Authors/Thomas Aquinas/metaphysics/liber4/lect8

Lecture 8

Latin	English
lib. 4 l. 8 n. 1 Ponit tertiam rationem, quae sumitur ex uno et diverso: et est ratio talis. Si affirmatio et negatio verificantur simul de eodem, omnia sunt unum. Hoc autem est falsum; ergo et primum. Circa hanc rationem tria facit. Primo ponit conditionalem et exemplificat, quia scilicet sequeretur si contradictiones simul verificantur de eodem, quod idem essent triremis, idest navis habens tres ordines remorum, et murus et homo.	636. Then he gives a third argument, which involves oneness and difference. The argument runs thus: if an affirmation and a negation are true of the same subject at the same time, all things will be one. But the consequent is false. Hence the antecedent must be false. In regard to this argument he does three things. First (343)C 636), he lays down a conditional proposition and gives an example, namely, that if contradictories are true of the same subject at the same time, it will follow that the same thing will be a trireme (i.e., a ship with three banks of oars), a wall and a man.
lib. 4 l. 8 n. 2 Secundo cum dicit quemadmodum est ostendit quod idem inconveniens sequitur ad duas alias positiones. Primo ad opinionem Protagorae, qui dicebat quod quicquid alicui videtur, hoc totum est verum; quia si alicui videtur quod homo non sit triremis, non erit triremis; et si alteri videtur quod sit triremis, erit triremis; et sic erunt contradictoria vera.	637. And this is what (344). Then he shows that the same impossible conclusion follows with regard to two other positions. He does this, first, with regard to the opinion of Protagoras, who said that whatever seems so to anyone is wholly true for him; for if it seems to someone that a man is not a trireme, then he will not be a trireme; and if it seems to someone else that a man is a trireme, he will be a trireme; and thus contradictories will be true.
lib. 4 l. 8 n. 3 Secundo ad opinionem Anaxagorae, qui dicebat omnes res simul esse, quasi nihil sit vere unum ab aliis determinatum, sed omnia sint unum in quadam confusione. Dicebat enim, quod quodlibet sit in quolibet, sicut in primo physicorum ostensum est. Quod ideo accidebat Anaxagorae, quia ipse videtur loqui de ente indeterminato, idest quod non est determinatum in actu. Et cum putaret loqui de ente perfecto, loquebatur de ente in potentia, sicut infra patebit. Quod autem est in potentia et non endelechia, idest in actu, est indefinitum. Potentia enim non finitur nisi per actum.	638. Second, he does this with regard to the opinion of Anaxagoras, who said that all things exist together, so that nothing which is truly one is distinguished from other things, but all are one in a kind of mixture. For he said that everything is found in everything else, as has been shown in Book I of the Physics. This is the position which Anaxagoras adopted because he seems to be speaking about indeterminate being, i.e., what has not been made actually determinate. And while he thought he was speaking about complete being, he was speaking about potential being, as will become clear below (355)C 667). But the indeterminate is what exists potentially and is not “complete,” i.e., actual; for potency is made determinate only by actuality.
lib. 4 l. 8 n. 4 Tertio cum dicit sed dicenda probat conditionalem primo propositam esse veram. Et primo quantum ad hoc quod omnia affirmative dicta unum essent. Secundo quantum ad hoc quod affirmationes a suis negationibus non distinguerentur in veritate et falsitate, ibi, et quia non est necesse et cetera. Dicit ergo primo, quod illud primum est ab eis supponendum ex quo ponunt affirmationem et negationem simul verificari de eodem, quod de quolibet est affirmatio et negatio vera. Constat enim quod de unoquoque magis videtur praedicari negatio alterius rei, quam negatio propria. Inconveniens enim esset si alicui inesset sua negatio et non inesset negatio alterius rei, per quam significatur quod illa res non inest ei: sicut si verum est dicere quod homo non est homo, multo magis est verum dicere quod homo non est triremis. Patet ergo, quod de quocumque necessarium est praedicari negationem, quod praedicatur de eo affirmatio. Et ita per consequens praedicabitur negatio, cum affirmatio et negatio sint simul vera; aut si non praedicabitur affirmatio, praedicabitur negatio alterius magis quam negatio propria. Sicut si triremis non praedicatur de homine, praedicabitur de eo non triremis, multo magis quam non homo. Sed ipsa negatio propria praedicatur, quia homo non est homo: ergo et negatio triremis praedicabitur de eo, ut dicatur quod homo non est triremis. Sed si praedicatur affirmatio, praedicabitur negatio, cum simul verificentur: ergo necesse est quod homo sit triremis et eadem ratione quodlibet aliud. Et sic omnia erunt unum. Hoc igitur contingit dicentibus hanc positionem, scilicet quod contradictio verificetur de eodem.	639. But the affirmation (345). Third, he proves that the first conditional proposition is true. He does this, first, on the grounds that all things would have to be affirmed to be one; and second (346:C 640), on the grounds that affirmations would not be distinguished from their negations from the viewpoint of truth and falsity (“And it also follows”). He accordingly says, first (345), that the first conditional proposition must be admitted by them inasmuch as they hold than an affirmation and a negation are true of the same subject at the same time because an affirmation and a negation are true of anything at all. For it is clear that the negation of some other thing seems to be predicable of each thing to a greater degree than its own negation. For it would be absurd if some subject should have its own negation predicated of it and not the negation of something else by which it is signified that this other thing is not predicable of it. For example, if it is true to say that a man is not a man, it is much truer to say that a man is not a trireme. Hence it is clear that anything of which a negation must be predicated must also have an affirmation predicated of it. Therefore a negation will be predicated of it since an affirmation and a negation are true at the same time; or if an affirmation is not predicated of it, the negation of the other term will be predicated of it to a greater degree than its own negation. For example, if the term trireme is not predicable of man, non-trireme will be predicated of him inasmuch as it may be said that a man is not a trireme. But if the affirmation is predicable, so also must the negation be, since they are verified of the same thing. A man, then, must be a trireme, and he must also be anything else on the same grounds. Hence all things must be one. Therefore this is what follows for those who maintain the position that contradictories are true of the same subject.
lib. 4 l. 8 n. 5 Deinde cum dicit et quia non deducit aliud inconveniens, quod scilicet non distinguatur negatio ab affirmatione in falsitate, sed utraque sit falsa. Dicit ergo quod non solum praedicta inconvenientia sequuntur ad praedictam positionem, sed etiam sequitur quod non sit necessarium affirmare et negare, idest quod non sit necessarium affirmationem vel negationem esse veram, sed contingit utramque esse falsam. Et sic non erit distantia inter verum et falsum. Quod sic probat.	640. And it also follows (346). He now draws the other impossible conclusion which follows from this view, namely, that a negation will not be distinguished from an affirmation as regards falsity, but each will be false. Thus he says that not only the foregoing impossible conclusions follow from the above-mentioned position, but also the conclusion that it is not necessary “either to affirm or to deny,” i.e., it is not necessary that either the affirmation or the negation of a thing should be true, but each may be false; and so there will be no difference between being true and being false. He’ proves this as follows.
lib. 4 l. 8 n. 6 Si verum sit quod aliquid sit homo et non homo, verum est quod id non erit homo, nec erit non homo. Et hoc patet. Horum enim duorum quae sunt homo et non homo, sunt duae negationes, scilicet non homo et non non homo. Si autem ex primis duabus fiat una propositio, ut dicamus, Socrates non est homo nec non homo, sequitur quod nec affirmatio nec negatio sit vera, sed utraque falsa.	641. If it is true that something is both a man and a not-man, it is also true that it is neither a man nor a not-man. This is evident. For of these two terms, man and not-man, there are two negations, not man and not not-man. And if one proposition were formed from the first two, for example, if one were to say that Socrates is neither a man nor a not-man, it would follow that neither the affirmation nor the negation is true but that both are false.
lib. 4 l. 8 n. 7 Deinde cum dicit amplius autem ponit quartam rationem quae sumitur ex certitudine cognitionis; et est talis. Si affirmatio et negatio simul verificantur, aut ita est in omnibus, aut ita est in quibusdam, et in quibusdam non: si autem non est verum in omnibus, illae, in quibus non est verum, erunt confessae, idest simpliciter et absolute concedendae, vel erunt certae, idest certitudinaliter verae secundum aliam translationem; idest in eis ita erit vera negatio, quod affirmatio erit falsa, vel e converso.	642. Again, either this (347). Then he gives a fourth argument, and this is based on certitude in knowing. It runs thus. If an affirmation and a negation are true at the same time, either this is true of all things, or it is true of some and not of others. But if it is not true of all, then those of which it is true will be “admitted”; i.e., they will be conceded simply and absolutely, or according to another translation “they will be certain,” i.e., true with certainty; that is, in their case the negation will be true because the affirmation is false, or the reverse.
lib. 4 l. 8 n. 8 Si autem hoc est verum in omnibus, quod contradictio verificetur de eodem, hoc contingit dupliciter. Uno modo quod de quibuscumque sunt verae affirmationes, sunt verae negationes, et e converso. Alio modo quod de quibuscumque verificantur affirmationes, verificentur negationes, sed non e converso.	643. But if it is true in all cases that contradictories are verified of the same subject, this might happen in two ways. In one way anything of which affirmations are true, negations are true, and the reverse. In another way anything of which affirmations are true, negations are true, but not the reverse.
lib. 4 l. 8 n. 9 Et si hoc secundum sit verum, sequitur hoc inconveniens, quod aliquid firmiter vel certitudinaliter est non ens; et ita erit firma opinio, quae scilicet est de negativa; et hoc ideo, quia negativa semper est vera, eo quod quandocumque est affirmativa vera, est etiam negativa vera. Non autem affirmativa semper erit vera, quia positum est, quod non de quocumque est vera negativa, sit vera affirmativa; et ita negativa erit firmior et certior quam affirmativa: quod videtur esse falsum: quia dato quod non esse sit certum et notum, tamen semper erit certior affirmatio quam negatio ei opposita, quia veritas negativae semper dependet ex veritate alicuius affirmativae. Unde nulla conclusio negativa infertur, nisi in praemissis sit aliqua affirmativa. Conclusio vero affirmativa ex negativa non probatur.	644. And if the second is true, this impossible conclusion will follow: there will be something that firmly or certainly is not; and so there will be an unshakeable opinion regarding a negative proposition. And this will be the case because a negation is always true since whenever an affirmation is true its negation is also true. But an affirmation will not always be true, because it was posited that an affirmation is not true of anything at all of which a negation is true; and thus a negation will be more certain and knowable than an affirmation. But this seems to be false because, even though non-being is certain and knowable, an affirmation will always be more certain than its opposite negation; for the truth of a negation always depends on that of some affirmation. Hence a negative conclusion can be drawn only if there is some kind of affirmation in the premises. But an affirmative conclusion can never be drawn from negative premises.
lib. 4 l. 8 n. 10 Si autem dicatur primo modo, scilicet quod de quibuscumque est affirmare, ita de eis est negare; similiter de quibuscumque est negare, de eis est affirmare, ut scilicet affirmatio et negatio convertantur: hoc contingit dupliciter: quia si semper negatio et affirmatio sunt simul verae, aut erit divisim dicere de utraque quod sit vera, verbi gratia, quod sit divisim dicere quod haec est vera, homo est albus, iterum haec est vera, homo non est albus: aut non est divisum utramque dicere veram sed solum coniunctim, ut si dicamus quod haec copulativa sit vera, homo est albus et homo non est albus.	645. Now if one were to speak in the first way and say that of anything of which an affirmation is true the negation is also true, and similarly that of anything of which the negation is true the affirmation is also true, inasmuch as affirmation and negation are interchangeable, this might happen in two ways. For if an affirmation and a negation are both true at the same time, either it will be possible to state what is true of each separately, for example, to say that each of these propositions is true separately—“Man is white” and “Man is not white”; or it will not be possible to state that each is true separately but only both together. For example, if we were to say that this copulative proposition is true —“Man is white and man is not white.”
lib. 4 l. 8 n. 11 Et siquidem dicamus hoc secundo modo, ut scilicet non sit utraque vera divisim sed solum coniunctim, tunc sequuntur duo inconvenientia: quorum primum est, quod non dicet ea, idest quod non asseret nec affirmationem nec negationem, et quod ambae erunt nihil, idest quod ambae sunt falsae: vel secundum aliam translationem et non erit nihil, idest sequitur quod nihil sit verum, nec affirmatio nec negatio. Et si nihil est verum, nihil poterit dici nec intelligi. Quomodo enim aliquis pronuntiabit vel intelliget non entia? Quasi dicat, nullo modo.	646. And if we were to speak in the second way and say that neither one is true separately but only both together, two impossible conclusions would then follow. The first is that “an opponent will not be saying what he professes to say,” i.e., he will assert neither the affirmation nor the negation of something, and “neither will exist,” i.e., both will be false; or according to another text, “nothing will exist,” i.e., it will follow that nothing is true, neither the affirmation nor the negation. And if nothing is true it will be impossible to understand or to express anything. For how can anyone understand or express non-being? Implied is the reply: in no way.
lib. 4 l. 8 n. 12 Secundum inconveniens est, quia sequitur quod omnia sint unum, quod in priori ratione est dictum. Sequitur enim quod sit idem homo et Deus et triremis, et etiam contradictiones eorum, scilicet non homo et non Deus et non triremis. Et sic patet, quod si affirmatio et negatio simul dicuntur de unoquoque, tunc nihil differt unum ab alio. Si enim unum ab alio differret, oporteret quod aliquid diceretur de uno, quod non diceretur de alio. Et sic sequeretur quod aliquid esset verum determinate et proprium huic rei, quod non conveniret alteri. Et sic non de quolibet verificaretur affirmatio vel negatio. Constat autem quod ea quae nullo modo differunt, sunt unum; et ita sequetur omnia unum esse.	647. The second impossible conclusion would be that all things are one, as has been stated in a previous argument (345:C 639). For it would follow that a man and God and a trireme, and also their contradictories, a notman, not-God and not-trireme, are the same. Thus it is clear that, if an affirmation and a negation are true of any subject at the same time, one thing will not differ from another. For if one were to differ from another, something would have to be predicated of the one which is not predicated of the other; and so it would follow that something is definitely and properly true of this thing which does not fit the other. Therefore an affirmation and a negation will not be true of anything whatever. But it is clear that things which differ in no way are one. Thus it would follow that all things are one.
lib. 4 l. 8 n. 13 Si autem dicatur primo modo, scilicet quod non solum coniunctim est dicere affirmationem et negationem, sed etiam divisim, sequuntur quatuor inconvenientia: quorum unum est, quod haec positio significat ipsum dictum, idest demonstrat hoc esse verum quod immediate est dictum. Unde alia litera habet accidit quod dictum est, scilicet quod omnia sunt unum; quia sic etiam similiter affirmatio et negatio de unoquoque dicetur, et non erit differentia unius ad aliud.	648. But if one were to speak in the first way and say that it is possible for an affirmation and a negation to be true, not only together but also separately, four impossible conclusions will follow. The first is that this position “indicates that this statement is true”; i.e., it proves that the statement just made is true. Hence another text reads, “the results described will follow,” i.e., all things will be one, because it will then be possible both to affirm and to deny each thing, and one will not differ from the other.
lib. 4 l. 8 n. 14 Secundum est quod omnes verum dicerent, quia quilibet vel dicit affirmationem vel negationem, et utraque est vera; et omnes mentientur, quia contradictorium eius quod quisque dicit, erit verum. Et idem etiam homo seipsum dicere falsum confitetur; quia cum dicit negationem esse veram, dicit se falsum dixisse cum dixit affirmationem.	649. A second impossible conclusion is that all will speak the truth, because anyone at all must make either an affirmation or a negation, and each will be true. And each man will also admit of himself that he is wrong when he says that the affirmation is true; for, since he says that the negation is true, he admits that he was in error when he made the affirmation.
lib. 4 l. 8 n. 15 Tertium est quia manifestum est quod adhuc non poterit esse perscrutatio vel disputatio. Non enim potest disputari cum aliquo qui nihil concedit. Ille enim nihil dicit, quia nec dicit absolute quod est ita, nec dicit quod non est ita; sed dicit quod est ita et non est ita. Et iterum ambo ea negat dicens quod nec est ita nec non ita, sicut ex praecedenti ratione apparet. Si enim non omnia ista neget, sequitur quod ipse noverit aliquid determinate verum; quod est contra positum. Vel secundum quod alia translatio habet, et planius, iam utique erit determinatum.	650. A third impossible conclusion is that up to this point there obviously could not be any investigation or dispute. For it is impossible to carry on a dispute with someone who admits nothing, because such a person really says nothing since he does not say absolutely that something is so or is not so; but he says that it is both so and not so. And again he denies both of these, for he says that it is neither so nor not so, as is evident from the preceding argument. For if he does not deny all of these he will know that something is definitely true, and this is contrary to his original position. Or according to another translation which expresses this more clearly, “there would already be some definite statement.”
lib. 4 l. 8 n. 16 Quartum sequitur per definitionem veri et falsi. Verum enim est cum dicitur esse quod est vel non esse quod non est. Falsum autem est cum dicitur non esse quod est, aut esse quod non est. Ex quo patet per definitionem veri et falsi, quod quando affirmatio est vera, tunc negatio est falsa: tunc enim dicit non esse, quod est: et si negatio est vera, tunc affirmatio est falsa: tunc enim dicitur esse de eo quod non est. Non ergo contingit vere idem affirmare et negare. Sed forte adversarius ad hoc ultimum poterit dicere, quod hic est petitio principii. Qui enim ponit contradictionem simul esse veram, non recipit hanc definitionem falsi, scilicet quod falsum est dicere quod non est esse, vel quod est non esse.	651. A fourth impossible conclusion will follow because of the definition of the true and the false. For truth exists when one says that what is, is, or that what is not, is not. But falsity exists when one says that what is, is not, or that what is not, is. Hence from the definition of the true and the false it is clear that, when an affirmation is true, its negation is false; for one then says that what is, is not. And when a negation is true, its affirmation is false; for what is not is then said to be. Therefore it is impossible both to affirm and to deny the same thing truly. But perhaps an opponent could say that this last argument is begging the questiofi; for he who claims that contradictories are true at the same time does not accept this definition of the false: the false is to say that what is not, is, or that what is, is not.