Book I, lectio XXXVOSTENDITUR ANALYTICE QUOD IN PRAEDICATIS NON EST IN INFINITUM PROCEDERE, NEQUE IN SURSUM NEQUE IN DEORSUM

Analytice autem manifestum est per hoc velocius quod neque in sursum neque in deorsum infinita praedicantia contingit esse in demonstrativis scientiis, de quibus intentio est. Demonstratio quidem enim est, quaecunque ipsa insunt secundum seipsa rebus. Secundum seipsa autem dupliciter: quaecunque enim illis insunt in eo quod quid est, et in quibus ipsa in eo quod quid est insunt ipsis: ut numero impar, quod inest quidem numero, est autem ipse numerus in ratione ipsius; et iterum multitudo aut divisibile in ratione numeri est. Horum autem neutra contingit esse infinita, nec ut impar numeri: iterum enim si impari aliud insit, cui inerat existenti; hoc autem si est, primum numerus inerit his quae insunt ipsi. Si igitur non contingit infinita huiusmodi esse in uno, neque in sursum erunt infinita. At vero necesse est omnia inesse primo, ut numero, et in illis numerum: quare convertibilia erunt, sed non excedentia. Neque etiam quaecunque sunt in eo quod quid est, nec haec infinita sunt: nec enim esset definire. Quare si praedicantia quidem per se omnia dicuntur, haec autem non infinita sunt, stabunt utique in sursum; quare et in deorsum. Si autem sic est, et quae sunt in medio duorum terminorum semper sunt finita. Si vero hoc est, manifestum iam est et demonstrationum quod necesse est principia esse, et non omnium esse demonstrationem, quod vere diximus quosdam dicere iuxta principium. Si enim sunt principia, non omnia sunt demonstrabilia, neque in infinitum possunt ire: esse enim horum quodlibet nihil aliud est, quam esse nullum spatium sine medio et indivisibile, sed omnia divisibilia. Intus enim immitendo terminum, sed non assumendo, demonstratur id quod demonstratur. Quare si hoc in infinitum contingit ire, contingeret utique duorum terminorum infinita esse interius media. Sed hoc impossibile est, si praedicamenta steterint superius et inferius. Quod autem stent, demonstratum est logice prius, analytice vero nunc.

The Latin version St Thomas commented, as the Leonine edition prints it.

In things predicated therefore as to what a thing is, this is clear, for if it is possible to define, or if the very nature of a thing may be known, but infinites cannot be passed through, it is necessary that those things should be finite which are pre-dicated with respect to what a thing is. We must however speak universally thus: a white thing we may truly say walks, also that that great thing is wood; more-over, that the wood is great, and that the man walks, yet there is a difference between speaking in this way and in that. For when I say that that white thing is wood, then I say that what happens to be white is wood, but what is white is not, as it were, a subject to wood, since neither being white, nor what is a certain white thing, became wood, so that it is not (wood) except from accident. But when I say that the wood is white, I do not say that something else is white, but it happens to that¹ to be wood, (as when I say that a musician is white, for then I mean that the man is white, to whom it happens to be a musician,) but wood is the subject which became (white), not being any thing else than what is wood, or a certain piece of wood. If indeed it is necessary to assign names, let speaking in this way² be to predicate, but in that way be either by no means to predicate, or to predicate indeed, not simply, but according to accident. That which is predicated is as white, but that of which it is predicated as wood; now let it be supposed that the predicate is always spoken of what it is predicated of simply, and not according to accident, for thus demonstrations demonstrate. Therefore when one thing is predicated of one, it will be predicated either in respect of what a thing is, or that it is a quality, or a quantity, or a relative, or an agent, or a patient, or that it is some where, or at some time.

Moreover, those which signify substance, signify that the thing of which they are predicated, is that which it is, or something belonging to it, but whatever do not signify substance, but are predicated of another subject, which is neither the thing itself, nor something belonging to it, are accidents, as white is predicated of man, since man is neither white, nor any thing which belongs to white, but is perhaps animal, for man is that which is a certain animal. Such as do not signify substance it is necessary should be predicated of a certain subject, and not be something white, which is white, not being any thing else. For, farewell to ideas, for they are mere prattlings, and if they exist, are nothing to the subject, since demonstrations are not about such things.³ Again, if this is not a quality of this, and that 2. of this, neither a quality of a quality, it is impossible that they should be thus mutually predicated of each other, still they may possibly be truly said, but cannot truly be mutually predicated. For will they be predicated as substance, as being either the genus or the difference of what is predicated? It has been shown that these will not be infinite, neither in a descending nor in an ascending progression, as for instance, man is a biped, this an animal, this something else; neither can animal be predicated of man, this of Callias, this of something else, in respect to what a thing is. For we may define the whole of this to be substance, but we cannot penetrate infinites by perception, wherefore neither are there infinites upwards or downwards, for we cannot define that of which infinites are predicated. They will not indeed be mutually predicated of each other as genera, for genus would be a part itself, neither will quality nor any of the other categories be (mutually) predicated, except by accident, for all these are accidents, and are predicated of substances. But neither will there be infinites in ascending series, for of each thing, that is predicated, which signifies either a certain quality, or a certain quantity, or something of this kind, or those which are in the substance, but these are finite, and the genera of the categories are finite, since (a category) is either quality, or quantity, or relation, or action, or passion, or where, or when. One thing is however supposed to be predicated of one, but those not to be mutually predicated which do not signify what a thing is, since all these are accidents, but some are per se, others after a different manner, and we say all these are predicated of a certain subject, but that accident is not a certain subject, for we do not assume any thing of this kind to be, which not being any thing else, is said to be what it is said to be, but we say that it is predicated of something else, and certain other things of another thing.⁴ Neither then can one thing be predicated of one (infinitely) upwards, nor downwards, for those of which accidents are predicated, are such as are contained in the substance of each thing, but these are not infinite. Both these indeed and accidents are ascending, and both are not infinite, wherefore it is necessary that there should be something⁵ of which primarily something⁶ is predicated, and something else of this, also that this should stop, and that there should be something|| which is neither predicated of another prior thing, nor another prior thing of it. This then is said to be one mode of demonstration, but there is another besides, if there is a demonstration of those of which certain things are previously predicated, but of what there is demonstration, it is not possible to be better affected towards them than to know them, nor can we know without demonstration.⁷ Still if this⁸ becomes known through these, but these we do not know, nor are better affected towards them than if we knew them, neither shall we obtain scientific knowledge of that which becomes known through these. If then it is possible to know any thing simply through demonstration, and not from certain things, nor from hypothesis, it is necessary that the intermediate predications should stop; for if they do not stop, but there is always something above what is assumed, there will be a demonstration of all things, so that if we cannot pass through infinites, we shall not know by demonstration those things of which there is demonstration. If then we are not better affected towards them than if we knew them, it will be impossible to know any thing by demonstration simply, but by hypothesis. Logically then from these things a person may believe about what has been said, but analytically⁹ it is more concisely manifest thus, that there cannot be infinite predicates in demonstrative sciences, the subject of the present treatise, either in an ascending or descending series. For demonstration is of such things as are essentially present with things, essentially in two ways, both such as are in them in respect of what a thing is, and those in which the things themselves are inherent in respect of what a thing is, thus the odd in number which indeed is inherent in number, but number itself is inherent in the definition of it, again also, multitude or the divisible is inherent in the definition of number. Still neither of these can be infinites, nor as the odd is predicated of number, for again there will be something else in the odd, in which § being inherent,|| (the odd) would be inherent, and if this be so, number will be first inherent in those things which are inherent in it. If then such infinites cannot be inherent in the one, neither will there be infinites in ascending series. Still it is necessary that all should be inherent in the first, for example, in number, and number in them, so that they will reciprocate, but not be more widely extensive. Neither are those infinite which are inherent in the definition of a thing, for if they were, we could not define, so that if all predicates are predicated per se, and these are not infinite, things in an upward progression will stop, wherefore also those which descend.

If then this be so, those also which are between the two terms will be always finite, but if this be the case, it is clear now that there must necessarily be principles of demonstrations, and that there is no demonstration of all things, as we observed in the beginning, certain persons assert. For if there be principles, neither are all things demonstrable, nor can we progress to infinity, since that either of these should be, is nothing else than that there is no proposition immediate and indivisible, but that all things are divisible, since what is demonstrated is demonstrated from the term¹⁰ being inwardly introduced, and not from its being (outwardly) assumed. Wherefore if this § may possibly proceed to infinity, the media between two terms|| might also possibly be infinite, but this is impossible, if predications upwards and downwards stop, and that they do stop, has been logically shown before, and analytically now.

The whole chapters, in the translation of 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).