is; and therefore two is the first number. But composite among numbers is a number which is composed from unity and a number or numbers. And again, as in number and in the continuous there are equilateral and longer on the other side, for in the definitions of these the subject falls: because whether in numbers or in continua, equilateral is that whose multiplication into itself is equal to the root, as a line drawn into itself or a number multiplied by itself; and each makes a square number, as is said in the second book of Arithmetic, that the multiplication of any number whatever into itself makes a square number; or concerning a continuous square, that it happens so is said in the fourth book of Euclid.
But that a square number multiplied into itself makes a square among numbers is said in the second book of Arithmetic, which Pythagoras made. And speaking generally, we say that in all these predicates the subjects are present in the account saying what the property is; as on this side, that is, in the definition of straight and curved, line is present; and on that side, that is, in the definition of even and odd, or prime and composite, or of square and of a rectangle longer on one side, in one part line is present, in another part number is present. For a rectangle longer on one side is a number or line whose product is longer than the root, as when a smaller number is multiplied by a greater, or conversely, as three by four, or when a two-cubit line is led into a circular one. But it is similar in all other things of this kind. I say that whatever things are either in the first mode, in which the predicate is present in the subject, or in the second mode, when the subject is in the account of the predicate, all such things, I say, are per se.
But whatever predicates or subjects are neutrally present in predicates or subjects are accidents and are present accidentally, as musical and white are present in animal, such that neither is the predicate of the account of the subject, nor the subject in the account of the predicate. And therefore such a predicate happens to the subject, and it is common, not proper, and the subject happens to the predicate 3. But it must be attended that in this second mode the subject entering into the definition of the predicate is in the place of a contracting and specifying difference; and that which is the genus of the property is in potency with respect to it, as is evident in the definition of snub and aquiline concerning the nose. For concavity in the middle of the nose makes the snub, but convexity makes the aquiline; in these, curvature and convexity are in the place of a genus, but nose determines to the species of the property as the last difference. And therefore the subject is the proper cause of the property, and the definition of the subject says why and that the property is in the subject.
Amplius autem tertio modo dicitur esse per se potius quam dici per se, quod de alio quodam, hoc est, alterius naturae subjecto, non dicitur secundum suum proprium modum essendi sive existendi modum, ut ambulans, cum secundum modum existendi alterum et alterius naturae sit ambulatio quae inest, et id quod ambulat cui inest ambulatio, et a quo ut a subjecto egreditur actus ambulationis: et album cum alterius naturae sit albedo, et id cui inest albedo et a quo sicut a subjecto proprio causatur albedo: et ideo talia non dicuntur esse per se: quia eorum esse est inesse alteri. Substantia autem et praecipue substantia prima et quaecumque ut prima substantia, hoc aliquid signant, non alterum aliquid quidem sunt quam quod vere est proprio modo existendi per seipsum: et non per hoc habet esse, quod ipsa sit in alio: sed a seipsa habet suum esse secundum hoc quod ipsa est, et vere est quod est. Quaecumque igitur non de subjecto aliquo praedicata sunt, quo esse habeant, dico esse per seipsa: quae vero de subjecto sunt praedicata, a quo esse habent, dico esse accidentia.
Si autem quaeritur, quid iste modus facit ad demonstrationem? Dico, quod sicut in demonstratione est passio per se quae immediate exit a subjecto, ita quod inter eam et subjectum non est aliud subjectum mediante quo insit, sicut habere tres angulos aequales duobus rectis inest triangulo non mediante superiore quae est figura, et non mediante inferiore quod isosceles vel isopleurus: ita igitur, quod in demonstratione sit per se substans et stans subjectum, sicut nasus per se, hoc est per suam rationem qua diffinitur ut subjectum immediate, ita quod non per aliam aliquam passionem substat passioni: et triangulus substat tribus angulis aequis duobus rectis. Et ad hoc determinandum in vera et potissima demonstratione necessarius est iste tertius modus: est enim proprius modus subjecti substare per propriam rationem et non inesse alicui.
Si autem talis est tertius modus, ut dictum est, tunc tertius non videtur differre a modo secundo in his quae dicuntur etiam per se: quia in secundo modo quando subjectum est in ratione praedicati, ex subjecti ratione contrahitur ratio praedicati propter quam praedicatum inest ipsi subjecto, et sic subjectum per se ostenditur substare per passionem. Sed ad hoc dicendum est, quod in veritate secundus modus et tertius conveniunt in hoc quod uterque dicit causam per se inhaerentiae praedicati in subjecto, sed converso modo. Quia secundus dicit qualiter per se praedicato inest subjectum per id quod subjectum est principium praedicati. Tertius autem modus dicit causam propter quam subjectum non alii substat, quam praedicato, non ex ratione subjecti, sed ex ratione praedicati, in cujus diffinitione cadit hoc non aliud subjectum sive superius sive inferius acceptum, et sic conveniunt in causa inhaerentiae quae est per se inhaerentia: uterque enim dicitur ideo modus inhaerendi per se, quia per se praedicatum est in subjecto: et ideo modus secundus non excluditur a tertio quantum ad hoc.
Furthermore, in the third mode to be per se is said rather than to be said per se, namely what is not said of some other, that is, of a subject of another nature, according to its own proper mode of being or mode of existing. For example, walking, since according to the mode of existing the walking which is present is another thing and of another nature, and that which walks, in which walking is present and from which, as from a subject, the act of walking proceeds, is another thing; and white, since whiteness is of another nature, and that in which whiteness is present and from which, as from a proper subject, whiteness is caused, is another thing. And therefore such things are not said to be per se, because their being is to be in another. But substance, and especially first substance, and whatever things signify this something as first substance does, are not some other thing than what truly exists in its own mode of existing through itself; and it does not have being through this, that it is in another, but from itself it has its being according to this, that it is itself, and truly is what it is. Therefore whatever things are not predicated of some subject from which they have being, I say are through themselves; but those which are predicated of a subject from which they have being, I call accidents.
But if it is asked what this mode contributes to demonstration, I say that just as in demonstration there is a property per se which immediately goes out from the subject, so that between it and the subject there is no other subject by means of which it is present, as having three angles equal to two right angles is present in triangle not by means of a higher thing, which is figure, and not by means of a lower thing, which is isosceles or equilateral, so therefore in demonstration there must be a subject standing under and standing per se, as nose is per se, that is, through its account by which it is defined as immediate subject, so that not through some other property does it stand under the property; and triangle stands under three angles equal to two right angles. And for determining this in true and most powerful demonstration, this third mode is necessary; for it is the proper mode of the subject to stand under through its proper account and not to be present in something.
But if the third mode is such as has been said, then the third does not seem to differ from the second mode in those things which are also said per se, because in the second mode, when the subject is in the account of the predicate, from the account of the subject the account of the predicate is contracted, on account of which the predicate is present in that subject, and thus the subject is shown to stand under the property per se. But to this it must be said that in truth the second mode and the third agree in this, that each states the cause of the per se inherence of the predicate in the subject, but in a converse mode. For the second states how the subject is present per se in the predicate through the fact that the subject is the principle of the predicate. But the third mode states the cause on account of which the subject stands under no other thing than the predicate, not from the account of the subject, but from the account of the predicate, in whose definition this and not another subject falls, whether it is taken as higher or as lower. And thus they agree in the cause of inherence which is per se inherence. For each is therefore called a mode of inhering per se, because the predicate is in the subject per se; and therefore the second mode is not excluded from the third with respect to this.
Sed est notandum quod secundus modus dicitur per se secundum quod opponitur per se et id quod est per accidens: quia immediata est inhaerentia in subjecto, in cujus ratione diffinitiva cadit ipsum subjectum: quia inter passionem et subjectum non est aliud subjectum per quod insit passio, ut propterea quod per aliud insit, dicatur inesse per accidens. In tertio autem modo est per se secundum quod per se est primo esse, et non est hoc oppositum ei quod est per accidens, sed ei quod est non primo, sicut sit non primo substat quod ratione alterius substat. Et totum hoc quod dictum est, consistit in hoc, quod in secundo modo inest passio non per accidens, sed per se. In tertio autem modo subjectum est per se, ita quod non per aliud subjectum, quamvis illud subjectum non sit per accidens.
Sed tamen contra ea quae dicta sunt esse videtur, quod passio propria dicitur de subjecto primo et immediate praedicari. Sed ad hoc dicendum quod revera primum et immediatum sunt eadem subjecto, sed differunt ratione: quia immediatum dicitur dupliciter: dicitur enim immediatum a privatione medii quod est causa, aut a privatione medii quod est subjectum. Dico autem a privatione causae quae sit causa essendi subjectum, et a privatione subjecti quod sit subjectum proprium et immediatum et per se. Modus quidem secundus est per se et immediatus immediatione passionis et subjecti, ita quod passio immediata ex substantialibus subjecti egressa et causata praedicatur de primo suo et immediato subjecto, ita quod inter eam et subjectum non est aliud subjectum. In modo autem tertio stat subjectum quod per se subjectum est, et suae subjectionis causa propter quam sit subjectum, et non habet aliam causam: et ideo a privatione causae dicitur per se et non per aliud subjectum: et hoc subjectum est primum, quia non habet aliud a quo subjiciatur quod sit causa subjectionis ejus. Et sic secundus modus est per se, eo quod subjectum non per accidens, sed per sua essentialia a quibus fluit passio, tali subjicitur passioni. Tertius autem modus est per se, eo quod subjectum non habet ante se et praeter se quo substet omnibus quae sunt in demonstratione et circa demonstrationem. Tamen in sequenti capitulo adhuc dicemus verba Alfarabii de hoc: et tunc melius intelligetur hujusmodi sententia.
But it must be noted that the second mode is called per se insofar as per se is opposed to that which is by accident, because the inherence is immediate in the subject, in whose definitive account the subject itself falls, since between the property and the subject there is no other subject through which the property is present, so that because it is present through another, it would be said to be present by accident. But in the third mode there is per se insofar as through itself it is first in being, and this is not opposed to that which is by accident, but to that which is not first, as what stands under not first is what stands under by reason of another. And this whole thing that has been said consists in this, that in the second mode the property is present not by accident, but per se. But in the third mode the subject is per se, so that it is not through another subject, although that subject is not by accident.
Yet against the things that have been said there seems to be this: that a proper property is said to be predicated of the first and immediate subject. But to this it must be said that in reality first and immediate are the same in subject, but they differ in account, because immediate is said in two ways. For immediate is said from the privation of a middle which is a cause, or from the privation of a middle which is a subject. But I mean from the privation of a cause which would be the cause of the subject's being, and from the privation of a subject which would be a proper and immediate and per se subject. The second mode, indeed, is per se and immediate with the immediacy of property and subject, so that an immediate property proceeding and caused from the substantial things of the subject is predicated of its first and immediate subject, so that between it and the subject there is no other subject. But in the third mode the subject stands, which is subject per se, and the cause of its subjection on account of which it is subject stands, and it does not have another cause; and therefore from privation of cause it is called per se and not through another subject. And this subject is first, because it does not have another from which it is subjected which is the cause of its subjection. And thus the second mode is per se because the subject is subjected to such a property not by accident, but through its essentials from which the property flows. But the third mode is per se because the subject does not have before itself and besides itself that by which it may stand under all the things which are in demonstration and around demonstration. Nevertheless in the following chapter we shall still state the words of Alfarabi concerning this; and then the judgment of this kind will be understood better.
Tres ergo modi ejus quod est per se, sunt, quod primus est quando praedicatum inest subjecto per hoc quod in subjecto est primum et causa propter quam praedicatum est in ipso: quia essentiam trahit ab ipso, et ideo in ipso est actu et intellectu. Secundus autem modus est quando subjectum est in praedicato, ita quod praedicatum est in subjecto, eo quod passionis esse est in subjecto esse: et ideo quod insit, est in passione et non in subjecto: quia subjecti esse non est inesse, sed causa illius inhaerentiae propter quam huic subjecto insit, cum in subjecto non in passione insit, causa est passionis. Sed causa quod huic insit, est in subjecto: quia materialiter passio diffinitur per subjectum ut per causam, et sic per diffinitionem materialem probatur subjecto inesse. Tertius autem modus ita ponit subjectum per seipsum, quod non habet aliud his omnibus quae sunt in demonstrationem et circa demonstrationem.
Ex his patet quod primae substantiae et quae substant in eis, ut secundae substantiae quae substant in prima, sunt, quae non dicuntur de subjecto aliquo quod illis conferat esse, subjecta: sicut ambulans quod de quodam alio dicitur, quod alterius naturae et praedicamenti est quam ambulatio: et album quod denominative dicitur ab alio quod alterius naturae et praedicamenti est, quam albedo: eo quod alterum et alterius naturae est id quod denominatur ab actu ambulationis, cum dicitur ambulans, quam ambulatio: et album quod denominatur ab albedine, alterius naturae est quam albedo: substantia autem secunda et praecipue quaecumque substantiae hoc aliquid significant, non sunt alterum aliquod subjectum, quam id quod vere sunt secundum id quod sunt: quamvis enim dicam, hic homo est homo, tamen eadem natura est hic homo qui in uno sumitur, non particularizata secundum essentiam, in altero autem particularizata secundum esse: et hoc naturam non facit diversam.
Sed hoc observandum est, quod cum hic dicitur quod id per se est quod non est de subjecto quodam alio, aliter sumitur dici de subjecto quam in Praedicamentis. In praedicamentis enim de subjecto est, quod est praedicatum in eo quod subjicitur naturae communi: hic autem non dicitur de subjecto, sed de alio quodam subjecto, et non convenit nisi accidenti: et ideo quae quidem non sic de subjecto sunt, dico esse per se stantia: quae vero sunt de subjecto alio quodam secundum naturam, sunt accidentia, quae per se secundum tertium modum dicendi per se esse non possunt, et tamen possunt esse per se secundum primum modum aliquando, ut cum dicitur, album est coloratum, et aliquando secundum secundum, ut cum dicitur, linea est recta vel curva. Unde omnes praedicationes in quibus effectus praedicatur de causa, reducuntur ad secundum modum. Omnes autem in quibus causa praedicatur de effectu, reducuntur ad primum. Omnes autem in quibus aliquid gratia suiipsius substat, reducuntur ad tertium.
Therefore there are three modes of that which is per se: the first is when the predicate is present in the subject through this, that in the subject there is the first thing and the cause on account of which the predicate is in it, because it draws essence from it, and therefore it is in it in act and in intellect. But the second mode is when the subject is in the predicate, so that the predicate is in the subject, because the being of the property is to be in the subject; and therefore that it is present is in the property and not in the subject, because the being of the subject is not to be present, but the cause of that inherence on account of which it is present in this subject, since it is present in the subject and not in the property, is the cause of the property. But the cause that it is present in this is in the subject, because the property is defined materially through the subject as through a cause, and thus through the material definition it is proved to be present in the subject. But the third mode posits the subject through itself in such a way that it does not have anything else for all these things which are in demonstration and around demonstration.
From these things it is evident that first substances and those which stand under in them, as second substances which stand under in the first, are subjects, which are not said of some subject which confers being on them; as walking, which is said of some other thing which is of another nature and predicament than walking, and white, which is said denominatively from another thing which is of another nature and predicament than whiteness, because that which is denominated from the act of walking, when walking is said, is another thing and of another nature than walking; and the white thing which is denominated from whiteness is of another nature than whiteness. But second substance, and especially whatever substances signify this something, are not some other subject than that which they truly are according to that which they are; for although I may say, this man is man, nevertheless the same nature is this man, which in one case is taken as not particularized according to essence, but in the other as particularized according to being; and this does not make the nature diverse.
But this must be observed, that when here it is said that that is per se which is not of some other subject, to be said of a subject is taken otherwise than in the Predicaments. For in the Predicaments, of a subject is that which is predicated in that which is subjected to a common nature. But here it is not said of a subject, but of some other subject, and this belongs only to an accident. And therefore the things which are not thus of a subject, I say are standing per se; but those which are of some other subject according to nature are accidents, which cannot be per se according to the third mode of saying to be per se, and yet can sometimes be per se according to the first mode, as when it is said, white is colored, and sometimes according to the second, as when it is said, line is straight or curved. Hence all predications in which the effect is predicated of the cause are reduced to the second mode. But all in which the cause is predicated of the effect are reduced to the first. And all in which something stands under for the sake of itself are reduced to the third.
Caput X. De quarto modo dicendi per se, qualiter se habet ad demonstrationem.
Item alio modo et quarto dicitur per se quod propter ipsum et causam immediatam inest unicuique subjecto, quod indefinite signatur et subjicitur ut causa indefinite implicite vel explicite circa subjectum vel subjecta signata: et quod non sic praedicatur de subjecto, ut causa signata quae sit immediata causa praedicati, sive quod non convenit secundum ipsum et quod non concernit causam, dicitur quod est accidens: cujus exemplum in eo quod est per accidens isti modo oppositum, est in casualibus et fortuitis, et in omnibus in quibus subjectum non concernit in se veram causam praedicati: ut si dicam, quod ambulante aliquo homine vel equo indefinite signato coruscavit: ambulatio enim quam concernimus cum subjecto, non est causa coruscationis: unde dicimus, quod talis praedicatio est accidens sive per accidens ejusdem temporis in quo iste ambulavit, et de coruscatione nihil intendit, et nubes sonuit et nihil intendit de ambulatione: haec enim duo non habent unum ad aliud ordinem causalitatis, sed casus, in quo semper duae causae concurrunt, quarum neutra habet ordinem causalitatis ad alteram.
Si vero praedicatum est propter ipsum, quod cum subjecto concernitur implicite vel explicite, tunc est per se. Et hujus exemplum est si aliquod interfectum sive decollatum interiit secundum interfectionem vel decollationem: tale enim praedicatum inest subjecto propter causam quae consignificatur in subjecto: cum enim dicitur interfectum, subjectum significatur indefinite ut aliquid interfectum et per interfectionem quae consignificatur circa illud indefinitum subjectum quod causa est praedicati quod est interiisse. Et quod additur secundum interfectionem, non est de substantialibus hujus exempli, sed de expositione, ut explicite significetur quod implicite erat in subjecto de causa praedicati, propter quam tale praedicatum inest cuicumque.
Unde in hoc nec subjectum est per se determinatum quod gratia sui substet sicut fuit in tertio, nec praedicatum necessario est propria passio sicut in secundo modo fuit, sed praedicatum est generaliter propria passio vel aliud quod per causam significatam inest cuicumque subjecto. Nec modus inhaerentiae similis est secundo modo: quia quamvis causa quare passio est in subjecto, sit in subjecto in modo secundo: tamen non concernitur aliqua causa cum subjecto diffinito et determinato: sed ipsa natura subjecti causa est passionis. Hoc autem concernitur implicite vel explicite. Implicite quidem quando ipsa forma subjecti causa est, quare inest hoc vel illud praedicatum: sicut cum dicitur, homo est homo, et asinus est asinus: causa enim quod homo est homo, non est alia quam humanitas vel homo: eo quod hoc talis propositio a nullo habet. In secundo autem modo determinatum et definitum est subjectum. Adhuc autem in secundo diffinitum et determinatum est praedicatum quod est propria passio: hic autem talis causa est relata ad quodcumque praedicatum: unde in hoc modo dicendi per se sunt omnes propositiones, in quibus idem de seipso praedicatur. In talibus enim omnibus causa inhaerentiae praedicati in subjecto est in subjecto, et est forma ipsius subjecti in subjecto significata.
Chapter X. On the fourth mode of speaking per se, how it is related to demonstration.
Again, in another and fourth mode, that is called per se which is present in each subject on account of itself and an immediate cause, a subject which is signified indefinitely and is subjected as a cause indefinitely, implicitly or explicitly, around the subject or signified subjects. And what is not thus predicated of the subject, as a signified cause which is the immediate cause of the predicate, or what does not belong according to itself and what does not concern a cause, is said to be an accident. An example of this in what is by accident, opposed to this mode, is in casual and fortuitous things, and in all things in which the subject does not concern in itself the true cause of the predicate: as if I say that while some man or horse, indefinitely signified, was walking, it flashed. For the walking which we concern with the subject is not the cause of the flashing. Hence we say that such a predication is an accident or is by accident of the same time in which that one walked, and it intends nothing about the flashing; and the cloud sounded and intends nothing about the walking. For these two do not have an order of causality of one to the other, but chance, in which two causes always concur, neither of which has an order of causality to the other.
But if the predicate exists on account of that very thing which is concerned with the subject implicitly or explicitly, then it is per se. And an example of this is if some slain or beheaded thing perished according to the slaying or beheading. For such a predicate is present in the subject on account of the cause which is co-signified in the subject. For when slain is said, the subject is signified indefinitely as something slain and through the slaying which is co-signified around that indefinite subject, which is the cause of the predicate which is to have perished. And what is added, according to the slaying, is not among the substantial things of this example, but belongs to exposition, so that what was implicitly in the subject about the cause of the predicate may be signified explicitly, on account of which such a predicate is present in anything whatever.
Hence in this neither is the subject determined per se so that it stands under for its own sake, as it was in the third mode, nor is the predicate necessarily a proper property, as it was in the second mode, but the predicate is generally a proper property or something else which is present in any subject whatever through a signified cause. Nor is the mode of inherence similar to the second mode, because although the cause why the property is in the subject is in the subject in the second mode, nevertheless no cause is concerned with a defined and determinate subject; rather the very nature of the subject is the cause of the property. But here this is concerned implicitly or explicitly. Implicitly, indeed, when the very form of the subject is the cause why this or that predicate is present; as when it is said, man is man, and ass is ass. For the cause that man is man is no other than humanity or man, because such a proposition has this from nothing else. But in the second mode the subject is determinate and defined. Furthermore, in the second mode the predicate which is a proper property is defined and determinate; but here such a cause is related to any predicate whatever. Hence in this mode of speaking per se are all propositions in which the same thing is predicated of itself. For in all such things the cause of the inherence of the predicate in the subject is in the subject, and is the form of the subject itself signified in the subject.
Aliquando tamen aliter praedicati causa implicatur in subjecto cum causae reduplicatione, ut cum dicitur, interfectum interiit secundum interfectionem. Cum enim dicitur interfectum, circa subjectum concretive significatur causa praedicati talis: et cum additur reduplicatio, secundum interfectionem, hoc est de bene esse ad illius causae declarationem: quia sine hoc tota causa praedicati significatur cum dicitur, interfectum interiit. Et cum dicitur secundum interfectionem, quamvis reduplicatio ponatur ad praedicatum, tamen non est praedicati, sed subjecti, et ideo refertur ad subjectum sic, interfectum secundum interfectionem interiit: determinat autem subjectum secundum quod est causa talis praedicati: quorum nihil est in modo secundo. Patet igitur quod cum dicitur, interfectum interiit, per se est, quia interiit propter id quod interfectum est, et non propter causam accidentalem qua accidat interfectum interire. Conveniunt ergo secundus modus et quartus in hoc, quod in utroque causa inhaerentiae praedicati ponitur in subjecto: sed differunt modo subjecti et modo praedicati et modo causalitatis inhaerentiae, sicut dictum est.
Si autem quaeritur qualiter iste modus habeat se ad demonstrationem? Dicendum quod semper cadit in majori propositione syllogismi demonstrativi, sive debeat demonstrari passio de subjecto, sive demonstrari debeat diffinitio materialis per formalem: et hoc est ideo, quia in majori propositione demonstrationis subjectum semper est praecise de medio prout medium est causa talis praedicationis. Et ad hoc autem intelligendum, notandum quod demonstratio quae simpliciter demonstratio est, aliquando demonstrat passionem de subjecto: et tunc semper secundus modus est in conclusione: tunc enim praedicatur propria passio de subjecto. Aliquando autem demonstratur diffinitio materialis subjecti de subjecto per diffinitionem formalem ejusdem subjecti: et tunc primus modus est in conclusione: praedicatur enim diffinitio materialis in conclusione de subjecto: cujus exemplum est, quidquid habet appetitum contrarii doloris, habet circa cor accensionem sanguinis ex cooperatione fellis: iratus habet appetitum contrarii doloris: ergo circa cor habet accensionem sanguinis ex cooperatione fellis. In majori autem potest dici quartus modus, quia comparat causam ad causatum: quia appetitus contrarii doloris est causa accensionis sanguinis circa cor ex cooperatione fellis, hoc modo quo accidentia animae sunt causa accidentium corporis, ut dicit medicus. In minori vero est tertius modus, quia praedicatur diffinitio formalis de subjecto quod substat primo.
Yet sometimes the cause of the predicate is implicated otherwise in the subject with a reduplication of the cause, as when it is said, the slain thing perished according to the slaying. For when slain is said, around the subject the cause of such a predicate is signified concretely; and when the reduplication is added, according to the slaying, this belongs to well-being for the declaration of that cause, because without this the whole cause of the predicate is signified when it is said, the slain thing perished. And when according to the slaying is said, although the reduplication is placed toward the predicate, nevertheless it is not of the predicate but of the subject; and therefore it is referred to the subject thus: the thing slain according to the slaying perished. But it determines the subject according as it is the cause of such a predicate, none of which is in the second mode. Therefore it is evident that when it is said, the slain thing perished, it is per se, because it perished on account of that through which it was slain, and not on account of an accidental cause by which it would happen that the slain thing perished. Therefore the second mode and the fourth agree in this, that in each the cause of the inherence of the predicate is placed in the subject; but they differ in the mode of the subject, and in the mode of the predicate, and in the mode of the causality of inherence, as has been said.
But if it is asked how this mode is related to demonstration, it must be said that it always falls in the major proposition of a demonstrative syllogism, whether a property must be demonstrated of a subject, or a material definition must be demonstrated through a formal one. And this is so because in the major proposition of demonstration the subject is always precisely about the middle insofar as the middle is the cause of such predication. And to understand this, it must be noted that demonstration which simply is demonstration sometimes demonstrates a property of a subject, and then the second mode is always in the conclusion, for then a proper property is predicated of the subject. But sometimes the material definition of the subject is demonstrated of the subject through the formal definition of the same subject, and then the first mode is in the conclusion; for the material definition is predicated in the conclusion of the subject. An example of this is: whatever has appetite for contrary pain has around the heart a kindling of blood from the cooperation of bile; an angry person has appetite for contrary pain; therefore around the heart he has a kindling of blood from the cooperation of bile. But in the major there can be said to be the fourth mode, because it compares cause to caused, since appetite for contrary pain is the cause of the kindling of blood around the heart from the cooperation of bile, in that mode in which accidents of the soul are the cause of accidents of the body, as the physician says. But in the minor there is the third mode, because the formal definition is predicated of the subject which stands under first.
In praemissis autem illius demonstrationis quae concludit passionem de subjecto, si diffinitio passionis sit medium, cum illa diffinitio exprimat causam passionis, dicitur quod in majori propositione est quartus modus, qui comparat causam ad causatum, vel modus primus conversus. In minori autem propositione potest dupliciter contingere: causa enim passionis per modum causae expressa vel est aliquid subjecti, et tunc in minori propositione est primus modus: vel est aliquid consequens ad subjectum, et sic est secundus. Verbi gratia, omne continuo sonans propter extinctionem ignis in nube, est tonitru: nubes humida in qua est extinctus vapor igneus, est continuo sonans propter extinctionem ignis in nube: ergo nubes talis tonat vel est tonitru. Si autem in demonstratione quae concludit passionem de subjecto, sit formalis diffinitio subjecti medium, tunc in majori propositione est modus secundus: quia praedicatur passio de diffinitione subjecti, et eadem est comparatio passionis ad subjectum et ad suam diffinitionem. In minori autem propositione tunc erit modus primus: quia praedicatur diffinitio de diffinito: cujus exemplum est, omne quod est superficies plana, tribus lineis contenta, habet tres angulos aequos duobus rectis: triangulus est superficies plana, tribus rectis lineis contenta: ergo habet tres angulos aequos duobus rectis. Hoc ergo modo faciunt ad demonstrationem modi per se qui determinati sunt.
But in the premises of that demonstration which concludes a property of a subject, if the definition of the property is the middle, since that definition expresses the cause of the property, it is said that in the major proposition there is the fourth mode, which compares cause to caused, or the first mode converted. But in the minor proposition it can happen in two ways. For the cause of the property expressed by the mode of a cause either is something of the subject, and then in the minor proposition there is the first mode, or it is something consequent upon the subject, and thus it is the second mode. For example: everything continuously sounding on account of the extinction of fire in a cloud is thunder; a humid cloud in which fiery vapor has been extinguished is continuously sounding on account of the extinction of fire in the cloud; therefore such a cloud thunders or is thunder. But if in a demonstration which concludes a property of a subject the formal definition of the subject is the middle, then in the major proposition there is the second mode, because the property is predicated of the definition of the subject, and the comparison of the property to the subject and to its definition is the same. But in the minor proposition there will then be the first mode, because the definition is predicated of the defined; an example of which is: everything which is a plane surface contained by three lines has three angles equal to two right angles; a triangle is a plane surface contained by three straight lines; therefore it has three angles equal to two right angles. Therefore in this mode the modes per se which have been determined contribute to demonstration.
Caput XI. De comparatione modorum dicendi per se ad demonstrationem et de sufficientia eorumdem.
Comparantur autem isti modi ad demonstrationem, et accipitur numerus eorum per hunc modum: quia quaecumque dicuntur in simpliciter scibilibus, hoc est, in scientia conclusionum demonstrativarum et vere scitarum sic se habent aut sicut inesse subjectis praedicantibus ipsis, hoc est, praedicatis, ita quod praedicata insunt subjectis sicut in primo modo: illa enim omnia insunt subjectis et rationi subjectorum, sicut ea quae insunt praedicantibus essentialia praedicata de subjectis per illud in Praedicamentis determinatum, quando alterum de altero ut de subjecto praedicatur, tunc quaecumque de praedicato dicuntur, omnia de subjecto dici necesse est. Aut inesse ea quae insunt ex necessitate propter ipsa subjecta quae sunt ex necessitate in ipsis praedicatis sive in diffinitionibus suorum praedicatorum.
Quod autem haec ex necessitate insint quaecumque contingit altero duorum modorum inesse in simpliciter scibilibus, hoc est, in his quae simpliciter sciuntur per demonstrationem factam per medium quod est diffinitio praedicati vel subjecti, patet ex hoc quod talia non contingit non inesse aut simpliciter, hoc est, sine disjunctione, ut triangulo habere tres aequos duobus rectis: aut opposita sub disjunctione, ut lineae rectum aut curvum, et numero par aut impar. Quaecumque enim insunt et non contingit non inesse, illa insunt de necessitate. Omnia autem quae ex praedicato essentiali insunt subjecto, et ex subjecto intrante in diffinitione praedicati insunt praedicato, ita insunt quod non contingit non inesse vel ipsa absolute vel sub disjunctione ad opposita: ergo omnia talia insunt aliquo istorum modorum. Aut enim est contrarium immediatum sub disjunctione acceptum ad suum contrarium, ut omne animal aut sanum aut aegrum, et omnis linea aut recta aut curva, et omnis numerus aut par aut impar, et universaliter loquendo quaecumque immediata sunt circa idem subjectum, quorum utrumque per positionem formae significat contrarium in specie determinatum. Aut talia sunt opposita ut privatio et habitus, ut omne animal, vel omnis homo, aut caecum, aut videns, quorum unum significat habitus alicujus positionem, et alterum ejusdem privationem cum positione ordinis naturae ad habendum habitum illum. Aut sunt opposita ut contradictio sive contradictoria in genere eodem et non extra genus, ut par et impar: hoc non est par in genere numeri: par et impar sunt sicut contradictoria secundum quod de omnibus sequitur alterum intra genus, et de nullo simul proprie. Quia dicitur quod si necesse est affirmare et negare sive aut negare de omnibus extra genus, tunc etiam necesse est in eodem genere alterum talium oppositorum inesse: et ideo necesse est haec quae dicta sunt per se ex necessitate inesse. De duobus ergo principiis seu conditionibus principiorum de omni, et de hoc quod est per se, determinatum sit hoc modo quo dictum est.
Chapter XI. On the comparison of the modes of speaking per se to demonstration and on their sufficiency.
But these modes are compared to demonstration, and their number is received in this mode: because whatever things are said in things knowable simply, that is, in the science of demonstrative conclusions and of things truly known, are related either as being present in subjects predicating them, that is, in predicates, so that predicates are present in subjects as in the first mode; for all those things are present in subjects and in the accounts of subjects, as those things which are present in predicates are essential predicates about subjects through that determined in the Predicaments: when one thing is predicated of another as of a subject, then whatever things are said of the predicate must all be said of the subject. Or they are related as those things being present which are present from necessity on account of the subjects themselves, which are from necessity in those predicates or in the definitions of their predicates.
But that whatever things happen to be present by one of the two modes in things knowable simply are present from necessity, that is, in those things which are simply known through demonstration made through a middle which is the definition of the predicate or of the subject, is evident from this, that such things cannot not be present, either simply, that is, without disjunction, as for a triangle to have three angles equal to two right angles, or with opposites under disjunction, as straight or curved for a line, and even or odd for a number. For whatever things are present and cannot not be present are present of necessity. But all things which from an essential predicate are present in a subject, and from a subject entering into the definition of the predicate are present in the predicate, are present in such a way that they cannot not be present, either absolutely themselves or under a disjunction toward opposites. Therefore all such things are present by some one of these modes. For either it is an immediate contrary taken under disjunction toward its contrary, as every animal is either healthy or sick, and every line either straight or curved, and every number either even or odd, and speaking universally, whatever things are immediate around the same subject, each of which through the position of a form signifies a contrary determinate in species. Or such things are opposites as privation and habit, as every animal, or every man, is either blind or seeing, one of which signifies the position of some habit, and the other the privation of the same with the position of an order of nature toward having that habit. Or they are opposites as contradiction or contradictories in the same genus and not outside the genus, as even and odd: this is not even in the genus of number; even and odd are like contradictories according as one follows concerning all things within the genus, and properly not both at once concerning anything. For it is said that if it is necessary to affirm and deny, or to deny of all things outside a genus, then it is also necessary that one of such opposites be present in the same genus. And therefore it is necessary that these things which have been said to be per se be present from necessity. Therefore concerning the two principles or conditions of principles, of every and that which is per se, let it have been determined in the mode that has been stated.
Numerus autem modorum eorum quae sunt per se, sic accipi potest. In natura enim subjectorum et praedicatorum non sunt nisi tria, scilicet quod est, et quod inest, et causa propter quam unum alteri inest. Modi igitur qui sunt per se, in subjectis et praedicatis multiplicantur penes haec tria. Omnis ergo modus ejus quod est per se, aut est circa hoc quod inest, et hoc dupliciter: omne enim inhaerens alteri per se, aut dat esse ei cui inest, et sic est modus primus, aut egreditur ab essentia ejus cui inest, et sic est modus secundus: aut dicit causam propter quam inest, et sic est modus quartus. Vel sic, per se aut est dispositio alicujus entis per se perfecte et absolute, et sic est modus tertius: vel est dispositio entis unius ordinati ad alterum, aut ordine essendi sicut causa dicit ordinem essendi unius ad alterum, et sic est quartus modus: aut ordine praedicandi et subjiciendi: et hoc dupliciter: si enim ordo est ingrediendi praedicatum in ratione subjecti, est modus primus: aut e converso, ita quod subjectum sit de quidditate praedicati, et sic est modus secundus. Et sic patet etiam ordo: tres enim primi accipiuntur absolute: quartus autem cum reduplicatione causae quae est in subjecto in comparatione ad praedicatum. Adhuc primi duo sic pertinent ad demonstrationem, quod cadunt in simpliciter scibilibus: tertius autem non sic, sed cadit in subjectis eorum quae sciuntur.
Scias autem quod Alfarabius super locum istum in commento aliquantulum sequens Porphyrium et Alexandrum, aliter dicit: dicit enim quod tres sunt modi dicendi per se subjectum de praedicato, et praedicatum de subjecto: et ponit primum modum qui potissimus est, quando in natura principii et principiantis est ut sit in natura principiati: et iterum cum hoc in natura subjecti est ut praedicatum sit in eo, sicut est in natura principiati per essentiam ut principians ipsum sit in ipso, sicut in natura animalis est, quod sit in homine, et in natura hominis est ut animal sit in ipso: quia natura animalis ad actum determinatur in homine, et natura hominis inchoatur in animali et perficitur in rationali: et quia hic modus est et in natura subjecti et praedicati, ideo est primus et potissimus. Secundus autem modus est, quando in natura et in diffinitione praedicati quidem est ut dicatur de subjecto, et non est in natura subjecti ut praedicatum dicatur de eo, sicut se habent ad invicem corpus et coloratum. In natura enim colorati est ut dicatur de corpore terminato, quia non est nisi in corpore terminato: sed non est in natura vel ratione corporis ut substet colorato, quia potest esse secundum diffinitionem et non substare colorato: et hoc modo se habent risibile et homo, et generaliter loquendo passio et subjectum. Tertius autem modus est ut sit quidem in natura subjecti ut praedicatum de eo dicatur, et non in natura praedicati et ratione ut ipsa sit in tali subjecto, sicut mors et decollatio se habent ad invicem. In natura enim decollationis est ut sit in ea mors: sed in natura mortis non est ut sit in decollatione, potest enim mors esse sine decollatione. Et haec sunt verba Alfarabii sine additione et diminutione et sine expositione.
But the number of the modes of those things which are per se can be received thus. For in the nature of subjects and predicates there are only three things, namely what is, what is present, and the cause on account of which one is present in the other. Therefore the modes which are per se are multiplied in subjects and predicates according to these three things. Therefore every mode of that which is per se is either around this, what is present, and this in two ways: for everything inhering in another per se either gives being to that in which it is present, and thus it is the first mode, or it goes out from the essence of that in which it is present, and thus it is the second mode; or it states the cause on account of which it is present, and thus it is the fourth mode. Or thus: per se is either the disposition of some being per se perfectly and absolutely, and thus it is the third mode; or it is the disposition of one being ordered to another, either by the order of being, as cause states the order of being of one to another, and thus it is the fourth mode, or by the order of predicating and subjecting. And this is twofold: for if the order is of the predicate entering into the account of the subject, it is the first mode; or conversely, so that the subject is of the quiddity of the predicate, and thus it is the second mode. And thus the order too is evident: for the first three are received absolutely, but the fourth with reduplication of the cause which is in the subject in comparison to the predicate. Further, the first two pertain to demonstration in such a way that they fall within things knowable simply; but the third not in this way, but it falls in the subjects of those things which are known.
But you should know that Alfarabi, on this place in the commentary, following Porphyry and Alexander somewhat, speaks otherwise. For he says that there are three modes of saying per se the subject of the predicate and the predicate of the subject. And he posits the first mode, which is the most powerful, when in the nature of the principle and of the one principiating it is that it be in the nature of the thing principiated; and again, along with this, in the nature of the subject it is that the predicate be in it, just as it is in the nature of the thing principiated through essence that the thing principiating it be in it, as it is in the nature of animal to be in man, and in the nature of man that animal be in him; because the nature of animal is determined to act in man, and the nature of man is begun in animal and completed in rational. And because this mode is both in the nature of the subject and of the predicate, therefore it is first and most powerful. But the second mode is when in the nature and definition of the predicate, indeed, it is that it be said of the subject, and it is not in the nature of the subject that the predicate be said of it, as body and colored are related to one another. For in the nature of colored it is that it be said of a terminated body, because it exists only in a terminated body; but it is not in the nature or account of body that it stand under colored, because it can exist according to definition and not stand under colored. And in this mode risible and man are related, and generally speaking, property and subject. But the third mode is that it indeed be in the nature of the subject that the predicate be said of it, and not in the nature and account of the predicate that it be in such a subject, as death and beheading are related to one another. For in the nature of beheading it is that death be in it; but in the nature of death it is not that it be in beheading, for death can exist without beheading. And these are the words of Alfarabi without addition and diminution and without exposition.
De tertio autem modo quem posuit Aristoteles dicit Alfarabius: Substantias primas esse per se dicit Aristoteles et substantias primas intelligit esse individua, sive sint extra intellectum, sive in intellectu: et dicuntur per se, non quod sint praedicata de aliis, sed quod existant per se, non quod sint aliis essentialia, et non continentur sub aliquo trium modorum: sed ideo dixit ea esse per se ut ostenderet quod non sunt per accidens, quamvis non sint subjecta demonstrationis. Haec sunt verba Alfarabii et hoc videtur esse intellectus Aristotelis plus quam omnia alia quae dicta sunt.
Et patet numerus et ordo eorum quae dicuntur per se ex ipsius verbis: quia per se est, aut dispositio tam praedicati quam subjecti, et est modus primus: aut est dispositio praedicati tantum, et est modus secundus: aut subjecti tantum, et est modus tertius. Dicit etiam quod per se et secundum ipsum in tertio modo qui est per causam est reduplicatio subjecti secundum quod stat sub causae determinatione, sed respectu praedicati: ut sit sensus, homo secundum quod homo est animal: si enim poneretur reduplicatio ad praedicatum sic, homo est animal secundum quod animal, esset sensus, quod homo esset omne animal, quod falsum est: sed hoc in ante habitis expositum est. Haec igitur dicta sunt de conditione demonstrationis quae est per se.
But concerning the third mode which Aristotle posited, Alfarabi says: Aristotle says first substances are per se, and he understands first substances to be individuals, whether they are outside the intellect or in the intellect; and they are called per se not because they are predicates of others, but because they exist per se, not because they are essential to others, and they are not contained under any of the three modes. But he therefore said that they are per se in order to show that they are not by accident, although they are not subjects of demonstration. These are the words of Alfarabi, and this seems to be the understanding of Aristotle more than all the other things which have been said.
And the number and order of those things which are called per se is evident from his words: because per se is either a disposition both of the predicate and of the subject, and this is the first mode; or it is a disposition of the predicate only, and this is the second mode; or of the subject only, and this is the third mode. He also says that per se and according to itself in the third mode, which is through cause, is a reduplication of the subject according as it stands under the determination of the cause, but with respect to the predicate, so that the sense is: man, according as he is man, is animal. For if the reduplication were put to the predicate thus, man is animal according as it is animal, the sense would be that man was every animal, which is false. But this has been explained in what was held before. Therefore these things have been said concerning the condition of demonstration which is per se.
Caput XII. De universali quid sit in demonstrativis.
Universale autem dico, secundum quod universale in necessariis et demonstrativis accipitur, quod cum sit de omni, hoc est, omnibus partibus essentialibus subjecti praedicatum, et sit per se praedicatum de illis omnibus, est praedicatum de illo subjecto et partibus secundum quod ipsum est nomine et diffinitione acceptum. Propter quod patet, quod hoc quod dico de omni et per se, conditiones sunt praedicati, relatae tamen ad subjectum. Id autem secundum quod ipsum est, est conditio subjecti: ut sit sensus, quod universale sit alicujus subjecti praedicatum de ipso quoad omnes partes subjecti, non secundum quod partes sunt, sed secundum quod univocantur et uniuntur in forma speciei communis: et per se, sive essentialiter, ita convenit omnibus partibus subjecti, quod cuilibet convenit in quantum stat sub forma speciei, et non secundum quod est determinata in substantia et forma partis.
Per se autem et secundum quod ipsum est idem quoad suppositum, quamvis differant haec secundum rationem: sunt enim idem sicut particulare et universale: quia per se communius est quam secundum quod ipsum, sicut paulo inferius patebit. Et hujus exemplum est, quod lineae inest punctum per se secundum primum modum dicendi per se, sicut principium essentiale non praedicabile secundum rectum: et rectitudo et curvitas insunt lineae sicut passiones, et secundo modo dicendi: et haec alio modo insunt lineae secundum quod linea. Sed hic intelligendum quod haec insunt lineae secundum quod ipsum sive secundum quod linea est, secundum quod linea contrahitur ad extensionem quae fit inter duo puncta: et secundum hoc rectitudo cum suo opposito accipitur per disjunctionem, ut dicatur, quod linea extensa inter duo puncta, recta est vel curva secundum quod talis est linea. Et hoc modo in secundo modo dicendi per se triangulus secundum quod ipsum, hoc est, secundum quod triangulus est perfectus habens speciem et rationem trianguli, est duo recti per angulorum trium aequalitatem ad duos rectos: cujus ratio: quia triangulus, in angulis tribus quibus terminatur, duobus rectis angulis est aequalis. Et haec jam ante ostendimus intelligi de triangulo rectilineo: quia si sphaericas vel portiones circuli vel curvas habeat lineas, potest habere tres angulos tribus et duobus rectis majores.
Universale autem tunc esse dicitur in demonstrativis secundum inductam determinationem, cum demonstratur esse in quolibet, hoc est, in qualibet parte subjecti: quia aliter non esset de omni: et monstratur primo, hoc est, immediate inesse cuilibet per subjectum primum. Et sic primum est quod inter ipsum et passionem aliud subjectum non intercidit, sicut quod convenit omni triangulo in quantum triangulus, et convertitur cum ipso in quantum est triangulus: ita quod hoc subjectum ita est causa passionis, quod non indiget majori se et superiori quod est figura in triangulo, ad hoc quod fluat ex ipso: nec sufficiat minus et inferius quod in triangulo est isosceles ad causandum totum secundum ambitum et communitatem praedicationis ipsius passionis: habere enim tres aequos duobus rectis et isosceles in minus est quam quod totum causare possit.
Chapter XII. What the universal is in demonstrative matters.
But I call universal, according as universal is taken in necessary and demonstrative matters, that which, since it is of every, that is, a predicate of all the essential parts of the subject, and is predicated per se of all those, is predicated of that subject and its parts according to what it itself is when received by name and definition. On account of this it is evident that what I call of every and per se are conditions of the predicate, yet related to the subject. But that according to which it itself is is a condition of the subject, so that the sense is that the universal is the predicate of some subject, predicated of it with respect to all the parts of the subject, not according as they are parts, but according as they are named univocally and united in the form of the common species; and it belongs per se, or essentially, to all parts of the subject in such a way that it belongs to each insofar as it stands under the form of the species, and not according as it is determined in the substance and form of a part.
But per se and according to what it itself is are the same with respect to supposit, although these differ according to account; for they are the same as particular and universal are, because per se is more common than according to what it itself is, as will be evident a little below. And an example of this is that a point is present in line per se according to the first mode of speaking per se, as an essential principle not predicable according to a direct case; and straightness and curvature are present in line as properties, and in the second mode of speaking; and these are present in line in another mode according as it is line. But here it must be understood that these are present in line according to what it itself is, or according as it is line, according as line is contracted to the extension which happens between two points; and according to this straightness with its opposite is received through disjunction, so that it is said that a line extended between two points is straight or curved according as it is such a line. And in this mode, in the second mode of speaking per se, triangle according to what it itself is, that is, according as triangle is perfect, having the species and account of triangle, is two right angles through the equality of three angles to two right angles. The reason for this is that triangle, in the three angles by which it is terminated, is equal to two right angles. And we have already shown before that these things are understood of a rectilinear triangle, because if it has spherical lines or portions of a circle or curved lines, it can have three angles greater than three and two right angles.
But the universal is then said to be in demonstrative matters, according to the determination introduced, when it is demonstrated to exist in any one whatever, that is, in any part whatever of the subject, because otherwise it would not be of every, and it is shown first, that is, immediately, to be present in each through the first subject. And thus the first is that between which and the property no other subject intervenes, as what belongs to every triangle insofar as it is triangle, and is converted with it insofar as it is triangle, so that this subject is the cause of the property in such a way that it does not need something greater and higher than itself, which is figure in triangle, in order that the property flow from it; nor is the lesser and lower thing which is isosceles in triangle sufficient for causing the whole according to the scope and community of the predication of that property. For having three angles equal to two right angles and isosceles is too narrow for it to be able to cause the whole.
Unde duos rectos habere, neque cuilibet figurae inest: quod pro certo sequeretur, quod omni inesset figurae: et ideo non omni inest figurae: et tamen hanc passionem est demonstrare de figura, non qualibet sed de tali quae duos habet secundum aequalitatem ad tres, et illa est triangulus, quae est figura tres habens duobus rectis aequales. Sed tamen talis passio non cujuslibet figurae est, quia quadrati vel quadranguli non est: neque demonstrans eam de proprio subjecto in demonstrando utitur pro subjecto qualibet figura, sed illa sola quae in specie et forma triangulus est: quadrangulus enim, sicut diximus, figura est: non autem habet tres angulos duobus rectis aequales: sed isosceles habet quidem fortasse duobus rectis aequales tres angulos, sed non habet tres primum sive primo vel primitus, hoc est, sicut immediatum subjectum ex quo tota illa fluit passio. Et dico fortassis: quia jam fortuito sortitur aliquid, quod per aliud quoddam sortitur ipsum. Primum autem dico: quia isosceles non est primum sive immediatum subjectum passionis secundum se totius: sed dicitur capi in tempore secundum quod triangulus est: sed triangulus habet hanc passionem prius sive immediatius quam isosceles.
Id igitur subjectum quod demonstratur habere tres aequos duobus rectis quodlibet, hoc est, pro qualibet parte sua, et primum sive immediatum, ita quod non attribuatur ei passio propter aliud propinquius subjectum potissimum, huic primo inest et inesse attribuitur universale praedicatum quod est passio. Et hujus subjecti est demonstratio ostendens passionem inesse subjecto universaliter et per se. Et dico per se esse hujusmodi: quia ut est de hoc, sicut ante diximus, subjecto quod est triangulus: ita est de alio subjecto tali quodcumque est illud de quo passio demonstratur. Hujus autem talis subjecti passio talis est universaliter pro omnibus partibus conveniens. Aliorum autem subjectorum sive sint superiora sive inferiora, sunt quodammodo et non per se neque secundum ipsa: est enim superioris, sicut figurae, in quantum determinatur ad species hujus inferioris: inferioris autem est, ut isoscelis, in quantum stat in specie trianguli: et sic utriusque est non per se, sed quodammodo. Neque est isoscelis universaliter accepta passio in omni ambitu suae praedicationis, sed ut frequentius, hoc est, prout est in
Hence to have two right angles does not belong to every figure, which would follow for certain if it belonged to every figure; and therefore it does not belong to every figure. And nevertheless this property can be demonstrated of figure, not of any figure whatever, but of such a figure which has two according to equality to three, and that is triangle, which is a figure having three angles equal to two right angles. But nevertheless such a property is not of any figure whatever, because it is not of square or quadrangle; nor does the one demonstrating it of its proper subject, in demonstrating, use as subject any figure whatever, but only that which in species and form is triangle. For quadrangle, as we have said, is a figure, but it does not have three angles equal to two right angles. But isosceles indeed perhaps has three angles equal to two right angles, but it does not have the three first, or in the first way, or primarily, that is, as an immediate subject from which that whole property flows. And I say perhaps because it now obtains something by chance, which it obtains through some other thing. But I say first because isosceles is not the first or immediate subject of the property according to the whole of itself, but it is said to be taken in time according as it is triangle; but triangle has this property prior or more immediately than isosceles.
Therefore that subject which is demonstrated to have three angles equal to two right angles, any one whatever, that is, with respect to any part whatever of itself, and first or immediately, so that the property is not attributed to it on account of another nearer and most powerful subject, to this first subject the universal predicate which is the property is present and being present is attributed. And of this subject there is demonstration showing the property to be present in the subject universally and per se. And I say that this sort is per se because as it is concerning this subject, as we said before, which is triangle, so it is concerning another such subject, whatever that is about which the property is demonstrated. But the property of such a subject of this sort is such as belongs universally for all parts. But the properties of other subjects, whether they are higher or lower, belong in a certain way and not per se nor according to themselves. For it belongs to the higher, as to figure, insofar as it is determined to the species of this lower thing; but it belongs to the lower, as to isosceles, insofar as it stands in the species of triangle; and thus it belongs to each not per se, but in a certain way. Nor is isosceles a property accepted universally in the whole scope of its predication, but as more often, that is, insofar as it is in
Notes
- Aristotle, in the fifth book of first philosophy, text-commentary 23. (ARISTOTELES, In 5 primae philosophiae, tex. com. 23.) ↩
- Text-commentary 1. (Tex. com. 1.) ↩
- See the exposition of Themistius on that part: Whatever things, however, are neutrally present, and so forth, because he explains it otherwise than other expositors do. P. J. (Vide expositionem Themistii super illa parte: Quaecumque vero neutraliter insunt, etc., quia aliter exponit quam alii expositores. P. J.) ↩
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