Plato, a Reality Game in Four Levels (Session 7)

hello and welcome to the seventh section session of Plato a reality game in four levels and pass the mic off to the instructor as a Negrastani thanks everyone okay today other promise we will look a little bit more into the third man argument and also go over very briefly and it you know the first parts of Parmenides just kind of contextualizing what exactly is the context for those conversations that are happening between Socrates, Zeno and Parmenides. So before that, if anyone has a question, comment, thoughts, I will be happy to answer

or listen to nothing everyone silent not presently okay so okay then I'm going to jump into a little bit more technical stuff. Technical is always good. Yes. But before then, very, very, very brief comments about, you know, at least the beginning

parts of Parmenides. So two things, just so you get the kind of context for this dialogue, in the historical context and why Plato wrote it and who is Parmenides of this dialogue. One is that you see this is essentially a dialogue between a young Socrates. Socrates who is kind of very arrogant, he's brilliant, but he hasn't really shed his doxastic conservatism, namely vulgar thoughts.

He still thinks like a person. who has just touched the edges of philosophy but he hasn't really initiated to what does it mean to think philosophically. So he does not have, he has brilliant ideas but he doesn't have the profundity to work out the details of what these thoughts lead to, their implications and also the presuppositions. So we know that Socrates himself is usually associated with a method of leading, you know,

taking an opponent's claim, using it and ultimately leading it to aporia. But the thing is that in Parmenides, the actual inventor of this method, he uses this method against Socrates himself, and that's Parmenides. Because Parmenides is the one who comes up with the idea of rational argumentation, rational philosophy, and the force of the dialectical thinking. This is one thing,

Two is that here the kind of Parmenides that you are approaching is not the Parmenides of our nature, it's not the true Parmenides. There are narrative insinuations as that this Parmenides is essentially a very mature Parmenides, So as Zeno participates in some of the dialogues. By mature, I mean they have already come to the conclusion that some of their earlier claims were bogus, including that thinking and being is one.

This is interesting. So suspend your belief, do not associate this Parmenides with the actual Parmenides. It might be true that this Parmenides, because you get in Theaetetus almost some references that there is in fact a more mature Parmenides who had already started like Plato, like any philosopher, I start to question his earlier assumptions, and this is exactly that Parmenides. So Socrates in fact wants to boast his Parmenidian knowledge to Parmenides himself, whereas Parmenides

now has become mature, he doesn't accept those early Parmenidian claims. thinks that they can be led to aporia, to absurdities. And in fact that's exactly what he does to Socrates here. And this is one of those very few instances where Socrates is absolutely being crushed by a force beyond his imagination. If I had to formulate the most reductive but nevertheless helpful way of understanding

the topic of these conversations, at least at the beginning, would be just one piece of advice. It is always dangerous to use the names that pertain to concrete facts, to abstract categories. It's always dangerous to use names that concern concrete facts, namely things, particularities,

existence, to abstract categories. And this is exactly what Parmenides tries to show Socrates. Socrates implicitly knows this, but nevertheless he doesn't know the implications of this. By virtue of that, Socrates is shown repeatedly to be ignorant of the claim that he makes. So throughout the dialogues as it unfolds, Parmenides tries to unpack the implication of this, that Socrates himself had already affirmed.

Nevertheless, he doesn't know the implication of it, and by virtue of not knowing the implications or the consequences of his assumption, he always falls into traps. Third Man argument also encapsulates this because at the center of the Third Man argument is the idea that under certain misassumptions or wrong assumptions, forms can be reduced

to things, abstract categories can be reduced to concrete facts in modern lexicon, but also a more adverse situation, which Parmelides points out. Under these wrong assumptions, it would be possible to attribute the characteristics of things to the characteristics of forms. But insofar as forms are the ones that are ontologically prior to our talks, our posterior

talks about things and existence, that lead to vicious circularity. Again, the Third Man argument, as we were just talking about, has also two dimensions. a logical dimension, one an epistemological dimension. The idea is that the third man argument, even in its most extreme degree, simply leads to generation of infinite series of arguments. From a logical standpoint, there is absolutely nothing wrong with it. Generation of infinite series, there's nothing wrong with that. But when you bring the epistemic dimension to this argument, that's when it becomes regressive,

leads to vicious circularity. So I just want to make this clear. The Thurman argument, as we will look at, has two dimensions, logical dimension and systemic dimension by it I think at the level of the logical dimension it leads to infinite series but infinite series is not essentially a negative thing but so epistemically it's a problem because an infinite regress doesn't provide a foundation for knowledge like like if you need to know an extra form yes yes we never know okay yes absolutely yes so just wanted to give these tidbits about

the context of the dialogue so let's look at the last this essay can I ask a question sure um you were talking about how the um the philosopher is able to lead the sophist into an infinite regress? Is there like a particular thing that ends up having that interaction be terminated somehow? Can you elaborate on this? Like, how would you get out of the infinite regress between a sophist and a philosopher? No, no, no, I I didn't mean that. I was saying that philosophers can force, can corner sophists on their own assumptions and lead them to infinite regress based on their own assumptions.

Okay, and then after that, they're able to end up having the sophists see that their assumptions are leading to infinite regress. yes and that's exactly what does the socket is because success here in the softest yeah yes because he's ignorant of being ignorant of his own claim namely it is it were forms and things are separate he knows this but he's ignorant of its implications hence it ignorant of what it means so he hence is a sophist. And what Parmenides does is that he tries to push him on different fronts by unpacking the implications of this claim or scrutinizing, interrogating Socrates about

its different aspects, show that Socrates really hasn't grasped what it means for forms to be separate from things. As I mentioned, there are a number of times that Parmenides simply tries to show Socrates that he's essentially, he's what you might call to be a, has a common understanding of these issues, as a vulgar, naive understanding of this issue. Precisely because his ideas are based on duck sauce.

He tries to, he tries hard to say that all forms are different from things, but when he tries to explain them, he always uses metaphors, you know, allegories, or some sort of connection with things, understanding forms in terms of things. And that's, you know, for Parmenides is the doxastic residue of Socrates, which, you know, later on in Parmenides, he tries to come up with a recipe for training, which

he calls some sort of gymnastic regimen for a philosopher to be capable of shedding these doxastic residues. So it's famous that Velastus opens his argument against his theory of forms as quoted by Parmenides this with this line of attack it says this is quote from Parmenides glasses

using in order to start his construct his argument third man argument version of certain argument I suppose this is what leads you to suppose that there is in every sense that in every case a single form when several things seem large to you it seems perhaps that there is a single form which is the same in your view of all of them hence you believe that largeness is a single thing this is what Wallace's calls the first step of a third man argument so the The generalization of this paragraph constitute the first step of the last argument, let's

call it A1, which can be formulated as follows. If a number of things A, B, C are all F, F for form, there must be a single form F-ness in virtue of which we apprehend A, B, C as all F, as all being large. Now then Velasquez goes on in explaining the generality of A1, of this formulation, by saying that F stands for any discernible character or property. He then adds, the

use of the name symbol F in F-ness, the symbolic representation of the single form, records the identity of the character discerned in the particular, large and conceived in the form largeness through which we see that this or any other particular has this character. Now A1, this general formulation that Velasquez presents, tells us that the role of ethness is that of making possible the apprehension of A, B, C as well as all F. But surely the

point of the theory of ideas that Dr. Reno forms is that F-ness makes possible the apprehension of say A, B, C as F, this dog, that dog, and the other dog as being large, thus and so. So apprehending something as being thus and so, being such and such. Because F-ness is that by virtue of which, by virtue of participating in which, A, B, C, R, F. Therefore, at the very least, A-1, the argument A-1, should read, if a number

of things A, B, C are all F, then there must be a single form of F-ness by virtue of which A, B, C are all F and can be apprehended as such. But doesn't reference to our apprehension of A, B, C as F belong in the A1 argument at all? Granted that Vlastos' essay reads, when several things seem large to you, it seems perhaps that there is a single form which is the same in your view of all of them.

Now here, can't we take the scening and the viewing to pertain to discovery of the principle, which is the function as a premise of the third man argument, rather than as constitutive elements in the principle itself? So then why does Velastus think that the reference to apprehension belongs in the principle? The answer is that Velastus sees that even if the third man establishes as infinite series of largenets as a consequence of the doctrinal forms, this fact as such would not suffice

to refute the theory in the strict sense of showing it to be logically absorbed. for there is no logical absurdity in an infinite series as such. On the other hand, if this series could be shown to involve a vicious regress, the job would indeed be done. But then wouldn't Plato himself have regarded the infinite series as already unacceptable, and sufficient to refute the theory if it could be shown to be a consequence of it. Now, Velasquez, in his essay, recognizes this, this is the case, but since he thinks that

Plato is anyway committed to an epistemological principle, which when combined with the infinite theories of largeness does yield a vicious regress, he feels justified in putting it into the argument. This principle which Velasquez no more carefully formulates is to the effect that we apprehend an item as eth by virtue of apprehending the ethness in which it participates as being what in turn is. Therefore, on the assumption that all F-ness are F, the principle becomes, we apprehend

an item as F, in virtue of apprehending the F-ness in which it participates as also F. But while F-ness must indeed be apprehended to play its epistemological role, need it be apprehended as being F. There is an important distinction between the apprehension of X and the apprehension of X being dot and so. And if Vlastos sees this distinction, but nevertheless is convinced that the former cannot take place without the latter, he has given no reason for foisting this conviction

on Plato. Well whether or not Plato has implicitly mobilized an epistemic premise to ensure the unacceptability of an infinite series of largeness, it is clear that it is not necessary to the establishing of the series itself. And in his reconstruction of these aspects of Plato's argument, Velasquez makes no use of this premise, since it is this reconstruction which I try to explain to be problematic, try to criticize.

So from this perspective, I will try to get rid of this old reference to apprehension because that doesn't really can't really be justified given the Plato's given the Parmenides discussion himself is I I think this is more of a you know ad hoc modification that Velasquez himself has done to Plato's argument. One other comment before we get to Velasquez's reconstruction of what it takes to be the second

step is that in the passage which follows his formulation of A1, Velasquez lays down a plausible precision argument. It tells that Plato's argument prophesies to be a deductive argument, and that's a quote from Blastus, so I propose to treat it as a formal structure of inferences from premises, as stated or implied. For this reason I raise no questions about the theory of forms and presume no more information about it than I can extract from the text before me."

So already, Vlastus has already made a mistake. He says that he wants to treat Plato's, you know, Carmeniz argument as a deductive influence in which, you know, all the contents of your conclusions need to be contained in the contents of your premises, but nevertheless he adds an additional premise. And that's, you know, we saw that was the apprehension, but also another thing is that whether or not this procedure is a viable one, Volastis has already violated it by importing

into its explication of A1 a distinction between large as a character or property of large large things and the form largeness in which they participate. Large as a character or property of large things and the form largeness in which they participate. There's already a duxastic assumption that is completely unfounded according to the theory of forms. And according to Parmenides himself, the idea that he has already introduced, Velasquez

has already introduced a distinction between large as a character or property of large things and the form-largeness in which they participate. You see, the idea is that if forms are distinct from things, then the characteristics, then the form as such cannot be reduced to the characteristics of things which are separate from forms in their essence. So he has already done what I mentioned to you, he has already committed the sin of applying

the name of concrete facts to abstract categories. You see, this is the whole idea of reification. is not just you see abstract categories as concrete things, but the worst happens when you start to apply the name of concrete things to abstract categories. So, is this like substantiating forms? Yes.

But also aligning the distinction that you already made clear. This is exactly, you see, exactly, Velasquez tries to, in fact, Velasquez falls in the same traps as Socrates himself does in his conversation with Parmenides. He has already assumed, accepted that forms are distinct from things, but nevertheless he goes on, because he doesn't know the implications of the separation, he goes on and applies the concrete names of things to abstract categories large is a character of

property of large things to largeness as a forms in which those things participants I have a question sure um it isn't couldn't you argue that there's some like question begging going on in this view in that um the burden kind of on Socrates to show that there could be something between the one and the world of things and that like because the forms the whole thing about the forms is that they they do have something like characteristics

and that they can apply to one another they participate in multiplicity they have relations yes but you see that's the whole point that Plato and Parmenides want to make the plurality of forms is different from plurality of things and this is the this is this is the point that Socrates doesn't grasp because he tries to always is the young Socrates not the older Socrates of the Republic. Young Socrates can't really understand the significance of what it means that forms to be different from things as ontologically prior in the domain of thought. Hence he always thinks that the plurality of forms is on the same level or in fact is

identical with the plurality of things. And then this creates a kind of nebulous space where he can shuttle back and forth unfounded premises, both about nature of things and about the nature of forms. I noticed this a lot with like sort of extraordinarily like mythical animistic thinking. Is that just complete like fascination with the image and just focusing on the image and playing with that.

Yeah, well. There's a nebulous space of shuffling around. Yeah, well, you see, this is already in the divided line in the Republic that things, according to Plato, belong at their basic core to the realm of the perceptible, whereas forms are not perceptible. So you can't treat forms with the same characteristics that you treat perceptibles with. The thing is that Plato and Parmenides both want to argue against this young Socrates

that we should stop, treat forms imagistically and treat them instead noetically. So any question? Yeah, I was just going to ask. I'm not sure how. Now I feel like I've lost the thread on how forms relate at all to concrete particularities. And how would we know forms?

Well, this is an interesting question. You see, knowing forms, Plato wants to talk about both Plato and Parmenides, and knowing form is very different from knowing forms in terms of things which participate in those forms. In fact, for us to understand what it means for some things participating in forms, and by virtue of this participation or falling under forms, we can start knowing things we need to know forms in themselves. You see this is a very Hegelian gesture, I mean Hegel borrows this gesture against Kant.

But categories, and of course, let's not think about categories as form, just to spend. But nonetheless, I just want to make a kind of a parallel scenario for Hegel and Kant. The categories in Kant are bound to the transcendental subjectivity, mainly to the structure of experience. Now, because of that, they are constricted to the structure of the transcendental, what you might call, subject, namely its locality, its contingent formation, so on and so forth.

So Hegel tries to open this up that if categories are really, you know, constitute the infrastructure of science, then by virtue of you shackling them to a structure of transcendental subjectivity, You are already undercutting the possibility of scientific advance, scientific progress or cognitive progress. So Hegel's prescription is that before we apply categories to objects of experience,

the Kant's idea of transcendental, we ought to treat categories in themselves. That's exactly what science of logic is. Science of logic in fact allows you to unbind the real sciences, including the science that applies to experiential domain, namely empirical sciences. So this is important, that if you don't do this, then you are essentially bound to the restriction of the transcendental structure. And that basically ultimately leads Kant to be a conservative thinker on this point,

whereas Hegel is the one who is not conservative. The same thing about Plato and Parmenides is that before, in fact, yes, forms, we can know things through forms by virtue of those things that participate in them, but we can't really apply forms to things properly or understand which things participate in forms unless we take the idea of forms in themselves very seriously in order for Anders to to think about the logical forms or what Plato might call the ontology of forms the being of forms you need to suspend at least at the beginning any reference

or any insinuation of characteristics that belong to things rather forms as such so essentially you see Plato tries to open a logical a space for forms and this logical without this logical space forms the application of forms the study of forms, a study of what things fall, participate in what forms they can go all wrong. So first you reclaim the noetic dimension.

You understand how it works in itself and then by virtue of this understanding you are capable of the right epistemological application of these forms. Would you say that you do have to start, like when you're sort of discovering the forms in your Plato, you have to start out thinking them by analogy with things and then sort of experimentally refining your account from there? That's what Socrates wants to do. Yes, for Parmenides and for Plato, that's what you might call to be a student of philosophy

should do, experimentation via analogies and stuff. But for a philosopher, Plato says that this is a duxas, it's a part of a duxa. Why is it duxa? Because you really can't understand, you can't really apply or make these analogies correctly or sufficiently unless you have already learned the logic of forms, what forms are. And in order for you to understand what forms are, you absolutely need to suspend any reference to characteristics of things at that level. Because only the refinement of the logic of forms can lead to a healthy and potentially

correct or less wrong application of forms to things. a modern perspective it is very much acceptable this claim rather than you know at the time of Plato precisely because if you do not have no like okay let's go like this epistemology mathematical like in any field of science if you do not know the logic if you're not mathematics which are need to be treated in themselves regardless of their epistemological import,

if you can't do that, you will be led to the wrong application of these logical or mathematical structures in the domain of epistemology and science. Science. Does treating them in themselves sort of suspend for a moment epistemology in order to develop it and then bringing it back to epistemology, like epistemology becomes changed?

Yes, but you see Plato doesn't, in fact, doesn't, Parmenides at least, not Plato, But Armonie at this point, he just doesn't, he's not interested in the epistemological aspect. He just wants Socrates to understand that what does it mean really to treat forms in themselves as the dimension of thinking. Because form is kind of the dimension of thinking, not being or existence. He wants to argue, this is exactly, as I mentioned, this is mature Parmenides, he wants to show to Socrates that thinking as being undergirded by forms is truly different from being, from

the domain of the existence and things. And in order for you to understand what thinking is, what forms are, so then you can go on about how I can think things, you need to learn to understand the true, pure dimension of thought as such or forms as such by themselves. I'm just getting tripped up on the difference between truly having accurate knowledge of, a particular form and having knowledge of the nature of logical space as such.

You see, you see. Sort of knowing what, like could Plato really answer this question until Kant or something, you know, like, until transcendental subjectivity. No, I don't think so, but nevertheless, there is one thing here is that Plato doesn't... Okay, what we call the knowledge of forms is not an epistemological... for Plato, at least, it's not an epistemological thing, not an epistemological knowledge as pertaining to domain of objects. It is essentially what we talked about, it's a process of expanding the domain of intelligibility

in the so-called form of forms. It's a process of construction. So Plato doesn't want to make... First of all, as you say, I don't think that Plato can answer this question, but also as I mentioned Plato is not really uninterested that much about this kind of transcendental epistemic dimension of what forms are. All he is interested in is that what forms are themselves without being particularized to this form versus that form, namely the logic

of forms. The logic of forms I think is Plato in fact approaches more profoundly than Kant and it's only matched by Hegel. With Hegel's conception of reason? Or as like an unfolding? Yes. Yes. And the reason why I wouldn't care about the transcendental epistemic dimension is because the investigation of the forms would determine what the epistemic dimension is in the first place. Right? It is really hard to answer this question with regard to Plato.

Yes, I think Plato would say that insofar as forms adequately understood are the domain are basically are warranting the process of making the world intelligible through the function of the soul or mind. yes I think the plate would say yes to this question because without forms there is no intelligibility without and without intelligibility there is nothing that can ever be known about existing things in the world and essentially

Plato tries to at least in not in Parmenides essentially but you know in Philebus and in Fido he tries to argue that how soul and forms come together so is mind for Plato and forms are what you might call to be the archetypes of intelligibility or simply the dimension of the intelligible, formal intelligibility how they can, how mind can use these forms in order to craft a world that is intelligent, a structure to do. So before moving forward, let's have a cigarette and it gets a little bit technical from here.

Sounds good. Sure. Thank you.

Thank you. Thank you.

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Thank you. Thank you.

Okay, should we start? Yeah, sounds good. Okay, so... So as I mentioned, you know, that... Velastus has already violated in the first step of his arguments the distinction between large as a character or property of large things and form largeness in which they participate.

And there is no reason to assume, because Velasquez already said that he doesn't really, he doesn't want to introduce any more assumptions, more premises than what is already available in dialogues about the Doctrine of Forbes. But Plato himself in Phyto has made the distinction between a large thing, the large in the thing, thing, the large in the thecacteries of large in the thing and the large itself, in largeness.

In fact, in Parmenides also there is this section where Parmenides asks Socrates, have Have you yourself drawn the distinction you speak of and separated apart on the one side formed themselves and on the other the things that share in them? Do you believe that there is such a thing as likeness itself apart from the likeness that we possess? and so on with unity and plurality and all the terms in Zeno's argument. So nevertheless, while all this is true, the troicotomy in question can't be found in the

passages which constitute the Thurman argument. Velastus claims that F and F-ness are logically and ontologically distinct is crucial to the argument. But what he must mean is that it is crucial to his explanation of why Plato offers the Third Man argument, which he, Velastus, attributes to him and why Plato failed to refuse this. this crucial thesis doesn't occur in the Third Man argument itself, even as Blastus reconstructs it. So, as we will find out, we will find it wise to interpret large not as a standing

for or a character, whereas largeness names a form, but rather more neutrally as the adjectival expression corresponding to the abstract noun largeness, which latter, according to Platonic theory, is the name of an idea. So in the light of these remarks, let's reformulate the first step of Lastus's argument, A1. If a number of things A, B, C are all F, there must be a single form, F-less, in virtue of which they are all F. Now let us turn our attention to Velasquez's reconstruction of

what he calls the second step. This he translates as follows. Of which all these largeness and other large things appear large, it seems so. Consequently, another form of largeness will appear over and above largeness, itself and the things which participate in it. He then boils it down and generalizes it into the following principle, from the formulation of which, as before, we have omitted his reference to apprehension. This is the second step, A2.

If A, B, C and F-ness are all F, there must be another form, F-ness, in virtue of which A, B, C and F-ness are all F. So the question now is that why Vlastis writes F-oneness, like subscript, F-oneness, numerically distinct, instead of F-ness one. He writes F-ness one rather than F-oneness. By doing so, he introduces an unnecessary complication into the argument, making it

loose as though Plato had in mind a principle of which the following would be an illustration. If A, B, C and redness are all red, say scarlet, then there must be another form, red oneness, say crimson, in virtue of which A, B, C and red zero-ness are all red zero. But not only is there nothing in the text which requires him to attach the subscripts

to the F in F-ness, nothing in his formal reconstruction of the argument hinges on displacing of the subscripts. And while there would be no objection to so attaching them if it were clearly understood that it was to have no other force than if it were attached to the nes , actually the temptation to construe a oneness and a twoness as a standing for two different, specific or determinate forms of a generic fness is so strong as to rule out displacing of the subscripts.

So, Volastus indeed lays great stress on the determinations and the determinants which as he sees it are lurking in the argument. He sees that the theory of forms, the doctrine of forms against which it is directed and which he mistakenly believes to be the theory Plato actually held, which I mentioned last session, is not really Plato, this is more a lesson, this is not really what Plato really holds in terms of the doctrine of forms. So he sees that the theory of, Blastus sees the theory of forms against which it is directed, the third non-argument is directed, at which he mistakenly believes to be the theory Plato

actually held involves that the form F-ness is superlatively F, particulars being by contrast F. He concludes... One second. I think I have missed some of my... So involves that the form fness is superlatively f, particulars being by contrast monotonously

f. All monotonously are f. He concludes that being superlatively f and being monotonously f are two determined ways of being F. So it's doubtless this reasoning which underlines the choice of F-oneness in the formulation of A2, the second step of argument. But it fails to justify the placing of the subscript after the F in ethness, for these These metaphysically different ways of being F are not, in the usual sense, specific or determined ways of being F. The subscripts would belong to the being rather than to the

F in being F. So you see, remember that the doctrine of forms distinguishes being as attributed to forms and forms only. That being is very different from the being of things. The subscript that Velastus associates with F-ness in order to construct the Bergman argument essentially, illicitly, smuggles an implicit metaphysical assumption that Plato doesn't

hold, and that creates a conflation, a light distinction between being a form rather than the F in the being F as attributed to a particular thing. One more comment before we see how Vlastus combines A1 and A2 together. So even a casual reading of the passage which boils down to the second step of the argument, etut, shows that something is wrong.

For the text actually gives us two steps, Parmenides, by the text I mean Parmenides. One, when one views largeness itself and the other large things, a single largeness appears once again in virtue of which all these are large. Two, therefore we discover a new largeness which is over and above the largeness already noted. And if we ask what does the second of these steps add to the first, the answer is that

the largeness which appears in one is other than the largeness previously deserved. Like last session, at the end we were A, B, C, largeness, becomes one set and then you add a new largeness. It seems that the whole Thurman argument presupposes that the new largeness that is added to the previous set is essentially distinct from the previous largeness. So the significance of this point will emerge at the conclusion of how I'm going to talk

of this critical reconstruction of Blastus' argument. So after reconstructing the text of the Third Man argument into two steps, A1 and A2, and before he introduces two additional premises which he finds implicit in the text, Blastos pauses to make the following comment. This is from Blastos. Merely to compare A2 with A1 above is to see a discrepancy in the reasoning, which, so far as I know, has never been noticed before. Though it leaps to the eye the moment one takes the trouble to transcribe the full content

of the two-step in symbolic form. In A1, we are told that if several things are all F, they are all seen as such in virtue of F-ness. But A2 tells us that if several things are all F, they are all seen as such not because of F-ness but because of a form other than F-ness, namely F- oneness. To be sure there is a difference in the protesis of A1 and A2, and this is doubtless what has misled patrons or critics of the arguments. A2 includes, while A1 does not, F-ness among the things which have the property F.

The significance of the assumption which prompts this inclusion will be discussed directly and will remain the most important single issue throughout the whole of this paper. But if we simply stick to the logical form of the two statements, the disparity of reasoning as between A1 and A2 remains glaringly abrupt and unwarranted." This was from Velastus. Now, Velastus in this comment is pointing out that whereas according to A1, the members of the class of F particulars A, B, C, etc. are F by virtue of F-ness, according to the second step A2, the same particulars and F-ness as well are F by virtue of a different form

F-oneness. This accordingly, this according to Vlastus, is a glaring inconsistency, so that we can say straight away that if the theory of forms commit us to A1 and A2, we are in a position to reject it without waiting to derive further consequences, in particular a regress form A1 and A2. Now, two comments here are in order. In the first place, it must indeed be granted that the Thurman argument, as formulated by Plato involves that each large item, whether it be a particular or a form, participates

in an infinite number of largeness, and that it is large many times over by virtue of participating in these many largenesses. But notice that as being large by virtue of participating in a given largeness, an item is a member of a certain class of large items. Therefore, A, B, C, etc. would be members of the class of large particulars by virtue of the fact that each participates in the first largeness. On the other hand, A, B, C, etc., together with this first largeness, are members of

a more inclusive class by virtue of their common participation in the second largeness and so on. Thus, it does not follow from Plato's premises that the members of one and the same class of large items, example the class of large particulars, are members of that class by virtue of two different largenesses. It's simply a more generic largeness, not two different forms of largeness. The latter would indeed be a gross inconsistency. Therefore, unless we are going to rule out of court as absurd the idea that a large item

participates in many largenesses, all we are entitled to do at this stage is note that the regress as Plato sets it up requires that it be incorrect to speak of the form by virtue of an item, x is large, without going on to specify the class of large things with respect it is being considered. So if it is pointed out that the class whose members are large particulars can be different

as it must be from the class whose numbers are large particulars plus largeness only Clearly if large connotes a different property in each case, whereas the theory of forms that is under attack clearly involves that large is not ambiguously applied to both large particulars and largeness. This must indeed be granted. But must it also be granted that the difference between the properties which is necessary to make the two classes different in such as to entail that the word large is ambiguous

in the ordinary sense of ambiguous, that the regress involves that large be ambiguous in an old metaphysical sense is clear. There is indeed an absurdity in the idea that large particulars are many times large in the same sense of large. So what I said here is to show is that the absurdity is no matter of a single contradiction. The second and more important comment on this inconsistency is that Velastus is assuming that first step A1 and the second step A2 are both premises of the third minority.

Consequently, he supposes that the absurdity which we all find in the regress of the third man is already manifest in the premises. The whole idea that Glasses says that is deductive. So if the idea that it leads to the regress according to the principle of truth preservation and non-ampliativeness of deductive reasoning means that if the conclusion is that the third man A1 and A2 lead to internet regress, it means that the internet regress should have already been contained and included in the premises of the argument.

Consequently, he supposes the absurdity which we all find in the regress of the third man is already manifest in the premises. At a later stage, we'll talk about that A2 is not a premise of the argument, and therefore Velastus has not, as he supposes, given a good reason for holding that Plato was a puzzled a spectator of his own argument in Parmenides. Now, if we now ask how does Velastus conceive the role of etou in the argument, the answer seems to be that it is a hypothetical from which, by modus ponens, we are to draw the

conclusion. There is another rule, ethness, sorry, eth-oneness. this point of view two questions arise. One, what authorizes the hypothetical? Two, what authorizes the affirmation of its antecedents? Now, Velasquez sees the first of these questions. One, in terms of how to get from A1 to A2, and as it is immediately clear that A2 does not follow logically from A1 by itself. He looks for additional premises, which we end combined with A1 will do the job, and which can reasonably be said to be implicit in Plato's formulation.

But before rummaging into other texts to discover what further assumptions Plato made about of the real force. Blastus asks the purely logical question, what are the simplest premises, not given in the present argument, which would have to be added to its first step to make a too illegitimate conclusion? He finds two additional premises to be necessary. The first of these is the assumption of self-predication, which he formulates as follows. This is the third step of the argument.

Any form can be predicated of itself. Largeness is itself large. Ethness is itself eth. Now, this phrase self-predication is a misleading one. To begin with, there is the obvious point that it is not largeness which is predicated of largeness, but rather large or material mode of being large. It is not largeness that is being large, but the material mode of being large, being large, as attributed to a thing.

So, what is needed is indeed a principle of predication. But to speak of self-predication in connection with forms is to run the risk of confusing the principle needed with the principle of self-participation, i.e. to confuse largeness is large, with largeness participates in itself.

So since the second additional premise required by the argument will turn out to be a principle of non-self-participation, i.e. the very denial of self-participation, it is clear that the above confusion would lead to the discovery of inconsistent premises in Plato's argument, erroneously. Velastus does indeed discover an inconsistency between two additional premises required by the argument, and it is confusion which leads him to do so. But it is more radical confusion in which the danger to which we have been calling attention

plays at most an auxiliary role. The assumption Velasquez has in mind would be formulated more correctly as the adjective corresponding to the name of any form can correctly be predicated of that form. The adjective, this is quote from Glasses, the adjective corresponding to the name of any form can correctly be predicated of that form. This might well be called the F-ness is F assumption. However, there is enough appropriateness to the name assumption of self-predication to

warrant its use, provided the above points are kept in mind. Now A3, which was, you know, any form can be predicated of itself, large message itself, large, etless is itself, which was the third step, A3. Now A3 seems more relevant to the question. What authorizes the affirmation of the antecedent A2 than to the establishing of A2 itself?

So let's turn our attention to the second of the additional premises. This he calls the non-identity assumption and formulates it as follows. This is called A4 in Blastoise. If anything has a certain character, it cannot be identical with the form in virtue of which we apprehend that character. If x is f, then x cannot be identical with f-ness. So I'm going to skip this one precisely because what I said earlier about a3 is already implicit

in a4. Namely, the idea that the illicit transfer of F, F-ness, and being in F, as being, you know, a characteristic of a thing. So Velasquez is clearly correct in saying that both self-predication and non-identity are essential to the Thurman argument.

Now, are they also sufficient when joined with one to generate a two? Velasquez thinks so, though he qualifies this by adding, in quotes, though in a very odd way. And the reason for this is that he has just shown to his own satisfaction that these two additional premises are mutually inconsistent, so that we should not be surprised to see them justify all kinds of contradictory conclusions. Now, let us look at his demonstration of this inconsistency. He begins by giving a very dense formulation of namely fness is f.

He follows this with a more dense formulation of a form, namely if x is f then x cannot be identical with fness, where x is a variable which includes not only particulars but also forms in its range of values. He continues to the fifth step of the argument. Substituting fness for x in A4, we get A5, which says if fness is f, fness cannot be identical with fness. And since the consequence of A5 is plainly false because self-contradictory at least one of the premises from which it follows.

A3 and A4 must be false. But this demonstration is a result of a series of confusions. The passage which is most clearly diagnostic of this confusion is that in which Vlastus' analysis comes to this, in quotes, it says that the odd way, in which as he sees it, A1, A3, and A4 are jointly sufficient to establish

Or in Blastus' words, since these premises warrant the proposition that F-ness is not identical with F-ness, they will warrant the presupposition, sorry, the pro... Since these premises warrant the proposition that F-ness is not identical with F-ness, they will warrant the proposition that F-ness is identical with F-oneness, which is a form not identical with fness. And a2 will then follow from a1. Now at this point, Velasquez replaces to a footnote his formal analysis of this reasoning. He says, for we know from a1 that if a number of things are f, there must be a form.

The number of dogs being large, there must be a form. Largeness. through which they are apprehended as F being thus and so. Whence it follows that A to B if A, B, C and F-ness are all F there must be a form F-ness through which they are apprehended as F. but if f-ness is identical with f-oneness we may substitute f-oneness for f-ness in the second clause of a2b which will produce a2 the second step of the argument but now here notice the use

that is made of A1 in the argument. Whereas A1, as initially formulated, told us that if a set of particulars A, B, C, etc. are F, there must be a form F-ness by virtue of which they are F, it is now being used as a more general principle to the effect that if a member of things are F, there must be a form F-ness. where the things in question may be either particulars or forms. Let us call this more general principle G. Now clearly something like the original A1 results from applying G to the case where the things which are F are particulars.

This suggests that A2 might be the result of applying G to the case where the things which are F are F particulars together with the form, ABC large being one set and then it admits another largeness. This suggests that A2 might be the result of applying G to the case where the things which are F are F particulars together with the form, F-ness, in which they all participate. Clearly, however, the second step, A2, requires, in addition, the use of an assumption of non-identity.

But it is even more important to note the role played by the expression f-ness in A1 as it is used in the above footnote. An expression such as f-ness may be a variable in either of the two senses. 1. It can serve as a representative symbol. In this use, ethness would represent the name of a form, an idea. To assert a formula which includes a representative name is in effect to assert each and every sentence which results from the formula by replacing the representative name by a name.

Consequently, to formulate an argument in terms of ethness, where ethness represents the name of a form is in effect to propound a class of arguments, in each of which there occurs not fness but the name of a single form, largeness, for example. 2. fness can serve as a variable proper. The distinct feature of a variable proper is that it makes sense to say for all values of, for example, v for some values of v, etc. Therefore, where fness is a variable proper, it makes sense to say all fness, some fness,

the fness which, there must be an fness which, etc. These contexts are improper for representative names. These are two different things. Now I said just now that an expression such as f-ness may be a variable in either of these two senses. However, I didn't say that either or both of two senses. But it can readily be seen that provided care is taken, these two modes of variability, symbol and variable proper can be embodied by one and the same symbol.

In this case, a formula involving ethness would represent a class of sentences in each of which there would occur, instead of ethness, one of the following, largeness, triangularity, where the latter however are to be constructed not as names of single forms but rather as variables said differently the latter would be used in such a way as to admit of such context as all largeness there is a triangularity etc and the substituents for these variables for example largeness would be

designated by some such device as the use of numerical subscripts example largeness one largeness two etc now here note that it would be obviously inappropriate to put the subscripts inside the variable like large one-ness large two-ness the way that Vlastos does F1-ness F2-ness so on so forth now if we now ask which of these uses of F-ness is appropriate the answer is obvious F-ness here must be a symbol which represents a class of variable things,

particulars. Indeed the generalization G that Vlastus has made for moving from A4 to A5 correctly formulated as if a number of entities are all F there must be an f-ness by virtue of which they are all f is a formula which represents a class of propositions the one of which would be general largeness which says if a number of entities are all large there must be a largeness by virtue of which they are all large and an application of this proposition to the case of large particulars would yield

If a number of particulars A, B, C are all large, there must be a largeness by virtue of which they are all large. This again, in turn, must be carefully distinguished from this statement. If a number of particulars A, B, C are all large, they are so in virtue of a form, namely largeness. For in the latter, the one that I just mentioned, the largeness appears as the name of a single form, whereas in the previous one it is a variable.

If we approach a Third Man argument in the light of these distinctions, which Velasquez has surreptitiously elided, puzzles and perplexities melt away. The movement of thought is from L, which was saying, if a number of particulars, ABC, are all large, they are so in virtue of a form, namely largeness, and this is by induction, to G largeness, which was saying, if a number of entities are all large, there must be a

largeness by virtue of which they are all large. And from G largeness, which was saying if a number of entities are all large, there must be a largeness by virtue of which they are all large. To the series of hypotheticals which are its applications. These hypotheticals would be H1 largeness as above, H2 largeness. If a number of particulars, A, B, C, etc., and the largeness they jointly exemplify are large, there must be a largeness by virtue of which they are all large. H3 largeness. If a number of particulars A, B, C, etc., the largeness they exemplify, and the largeness exemplified by all the preceding items are large,

there must be a largeness by virtue of which they are all large. So, indeed, since the Third Man argument, though phrased in terms of largeness, is intended to have a more general validity, largeness has a representative function, and at a certain stage in the logical movement of thought, plays the role of ethness in the last paragraph of the preceding section, much more than the self-predication and non-identity must be found implicit in Parmenides, embody a cogent argument, is to embody a cogent argument.

But what about the charge that self-predication and non-identity are mutually inconsistent, which is the last this as I mentioned last session the whole idea of self predication is really bugbear of the whole third and that's where basically blasts are glasses critique emerges and I can ask a quick question about the self-predication thing sure is that is that okay or do you want to absolutely absolutely go on well I mean we were talking about reading Plato through a Hegelian lens and if we do that isn't like isn't this the failure of a form to self-predicate actually a good thing in

a way to preserve because it's the motor of dialectical yes yes yes that's absolutely correct and Parmenides exactly makes this point in a very implicit way first of all the thing is that our men in this choice to show that if you do not have a form that doesn't surrender self-reducation the whole idea of dialectic is impossible whether in the common sense or in the technical platonic sense yes this is absolutely true ok thanks but but but then it almost almost seems like that like that we're talking about right now is an effort to like explain away self-predication or well yeah I guess I'm not sure where you're gonna use yourself

predication is essentially comes down is not so subredication cannot be applied to forms as such self-predication is a property that can only be applied in to being in a form being in a form being in large being in large it's being in large self predication here tries to show that this kind of self-predication and that's a transition that you see if you take forms in themselves as a kind of a lot logic of forms as such the transition from forms in themselves to being in a

particular form is that epistemic transition so okay so it's like the tension between the form and particulars to which the form applies yes and and the thing is that's Plato tries to show that self-ready once after you apply self-predication the forms you simply mess up the whole doctrine of forms or by virtue of that you undermine this transition what actually can make this transition to understand what it means to be a form and what it means for something to participate in for being in for example ethness which where you can actually apply self-predication or understand self-predication. Okay, thanks, that makes sense.

So for... So as I said, what are the charge... What about the charge that self-predication and non-identity are mutually inconsistent? Now a quick look at these principles in the light of the distinction we just investigated, This is the groundlessness of this claim. For properly formulated, the assumption of self-predication becomes, let's call this SP, self-predication, all ethnicities are F. And the assumption of non-identity, NI, if X is F, then X is not identical with the

f-ness by virtue of which it is f. So you see the whole idea that the Thurman argument hinges on these two, on the functioning of these two. And the one is the self-gradication of all f-ness are f, and then trying to create a sets, increasing infinite series of sets series of sets where in the previous forms of F-ness are being you know treated at the same level of things a b c largeness one or large one-ness and then another

large two-ness comes and then will be added to this set this is because the law of because of because the assumption of non-identity which says that if x is f then x is not identical with the f-ness by virtue of which it is f and that's how it creates an infinite series and a moment at a moment of reflection makes it clear that vlastus found an inconsistency because he treated the f-ness in its formulation as a representative name, once it is realized rather than variables, proper variables, once it is realized that what is needed are formula in which ethness

function as a representative variable, it is seen that the assumption of self-predication and non-identity are to be formulated as above and the inconsistency vanishes. This is the schema of such a construction of where the consistency of the Doctrine of Forms can go away. F-ness one, rather than F-oneness, F-ness one is F. A, B, C, etc. and F-ness 1 are all F.

Now the generalization. If A, B, and C, etc. and F-ness are all F, then there is an F-ness by virtue of which they are all F. Next step. There is an F-ness by virtue of which A, B, and C, etc. and F-ness 1 are all F. call this fness fness 2 rather than f2ness if fness 1 is f then fness 1 is not identical with the fness by virtue of which it is in f it is f sorry fness 1 is not identical with fness 2 if a b c etc and fness 1 and fness 2 are all f then there is an fness by virtue of which they

they are all F. Fnest 2 is F. It can be constructed as a last stage, A, B, C, etc., and Fnest 1 and Fnest 2 are all F, ad in Freudian, reconstruct. So is the argument that we just constructed to be found in Parmenides? Certainly not. But what about explicit, it's explicit for? But then, there are many ways in which formally complete arguments are found in arguments

and actually pronouncing it. And I would be willing to say that the above is merely implicit in the text of the Parmenides only if this phrase is so understood as to be compatible with the idea that this argument is fair, albeit idealized, representation of Plato's thoughts, and in particular with the idea that its premises can be said to have been Plato's premises. But it is not, of course, my claim here. in the, you know, treatment of Velasquez's third man argument.

I think on the other hand that the careful reading of the complete argument as Plato gave it is sufficiently convincing. I say complete because nowhere in his article does Velastus reproduce, let alone analyze what can be called the third step of the argument. This is a quote from Velastus, which is actually based on Velastus's translation of Parmenides.

I suppose this is what leads you to suppose that there is in every case a single form. several things seem large to you, it seems perhaps that there is a single form which is the same in your view of all of them. Hence you believe that largeness is a single thing. What then, if you similarly view mentally largeness itself and the other large things? Will not a single largeness appear once again in virtue of which all these appear large? It seems so. Consequently, another form of largeness will appear over and above largeness itself and the things which participate in it, and, again, covering all these yet another, which will

make all of them large, so each of your forms will no longer be one, but an indefinite number. So if Vlastis had devoted as much care and attention to bringing out the logical form of the third step as explicitly stated in Parmenides as he did to the other steps, he must surely have been led to distinction between a matrix of general principles and the specific steps in the regress constituted by recurrent application. And this in turn must have led him to appreciate the diversity of roles played by largeness,

failure to discern which is responsible for the most of the confusion in his analysis. It is Velas' diagnosis of Plato's philosophical frame of mind at the time of writing Parmenides, which is the target of this portion of this argument against Velastus. This diagnosis occupies the second and larger part of Velastus' paper, and if Velastus is right in his main contentions, then Plato could not have had in mind the argument with which we conclude the above section. Fortunately, this part of Velastus's paper rests on a few key premises in the discussion

which we can be very brief. Velastus summarizes as follows the conclusion to be drawn from what he takes to be the fact that Plato presented the Third Man argument with no clear indication of a reputation. If Plato had identified all of the premises which are necessary and sufficient to warrant the second step of the third man argument, he would not have produced the third man argument at all unless he were simply pursuing a logical game for its own sake, which is not what he is doing in the first part of the Parmenides. inestating the third man argument and in leaving it unrefuted is revealing a that he did not

know all of its necessary premises whence it would follow that be he had no way of determining whether or not it was a valid argument. Now the crucial step in this reasoning is the contention that if Plato had realized that self-predication and non-identity are indispensable premises of the argument, it would have detected their inconsistency and would therefore, instead of playing with a regress, have turned directly to the problem, does my theory of form involve the commitment to these inconsistent principles? But we have undercut this step by showing that the idea on which it rests, namely that self-predication

and non-identity are patently incompatible is mistaken. Up to this point, therefore, Velastus has given no good reason whatsoever for supporting that Plato had not identified all of the premises and therefore had no way of determining whether or not it was a valid argument. But Velastus has another restraint to his bow. He claims to have independent evidence, evidence that is, which does not spring from his analysis of the Thurman argument, for the thesis that Plato had not identified all of the necessary premises. specifically he proposes to establish one that Plato's theory of ideas even

its later form is through and through committed to self-predication but also be that Plato never came to an explicit recognition of this fact The first one is clearly the crucial step, for unless, if it were to, the fact upon which Velazquez lays such a stress that Plato nowhere explicitly formulates the principle of self-predication, could scarcely be that Plato failed to recognize an essential feature of this theory. Nor could evidence be found in the fact that Plato in the later dialogues arrived at a

conclusion about the realm of ideas, for example the genus-species structure, the existence of a form motion or change which must have been seen to be incompatible with an explicitly entertained principle of self-predication. On the other hand, if Velasquez can establish that Plato's theory of ideas, even its later form, is committed to self-predication, then one can hold that Plato was cognizant of the logical force of the Third Man argument as we structured it, and therefore that he recognized that self-predication is its key premise. at the expense of supposing either that Plato believed that the argument refuted his theory of ideas,

or that it could be saved by dropping the generalized assumption of non-identity. I think it's fair to say that when Plato was writing the earlier dialogues, he had not yet been led to the question the self-predicational force of the language of his theory but this by no means equivalent to the idea that he was implicitly thinking of his forms as self-predication are you taking this for granted to establish this we will have to show that significant features of the

early theory of ideas or of the arguments developed in connection with it imply a commitment to self predication in other words one would have to show that self-predication plays a role in the philosophical use to which plato put the language of the theory to do this is no simple task and And I'm not going to attempt to settle the matter one way or another in terms of Plato's theory of forms, that whether it actually presupposes an implicit account of self-reeducation borrowed from the earlier work or not.

I do however want to call attention to at least two considerations which contribute to an explanation of the fact that Plato used language with self-predicational forces, yet do not require us to say that even implicitly thought of the ideas as self-predication. So in the first place, There is the obvious fact that the names of the ideas had to be formed from the roots of the class terms and adjectives, the applicability of which to particulars was to be explained

by the theory. Thus, the name of the idea in terms of which statements of the form is a triangle are to be explained would be a noun or noun phrase built from the root of the triangular and triangle. Only when the concept of universal had been hammered out in philosophical debate would it come to be seen that there is something bizarre about the use of the triangle itself to designate this idea, and until the concept of a universal had been hammered out, the

distinctive expressions which philosophers used to designate them, for example triangularity, large-ness, largeness, etc., did not exist. In short, Plato did exactly what we should expect. He took the existing noun triangle and put it to a new use. But the fact that by referring to the idea as a triangle itself, he was using language which implies that the idea is a triangle does not suffice to establish that Plato thought even implicitly that the triangle itself was a triangle.

To show this, as I have mentioned, one must show that this implication of the language is put to philosophical use. In the second place, the early dialogue asserts the role of the ideas as standards or norms which objects in the world of becoming strive to realize, but necessarily fail to realize fully because of the inherent fuzziness of becoming. Now if we thought along these lines, we should carefully distinguish between the idea or universal and the nonexistent ideal which it specified, example, between a straight linearity

and a perfect straight line. But this distinction was not a datum for Plato, and he could have led to draw it only by the pressure of the perplexities which arise from a failure to draw it. Plato ever draw in his own mind this distinction between ideas and ideal particulars. You see, two different things. Ideal particulars are different from ideas themselves. One immediately thinks of the Mathematica. As usually conceived by those who find them in Plato, they are

existent ideal particulars, the so-called analytical idealities, the third segment. They are existent ideal particulars which are other than the ideas that they exemplify. As for a distinction between ideas and non-existent ideal particulars, Plato was not in a position to draw it until he had acquired the insight into non-being, which is embodied in that most wonderful of the dialogues, the sophists. Now the resolution of this problem is not our present concern. We will get back to this.

The point which I would like to make is that to say that Plato language embodies no distinction whatsoever between the circle itself and the ideal circle. And in general, between an idea and the ideal it specifies. is not the same as to say that Plato implicitly thinks of the circle itself as an ideal circle. Two different things. So, one more time. There is nothing virtually in Plato's language, no distinction to distinguish between the circle itself and an ideal circle.

And in general, between an idea and the ideal it specifies. But this is not to say that Plato implicitly thinks of the circle itself as an ideal circle. The latter statement is much stronger in its own force than the former. That Plato failed to draw an explicit distinction is indeed a reason for supposing that he implicitly thought of the ideas as ideal objects. But it is not a compelling reason, as is made clear by the fact that we can conceive of considerations which would lead us to say that although Plato drew no such explicit distinction, he implicitly distinguished between ideas and ideals.

Those considerations would spring from an examination of the different philosophical uses to which such expression as the circle itself was put in the context of different problems. Well, whether or not a careful examination of the evidence would lead us to the conclusion that in the early dialogues Plato thought of the idea as self-predicational, I think that by the time he wrote the first part of Parmenides, he had faced up to the question, is, for example, the large itself large, and answered it in the negative, no. This thesis is by no means a novel.

As Velasius himself has pointed out, it is the orthodox view of Plato. On what grounds does he reject it then? There is a quote from Glasses, if Plato never stated it, the assumption of self-predication, what reason can be given for saying that he did make it after all? The reason is that it is certainly implied by various things he said and believed. It is implied first of all both by his degree of reality theory and by his copy theory of the relation of things to forms. Now, the thing is that, first of all, it is highly dubious comment to hold that if Plato

ever held a copy theory of the relation of things to forms. This is in fact, when you read Parmenides, right around, I think it's 135 or 136, this This is in fact what Parmenides tries to prevent Socrates from arguing, that the relation between form, this is, I think we will talk about this in the next session because this is a little bit more complicated and requires more thinking. The relation between form and a thing is not the relation between a model and its exemplification. So many of us think that forms are in fact some archetypal models which things exemplify.

This already, according to Parmenides, confronted with the abyss of senselessness, Namely, duxastic domain. In the sense that it reduces the idea of form into part-whole relationships, which simply reduces to a thing again. Anything that can be divisible is a thing. When so far as forms cannot be divided, we cannot reduce it, we cannot understand in terms of part-whole relationships. And in so far as we cannot understand in terms of part-whole relationships, we cannot attribute to it properties that we attribute to models or archetypes.

Is the basic idea kind of that Vlastos is accusing Plato of illegitimately applying linguistic structures that are only appropriate for the manifest image to sort of a realm of the scientific image and that if you replace that with the form of a mathematical structure that then that's like then you sort of get around get around it seeming like forms need to have thinghood or properties yes but yes yes but not really I don't think that like in terms of manifest scientific frameworks.

But yes, this is exactly, as I mentioned, that's when I mentioned. He accuses him of basically playing that illicit game of attributing the names of concrete facts to abstract categories and shuttling back and forth implicit assumption. But it's Volacis that does this. Not Plato. Right. Parmenides, I think we need to, we'll get next session to this core that Theo pointed out, the first few paragraphs until 137, where Parmenides essentially challenges Socrates,

who sees forms as models. and things as their copies. Parmenides is essentially this mature Parmenides, as I mentioned, is not that Parmenides that we usually understand Parmenides. Essentially Plato himself here, who tries to educate the, so this is famous, Miller's interpretation particularly, that Socrates here in Parmenides is simply an avatar for a philosophy student. Parmenides himself is the philosopher, Plato. So what course of training should the philosopher provide the student of philosophy with

so as for the student to be capable of shedding such assumptions, but also be cheerful of not making these illicit movements between premises and conclusions. I have a question about this relationship between the form and the model. So I'm sort of imagining it as kind of like in Macbeth's article back from the mathematics from Antiquity of the Renaissance class where she's comparing the Euclidean line to representations of Euclidean line and Euclid, but that's fundamentally different from the relationship between Platonic forms to their models, right? Yes, yes, absolutely. You see, there is, however, you remember that we talked about Proclus' commentary on Euclid.

And Proclus thinks that, so you have the universality in itself. And these are what you might call to be forms in themselves. They are not even models. But he creates an estrata of intermediary universals down to concrete universals. So I think the question ultimately comes down that yes, forms are not models, ideal things

don't represent ideas in themselves. Nevertheless, there should be a level of intermediary generalities that allow concrete things to participate in one or another idea so that they can create their ideal the ideal of their own copies this is this is I think this is where essentially the idea of demiurge and the craft sold as a

craftsman come into the picture in Plato so the thing is that we have we have two things here one is the idea of participation in a form what does it mean to participate in intelligibility this is not essentially you don't even need the idea of model and copy and these intermediary universals in it you just need to understand what the form is the form of beauty form of justice need to form itself the form of it rather than the content of it so that's one once you participate in it as a particular agent what you go through the process of this craftsmanship doesn't turn you to the idea because the idea is inexhaustible

it is not a model that you can give a perfect copy of what you the process that you undergo is the process of crafting an ideal an ideal exemplification of of this idea in a thing, namely yourself, for example. There's two different things, and that's where the idea of these intermediary universals come to the picture. For example, the Euclidean line, you have different levels of intermediary beside the Euclid's construction that allowed you to create, for example, such and such, thus and so, ideal triangles.

But the idea of triangularity, triangularity as such, is different even from these particular ideal triangles. In fact, we saw that even in Euclid, and that was Procru's commentary on him, without the idea of the triangle, completely dissociated its particulars, you couldn't in fact make such constructions in the realm of the particle and the concrete. We will, there is like 30 minutes of this term and argument to conclude it. We will do it

next session because I know that they was a little bit convoluted but one of the things that's one of the things that okay next session still read the early sections of Parmenides because they are extremely very important, and they can also be quite confusing. One of the most important things that we will look into next session in conjunction with the rest of the third argument is this use of is, something is large. That's another one of those traps that Parmenides

identifies in Socrates. This is, if you are not capable of distinguishing it, differentiating that what does this is, is, what does this is, what does this is denote or refer to, you will end up again in the same doxastic mousetrap. will be coming back and tweeting forms as things. Can next time can you talk about Plato's conception of time at all? Sure, okay.

Or like bring that into the discussion? I feel like that would help clarify some of this for me. Sure, sure, sure, sure I will try to. Yes, okay, let me just going down somewhere. So, did anyone want to say something? Yeah, I sort of want to hop in. Sure, go on. I mean, I feel stupid responding with these questions to that because so much of it, I feel like, went over my head. But, yeah, it would be helpful if you can send any links or anything to supplement that that'd be great or or if you can did you read did you read the beginning of any of you read the

beginning chapters of Miller's book because it is quite actually I think edifying in terms of some of this discussion and it implicitly shows like some of the illicit moves that Velasquez makes and Velasquez mistakenly attributes to Plato, it shows that in fact Parmenides as avatar of Plato, the mature philosopher, he has already talked about them. So basically if you want to read it, you need to read it from the beginning until page 50,

something like that particularly chapter chapter one yes the other thing I was going to ask was if the relationship of I actually I mean I don't even know if it would be called a relationship at this point what what then is the relationship of forms to the instances of its particularities because if forms don't need to be embodied in a particular instance if forms somehow

represent a set or a conceptual set of those instances then how do we even talk about those forms if not through their instances it's kind of like that's part of what I want to ask about time because it seems like don't they have like a certain future anteriority in relation to their instances like yes I think we sort of have a will have been quality yeah I mean I think this is a little bit complicated question because it has different dimensions just for one and And then that's exactly what I'm going to talk about next session in the continuation of the argument. But in terms of time, yes.

So you see from at least one perspective, is that the idea that the ideas, as Theo says, that the relation between forms is quite different from the relation between things. And also the relation between things and forms. So first the thing is that the Doctrina form is essentially and essentially about the forms in themselves. This is all Plato was trying to say that you can't small any assumption about relational things about things of things and ideas into them. One. Two, now how then can be they related now this comes to the idea of participation what is exactly

participation this is exactly also where the model comes the model the construction of a model corresponding to an idea but this model is not the idea itself. Model is what you might call to be an intermediary domain through which which we can participate in an idea. But this is not the model of idea, this is not the idea of copy model relationship because model, copy model

relationship essentially belongs into the realm of things participating in forms rather than forms in themselves so this brings again this brings back to the idea of craftsmanship according what does it mean to construct something according to a model and that model supposed to give a vague a vague nevertheless intelligible account of one form or another. This brings the idea of the process of construction, and ultimately Plato's demagogic principle in Philebus,

that this ultimately comes back to the question of the good, and the question of time in general, in the sense that this is the process, through which the idea that the relation between forms are in excess of the relation between things and forms. This very excess guarantees what you might call to be the construction or what you might call to be the movement of things toward ideas, without things and ideas ever become one.

This is the process of intelligibility as such. The process of intelligibility, or the principle of the good, requires the abolishment of any form of relation, suspension of any relation that might lead to totalization, to conclusion of this process. If a thing becomes the idea, because if there is a copy model, a copy at some point, the process of construction can become the archetype itself. But by virtue of getting rid of this distinction, I mean, understanding forms in terms of archetype

copy relation, Plato in Philippus tries to show that this is a process that is open-ended. Because if you hold it within such relations, the idea of intelligibility is retroactively ennurled and become voided. Means that there is something that you can ultimately reach and say that this is what the intelligible is. But the whole idea of Platonic good is the process of intelligibility needs to abolish any form of totalization or conclusion or perfection. That's why there is a massive charge of impiety against Plato, because this is already what

you might call to be an anti-theistic, fundamentally anti-God worldview. the whole principle of the perfect good needs to be abolished by this movement of the intelligible. It can never attain the perfect intelligible, but nevertheless, this being unshackled by these illusions of reaching the perfect, the perfect copy, the perfect model, it can move forward and forward and open, basically expand the order of intelligibility and that's what basically for Plato the good consistent which the good ultimately coincides with the figure of time in Plato. Time in the sense that it shatters as I mentioned

all illusions of temporal totalization as if the totality of history has been achieved, as if a totality of idea has been achieved. Plato, this is again part of the Republic implicit political message, social political message of the Republic, is that if there is in fact a form of doctrine that advances these kinds of things that you can reach these things, the thing in itself the idea in itself the totality of the of the form that's exactly where it leads to tyranny it creates a totality that mistake itself as a

totality of all there is and that's why I think but as I mentioned but use quite right with Plato as a communist in a very accurate sense of communism is a real movement that pierces through the present state of affairs achieved totality of history. Why ascribe this value judgment good to this movement of becoming? Because, you see, why is it good? Because essentially Plato and Parmenides believe that if there is not such a process that warrants

this piercing through of totality, we ultimately end up with totalities. And if there is a totality of the given, the totality of the achieved idea of form, the form of justice, so on and so forth, that leads to two things. One, tyranny, in the sense that it represents itself as the totality of all there is, hence completely basically justify what it does and what can be done under this form, for example, under this totality. Exactly like the present situation, in the sense of capitalistic system, that insofar

as capitalism is not a totality of history, as it presents itself as a totality of history, anything that is done under this totality and conformed to this form is considered to be good, which of course it creates more and more of problems. The second thing is that the question of totalization or perfect copies, perfect archetype, perfect ideas, perfection, for Plato leads the question of unintelligibility. the sense that again you come back to the idea of the given. The perfect becomes your given.

But for Plato is that intelligibility essentially needs to separate itself from the given in any form, whether coming before in advance as the given data, the given truth, or given at the end as the given truth of achieved totality or achieved perfection. But these are ultimately in different scenarios lead to obstruction of intelligibility, taking for granted of certain truths. But this is not what truth is that's that's exactly what Plato wants to show the truth is a product of

an ongoing process rather than something that can be taken as the given isn't it also that there's a certain teleological aspect to it and that and that it's not just any old becoming in itself but that there it's becoming that involves an increase in freedom and knowledge? Yes. Like a sort of destruction of transcendental absolutes and a kind of optimization? Yes, yes. No, it is. I mean, I didn't want to talk about this because you see, when you talk about teleology, Plato is really a teleological thinker, but he's not just any kind of teleological thinker.

It would require much more discussion about exactly what kind of teleological thinker Plato is and what exactly distinguishes his idea of Thielus from, for example, our Sotelian teleological system. But again, in answer to Theo, so what makes it good is the idea that it warrants the expansion of intelligibility, because anything that obstructs this process will lead either in the social domain, in the tyranny, or in the axiological, epistemological domain in obstruction

of the intelligible, and hence becomes the given, which essentially what the intelligible is not. See, what intelligible is not, is not given. And that's for, why is that Plato forms are essentially the exemplifications of the group, because they are intelligent, because they warrant the process of, infinite process of expanding the horizon of the intelligible. so then it's like even our account of what forms are as such is subject to revision kind of like as knowledge

progresses we would we define them and yes and more sort of yes find them better yes I mean the whole thing is that you recognize you you can you can you can talk about their logic but you don't know what they are in the context, for example, what justice exactly is. It's a matter of rendering it intelligently, unfolding it. And this is very much actually, again, Hegel brings this up in terms of self-consciousness. You see, self-consciousness is a form in its most basic way. Not in the sense of self-consciousness, not in the sense that I'm phenomenologically aware of myself,

but in the way that Hegel formulated, or even Kant formulated, in the sense that thoughts can explain actions, and actions falls not only under such thoughts, but also exhibit them in their practical dimension. So this is the formal dimension of self-consciousness. For Hegel, philosophers can, by way of logic, because logic access the realm of the formal, we can talk about the formal dimension of self-consciousness. But the achievement, the concrete knowledge of self-consciousness is a matter of practical achievement. And that's Hegel's thesis.

That it's the Geist, even though it has knowledge of the form of self-consciousness, for self-consciousness is a form of consciousness, But when it comes to say what it is and concretely elaborate it, then it becomes a matter of practical investigation, a matter of the whole idea of a geistic odyssey of how it becomes a matter of socialist struggle. So the same thing about Plato, the idea is that we know about the forms in the sense of the formal dimension of them, but that's just a minimal sense. We do not know what they are really as a matter of practical knowledge.

It becomes a matter of practical investigation, that form of expanding the order of intelligibilities. So there's a tension here between what intelligence is doing is intelligence is expanding itself and it's it is a seeking of completion of the forms it's seeking to render forms intelligible right yes yes but but what you're saying is that it can never fully render forms intelligible um so there is this sort of like opposition opposition happening on the one hand

intelligence wants to render the forms intelligible it wants full that's a practical that's a practical achievement you see that that's easy two things we have two theoretical theoretical and practical intelligibility essentially what you might say that that's the practical the Sisyphean for example adventure to move toward this might be from one perspective futile from another perspective is not futile from the perspective that it can never be achieved you cannot never create the or know the intelligibility of forms but through this very process that seems to be futile you render intelligible the connection new connection between forms

and you become capable of overcoming any what you might call examples of perfection or achieved so-called achieved totalities. So essentially from from the level of the terminal goal it is futile and fruitless but from the level of you moving forward and what you can do with it it is not futile it is the good for you it is the whole idea that that's why it's called good good for you good for the agent good for the soul is it is the death drive driving a

process I don't think so but I think that this there is nothing here that allow us, that would prevent us from not understanding nihilism as a positive force from this perspective. Precisely because what is exactly nihilism ultimately? You know, it's leveling power of death. Adequately understood its implications. and precisely because you can say that this is a positive condition why is it a positive condition? because it

levels anything that seems to be inevitable to be total to be perfect in your life it clears away it clears away for what you can do and what you think yes, and this is exactly the Platonist idea of the futility of achieving the perfection becomes a condition of enablement, a condition of emancipation. Okay, I think it's time to go home. Yeah, thank you for the extra time. Can I ask one brief question? Sure.

So it seems to me that it's first of all the intermediaries which sort of get us out of Vastasis' problem. And it's because they allow us to make a form, to make an intermediary that has a certain range of explaining certain particulars. And then it would be it um you see i think i know where you want to go with this it's basically the whole idea of

composteris the dialectical method integration and separation because once you capable of moving toward more general classes you are capable of you know bringing more of some of the relations under that class but also separating some other more broad you know relations so it's basically it allows you to find out new relations between particular general these intermediaries these classes and And that's exactly what the process of separation and combination entails. Separation and combination can go either two ways, toward more specific relations, specific

particular relations, or more general relations under which these specific relations can be combined or separated. Yeah, so it's, and then the, in the last class you said something interesting regarding movement and stasis and you said that only other can disclose the meaning of being. Yes. would be the the the the the sort of reconfiguration of the intermediaries which change our relationship to the particulars yes yes and I mean as you can

see that basically this whole again the idea if you understand this idea of transition from one mid intermediary to another more general intermediaries one and so forth can be understood as a dialectical process that entails process of separation and integration then you can see that that's exactly where the question of other the so-called the negative comes into play as what is capable of distinguishing things according to different classes so as to for you to be capable of putting them together according to their own classes. And that's why you can't ask self-predication because it's

ultimately a function of... Yes, but I think there's more to this and then you have to wait for next session. yes but there is still I think you can formulate in a different way as well I think Christian just froze Christian did I think we may have lost you but maybe now is a good time to end I do have a question if are these notes that you're working from are these being published somewhere I will I will yeah I'm going to just put them, it's going to be like some sort of,

I plan actually to write, so I'm going to just work on two things, one term and argument and then it was paradox. Yeah, I plan to publish them as an essay. Just for now, I'm just writing it. I haven't thought about where I'm going to publish it or what I'm going to do. But I can send, let me just edit some of these notes and then I have to send them to you. Great, I love that, thank you. Absolutely. Sorry, my computer, is Reza still there? Yes. All right, yeah, I just wanted to say one thing, just to make sure I got it right.

And it's because it's a function of alterity, which is responsible for the ordering and structuring of principles that annihilates the self-predication argument. precisely because it's alterity that is organizing the particular predicates according to... Yes, but remember that this alterity, you shouldn't think about that as the alterity in the sense that today people, content of laws, use alterity. This is formal negativity.

Alternative as basically a name for negation. Right, not an indeterminate alterity. Yes, yes, yes. It's a completely, we can think about it in terms of determinate negation, yes. Alright. Well, take care everybody. Absolutely, take care everyone. Bye, Rosa, thank you. See you next week, bye bye.