Authors/Thomas Aquinas/posteriorum/L1/Lect34

Lecture 34 Logical reasons why one does not proceed to infinity in predicates

Latin	English
	Lecture 34 (83a36-84a7) LOGICAL REASONS WHY ONE DOES NOT PROCEED TO INFINITY IN PREDICATES
lib. 1 l. 34 n. 1 Praemissis his, quae necessaria sunt ad propositum demonstrandum, de distinctione praedicatorum ad invicem, hic accedit ad propositum ostendendum, scilicet quod non procedatur in praedicatis in infinitum. Et dividitur haec pars in partes duas, secundum duos modos quibus ostendit propositum. Secunda pars incipit ibi: adhuc autem alius et cetera. Circa primum duo facit: primo, ostendit quod non est procedere in infinitum in praedicatis per modum circulationis; secundo, quod non procedatur in infinitum in eis secundum rectitudinem in sursum neque in deorsum; ibi: sed utique quod neque in sursum et cetera. Circa primum tria facit: primo, praemissis suppositis, addit quaedam adhuc necessaria ad propositum ostendendum; secundo, ex his et aliis praemissis concludit propositum; ibi: impossibile est aeque praedicari etc.; tertio, probat; ibi: aut enim sicut substantia et cetera.	Having set forth the distinction of predicates from one another as a necessary preliminary to demonstrating his proposition, the Philosopher now undertakes to show his proposition, namely, that there is no infinite process in predicates. And his treatment falls into two parts, according to the two ways in which he shows his proposition, the second part beginning at (83b33). Concerning the first he does two things. First, he shows that one does not proceed to infinity in predicates after the manner of circularity (see Lect. 8). Secondly, that one does not proceed to infinity in a direct line upwards or downwards (83b13). Concerning the first he does three things. First, granting what has gone before, he adds certain things required for showing his proposition. Secondly, from these and other established facts he concludes the proposition (83a37). Thirdly, he proves it (8309).
lib. 1 l. 34 n. 2 Primo ergo proponit duo: quorum unum est, quia cum praedicatum, quod significat accidens, significet aliquod genus accidentis, puta qualitatem, non potest esse quod duo se habeant hoc modo ad invicem, quod primum sit qualitas secundi, et secundum sit qualitas primi; alia est enim ratio qualitatis, et eius cui qualitas inest. Secundum est, quod universaliter non est possibile quod qualitas habeat quamcunque aliam qualitatem sibi inhaerentem; quia nullum accidens est subiectum alterius accidentis per se loquendo. Soli enim substantiae convenit proprie ratio subiecti.	First, therefore (83a6) he proposes two things: one of these is that since a predicate which signifies an accident signifies some genus of accident, such as quality, it cannot occur that two things be so related to one another that the first is a quality of the second and the second a quality of the first: for the nature of a quality and that of which it is the quality are diverse. The second is that universally it is not possible that a quality have some other quality inhering in it, because no accident is the subject of another accident, absolutely speaking. For to substance alone does the notion of subject properly belong.
lib. 1 l. 34 n. 3 Deinde cum dicit: impossibile est aeque etc., proponit, quasi ex praemissis concludens, quod intendit probare, et dicit: si ista sunt vera, quae praemissa sunt, impossibile est quod fiat mutua praedicatio ad invicem sic, idest secundum aliquem praedictorum modorum. Non autem ita hoc dicitur, quin contingat vere praedicari unum de alio, et e converso. Dicimus enim vere quod homo est albus, et album est homo. Sed hoc non fit aeque, idest secundum aequalem rationem praedicandi. Et similiter est in praedicatis essentialibus.	Then (83a37) he proposes, as though concluding from these antecedents, what he intends to prove. He says, “If our preliminary rules are true, it is impossible that there be equal reciprocal predication,” i.e., according to any of the above-mentioned ways. But this does not exclude the possibility of one thing’s being truly predicated of another and conversely. For we say truly that man is white and that something white is a man. However, this is not done equally, i.e., according to an equal manner of predicating. And it is the same in essential predicates.
lib. 1 l. 34 n. 4 Deinde cum dicit: aut enim sicut substantia etc., ostendit propositum: et primo, in praedicatis essentialibus; secundo, in accidentalibus; ibi: verum etiam ipsius qualis et cetera. Circa primum tria facit: primo, ponit quamdam divisionem essentialium praedicatorum; secundo, resumit quoddam, quod supra probatum est; ibi: haec autem ostensa etc.; tertio, probat propositum; ibi: si quidem igitur genera et cetera.	Then (83a39) he shows the proposition. First, in essential predicates Secondly, in accidental ones (83b10). In regard to the first he does three things. First, he lays down a division of essential predicates. Secondly, he recalls something established above (83b1). Thirdly, he proves the proposition (83b8).
Dicit ergo primo, quod ad ostendendum quod non sit ad invicem aeque praedicari, primo oportet hoc considerare in essentialibus praedicatis. Aut enim quod aeque praedicatur praedicabitur sicut substantia, aut alio modo. Et si sicut substantia, aut sicut genus aut sicut differentia. Haec enim duo sunt partes definitionis, quae significant essentiam.	He says therefore first (83a39) that in order to show that they are not reciprocally predicated equally, it will be necessary to consider this in essential predicates. For that which is predicated equally will be predicated either as a substance or some other way: and if as a substance, then either as a genus or as a difference. For these are the two parts of a definition which signify the essence.
lib. 1 l. 34 n. 5 Deinde cum dicit: haec autem ostensa sunt etc., resumit quod supra probaverat, scilicet huiusmodi praedicata non esse infinita: quia si in infinitum procederent, non haberet in eis locum reciprocatio, seu circulatio. Dicit ergo quod sicut supra de his ostensum est, in huiusmodi non contingit procedere in infinitum, neque in sursum neque in deorsum: sicut si bipes praedicatur de homine, et animal de bipede, et de animali aliquid alterum, non est hoc procedere in infinitum in sursum; neque in deorsum, ut si animal dicatur de homine in eo quod quid est, et homo de Callia, et hoc de quodam alio (supposito quod homo esset genus continens sub se multas species, quarum una esset Callias), non posset sic procedi in infinitum. Et resumit rationem ad ostendendum quod supra posuit, quia omnem huiusmodi substantiam, quae scilicet habet aliquid universalius, quod de ipsa praedicetur, et quae potest de alio inferiori praedicari, contingit definire: genera vero generalissima, de quibus alia universaliora non praedicantur, et singularia, quae non praedicantur de aliquibus inferioribus, non contingit definire. Solum ergo substantiam mediam definire contingit. Illam vero substantiam non contingit definire, de qua infinita praedicantur: quia oportet definientem intelligendo pertransire omnia illa, quae substantialiter praedicantur de definito; cum omnia cadant in definitione, vel sicut genus, vel sicut differentia. Infinita autem non contingit pertransire. Ergo oportet omnem universalem substantiam, quae non est supremum genus, neque infimum subiectum, non habere infinita, quae de ipsa substantialiter praedicentur. Sic ergo non est procedere in infinitum, neque in sursum neque in deorsum.	Then (83b1) he recalls what he had proved above at the beginning of the previous lecture, namely, that predicates of this kind are not infinite; because if they were to proceed to infinity, reciprocity or circularity would find no place therein. He says, therefore, that as has been shown above, an infinite process does not take place in such predicates either by ascending or by descending: for example, if “two-footed” be predicated of man, and “animal” of two-footed, something else of animal, there is no process to infinity either upwards or downwards. Thus, if “animal” were said essentially of man, and “man” of Callias, and this of somone else (supposing that there were a genus containing under it species, one of which would be Callias), it would not be possible to go on in this way to infinity. And he recalls the reason he used earlier to prove this: for every such substance which has something more universal that can be predicated of it and which can be predicated of some inferior is capable of being defined; but the most general genera of which other more universal things are not predicated, and singulars which are not predicated of any inferiors, are not capable of definition. Only the substance between these can be defined. But a substance of which an infinite number of things is predicated turns out to be indefinable, because one who would define it must go through and understand all the items which are substantially predicated of the defined, since all of them occur in the definition either as a genus or as a difference. But the infinite cannot be gone through. Therefore, it is required that neither a universal substance, which is not a supreme genus, nor a lowest subject, can have an infinitude of predicates which are predicated of it substantially. Consequently, there is no infinite process either upwards or downwards.
lib. 1 l. 34 n. 6 Deinde cum dicit: si quidem igitur etc., ostendit quod in substantialibus praedicatis non possit esse processus in infinitum per modum circulationis. Et dicit quod si aliqua praedicata substantialia praedicantur de aliquo ut genera, non praedicantur ad invicem aequaliter, idest convertibiliter, ita quod unum sit genus alterius et e converso. Et ad hoc probandum subdit: erit enim ipsum quod vere ipsum aliquid; quasi diceret: si aliquid praedicatur de aliquo ut genus, illud de quo praedicatur, est aliquid, quod vere est ipsum, idest est aliquid particulariter, quod substantialiter recipit praedicationem ipsius. Si ergo hoc praedicetur de illo ut genus, sequetur quod ipsum, quod particulariter conveniebat alicui, e converso particulariter recipiat praedicationem illius; quod est idem respectu eiusdem esse partem et totum, quod est impossibile. Et eadem ratio est de differentiis. Unde et in I topicorum dicitur quod problema de differentia reducitur ad problema de genere.	Then (83b8) he shows that there is no process to infinity after the manner of circularity in substantial predicates. And he says that if certain substantial predicates are predicated as genera of something, they are not predicated of one another equally, i.e., convertibly, i.e., so that one would be the genus of another and vice versa. To prove this he continues, “for the one will be what something truly is.” As if to say: if something is predicated of something as a genus, that of which it is predicated is something which truly is that, i.e., something particular which receives that predication substantially. Therefore, if this be predicated of that as a genus, it will follow that something which belongs to something particularly would conversely receive the predication of it, which is tantamount to saying that a same thing is both a whole and a part in relation to the same thing—which is impossible. And the same reasoning applies to differences. Hence in Topics I it is stated that problems concerning a difference are reduced to problems concerning the genus.
lib. 1 l. 34 n. 7 Deinde cum dicit: neque tamen qualis etc., ostendit quod non potest esse processus in infinitum per modum circulationis in praedicationibus, in quibus praedicatur accidens de subiecto. Et dicit quod neque etiam ipsius qualis potest esse conversio cum suo subiecto, aut aliorum nullum potest habere huiusmodi praedicationem, quae accidentaliter praedicantur, nisi fiat praedicatio per accidens; secundum quod dictum est quod accidentia non praedicantur de subiectis nisi per accidens. Qualitas enim et omnia alia huiusmodi accidunt substantiae: unde praedicantur de substantiis sicut accidens de subiecto.	Then (83b10) he shows that there cannot be an infinite circular process in predications in which an accident is predicated of a subject. And he says that there cannot be conversion of a quality with its subject; furthermore, none of the others which are predicated accidentally can have that sort of predication, unless the predication be made per accidens in the sense described above, namely, that accidents are not predicated of their subjects except per accidens. For quality and all these others are accidental to the subject; hence they are predicated of their substances as an accident of a subject.
lib. 1 l. 34 n. 8 Deinde cum dicit: sed utique neque in sursum etc., ostendit universaliter quod in nullo genere praedicationis sit procedere in infinitum in sursum aut deorsum. Et dicit quod non solum non est procedere in praedicationibus in infinitum secundum circulationem, sed neque etiam procedendo in sursum infinita erunt praedicata, et similiter nec in deorsum. Et ad hoc probandum, primo resumit quaedam supra posita; secundo ex his probat intentum; ibi: neque in sursum ergo et cetera.	Then (83b13) he shows universally that in no genus of predication is i liere an infinite process upwards or downwards. And he says that not only is there no infinite process in predications according to circulation, but also that in proceeding upwards or downwards the predicates will not be infinite. To prove this: First, he recalls certain things which were established above. Secondly, from these he concludes his proposition 83b24)]].
lib. 1 l. 34 n. 9 Circa primum, primo resumit quod de unoquoque possunt aliqua praedicari, quidquid significent: sive sit quale, sive quantum, vel quodcunque aliud genus accidentis, vel etiam quae intrant substantiam rei, quae sunt essentialia praedicata. Secundo, resumit quod haec, scilicet substantialia praedicata, sunt finita. Tertio, resumit quod genera praedicamentorum sunt finita; scilicet quale et quantum et cetera. Si enim aliquis dicat quod quantitas praedicetur de substantia, et qualitas de quantitate, et sic in infinitum; hoc excludit per hoc, quod genera praedicamentorum sunt finita.	In regard to the first he reaffirms (83b13) that certain things can be predicated of a subject, whether they signify quality or quantity or any other genus of accident, or even items which constitute the substance of a thing, i.e., essential predicates. Secondly, he reiterates, that the latter, i.e., the substantial predicates, are finite. Thirdly, he reaffirms that the genera of predicaments are finite, namely, quality, quantity and so on. For if someone were to say that quantity is predicated of substance, and quality of quantity, and so on to infinity, he excludes this on the ground that the genera of predicaments are finite.
Quarto, resumit quod, sicut supra expositum est, unum de uno praedicatur in simplici praedicatione. Et hoc ideo inducit, quia posset aliquis dicere quod primo praedicabitur unum de uno, puta de homine animal; et ista praedicatio multiplicabitur quousque poterit inveniri aliquod unum, quod de homine praedicetur. Quibus finitis, praedicabuntur duo de uno: puta, dicetur quod homo est animal album; et sic multo plura praedicata invenirentur secundum diversas combinationes praedicatorum. Rursus, praedicabuntur tria de uno: puta, dicetur quod homo est animal album magnum; et sic semper addendo ad numerum, magis multiplicabuntur praedicata, et erit procedere in infinitum in praedicatis, sicut etiam in additione numerorum. Sed hoc excludit per praedicationem unius de uno.	Fourthly, he reaffirms that, as stated above, one thing is predicated of one thing in simple predication. And he mentions this because someone might say that one thing may well be first predicated of one thing, as “animal” of man, and this predication will be multiplied until something else can be found predicable of man, and when this is found, two things, will be predicated of one, so that it will be said that man is a white animal. Thus, many more predicates might be found according to various combinations of predicates. And so by continually adding to this number, the predicates will be increased more and more, so that there will be a process to infinity in predicates, just as there is in the succession of numbers. But he excludes this by predicating one of one.
Quinto, resumit ut non dicamus aliqua simpliciter praedicari de ipsis, quae non aliquid sunt, idest de accidentibus, quorum nullum est aliquid subsistens. De accidente enim neque subiectum neque accidens proprie praedicatur, ut supra dictum est. Omnia enim huiusmodi, quae non sunt aliquid substantiale, sunt accidentia, et de his nihil praedicatur simpliciter loquendo: sed haec quidem praedicantur per se, scilicet de subiectis, vel substantialia praedicata vel accidentalia. Illa vero secundum alium modum, idest per accidens, scilicet cum praedicantur de accidentibus, aut subiecta, aut accidentia. Haec enim omnia, scilicet accidentia, habent de sui ratione quod dicantur de subiecto: illud autem quod est accidens, non est subiectum aliquod; unde nihil proprie loquendo potest de eo praedicari, quia nihil talium, scilicet accidentium, ponimus esse tale, quod dicatur id, quod dicitur, idest quod suscipiat praedicationem eius, quod de eo praedicatur, non quasi aliquid alterum existens, sicut accidit in substantiis. Homo enim dicitur animal vel album, non quia aliquid aliud sit animal vel album, sed quia ipsummet quod est homo, est animal vel album: sed album ideo dicitur homo vel musicum, quia aliquid alterum, scilicet subiectum albi, est homo vel musicum. Sed ipsum accidens inest aliis; et alia, quae praedicantur de accidente, praedicantur de altero, idest de subiecto accidentis; et propter hoc praedicantur de accidente, ut dictum est. Hoc autem introduxit, quia si accidens praedicatur de subiecto, et e converso, et omnia quae accidunt subiecto, praedicentur de se invicem, sequetur quod praedicatio procedat in infinitum, quia uni infinita accidunt.	Fifthly, he repeats that we should not say that certain items are predicated absolutely “of things which are not something,” i.e., of accidents, none of which is a subsistent being. For, as shown above, neither the, subject nor an accident is properly predicated of an accident. For all things of this sort that are not substantial are accidents, and nothing is predicated, simply speaking, of such things. Yet they whether they be substantial predicates or accidental, they are predicated per se of their subjects; but if they are subjects or accidents being predicated of an accident, they are predicated in another way, i.e., per accidens. For it belongs to the very notion of all accidents that they be said of a subject; and since an accident is not a subject, nothing can, properly speaking, be predicated of it, because “none of such,” i.e., no accidents, “are stated to be such that they are said to be that which is said,” i.e., stated to be such that they themselves, rather than something else distinct from them, receives the predication of that which is predicated of them, as happens in the case of substances. For man is not called “animal” or “white” because something else is “animal” or “white,” but because the very thing which is a man is animal or white; but a white thing is called “man” or “musician” because something else, namely, the subject of white is the man or musician. But the accident itself is in something distinct from it; and items which are predicated of an a accident are predicated of something other than that accident, namely, of the subject of the accident: it is on this ground that they are predicated of the accident, as has been stated. (Now he mentioned this because if an accident is predicated of a subject and vice versa, and all accidents of a subject can be mutually predicated of one another, it will follow that predication could proceed to infinity, because an infinitude of things can happen to one thing).
lib. 1 l. 34 n. 10 Deinde cum dicit: neque in sursum ergo etc., ostendit propositum ex praemissis, scilicet quod in praedicatione, qua praedicatur unum de uno, non proceditur in infinitum, neque in sursum neque in deorsum; quia omnia accidentia praedicantur de his, quae pertinent ad substantiam rei, quod erat quinta suppositio. Substantialia autem praedicata non sunt infinita (quod erat secunda suppositio); et ita ex parte subiectorum non proceditur in infinitum in huiusmodi praedicationibus, quasi in deorsum. In sursum autem neutra sunt infinita, scilicet neque substantialia praedicata, neque accidentalia: quia et genera accidentium sunt finita, et in unoquoque generum non est procedere in infinitum, neque in sursum neque in deorsum, sicut neque in substantialibus praedicatis; quia in quolibet praedicamento genus praedicatur de specie in eo quod quid est. Unde concludi potest universaliter quod necesse est esse aliquod primum subiectum, de quo aliquid praedicetur, existente statu praedicationis in deorsum: et de hoc aliquid aliud praedicabitur, et hoc habebit statum in sursum: et erit invenire aliquid quod non amplius praedicabitur de alio, neque sicut posterius praedicatur de priori per accidens, neque sicut prius praedicatur de posteriori per se. Hic igitur est unus modus logice demonstrandi propositum, qui sumitur secundum diversos modos praedicationis.	Then (83b24) from these premises he shows his proposition, namely, that in a predication in which one thing is predicated of one thing there is no upward or downward process to infinity, because, as the fifth supposition states, all accidents are predicated of items which pertain to the substance of the thing. Furthermore, according to the second supposition, substantial predicates are not infinite; consequently, on the part of the subjects there is no infinite process downwards in these predications. Again, neither of these is infinite in the upward movement, i.e., neither the substantial nor the accidental predicates, both because the genera of accidents are finite, and because there is no infinite process upwards or downwards in any of these genera any more than there is in substantial predicates, because in each predicament the genus is predicated of a species in regard to something essential. Hence we can conclude universally that there must be some first subject of which something is predicated, thus establishing a stop in downward predication; then something else will be predicated of this, but it will come to a stop in the ascending process, so that something will be found which is not found predicated of another, either as the subsequent is predicated of its prior per accidens, or as the prior is predicated per se of its subsequent. This, therefore, is one way of demonstrating the proposition logically, and it is based on the diverse modes of predicating.
lib. 1 l. 34 n. 11 Deinde cum dicit: adhuc autem alius etc., ponit secundum modum probationis, et dicit quod quando est aliqua talis propositio, in qua praedicatur aliquid de subiecto, si aliqua possunt per prius praedicari de illo subiecto, talis propositio demonstrabilis erit: puta haec propositio, homo est substantia, demonstratur per hanc, animal est substantia, quia de animali per prius praedicatur substantia quam de homine. Si autem aliqua propositio est demonstrabilis, non possumus eam melius cognoscere quam sciendo: sicut principia indemonstrabilia melius cognoscimus quam sciendo, quia cognoscimus ea ut per se nota. Et iterum huiusmodi demonstrabilia non possumus scire nisi per demonstrationem; quia demonstratio est syllogismus faciens scire, ut supra dictum est. Item considerandum est quod si aliqua propositio est nota per aliam, si illam per quam nota est nescimus, neque cognoscimus eam meliori modo quam sciendo, consequens est quod nec sciamus illam propositionem, quae per eam cognoscitur.	Then (83b33) he sets forth the second way of proving. And he says that when a proposition in which something is predicated of a subject is such that certain things can be predicated per prius of that subject, that proposition will be demonstrable: for example, this proposition, “Man is a substance,” is demonstrated by the proposition, “Animal is a substance,” because “substance” is predicated of animal before it is predicated of man. But if a proposition is demonstrable, there is no better way of knowing it than to know it by demonstration, just as we know indemonstrable principles better than by way of demonstration because we know them as self-evident. Besides, we cannot scientifically know such demonstrable propositions except through demonstration, because a demonstration is a syllogism productive of scientific knowledge, as we showed above. Furthermore, if a proposition is known through another one, and if we do not scientifically know the one through which it is known, or know it in the way which is better than knowing scientifically, then we do not scientifically know that proposition which is made known through it.
His igitur tribus suppositis, procedit sic. Si contingit aliquid simpliciter scire per demonstrationem, et non ex aliquibus nec ex suppositione, necesse est quod sit status in praedicatis, quae accipiuntur ut media. Dicit autem simpliciter, et non ex aliquibus, ad excludendum demonstrationes ducentes ad impossibile; in quibus proceditur contra positiones aliquas ex aliquibus propositionibus datis. Dicit autem neque ex suppositione, ad excludendum demonstrationes quia, quales fiunt in scientiis subalternis; quae supponunt conclusiones superiorum scientiarum, ut supra habitum est.	With these three suppositions in mind he proceeds thus: If one does know something purely through demonstration “and not from something or from supposition,” it is necessary that there be a stop in the predicates which are-taken as middles. (He says, “purely and not from something,” to exclude) demonstrations leading to the impossible, in which one proceeds, against certain positions by arguing from propositions that have been agreed upon. Furthermore, he says, “or from supposition,” to exclude such demonstrations as are formed in subalternate sciences, which suppose the conclusion of higher sciences, as explained above).
Est ergo simpliciter per demonstrationem scire, quando quaelibet propositionum praemissarum, si sit demonstrabilis, scitur per demonstrationem; et si non est demonstrabilis, intelligitur per seipsam. Et hoc supposito, necesse est quod sit status in praedicationibus, quia si non fuerit status, sed semper potest accipi aliquid superius, sequitur quod omnium sit demonstratio, ut primo dicebatur. Si ergo aliqua conclusio demonstratur, oportet quod quaelibet praemissarum sit demonstrabilis. Sic ergo ad eius cognitionem nullo modo possumus melius nos habere, quam sciendo eam per demonstrationem: ergo oportebit eam demonstrare per aliquas alias propositiones, et illas iterum per alias, et sic in infinitum. Quia igitur infinita non est transire, non poterimus ea cognoscere per demonstrationem, neque melius ea cognoscere possumus, cum omnia sint demonstrabilia. Ergo sequetur quod nihil contingat scire per demonstrationem simpliciter, sed solum ex suppositione. Ultimo autem epilogando concludit principale propositum.	Therefore, one knows purely through demonstration when each one of the premised propositions, if it is demonstrable, is known through demonstration; and if it is not demonstrable, is known in virtue of itself. Under these suppositions it is necessary that there be a stop in predications, because if there is no stop but something prior can always be taken, it follows that there is demonstration of everything, as was said above. Therefore, if a. conclusion is demonstrated, each of the premises must be demonstrable. But if we can have knowledge of it in no better way than by knowing it through demonstration, and if it will be necessary to demonstrate it through other propositions, and those through others again, and so on to infinity, then, since it is not possible to go through those infinites, we shall not be able to make it known through demonstration or through the method better than demonstration, since all things are demonstrable. The consequence will be that one knows nothing purely through demonstration, but only from supposition. Finally, by way of summary he concludes the main proposition.