Yes. So why was this difference not seized upon in the moment?

That's a difficult question, concerning a difficult subject. Space and time were not well understood back then, and still aren't. Notice even today, the common convention is space-time, which considers time to be a dimension of space. Under such conceptions time is not separable from space. It could even be the case the examples were presented by Plato as a way of demonstrating a difference between space and time. Aristotle gave principles to understand space and time separately.

I was thinking of the difference as something Plato, the author, has two of his characters say at a particular moment. It would have been a different work if the argument went elsewhere than it did.

That is a constant question when reading Plato that does not come up in theories presented directly by others.

That is a constant question when reading Plato that does not come up in theories presented directly by others. — Paine

I think this is something which really needs to be respected when talking about "Platonism". For the most part, Plato, following the Socratic method, worked to expose problems. He offered very little in the way of theories presented as a means of resolution to the exposed problems. So what we have is Plato analyzing the theories of others, and poking holes in them. The reader has a very challenging task of understanding his logic, and why the holes are holes, in order to understand why the theories analyzed are deficient.

This leads to a big difference in interpretation, and a corresponding difference in proposed resolutions which follow, such as the difference between Neoplatonism and Aristotelianism. I believe the true test, for determining the most accurate, or "best" interpretation, is to look for the places where Plato actually presents some direction for resolution of the problems in knowledge, exposed by Socrates.

There is a number of such places, such as in The Republic, and in The Timaeus. The offerings are generally metaphorical, as the pathway to resolution is very unclear to Plato, and metaphor provides a broad route due to an even wider range of possible interpretations. Some examples are the comparison of "the good" to the light of the sun, and the related cave allegory, in The Republic, along with his discussion of "matter" as the recipients of the Forms, in The Timaeus.

I believe That Aristotle demonstrates a better understanding of these principles than the classical Neoplatonists such as Plotinus. He provides a proper representation of "the good", as "that for the sake of which", final cause, and does much work on this subject in The Nicomachean Ethics, and Metaphysics. This principle allows for activity, actuality, within the realm of Ideas and Forms, breaking the interaction problem of idealism. Participation theory renders the Forms as inactive, and cannot explain how Form is an active cause in the generation of individual material beings.

You'll notice in Aristotle's Metaphysics, (much of this being material produced from his school, after his death), how the Aristotelians distance themselves from those other Platonists, whom we call Neoplatonists. The other Platonists adhere more strongly to Pythagorean idealism, not understanding the problems of participation theory, revealed by Plato. They understand "the One" as the first principle, and try to make this consistent with Plato's "the good". Aristotle's Metaphysics shows how "the One" is really just a first Form, and cannot be "the good" itself; "the good" being something beyond the realm of Forms, as cause of the intelligibility of intelligible objects. So we commonly see modern day Neoplatonists representing "the good" of Plato as "the idea of good", or "Form of good", when Plato talks of "the good" itself. And the ancient Neoplatonists, such as Plotinus, claim that "the One" is something which transcends the realm of Forms, as an attempt to make it consistent with "the good". But the Aristotelians show that "the One" cannot be anything other than a first Form, and Aristotle continues onward to address "the good" in its causal relation with the Forms, as distinct from the Forms, like it is described in Plato's Republic.

You'll notice in Aristotle's Metaphysics, (much of this being material produced from his school, after his death), how the Aristotelians distance themselves from those other Platonists, whom we call Neoplatonists. — Metaphysician Undercover

Do you have a source that touches on how Aristotle's text was produced? Are you suggesting that when "Platonists" are mentioned in Aristotle that others are speaking in his name?

It is likely that when Aristotle uses "Platonists", he is referring to his old pals at the Academy. It is unlikely that they shared all the views of Plotinus, a Neo-Platonists who wrote hundreds of years later in Rome.

While we can guess the first Academicians would have taken issue with Aristotle challenging the separate land of the forms, it is unlikely they would have disagreed with Parmenides who sharply protects the boundary between the divine and the world of becoming that we muck about in:

“For instance,” said Parmenides, “if one of us is the master or slave of someone, he is not, of course, the slave 133E of master itself, what master is; nor is a master, master of slave itself, what slave is. Rather, as human beings, we are master or slave of a fellow human. Mastery itself, on the other hand, is what it is of slavery itself, while slavery itself, in like manner, is slavery of mastery itself. But the things among us do not have their power towards those, nor do those have their power towards us. Rather, as I say, these are what they are, of themselves, and in relation to themselves, while things with 134A us are, in like manner, relative to themselves. Or do you not understand what I am saying?”

“I understand,” said Socrates, “very much so.”

“And is it also the case,” he asked, “that knowledge itself, what knowledge is, would be knowledge of that truth itself, what truth is?”

“Entirely so.”

“Then again, each of the instances of knowledge, what each is, would be knowledge of particular things that are. Isn’t this so?”

“Yes.”

“The knowledge with us would be knowledge of the truth with us, and furthermore, particular knowledge with us would turn out to be knowledge of particular things that are 134B with us?”

“Necessarily.”

“But the forms themselves, as you agree, we neither possess nor can they be with us.”

“No, indeed not.”

“And presumably each of the kinds themselves is known by the form of knowledge itself?”

“Yes.”

“Which we do not possess.”

“We do not.”

“So none of the forms is known by us since we do not partake of knowledge itself.”

“Apparently not.”

“So what beauty itself is, and the good, 134C and indeed everything we understand as being characteristics themselves, are unknown to us.”

“Quite likely.”

“Then consider something even more daunting.”

“Which is?”

“You would say, I presume, that if there is indeed a kind, just by itself, of knowledge, it is much more precise than the knowledge with us, and the same holds for beauty and all the others.”

“Yes.”

“Now if anything else partakes of knowledge itself, wouldn’t you say that a god, more so than anyone, possesses the most precise knowledge?”

“Necessarily.”

134D “In that case, will a god possessing knowledge itself be able to know things in our realm?”

“Why not?”

“Because, Socrates,” said Parmenides, “we have agreed that those forms do not have the power that they have, in relation to the things that are with us, nor do the things with us have their power in relation to those forms. The power in each case is in relation to themselves.”

“Yes, we agreed on that.”

“Well then, if this most precise mastery is with a god, and this most precise knowledge too, the gods’ mastery would never exercise mastery over us, nor would their knowledge 134E know us nor anything else that is with us. Rather, just as we neither rule over them with our rule nor do we know anything of the divine with our knowledge, they in turn by the same argument, are not the masters of us nor do they have knowledge of human affairs, although they are gods.”

“But surely,” he said, “if someone were to deprive a god of knowledge, the argument would be most surprising.”

“Indeed, Socrates,” said Parmenides, “the forms inevitably possess these difficulties and many others 135A besides these, if there are these characteristics of things that are, and someone marks off each form as something by itself. And the person who hears about them gets perplexed and contends that these forms do not exist, and even if they do it is highly necessary that they be unknowable to human nature. And in saying all this he seems to be making sense, and as we said before, it is extraordinarily difficult to persuade him otherwise. Indeed, this will require a highly gifted man who will have the ability to understand that there is, for each, some kind, a being just by itself, 135B and someone even more extraordinary who will make this discovery and be capable of teaching someone else who has scrutinized all these issues thoroughly enough for himself.”

“I agree with you, Parmenides,” said Socrates. “What you are saying is very much to my mind.”

“Yet on the other hand Socrates,” said Parmenides, “if someone, in the light of our present considerations and others like them, will not allow that there are forms of things that are, and won’t mark off a form for each one, he will not even have anywhere to turn his thought, since he does not allow that a characteristic 135C of each of the things that are is always the same. And in this way he will utterly destroy the power of dialectic. However, I think you are well aware of such an issue.” — Plato, Parmenides, 133e, translated by Horan

This is a far cry from the mono-logos of Plotinus where the divine is a continuity from the highest reality to the lowest. The dialectic descends into the silence of contemplation.

Do you have a source that touches on how Aristotle's text was produced? — Paine

I did some quick Google research for you, and dug up the following. References are at the bottom.

What is called "Metaphysics" is a collection of works, which were taught in a school in Rhodes. This was a separate school from Aristotle's school the Peripatetic school in the Lyceum at Athens. These papers were put together into a single collection, "Metaphysics" some time (a couple centuries I believe) after Aristotle's death by Andronicus of Rhodes. It is not known how much of the material was produced by Aristotle himself, because Andronicus provided no indication of how he authenticated the individual writings he collected together under that title.

Apparently, the writings now known as "Metaphysics" were in the possession of one of Aristotle's students, Eudemus of Rhodes, after Aristotle's death. The writings were unpublished and Eudemus supposedly had the only copy. Eudemus and Theophrastus were two of Aristotle's top students. Aristotle appointed Theophrastus to head his Peripatetic School, and Eudemus went back to Rhodes (supposedly with the only copy of what is now known as the Metaphysics) to open his own school.

You can see why there would be much debate concerning the authenticity of the Metaphysics, as truly Aristotelian writings. Eudemus of Rhodes apparently provided no solid evidence to support his claims that this material he taught was actually authored by Aristotle. It is commonly believed that this material was notes taken by Eudemus, from Aristotle's teaching.


https://plato.stanford.edu/entries/aristotle-commentators/supplement.html
https://www.britannica.com/biography/Andronicus-of-Rhodes
https://www.philosophy.ox.ac.uk/event/workshop-in-ancient-philosophy-thursday-week-4-tt21
https://www.philosophie.hu-berlin.de/de/lehrbereiche/antike/mitarbeiter/menn/editors.pdf
https://en.wikipedia.org/wiki/Eudemus_of_Rhodes
https://mathshistory.st-andrews.ac.uk/Biographies/Eudemus/

Are you suggesting that when "Platonists" are mentioned in Aristotle that others are speaking in his name? — Paine

You'll notice that much of the material which Eudemus of Rhodes taught was derived from notes taken from Aristotle's teachings, and this is probably the case with the Metaphysics. I believe that at the time when Aristotle was teaching, the divisions between different schools of Platonism had not yet been established. Eudemus is well known for his work on mathematics and principles of geometry, and Plato's academy was a school of skepticism. In the metaphysics, where there is a pronounced separation from the other Platonists it has to do with the nature of mathematical and geometrical ideas, forms. Iam not familiar with Eudemus' famous works on mathematics, so I cannot confirm this speculation.

While we can guess the first Academicians would have taken issue with Aristotle challenging the separate land of the forms, it is unlikely they would have disagreed with Parmenides who sharply protects the boundary between the divine and the world of becoming that we muck about in: — Paine

This boundary is exactly what is attacked in Aristotle's De Caelo. The eternal circular motions of the heavenly bodies are supposed to support the eternal existence of the divine. But Aristotle demonstrates how anything which moves in a circular motion must be a body composed of matter, and is therefore generated and will be destroyed. This effectively breaks the boundary between the divine (eternal) and the earthly world of becoming.

This is a far cry from the mono-logos of Plotinus where the divine is a continuity from the highest reality to the lowest. The dialectic descends into the silence of contemplation. — Paine

Very true, and this indicates the separation between Neoplatonism and Aristotelianism very well. This passage forms the foundation for Aristotle's hylomorphism. Each individual material thing has a form specific to itself (the law of identity), as well as its matter:

“Indeed, Socrates,” said Parmenides, “the forms inevitably possess these difficulties and many others 135A besides these, if there are these characteristics of things that are, and someone marks off each form as something by itself. And the person who hears about them gets perplexed and contends that these forms do not exist, and even if they do it is highly necessary that they be unknowable to human nature. And in saying all this he seems to be making sense, and as we said before, it is extraordinarily difficult to persuade him otherwise. Indeed, this will require a highly gifted man who will have the ability to understand that there is, for each, some kind, a being just by itself, 135B and someone even more extraordinary who will make this discovery and be capable of teaching someone else who has scrutinized all these issues thoroughly enough for himself.”

“I agree with you, Parmenides,” said Socrates. “What you are saying is very much to my mind.”

“Yet on the other hand Socrates,” said Parmenides, “if someone, in the light of our present considerations and others like them, will not allow that there are forms of things that are, and won’t mark off a form for each one, he will not even have anywhere to turn his thought, since he does not allow that a characteristic 135C of each of the things that are is always the same. And in this way he will utterly destroy the power of dialectic. However, I think you are well aware of such an issue.” — Plato, Parmenides, 133e, translated by Horan

Thank you for the links.

We have differed in the past on what the consequences of De Caelo are on the divinity of the celestial sphere and I remember you do not accept the account of divinity in Metaphysics book Lamda. So, I will leave all that be.

I am glad we could find common ground on the role of forms in the dialectic.

We have differed in the past on what the consequences of De Caelo are on the divinity of the celestial sphere and I remember you do not accept the account of divinity in Metaphysics book Lamda. So, I will leave all that be. — Paine

Do you not agree, that in De Caelo Aristotle begins by agreeing with those who promote it, explaining that eternal circular motion is a valid concept, and a real logical possibility. However, he then proceeds to assert that anything moving in a circular motion must be a material body, and as a material body it must have been generated and will be destroyed. If you agree with these two aspects of De Caelo, you ought to also agree that what Aristotle has done is that even though he has accepted the logic of eternal circular motion as a valid logical possibility, he has dismissed eternal circular motion as 'physically impossible'.

I am glad we could find common ground on the role of forms in the dialectic. — Paine

Yes, I agree that is an accomplishment. But the significant issue is the direction which Plato points us. And since Plato appears to be pointing in a number of different directions, people can take up a number of different ontological, or metaphysical positions, and claim the position to be Platonic. This we see in the difference between Aristotle and Plotinus for example. Aristotle argues that the first principle, i.e. anything that is eternal, must be something actual. Plotinus assumes the first principle "the One" to be pure potential. Notice above, that the eternal circular motions are for Aristotle, possibilities whose actuality is denied.

To me, the direction taken by the Neoplatonists which gives priority to mathematical objects, in the manner of maintaining Pythagorean idealism, is a dead end. The inquiring in this direction culminates with Plotinus, who meets the brick wall of assuming the first principle "the One" as a pure potential, because then he has no principle of causation to account for the emanation or procession of Forms and beings from the One, in a hierarchical order. The hierarchical order is very good, and well thought out and constructed, but the problem is with the first principle, pure potential provides no source of causation.

Aristotle, on the other hand effectively refutes Pythagorean idealism, and those Platonists who follow that path, by demonstrating that anything eternal must be actual, and showing that mathematical, and geometrical forms, like the one, and the circle, exist only as potential, prior to being discovered by the human mind. Therefore such forms cannot be eternal. Notice that Christian theology, following Aquinas, represents God as pure act.

I don't view the differences as schools of thought as you do. The expression the "One" has a different life in different texts as do so many other ideas and perspectives.

I will leave your statements unchallenged as an expression of your theology.

The expression the "One" has a different life in different texts as do so many other ideas and perspectives. — Paine

Have you read how these differences are explained in the Metaphysics, especially Bk3, ch4 and BK13, ch6? The issue I think, is that all of the different ways which "the One" is held to be first principle, are unacceptable.

I just read this post elsewhere, about Aristotle and number (that's pretty much the context), so I want to share it and see what the inhouse Aristotelians think:

The basic Greek conception of "number," or what we call number, is that it is an abstraction from the countability of "SOME CONCRETE countable things" (as in, a countable/counted set of things like 8 bowls or 9 cows) to the countability of "ABSTRACT countable things," so, some kind of "unit." But whereas we moderns do all sorts of strange things, like seeing the Hindu numerals as hypostatic entities of some sort, and trying to found numbers in non-geometrical non-intuitive notions like set theory, Greek number theory maintains the intuitive basis of number (it "sees" the abstract "units," in a special form of highly abstract seeing theorized chiefly by Plato). It then assumes that there are certain primal relationships or ratios among irreducibly important numbers, which are taken to form the rest of the higher numbers in some way or another. This leads to all sorts of theories now regarded as fanciful, like the idea of "perfect" numbers etc. The Greeks also didn't really see the single unit as the "number" "One," rather, they saw the singular abstract countable unit as the "basis" of the countable sets (which are necessarily higher than one, since counting begins when there is more than one "something"). You can see that the Greeks (a) lacked a fully abstract sense of number like we possess, and (b) were obsessed with ratios and relationships and the derivability of higher from lower numbers in a way we aren't.

Plato's thought included significant Neo-Pythagorean elements, and his successors leaned into these in formalizing his work at the Academy, probably including the editing and publication of the standard edition of Plato's dialogues that comes down to us. Part of the complex heritage of the work done by these guys is the formalization or furthering of certain so-called "esoteric" doctrines of Plato regarding the radical primacy or transcendence of the One, its interaction with duality or the "dyad" to generate multiplicity, and the creation of more complex reality from this interaction. As in the number theory described above, it is often emphasized that the One transcends and precedes all multiplicity so thoroughly that even the names we use to describe it are strictly speaking "wrong." This doctrine probably owes a lot to Parmenides.

Aristotle feuded to some extent or other with this first school of Plato's successors, particularly their "Pythagoreanizing" aspects, and he defended a different conception of number. He maintains number is an abstraction from concrete sets of countable entities, but rather than supposing like a Pythagorean or Pythagoreanizing Platonist that primal numerical relationships underlies and is in a certain sense "hidden in" the concrete multiplicity we see, Aristotle has a more "conceptualist" theory of number in which the mathematician's abstraction of purely abstract numerical units from concrete countable things is a CHOICE, something he must ACTUALLY enact. To make this clearer, compare it with what Aristotle says about the concept of the infinite (better translated, the un-bounded, or even un-finishable). For Aristotle, the infinite is always "potential," and must be MADE actual, for example by a mathematician DECIDING to continuously divide a line more and more finely. For Aristotle, the concretely existing line is complete, finished, finite on its own, but "potentially" infinitely divisible. It's the mathematician or philosopher who comes along and "actualizes" this potential by actually dividing it. Of course, this process can only go on as long as the mathematician decides to continue it, so it's a kind of notional infinity that is quite distinct from our conception of infinity as something that is "always there, waiting to be found." It's really Descartes and Leibniz who start to think of things in this way, and even then, it's only because they think of the Platonic-Christian God as being the mathematician who always infinitely sees and thus "performs" the real (actual) infinity of everything.

Aristotelian and Platonic conceptions of number were variously synthesized, reconciled, subordinated one to the other, etc., and practicing mathematicians often strained against them as the math they were doing simply couldn't be contained in their assumptions. (Although the infinity assumption did "limit" mathematical thinking about infinity for a long time - some say for the better, some say for the worse.) In reality, Hellenistic mathematicians couldn't fit their more expansive, practicing mathematics into the boxes created either by Neoplatonic number theorists or by Aristotle, so they bent and sometimes broke those boxes.

I started a thread on Plato's metaphysics a few years ago in which I discussed this. From that thread:

Aristotle identifies three kinds of number:

arithmos eidetikos - idea numbers
arithmos aisthetetos - sensible number
metaxy - between
(Metaphysics 987b)

Odd as it may sound to us, the Greeks did not regard one as a number. One is the unit, that which enables us to count how many. How many is always how many ones or units or monads that are being counted. Countable objects require some one thing that is the unit of the count, whether it be apples, or pears, or pieces of fruit.

Eidetic numbers are not counted in the same way sensible numbers are. Eidetic numbers belong together in ways that units or monads do not.

The eidetic numbers form an ordered hierarchy from less to more comprehensive.

... the "first" eidetic number is the eidetic "two"; it represents the genos of being as such, which comprehends the two eide "rest and "change". (Jacob Klein, Greek Mathematical Thought and the Origins of Algebra).

:up: :ok: