Authors/Thomas Aquinas/metaphysics/liber11/lect5

Lecture 5

Latin	English
lib. 11 l. 5 n. 1 Postquam ostendit philosophus quod principia communia demonstrationis sunt principaliter de consideratione huius philosophiae, hic determinat de primo principio inter ea. Necesse est enim quod sicut omnia entia reducuntur ad aliquod primum, ita oportet quod principia demonstrationis reducantur ad aliquod principium, quod principalius cadit in consideratione huius philosophiae. Hoc autem est, quod non contingit idem simul esse et non esse. Quod quidem ea ratione primum est, quia termini eius sunt ens et non ens, qui primo in consideratione intellectus cadunt.	2211. Having shown that a study of the common principles of demonstration belongs chiefly to the consideration of this philosophical science, the Philosopher now deals with the first of these principles (934)C 2212). For just as all beings must be referred to one first being, in a similar fashion all principles of demonstration must be referred to some principle which pertains in a more basic way to the consideration of this philosophical science. This principle is that the same thing cannot both be and not be at the same time. It is the first principle because its terms, being and non-being, are the first to be apprehended by the intellect.
lib. 11 l. 5 n. 2 Dividitur autem haec pars in duas. In prima determinat veritatem circa illud principium. In secunda excludit errorem, ibi, ad dicentem autem. Circa primum duo facit de isto principio. Primo dicit quod est quoddam principium demonstrativum in entibus circa quod non contingit mentiri, scilicet secundum interiorem rationem. Sed necessarium est semper facere contrarium, scilicet dicere verum circa ipsum. Et hoc principium est, quod non contingit idem esse et non esse secundum unum et idem tempus, et aliis conditionibus servatis quae consueverunt in contradictione apponi, scilicet secundum idem, simpliciter, et alia huiusmodi. Impossibile enim est quod aliquis opinetur hoc principium esse falsum: opinaretur enim contradictoria esse simul vera, et sic idem haberet simul contrarias opiniones: nam contrariae opiniones sunt quae sunt de contrariis. Sicut opinio, qua quis opinatur Socratem sedere, est contraria opinioni, qua quis opinatur eum non sedere.	2212. This part is divided into two members. In the first (934)C 2211) he establishes the truth of this principle. In the second (936:C 2214) he rejects an error (“Now anyone who”). In reference to the first part he does two things regarding this principle. First, he says that in regard to beings there is a principle of demonstration “about which it is impossible to make a mistake” (i.e., so far as its meaning is concerned), but of which we “must always do the contrary,” namely, acknowledge it as true. This principle is that the same thing cannot both be and not be at one and the same time, granted of course that the other conditions which it is customary to give in the case of a contradiction are fulfilled, namely, in the same respect, in an unqualified sense, and the like. For no one can think that this principle is false, because, if someone were to think that contradictories may be true at the same time, he would then have contrary opinions at the same time; for opinions about contradictories are contrary. For example, the opinion that “Socrates is sitting” is contrary to the opinion that “Socrates is not sitting.”
lib. 11 l. 5 n. 3 Et de talibus secundo dicit, quod de praedicto principio et similibus non potest esse simpliciter demonstratio, sed potest esse demonstratio ad hominem. Quod autem non possit simpliciter demonstrari, probat ex hoc, quod non contingit facere syllogismum ad hoc principium demonstrandum ex aliquo principio magis noto; quod oporteret si contingeret illud principium simpliciter demonstrare. Sed ad hominem contingit hoc principium demonstrare, qui concedit aliquid aliud, licet minus notum, et hoc negat.	2213. And while (935). Second, he says that, while there cannot be demonstration in the strict sense of the above-mentioned principle and other similar ones, one may offer an argument ad hominem in support of it. That it cannot be demonstrated in the strict sense he proves thus: no one can prove this principle by constructing a syllogism from some principle which is better known. But such would be necessary if that principle were to be demonstrated in the strict sense. However, this principle can be demonstrated by using an argument ad hominem against one who admits some other statement, though less known, and denies this one.
lib. 11 l. 5 n. 4 Deinde cum dicit ad dicentem excludit opinionem negantium illud principium; et dividitur in partes duas. Primo disputat contra negantes hoc principium. Secundo ostendit quomodo ad hanc opinionem possit responderi, ibi, solvetur autem. Circa primum, duo facit. Primo disputat contra negantes hoc principium simpliciter. Secundo descendit ad speciales opiniones, ibi, cito autem. Circa primum duo facit. Primo ponit modum disputandi contra hunc errorem; dicens, quod ille, qui contra ponentem contradictorias propositiones esse veras, vult ostendere quod sit falsum, debet sumere aliquid tale quod idem sit huic principio,- scilicet non contingere idem esse et non esse, secundum idem tempus,- sed non videatur idem. Si enim videretur idem, non concederetur ab adversario. Si autem non esset idem, non posset concludere propositum, quia huiusmodi principium non potest ex notioribus ostendi. Et ideo hoc solum modo potest sumi demonstratio contra dicentem, quod contradictoria verificantur de eodem; ut scilicet illud quod sumitur sit idem conclusioni, sed non videatur idem.	2214. Now anyone who (936). Then he rejects the opinion of those who deny this principle; and this is divided into two parts. First (936:C 2214), he argues against those who deny this principle. Second (943:C 2225), he shows how one can meet this opinion (“Now this difficulty”). In regard to the first he does two things. First (936:C 2214), he argues against those who unqualifiedly deny this principle. Second (940:C 2221), he turns his attention to certain particular opinions (“And perhaps”). In regard to the first he does two things. First, he gives the method of arguing against this error. He says that in arguing against an opponent who claims that contradictory propositions may be true, anyone who wants to show that this opinion is false ought to take some such principle which is the same as this one—that the same thing cannot both be and not be at the same time—but apparently is not the same. For, if it were evidently the same, it would not be admitted by an opponent. Yet if it were not the same, he could not prove his thesis, because a principle of this kind cannot be demonstrated from some principle which is better known. Hence, it is only in this way that a demonstration can be made against those who say that contradictories may be true of the same subject, namely, by assuming as a premise what is in fact the same as the conclusion but apparently is not.
lib. 11 l. 5 n. 5 Futuros itaque secundo procedit ad disputandum contra praedictum errorem. Et circa hoc facit tres rationes. Quarum prima est, quod si duo homines debeant adinvicem communicare rationem, ut scilicet unus alteri rationem suam communicet disputando, oportet unum ipsorum intelligere aliquid, quod ab alio dicitur: quia si hoc non esset, non communicarent adinvicem in sermone secundum rationem. Et ita frustra acciperetur disputatio contra eum, qui hoc negaret.	2215. Accordingly (937). Second, he begins to argue dialectically against the above-mentioned error; and in regard to this he gives three arguments, First, he argues as follows: if two men are to join in a discussion in such a way that one may communicate his view to the other in a dispute, each must understand something that the other is saying. For if this were not the case, no statement would be understood by both of them; and thus an argument with an opponent would be pointless.
lib. 11 l. 5 n. 6 Si autem unus ex eis intelligeret quod alius dicit, oportet quod unumquodque nominum quae proferuntur, sit notum in sua significatione; et per consequens, quod significet aliquid, et non multa, sed solum unum. Et si significet multa, quod manifestetur ad quod illorum multorum significandum utatur nomine; alias nesciret unus, quid alius vellet dicere.	2216. However, if one of them is to understand what the other is saying, each of the terms used must be understood according to its proper meaning and must therefore signify some one thing and not many things. And if it should signify many, it will be necessary to make clear which of the many things it signifies; otherwise one would not know what the other person means.
lib. 11 l. 5 n. 7 Hoc igitur supposito, quod nomen significet unum, manifestum est, quod ille, qui dicit esse hoc, et non est hoc, puta quod Socrates est homo, et non homo, illud unum quod attribuit Socrati, quod scilicet est homo, negat cum adiungit quod non est homo: et sic negat iam quod primo significavit. Unde relinquitur quod nomen non significet id quod significat, quod est impossibile. Sequitur ergo quod si nomen aliquid determinate significat, quod impossibile est contradictionem verificari de eodem.	2217. Now granted that a term signifies one thing, it is evident that one who says both that this is and that this is not, for example, that Socrates is a man and that he is not a man, denies the one thing which he attributed to Socrates, namely, that he is a man, when he adds that he is not a man; and thus he denies what he first signified. Hence it follows that a word does not signify what it signifies. But this is impossible. Consequently, if a term signifies some definite thing, the contradictory cannot be truly affirmed of the same subject.
lib. 11 l. 5 n. 8 Secundam rationem ponit ibi, adhuc autem quae talis est. Si nomen significet aliquid, et hoc quod significatur per nomen verificatur de eodem de quo primo praedicatur nomen, necesse est hoc inesse ei, de quo praedicatur nomen, dum propositio vera fuit. Manifestum est enim quod haec conditionalis est vera - si Socrates est homo, Socrates est homo. Omnis autem conditionalis vera est necessaria. Unde necesse est, quod si consequens sit verum quod antecedens sit verum; quoniam concluditur quod necesse est quamlibet propositionem esse veram dum vera est. Sed quod est aliquando non contingit tunc non esse, quia necesse esse et non contingens non esse aequipollent. Ergo dum haec est vera - Socrates est homo - non contingit hanc esse veram - Socrates non est homo. Et sic patet quod non contingit oppositas affirmationes et negationes simul verificari de eodem.	2218. Again, if a term (938). Then he gives the second argument, which runs as follows: if a term signifies some attribute, and the attribute signified by the term is truly affirmed of the same subject of which the term is first predicated, this attribute must belong to the subject of which the term is predicated so long as the proposition is true. For this conditional proposition, “If Socrates is a man, Socrates is a man,” is clearly true. Now every true conditional proposition is a necessary one. Hence, if the consequent is true, the antecedent must be true. But what is, cannot sometimes not be, because to be necessary and to be incapable of not being are equivalent. Therefore so long as the proposition “Socrates is a man” is true, the proposition “Socrates is not a man” cannot be true. Thus it is evident that opposite affirmations and negations cannot be true of the same subject at the same time.
lib. 11 l. 5 n. 9 Tertiam rationem ponit ibi, adhuc autem quae talis est. Si affirmatio non est vera magis quam negatio ei opposita, ille qui dicit Socratem esse hominem, non magis verum dicit quam ille qui dicit Socratem non esse hominem. Sed manifestum est, quod ille qui dicit hominem non esse equum, aut magis verum dicit, aut non minus, quam ille, qui dicit hominem non esse hominem. Ita ergo per locum a simili vel a minori, verum dicet, qui hominem dicet non esse equum. Sed, si opposita contradictorie sunt simul vera: si haec est vera - homo non est equus,- et haec erit vera - homo est equus. Et ita sequitur, quod homo sit equus et quodcumque aliud animalium.	2219. Again, if the affirmation (939). Then he gives the third argument, which is as follows: if an affirmation is not truer than the negation opposed to it, one who says that Socrates is a man does not speak with greater truth than one who says that Socrates is not a man. But it is evident that one who says that a man is not a horse speaks either with greater or with no less truth than one who says that a man is not a man. Hence, according to this argument, he who says that a man is not a horse will speak with equal or no less truth. But if contradictory opposites are true at the same time, for example, if the proposition “Man is not a horse” is true, and the proposition “Man is a horse” is also true, then it follows that a man is a horse and also any other animal.
lib. 11 l. 5 n. 10 Sed, quia posset aliquis calumniari praedictas rationes, ex hoc quod ea quae assumuntur in eis sunt minus nota quam conclusio quae intenditur; ideo respondet dicens quod nulla praedictarum rationum est demonstrativa simpliciter, sed tamen potest esse demonstratio ad hominem qui ponit hanc rationem, quem oportebit concedere ea quae assumuntur, licet sint minus nota simpliciter quam id quod negat.	2220. But because someone could criticize the foregoing arguments on the grounds that the things assumed in them are less known than the intended conclusion, he therefore answers this by saying that no one of the foregoing arguments is demonstrative in the strict sense, although there can be an argument ad hominem against an opponent who gives this argument, because the things assumed must be admitted to be true even though they are less known, absolutely than what he denies.
lib. 11 l. 5 n. 11 Deinde cum dicit cito autem excludit praedictum errorem descendendo ad speciales opinantes. Et primo ad Heraclitum. Secundo ad Protagoram, ibi, simile autem. Ponebat autem Heraclitus duo, scilicet quod affirmatio et negatio sit simul vera. Ex quo sequebatur quod omnis propositio tam affirmativa quam negativa sit vera. Item ponebat quod inter affirmationem et negationem sit aliquod medium. Et sic sequebatur quod contingeret neque affirmationem neque negationem esse veram. Et per consequens omnem propositionem esse falsam.	2221. And perhaps (940). Then he rejects the above error by considering certain particular thinkers. He does this, first (940:C 2221), with regard to Heraclitus; and second (942:C 2224), with regard to Protagoras (“The statement”). Now Heraclitus posited two things: first, that an affirmation and a negation may be true at the same time (and from this it would follow that every proposition, affirmative as well as negative, is true); and second, that there may be an intermediate between affirmation and negation (and from this it would follow that neither an affirmation nor a negation can be true). Consequently every proposition is false.
lib. 11 l. 5 n. 12 Primo ergo inducit rationem contra primum. Secundo contra secundum, ibi, adhuc autem. Dicit ergo, quod de facili aliquis hoc modo disputando ad hominem coget ipsum Heraclitum, qui fuit auctor huius propositionis, confiteri quod oppositae propositiones non verificantur de eodem. Videtur enim hanc opinionem accepisse quod verificentur de eodem, ex hoc quod non intellexit seipsum quid diceret. Hoc autem modo cogeretur negare quod dicit: quia si illud quod dictum est ab eo, verum est, scilicet quod contingat idem secundum unum et idem tempus esse et non esse, sequitur quod hoc ipsum non erit verum. Sicuti enim si divisim accipiantur affirmatio et negatio, non magis vera est affirmatio quam negatio, ita et si accipiantur affirmatio et negatio simul tamquam ex eis una affirmatio fiat, non erit minus negatio vera huius totius compositi ex affirmatione et negatione, quam ipsa tota affirmatio opposita. Manifestum est enim quod contingit aliquam propositionem copulativam esse veram, sicut aliquam simplicem propositionem, et contingit accipere eius negationem. Sive autem illa copulativa componatur ex duabus affirmativis, sicut cum dicitur - Socrates sedet et disputat,- sive ex duabus negativis, sicut cum dicitur - verum esse Socratem non esse lapidem neque asinum,- sive ex affirmatione et negatione, ut cum dicitur,- verum est Socratem sedere et non disputare,- semper tamen copulativa verificata sumitur in virtute unius affirmativae. Et ille qui dicit eam esse falsam, assumit negationem quasi totius copulativae. Qui ergo dicit simul esse verum, hominem esse et non esse, assumit hoc ut quamdam affirmationem; et hoc non esse verum est eius negatio. Si ergo affirmatio et negatio est simul vera, sequitur quod haec etiam negatio sit vera, qua dicitur non esse verum, scilicet quod affirmatio et negatio sint simul vera. Oportet enim, si aliqua negatio est simul vera cum affirmatione sibi opposita, quod omnis negatio sit simul vera cum affirmatione sibi opposita. Eadem enim est ratio in omnibus.	2222. First (940)C 2222), he raises an argument against Heraclitus’ first position; and second (941:C 2223), against his second position (“Again, if it is possible”). He accordingly says, first (940), that by giving an argument ad hominem in this way one may easily bring even Heraclitus, who was the author of this statement, to admit that opposite propositions may not be true of the same subject. For he seems to have accepted the opinion that they may be true of the same subject because he did not understand his own statement. And he would be forced to deny his statement in the following way: if what he said is true, namely, that one and the same thing can both be and not be at one and the same time, it follows that this very statement will not be true; for if an affirmation and a negation are taken separately, an affirmation is not truer than a negation; and if an affirmation and a negation are taken together in such a way that one affirmation results from them, the negation will not be less true of the whole statement made up of the affirmation and the negation than of the opposite affirmation. For it is clearly possible for some copulative proposition to be true, just as for some simple proposition; and it is possible to take its negation. And whether the copulative proposition be composed of two affirmative propositions, as when we say “Socrates is sitting and arguing,” or of two negative propositions, as when we say “It is true that Socrates is not a stone or an ass,” or of an affirmative proposition and a negative proposition, as when we say “It is true that Socrates is sitting and not arguing,” nevertheless a copulative proposition is always taken to be true because one affirmative proposition is true. And he who says that it is false takes the negation as applying to the whole copulative proposition. Hence he who says that it is true that man is and is not at the same time, takes this as a kind of affirmation; and that this is not true is the negation of this. Hence, if an affirmation and a negation are true at the same time, it follows that the negation which states that this is not true, i.e., that an affirmation and a negation are true at the same time, is equally true. For if any negation is true at the same time as the affirmation opposed to it, every negation must be true at the same time as the affirmation opposed to it; for the reasoning is the same in all cases.
lib. 11 l. 5 n. 13 Deinde cum dicit adhuc autem inducit rationem contra hoc, quod ponebatur quod nulla affirmatio sit vera. Si enim nihil contingat verum affirmare, qui autem dicit nullam affirmationem veram esse, aliquid affirmat, hoc scilicet quod verum sit nullam affirmationem esse veram; ergo hoc ipsum falsum erit. Et si aliquid affirmative dictum verum sit, removebitur opinio talium qui contra omnia instant. Et qui ista positione utuntur, auferunt totaliter disputationem; quia si nihil est verum, non potest aliquid concedi ex quo disputatio possit procedere. Et si affirmatio et negatio sint simul vera, non erit significare aliquid per sermonem, ut supra dictum est. Et sic cessabit disputatio.	2223. Again, if it is possible (941). Then he introduces an argument against the second position of Heraclitus: that no affirmation is true. For if it is possible to affirm that nothing is true, and if one who says that no affirmation is true does affirm something, namely, that it is true that no affirmation is true, then this statement will be false. And if some affirmative statement is true, the opinion of people such as those who oppose all statements will be rejected. And those who adopt this position destroy the whole debate, because if nothing is true, nothing can be conceded on which an argument may be based. And if an affirmation and a negation are true at the same time, it will be impossible to signify anything by a word, as was said above (937:C 2215), and then the argument will cease.
lib. 11 l. 5 n. 14 Deinde cum dicit simile autem descendit ad opinionem Protagorae: et dicit quod id quod dictum est a Protagora, simile est dictis ab Heraclito, et ab aliis qui ponunt affirmationem et negationem simul esse veram. Dicit enim Protagoras quod homo est mensura omnium rerum, scilicet secundum sensum et intellectum, ut in nono dictum est: quasi esse rei sequatur apprehensionem intellectus et sensus. Et sic qui dicit hominem esse mensuram omnium, nihil aliud dicit quam hoc esse verum quod videtur unicuique. Quo posito sequitur quod idem sit et non sit, et quod idem simul sit bonum et malum. Et simile est in aliis oppositis, eo quod multoties videtur hominibus aliquibus aliquid esse bonum, et aliis videtur contrarium, et ipsum videri est mensura rerum secundum opinionem Protagorae; ut scilicet intantum sit verum rem esse, inquantum videtur.	2224. The statement (942). Here he considers the opinion of Protagoras. He says that the statement made by Protagoras is similar to the one made by Heraclitus and by others who claim that an affirmation and a negation are true at the same time. For Protagoras says that man is the measure of all things, i.e., according to the intellect and the senses, as has been explained in Book IX (753:C 1800), as if the being of a thing depended upon intellectual and sensory apprehension. And one who says that man is the measure of all things merely says that whatever appears so to anyone is true. But if this is maintained, it follows that the same thing both is and is not and is both good and evil at the same time. The same thing is also true of other opposites, because often something seems to be good to some and just the opposite to others, and the way in which things seem or appear is the measure of all things according to the opinion of Protagoras; so that, inasmuch as a thing appears, to that extent it is true.