Are you referring to the very difficult second part of the Parmenides?

Is this the article?

yes

yes, section 5 and section 6

What is G? And what is F?
Is G an idea? Is F a property?
And if F is a property, con-F is the contrary to F, how could I explain "G is not F and not con-F"? — guanyun

If Plato were alive he would ask the same questions. The SEP has hundreds of articles on modern logic, and many on ancient Western and Eastern logic. Since there are so many different articles on the subject, it would seem not all logic is the same.

ok, so is there any way to understand this part of Plato's thought in a simple way?
Although I know that this content will probably not be tested in the entrance exam,but I always feel that something is missing if I don't understand it.

something is missing if I don't understand it. — guanyun

Yes, but everyone else is also missing that understanding. There is plenty of interpretation and opinion. Some people think it was just a lesson in logic or even a joke, but I just don't think anyone truly thinks like Plato did at the time he wrote that piece. It's obvious that the dialogue was an important turning point in Plato's thought therefore cannot be ignored.

The SEP article is amazing just for un-jumbling the details for us to try to follow.

There's no dummy's guide to the Parmenides, if that's what you're asking. It's one of the foundational texts of the whole tradition of Western metaphysics. Notice that in text above and below the examples you've quoted there's a whole set of references - more than a dozen, in fact. Drill down, there's a link to an enhanced bibiography. So taking those examples out of that context is, I'm afraid, a hopeless task, because they’re not algebra or even exercises in symbolic logic. They are an attempt to discern the underlying meaning of Parmenides by representing the arguments in symbolic form, so they can only be understood in the light of the debate about the nature and reality of the Forms. (I’m no Plato scholar, but I did get through two years of undergraduate classes in philosophy without encountering material as difficult as that.)

its another example of how notational calculus has no relation to life

Thanks, everybody. I think this discussion has came a conclusion which is I shall skip this arguement for now and come back after my exam. Thanks for reading this, I'm grateful that someone answered my question at such a moment in the first few steps of my philosophical journey.

Well, The G is the one, and F is another property. So, "G is not F and not con-F" says that G is a different from F.

The purpose is to bring out the structure of each argument, and show that each is valid.

I'd favour the reading that what is shown instead is that the arguments reach contrary conclusions, and hence that the One is an incoherent notion.

At Notre Dame Phil Reviews (NDPR), John Palmer responded to Rickless' Parmenides in some detail.

Socrates [... at Phaedo(76d7-e7)] marks the existence of forms as an unargued and as yet unsecured hypothesis — Palmer

Since the "theory of forms" is more accurately a hypothesis [... a hunch] under development in the Symposium, Phaedo, and Republic, Rickless's attempt to furnish a systematic reconstruction of the "theory" in would-be definitive fashion not only is misplaced but also makes it more difficult than necessary to understand what to make of Parmenides' criticisms. — Palmer

Don't get me wrong, I love modern logical reconstructions based on Plato's work because they make for fun reading. But that's not the same as reading and attempting to make sense of the original dialogue. Rickless's F and G only say what Rickless wants them to say.

I'd favour the reading that what is shown instead is that the arguments reach contrary conclusions, and hence that the One is an incoherent notion. — Banno

It would seem so.
Young Socrates fully agrees with the Parmenides character that particulars can't possibly exist but challenges Parmenides to show the same for the Forms. Part II is intended to prove that Forms are incoherent as well.

It is generally agreed that Plato was not fazed by this apparent debacle. That's because Plato had moved past these simple Aristotelian(!) modes of thought about the world, so that simple Aristotelian critique was no longer of direct concern to him. Correspondingly Plato wouldn't care what Rickless' logic said about a no longer Platonic "Theory of Forms".

The fact that Plato situates the dialogue at the time when Socrates was young suggests that the whole of the Socratic dialogues that take place after this early meeting were informed by the problem of the Forms raised in Parmenides. This is not to be understood historically but rather as a literary device. These are not problems that only occured to Plato at around the time Parmenides was written but rather that the problem of the Forms informed his writing of the dialogues from the beginning.

That the Forms are hypothesis should be understood in light of what is said about hypothesis in the Republic. They are "stepping-stones and springboards" (511b). They are intended to free us from what has been hypothesized. In the Phaedo Socrates calls the hypothesis of Forms “safe and ignorant” (105c).

Given all the problems with the Forms we might ask why Plato did not just abandon them. Plato gives us the answer in Parmenides: One who does not “allow that for each thing there is a character that is always the same" will “destroy the power of dialectic entirely” (135b8–c2). Something like the Forms underlies (hypo - under thesis - to place or set) thought and speech.

The problem is, despite the mythology of transcendence in the Republic, we cannot achieve transcendence through dialectic. This is why the dialogues frequently end in aporia. What is at issue is not simply the problem of Forms but the problematic nature of philosophy. It raises insoluble problems.

This is why the dialogues frequently end in aporia. What is at issue is not simply the problem of Forms but the problematic nature of philosophy. It raises insoluble problems. — Fooloso4

Plato was a sceptic. The forms are totalities which cannot be conceived. But Plato invented the concept, which is based in skepticism.

An aporia is because you believe a total comprehension is possible

Here's a nice little podcast for you.

https://shwep.net/podcast/platos-parmenides-and-metaphysics/

Are you referring to the very difficult second part of the Parmenides? — magritte

Yes, of course, it is very easy to find out in the Web that it's from Parmenides Dialogue, but I wonder how this could help you answering what the topic asks ...

Is this the article? — Banno

Isn't this too evident after reading that article??

Check this ref too: https://stanford.library.sydney.edu.au/archives/sum2012/entries/plato-parmenides/

I think we are generally in agreement.

Plato was a sceptic. — Jackson

It is important to distinguish Socratic skepticism from other types, both ancient and modern. It is zetetic - it proceeds by way of inquiry based on the knowledge that one does not know.

An aporia is because you believe a total compression is possible — Jackson

An aporia is an impasse. If, as in the Republic, there is a movement from hypothesis to knowledge, an aporia represents the failure of that movement. But zetetic skepticism is not the claim that total comprehension is not possible, but simply that it is not something that anyone possesses. The problem this raises, as described in the Phaedo, is "misologic" (89d-e). With the failure of logos Socrates turns to mythos. In terms of the image of the divided line in the Republic, it is recognition of the importance of eikasia, that is, the use of the imagination and image making.

Although things are said to be images of Forms, the Forms are themselves images. A kind of philosophical poiesis. What it seems must be if there is to be knowledge of things such as Justice, Beauty, and the Good.

But zetetic skepticism is not the claim that total comprehension is not possible, but simply that it is not something that anyone possesses. — Fooloso4

I do not see the difference.

Although things are said to be images of Forms, the Forms are themselves images. A kind of philosophical poiesis. — Fooloso4

Then reason depends on the imagination. Something which Plato spends his entire career denying.

I wonder how this could help you answering what the topic asks ... — Alkis Piskas

I thought the quote in the OP could be made more explicit for discussion. But if you like guessing that's OK too.

But zetetic skepticism is not the claim that total comprehension is not possible, but simply that it is not something that anyone possesses.
— Fooloso4

I do not see the difference. — Jackson

The zetetic skeptic, unlike some other skeptics, does not deny the possibility of knowledge, claiming only that we do not know. Nor is it the suspension of judgment, but rather leaves open the possibility that we might be wrong about our judgments. It relies on what seems most likely, but remains open to revising these judgment about what seems most likely.

Although things are said to be images of Forms, the Forms are themselves images. A kind of philosophical poiesis.
— Fooloso4

Then reason depends on the imagination. Something which Plato spends his entire career denying. — Jackson

The Republic is clear about the limits of reason (dianoia). It does not grasp each thing itself in its singularity (noesis), but always as it is in relation (ratio) to something else.That is to say, it makes use of likenesses (eikasia). Plato repeatedly points to the use of images for mathematics

The Republic is clear about the limits of reason (dianoia). It does not grasp each thing itself in its singularity (noesis), but always as it is in relation (ratio) to something else.That is to say, it makes use of likenesses (eikasia). Plato repeatedly points to the use of images for mathematics — Fooloso4

I must be missing the point.

OK, but I answered your question afirmatively myself. Has that helped you? Has that made any difference?

Plato gives us the answer in Parmenides: One who does not “allow that for each thing there is a character that is always the same" will “destroy the power of dialectic entirely” (135b8–c2). Something like the Forms underlies (hypo - under thesis - to place or set) thought and speech. — Fooloso4

This is an important point. It comes out much later with respect to the arguments about universals as the mechanism of meaning. As Plato believes that the objects of reason have a greater degree of reality than those of sense, then they must have something unchangeable as their object.

Could you say that Aristotle's later theory of essence and substance is foreshadowed here?

What is at issue is not simply the problem of Forms but the problematic nature of philosophy. It raises insoluble problems. — Fooloso4

I think, rather, that it indicates problems which can't be solved from the standpoint from which they are posed. In other words, that their resolution depends on reaching a higher perspective, in accordance with the steps of Diotima's ladder. That is something like 'the philosophical ascent'.

I've recently discovered why this notion of 'philosophical ascent' now seems such an implausible ideal. It is articulated quite clearly in this passage (referring to the 'scientific revolution'):

This scientific and philosophical revolution - it is indeed impossible to separate the philosophical from the purely scientific aspects of this process: they are interdependent and closely linked together - can be described roughly as bringing forth the destruction of the Cosmos, that is, the dissappearance from philosophically and scientifically valid concepts, the conception of the world as a finite, closed and hierarchically ordered whole (a whole in which the hierarchy of value determined the hierarchy and structure of being, rising from the dark, heavy and imperfect earth to the higher and higher perfection of the stars and heavenly spheres), and its replacement by an indefinite and even infinite universe which is bound toether by the identity of its fundamental components and laws, an in which all those components are placed on the same level of being. This, in turn, implies the discarding by scientific thought of all considerations based upon value-concepts, such as perfection, harmony, meaning and aim, and finally the utter devalorisation of being, the divorce of the world of value from the world of facts. — Alexander Koyré, From the Closed World to the Infinite Universe

That's the context in which 'the philosophical ascent' is unintelligible, for the simple reason that there is no longer a qualitative (i.e. vertical) axis along which there could be an 'ascent'.

As Plato believes that the objects of reason have a greater degree of reality than those of sense, then they must have something unchangeable as their object. — Wayfarer

Well, he certainly makes an argument in favor of this, but that is not the same as believing it. The Forms are posited as hypotheticals. A hypothetical does not have a "greater degree of reality" then sensible things. In various dialogues Plato gives us reasons to doubt the adequacy of the accounts of the Forms.

I discuss some of these problems

Here

and

Here

Could you say that Aristotle's later theory of essence and substance is foreshadowed here? — Wayfarer

The term essence (essentia) was a Latin invention used to translate Aristotle's Greek ousiai, or substance. Substance oressentia is the “the what it was to be” of a thing. His answer was not that what it is is a Form.

The term essence (essentia) was a Latin invention used to translate Aristotle's Greek ousiai, or substance. Substance oressentia is the “the what it was to be” of a thing. His answer was not that what it is is a Form. — Fooloso4

The Latin is wrong. By "essence" Aristotle means "form" or "shape." (eidos or morphê)

The term essence (essentia) was a Latin invention used to translate Aristotle's Greek ousiai — Fooloso4

'Ouisia' is a form of the Greek word 'to be', and so the word is nearer in meaning to 'being' or 'subject'. It was translated into Latin as 'substantia' and thence English as 'substance' but it has a completely different meaning in philosophical than in everyday discourse.

And the Platonic forms were 'immanetised' by Aristotle as the forms of hylomorphism where they live on to this day. In later Scholastic philosophy, the form of the particular was what was known by the intellect, as distinct from the matter, which was known by sense.

It was translated into Latin as 'substantia' and thence English as 'substance' but it has a completely different meaning in philosophical than in everyday discourse. — Wayfarer

@Jackson

From the Wike page on 'ousia':

There was no equivalent grammatical formation in Latin, and it was translated as essentia or substantia. Cicero coined essentia and the philosopher Seneca and rhetorician Quintilian used it as equivalent for οὐσία, while Apuleius rendered οὐσία both as essentia or substantia. In order to designate οὐσία, early Christian theologian Tertullian favored the use of substantia over essentia, while Augustine of Hippo and Boethius took the opposite stance, preferring the use of essentia as designation for οὐσία.[4][5] Some of the most prominent Latin authors, like Hilary of Poitiers, noted that those variants were often being used with different meanings.[6] Some modern authors also suggest that the Ancient Greek term οὐσία is properly translated as essentia (essence), while substantia has a wider spectrum of meanings.