METAPHYSICS

Argyropylus

23 ...and are now in the heavens and are brought into being: but they claim there is no other number besides this number from which the world is constituted. For when, according to their view, opinion and time are in one part, and slightly above or below are injustice, justice, or mixture, they demonstrate this is so because each of these is a number. It happens that in this place there is already a likeness of those magnitudes which constitute the world, because these qualities follow specific locations. Is this the same number which is in the heaven—which we must accept each of these things to be—or is it another besides this one? The Pythagoreans famously believed that "all things are number," assigning specific numerical values to abstract concepts like justice (4) or marriage (5). ¶ Plato, however, says it is another number, although he also thinks both these things and their causes are numbers; however, he considers the causes to be intelligible original: "intelligibiles"; things understood by the mind rather than perceived by senses. and these others to be sensible original: "sensibiles"; perceptible by the senses.. But let us omit speaking of the Pythagoreans for now, for it is enough to have touched upon them. ¶ Those who posit the Ideas original: "ideas"; Plato’s theory that perfect, eternal templates exist for all things., seeking first to grasp the causes of these existing things, introduced other things equal in number to them. It is as if someone wanting to count things thought he could not do so if there were few, but by creating more, he could then enumerate them. For the Forms original: "formæ" are almost equal to, or at least not fewer than, those things whose causes they were seeking, and from which they proceeded to the Forms. For in each case there is something with the same name, a Form; and besides the substances of other things, there is a "one over many" The logical principle that if multiple things share a name (like "large"), there must be a single Form they all share., both in these things and in eternal things. Furthermore, the Forms do not seem to exist by any of the methods by which we demonstrate they exist. For from some arguments, a necessary conclusion does not follow; from others, Forms are created even for things for which we do not believe Forms exist. For according to the principles of the sciences, there will be Forms of all things of which there are sciences. And by the principle of "one in many," there will even be Forms of negations If "not-white" is a single concept shared by many things, the theory implies there must be a Form of "Not-White," which Aristotle finds absurd.. And through the act of understanding something that has passed away, there will even be Forms of things that perish, for there remains a mental image of these things in the imagination, as is evident. Furthermore, the more exact arguments create Ideas of relations original: "ad aliquid"; things that exist only in relation to something else, like "double" or "greater.", of which we do not say there is a genus in itself. Other arguments bring in the Third Man term: Third Man (tertium hominem); a famous logical paradox. If a man is like the Form of Man, there must be a third "man" to explain the similarity between the two, leading to an infinite regress.. And overall, the arguments concerning the Forms do away with those things which those who speak of Forms wish to exist more than the Ideas themselves. For it happens that duality is not first, but number is.

Bessarion

...and are newly made in the heavens: but they claim there is no other number besides this number from which the world consists. For since in this part there is opinion and time for them, and a little further up or down is injustice and separation or mixture, they bring forth a proof that each of these is indeed a number. It happens, however, that in this place there is a multitude of already constituted magnitudes, because the qualities follow individual locations. But is this the same number which is in the heaven, which one must accept as being each of these things? Or is there another besides this? ¶ For Plato says there is another. Yet he also thinks numbers exist, and that they are both these things and the causes of these things. But he considers the causes to be intelligible, and these others to be sensible. Therefore, let us pass over the Pythagoreans for now. For it is sufficient to have touched upon them to this extent. ¶ Those who posit Ideas, while they were seeking to have the causes of these existing things, brought in other things equal in number to them. Just as if someone wishing to count, when there are fewer things existing, thinks he cannot do it, but makes them more numerous and so counts them. For the species original: "species"; here used synonymously with Plato's "Forms" or "Ideas." are almost equal to or not fewer than those things from which they proceeded to the Forms while seeking their causes. For according to each thing there is a shared name, and (besides the substances) there is a "one in many" for other things as well, both in these and in eternal things. Likewise, the ways in which it is shown that there are species do not appear valid by any of them. For from some, it is not necessary for a syllogism term: syllogism (syllogismū); a formal logical argument consisting of two premises and a conclusion. to be formed. From others, species are created even for things we do not expect. For according to the arguments from the sciences, there will be species of all things of which there are sciences. According to the "one in many," there will be species even of negations. And according to the fact that one understands something when it is destroyed, there will be species even of perishable things; since there is a phantasm original: "phantasma"; a mental image or representation. of any of these. Moreover, among the more certain arguments, some create Ideas of things that are relative, of which we do not say there is a genus in itself. Others speak of the Third Man. And simply put, these arguments about the species destroy those things which those who speak of species wish to exist more than the Ideas themselves. For it happens that duality is not first, but number.