Authors/Thomas Aquinas/metaphysics/liber3/lect14

Lecture 14

Latin	English
lib. 3 l. 14 n. 1 Postquam philosophus inquisivit utrum mathematica sint principia rerum sensibilium, hic inquirit utrum supra mathematica sint aliqua alia principia, puta quae dicuntur species, quae sunt substantiae et principia horum sensibilium. Et circa hoc tria facit. Primo movet dubitationem. Secundo inducit rationem ad unam partem, ibi, nam si ideo. Tertio obiicit ad partem contrariam, ibi, at vero si ponimus et cetera. Dicit ergo primo, quod supposito quod mathematica non sint principia rerum sensibilium et eorum substantia, ulterius aliquis dubitabit quae est ratio quare praeter substantias sensibiles et praeter mathematica quae sunt media inter sensibilia et species, oportet iterum ponere tertium genus, scilicet ipsas species, idest ideas vel formas separatas.	515. Having inquired whether the objects of mathematics are the principles of sensible substances, the Philosopher now inquires whether in addition to the objects of mathematics there are certain other principles, such as those which we call Forms, which are the substances and principles of sensible things. In regard to this he does three things. First, he presents the question. Second (516), he argues one side of the question (“For if it is because”). Third (518), he argues the other side (“But if we hold”). Accordingly, he says, first, that if one assumes that the objects of mathematics are not the principles of sensible things and their substances, one will next have the problem why, in addition to both sensible things and the objects of mathematics (which are an intermediate class between sensible things and the Forms), it is necessary to posit a third class of entities, namely, the specific essences, i.e., the Ideas or separate Forms.
lib. 3 l. 14 n. 2 Deinde cum dicit nam si ideo obiicit ad unam partem: et videtur haec esse ratio quare oportet species ponere praeter sensibilia et mathematica: quia mathematica a praesentibus idest a sensibilibus, quae in universo sunt, differunt quidem in aliquo, quia mathematica abstrahunt a materia sensibili; non tamen differunt in hoc, sed magis conveniunt, quia sicut in sensibilibus inveniuntur plura numero differentia eiusdem speciei, utpote plures homines, aut plures equi, ita etiam in mathematicis inveniuntur plura numero differentia eiusdem speciei, puta plures trianguli aequilateri, et plures lineae aequales. Et si ita est, sequitur quod sicut principia sensibilium non sunt determinata secundum numerum, sed secundum speciem, ita etiam sit in mediis idest in mathematicis. Manifestum est enim quod in sensibilibus propter hoc quod sunt plura individua unius speciei sensibilis, principia sensibilium non sunt determinata numero, sed specie, nisi forte accipiantur principia propria huius individui, quae sunt etiam in numero determinata et individualia. Et ponit exemplum in vocibus. Manifestum est enim quod vocis literatae, literae sunt principia; non tamen sunt aliquo numero determinato individualium literarum, sed solum secundum speciem sunt determinatae literae secundum aliquem numerum, quarum aliae sunt vocales, et aliae consonantes: sed haec determinatio est secundum speciem, non secundum numerum. Non enim unum solum est a sed multa, et sic de aliis literis. Sed si accipiantur hae literae, quae sunt principia huius determinatae syllabae vel dictionis aut orationis, sic sunt determinatae numero. Et eadem ratione, cum sint multa mathematica numero differentia in una specie, non poterunt esse mathematica principia mathematicorum determinata numero, sed determinata specie solum: puta si dicamus quod principia triangulorum sunt tria latera et tres anguli. Sed haec determinatio est secundum speciem: contingit enim quodlibet eorum in infinitum multiplicari. Si igitur nihil esset praeter sensibilia et mathematica; sequeretur quod substantia speciei non esset una secundum numerum, et quod principia entium non essent determinata in aliquo numero, sed erunt determinata solum secundum speciem. Si ergo est necessarium quod sint determinata secundum numerum (alioquin contingeret esse principia rerum infinita numero), sequitur quod necesse sit species esse praeter mathematica et sensibilia.	516. For if it is because (285) Here he argues one side of the question. The reason why it is necessary to posit separate Forms over and above sensible substances and the objects of mathematics seems to be that the objects of mathematics differ in one respect “from the things at hand,” i.e., from sensible things, which exist in the universe; for the objects of mathematics abstract from sensible matter. Yet they do not differ but rather agree in another respect. For just as we find many sensible things which are specifically the same but numerically different, as many men or many horses, in a similar way we find many objects of mathematics which are specifically the same but numerically different, such as many equilateral triangles and many equal lines. And if this is true, it follows that, just as the principles of sensible things are not limited in number but in species, the same thing is true “of the intermediate entities”—the objects of mathematics. For since in the case of sensible things there are many individuals of one sensible. species, it is evident that the principles of sensible things are not limited in number but in species, unless of course we can consider the proper principles of a particular individual thing, which are also limited in number and are individual. He gives as an example words; for in the case of a word expressed in letters it is clear that the letters are its principles, yet there are not a limited number of individual letters taken numerically, but only a limited number taken specifically, some of which are vowels and some consonants. But this limitation is according to species and not according to number. For a is not only one but many, and the same applies to other letters. But if we take those letters which are the principles of a particular syllable, whether written or spoken, then they are limited in number. And for the same reason, since there are many objects of mathematics which are numerically different in one species, the mathematical principles of mathematical science could not be limited in number but only in species. We might say, for example, that the principles of triangles are three sides and three angles; but this limitation is according to species, for any of them can be multiplied to infinity. Therefore, if there were nothing besides sensible things and the objects of mathematics, it would follow that the substance of a Form would be numerically one, and that the principles of beings would not be limited in number but only in species. Therefore, if it is necessary that they be limited in number (otherwise it would happen that the principles of things are infinite in number), it follows that there must be Forms in addition to the objects of mathematics and sensible things.
lib. 3 l. 14 n. 3 Et hoc est quod Platonici volunt dicere, quod sequitur ex necessitate ad positiones eorum quod sit in singularium substantia species aliquid unum, cui non conveniat aliquid secundum accidens. Homini enim individuo convenit aliquid secundum accidens, scilicet album vel nigrum; sed homini separato, qui est species secundum Platonicos, nihil convenit per accidens, sed solum quod pertinet ad rationem speciei. Et quamvis hoc dicere intendant, non tamen bene dearticulant, idest non bene distinguunt.	517. This is what the Platonists wanted to say, because it necessarily follows from the things which they held that in the case of the substance of sensible things there is a single Form to which nothing accidental belongs. For something accidental, such as whiteness or blackness, pertains to an individual man, but to this separate man, who is a Form, according to the Platonists, there pertains nothing accidental but only what belongs to the definition of the species. And although they wanted to say this, they did not “express themselves” clearly; i.e., they did not clearly distinguish things.
lib. 3 l. 14 n. 4 Deinde cum dicit at vero obiicit in contrarium: et dicit, quod si ponamus species separatas esse, et quod principia rerum non sunt solum determinata specie, sed etiam numero, quaedam inconvenientia sequuntur, quae superius in quadam quaestione sunt tacta. Hanc autem dubitationem philosophus determinat duodecimo et quartodecimo huius libri. Et veritas dubitationis est quod sicut mathematica non sunt praeter sensibilia, ita nec species rerum separatae praeter mathematica et sensibilia. Principia autem rerum efficientia et moventia sunt quidem determinata numero; sed principia rerum formalia quorum sunt multa individua unius speciei, non sunt determinata numero, sed solum specie.	518. But if wehold that (286). Then he counters with an argument for the other side of the question. He says that, if we hold that there are separate Forms and that the principles of things are limited not only in species but also in number, certain impossible consequences will follow, which are touched on above in one of the questions (464). But the Philosopher will deal with this problem in Book XII (2450) and Book XIV of this work. And the truth of the matter is that, just as the objects of mathematics do not exist apart from sensible things, neither do Forms exist apart from the objects of mathematics and from sensible substances. And while the efficient and moving principles of things are limited in number, the formal principles of things, of which there are many individuals in one species, are not limited in number but only in species.