Libro I, lezione XXXVIIIDEMONSTRATIO UNIVERSALIS POTIOR EST DEMONSTRATIONE PARTICULARI

Amplius si demonstratio est syllogismus demonstrativus causae et propter quid, universale autem magis est causa: cui enim per se inest aliquid, hoc idem ipsum causa est, universale autem primo est cui inest per se; causa ergo universale est. Quare et demonstratio dignior est: magis enim causa est et quod propter quid est.

Amplius usque ad hoc quaerimus propter quid, et tunc opinamur scire, cum non sit aliquod aliud quam hoc, aut quod fiat aut quod sit: finis enim et terminus ultimus iam sic est. Ut cuius causa venit? ut accipiat argentum: hoc autem est, quatenus reddat cui debuit; hoc autem est, ut non iniuste agat; et sic procedentes, cum non sit amplius propter aliud neque alterius causa, propter hoc sicut propter finem dicimus venire et esse et fieri, et tunc est cognoscere magis propter quid venit. Si igitur se habet similiter in aliis causis et quae sunt propter quid; in iis autem quaecunque causae sic sunt sicut quae est cuius causa, sic scimus maxime; et in aliis igitur tunc maxime scimus, quando non amplius sit hoc quoniam aliud est. Cum igitur cognoscatur quidem quod quattuor, qui sunt extra, aequales sunt, quoniam isosceles, adhuc deest propter quid, quia triangulus, et hoc quia est figura rectilinea. Si autem hoc non amplius propter quid aliud, tunc maxime scimus: et universale autem tunc; universalis itaque potior est.

Amplius quantocunque aliquid secundum partes est, in infinita cadit; universale autem in simplex et finem est. Secundum quod sunt infinita, non sunt scibilia, sed secundum quod sunt finita, scibilia sunt. Secundum itaque quod universalia sunt, magis sunt scibilia quam quae sunt secundum partem. Demonstrabilia ergo magis sunt universalia. De magis demonstrabilibus autem magis est demonstratio: simul enim magis ad aliquid sunt. Dignior ergo universalis est quam particularis, et magis demonstratio est.

Amplius si magis praeponenda est secundum quam hoc et aliud, quam secundum quam hoc solum cognovit; universale autem habens, cognovit et particulare; hoc autem, universale non scivit. Quare et sic utique magis praeponenda erit.

Amplius autem et sic. Universale enim magis demonstrare est, quod est per medium demonstrare cum propinquius sit principio. Proximum autem est immediatum; hoc autem est principium. Si igitur quae ex principio est, ea quae non est ex principio, et quae magis etiam ex principio, ea quae minus est, certior est demonstratio, est autem huiusmodi universalis magis; dignior utique erit universalis magis. Ut si oportet demonstrare A de D, media autem sint in quibus est B C, magis autem sursum sit B: quare si per B, universalis magis est. Sed eorum quae dicta sunt, quaedam logica sunt.

Maxime autem manifestum est quod universalis magis praecipua sit, quoniam propositionum hanc quidem priorem habentes, scimus quodammodo et posteriorem, et habemus potentia; ut si aliquis cognovit quod omnis triangulus habet angulos tres aequales duobus rectis, scivit quodammodo quod isosceles duobus rectis potentia sit, et si non cognovit isoscelem, quod triangulus sit; hanc autem habens propositionem universale nullo modo cognovit, neque potentia neque actu.

Et universalis quidem intelligibilis est: sed particularis in sensu perficitur. Quod universalis igitur dignior sit particulari, tot nobis dicta sint.

La versione latina commentata da san Tommaso, nel testo dell'edizione leonina.

As one demonstration is universal, but another particular, one also affirmative, but the other negative, it is questioned which is preferable, likewise also about what is called direct demonstration, and that which leads to the impossible. Let us first then consider the universal and the particular, and having explained this, speak of what is called direct demonstration, and that to the impossible.

Perhaps then to some considering the matter in this way, the particular may appear the better, for if that demonstration is preferable, by which we obtain better knowledge, for this is the excellence of demonstration, but we know each thing better when we know it per se, than when through something else, (as we know Coriscus is a musician, when we know that Coriscus is a musician rather than when we know that a man is a musician, and likewise in other things,) but the universal demonstrates because a thing is something else, not because it is that which it is, as that an isosceles triangle (has two right angles), not because it is isosceles, but because it is a triangle,) but the particular demonstrates because a thing is what it is, if then the demonstration per se is preferable, and the particular is such rather than the universal, particular demonstration would be the better. Besides, if the universal is nothing else than particulars, but demonstration produces opinion that this thing is something according to which it demonstrates, and that a certain nature of this kind is in things which subsist, (as of triangle besides particular (triangles), and of figure besides particular (figures), and of number besides particular (numbers), but the demonstration about being is better than that about non-being, and that through which there is no deception than that through which there is, but universal demonstration is of this sort, (since men proceeding demonstrate as about the analogous,¹ as that a thing which is of such a kind as to be neither line nor number, nor solid nor superficies, but something besides these, is analogous,) if then this is more universal, but is less conversant with being than particular, and produces false opinion, universal will be inferior to particular demonstration.

First then may we not remark that one of these arguments² does not apply more to universal than to particular demonstration? For if the possession of angles equal to two right angles is inherent, not in respect of isosceles, but of triangle, whoever knows that it is isosceles knows less essentially³ than he who knows that it is triangle. In short, if not so far as it is triangle, he then shows it, there will not be demonstration, but if it is, whoever knows a thing so far as it is what it is, knows that thing more.⁴ If then triangle is of wider extension (than isosceles), and there is the same definition, and triangle is not equivocal, and the possession of two angles equal to two right angles is inherent in every triangle, triangle will have such angles, not so far as it is isosceles, but the isosceles will have them, so far as it is triangle. Hence he who knows the universal, knows more in regard to the being inherent than he who knows particularly, hence too the universal is better than the particular demonstration. Moreover if there is one certain definition, and no equivocation, the universal will not subsist less, but rather more than certain particulars, inasmuch as in the former there are things incorruptible, but particulars are more corruptible.⁵ Besides, there is no necessity that we should apprehend this (universal) to be something besides these (particulars), because it shows one thing, no more than in others which do not signify substance, but quality, or relation, or action, but if a person thinks thus, it is the hearer, and not demonstration, which is to blame.⁶ Again, if demonstration is a syllogism, showing the cause and the why, the universal indeed is rather causal, for that with which any thing is essentially present, is itself a cause to itself, but the universal is the first, therefore the universal is cause. Wherefore the (universal) demonstration is better, since it rather partakes of the cause and the why, besides up to this we investigate the why, and we think that then we know it, when this is becoming, or is, not because something else (is), for thus there is the end and the last boundary. For example, on what account did he come ? that he might receive money, but this that he might pay his debts, this that he might not act unjustly, and thus proceeding, when it is no longer on account of something else, nor for the sake of another thing, then we say that he came, and that it is, and that it becomes on account of this as the end, and that then we especially know why he came. If then the same occurs, as to all causes and inquiries into the why, but as to things which are so causes as that for the sake of which, we thus especially know, in other things also we then chiefly know, when this no longer subsists because another thing does.⁷ When therefore we know that the external angles are equal to four right angles, because it is isosceles, the inquiry yet remains, why because isosceles, because it is a triangle, and this because it is a rectilinear figure. But if it is this no longer on account of something else, then we pre-eminently know, then also universally, wherefore the universal is better.

Again, by how much more things are according to the particular, do they fall into infinites, but the universal tends to the simple and the finite, so far indeed as they are infinite, they are not subjects of science, but so far as they are finite they may be known, wherefore so far as they are universal, are they more objects of scientific knowledge, than so far as they are particular. Universals however are more demonstrable, and of things more demonstrable is there pre-eminent demonstration, for relatives are at one and the same time more, whence the universal is better, since it is demonstration pre-eminently. Besides, that demonstration is preferable, according to which this and something else are known, to that, by which this alone is known, now he who has the universal knows also the particular, but the latter does not know the universal, wherefore even thus the universal will be more eligible. Again, as follows: it is possible rather to demonstrate the universal, because a person demonstrates through a medium which is nearer to the principle, but what is immediate is the nearest and this is the principle; if then that demonstration which is from the principle is more accurate than that which is not from the principle, the demonstration which is in a greater degree from the principle, is more accurate than that which is from it in a less degree. Now the more universal is of this kind, wherefore the universal will be the better, as if it were required to demonstrate A of D, and the media should be B C, but B the higher, wherefore the demonstration through this is more universal.

Some of the above arguments are logical, it is chiefly clear however that the universal is more excellent, because when of two propositions we have that which is the prior, we also in a certain degree know and possess in capacity that which is posterior; thus if a man knows that every triangle has angles equal to two right, he also in a certain respect knows in capacity that an isosceles triangle has angles equal to two right, even if he does not know that the isosceles is a triangle, but he who has this proposition by no means knows the universal, neither in capacity nor in energy. The universal proposition also is intuitively intelligible, but the particular ends in sense.1⁸

That universal is better than particular demonstration, let so much be alleged, but that the affirmative is preferable to the negative, will be evident from this. Let that demonstration be better, cæteris paribus, which consists of fewer postulates, or hypotheses, or propositions. For if they¹ are similarly known, quicker knowledge will be obtained through these, which is more eligible. The reason however of this proposition, that that which consists of fewer is better, universally is this; for if the media are similarly known, but things prior are more known, let the demonstration be through the media of B C D, that A is present with E, but through F G, that A is present with E.² That A is present with D, and that A is present with E subsists similarly,|| but that A is with D, is prior and more known than that A is with E, for that is demonstrated ¶ Viz. A E. through this, and that is more credible through which (a thing is demonstrated). Also the demonstration which is through fewer things is therefore better, cæteris paribus; both³ then are demonstrated through three terms, and two propositions, but the one assumes that something is, and the other, that something is and is not,⁴ hence through a greater number of things (the demonstration is made) so that it is the worse.

Moreover since it has been shown impossible for a syllogism to be produced with both propositions negative, but that one must of necessity be such (negative), and the other that a thing is present with, (that is affirmative,) we must in addition to this assume this,|| for it is necessary that affirmative (propositions) when the demonstration is increased, should become more, but it is impossible that the negatives should be more than one in every syllogism. For let A be present with nothing of those with which B is, but B be present with every C, if indeed, again, it should be necessary to increase both propositions, a middle must be introduced.⁵ Of A B then let the middle be D, but of B C let the middle be E, E then is evidently affirmative, but D is affirmative indeed of B, yet is placed negatively as regards A, since it is necessary that D should be present with every B, but A with no D; there is then one negative proposition, viz. A D. The same mode also subsists in other syllogisms, for the middle of affirmative terms is always affirmative in respect of both (extremes), but in the case of a negative (syllogism), the middle must be necessarily negative in respect to one of the two,|| so there is one proposition of this kind, but the others are affirmative. If then that is more known and credible through which a thing is demonstrated, but the negative is shown through the affirmative, and the latter not through the former, this, since it is prior, more known, and more credible, will be better. Again, since the principle of syllogism is an universal immediate proposition, but the universal proposition in an ostensive (demonstration) is affirmative, but in a negative is negative, and since the affirmative is prior to, and more known than, the negative, for negation is known through affirmation, and affirmation is prior, just as being is prior to not being, therefore the principle of affirmative is better than that of negative demonstration, but that which uses better principles is better. Moreover it partakes more of the nature of principle, since without affirmative there is no negative demonstration.⁶

I capitoli interi, nella traduzione di Octavius Freire Owen (London: George Bell & Sons, 1889 (Bohn's Classical Library), vol. I, from the plates of the first edition (London: H. G. Bohn, 1853), same pagination).