/lit/ - Literature

Also, Frater Asemlem, I see you in that poetry thread. Please grace my thread with a post if you have the time.

Here is a fascinating and comprehensive ~20 page summary of the debate from The St. John's Review:
https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/2b69b2ce561c611b2fc3cefb8e8bdaec.pdf

>>20926750
It's written by the same guy who wrote this. And there's a bit of niche scholarship that seeks to prove the plausibility of Plato's endorsement of the Golden Ratio, Harmonic Means, and other Pythagorean tropes.

>>20926679
There's a book on mostly Plato's later dialogues like the Philebus that claims to unearth in those dialogues a teaching that is tantamount to the Unwritten Doctrines. Worth checking out.

>>20926750
Quick rundown?

>>20927081
That 20 page paper is the quick rundown.

>>20927111
I need it faster!

>>20927119
I will do my best to summarize it. But it's going to sound like gibberish because 1) it references Platonic terminology; and 2) I don't fully understand it.

There is the one. I believe this is the Form of the Good, what is responsible for everything and makes everything intelligible. And then there is the many. But this many is strange. It is an indeterminate dyad. In some sense, the many is indefinite and hard to grasp (similar to the infinite, though I don't know the exact relationship). Kind of like experience: it is relative.

We can make it definite by putting a measure, allowing for absolute comparisons, but then we lose something here, because measurements are never as precise as we'd like it to be (see pic-related... another infinity). We bring certain things to the forefront, but other things fall to the wayside.

So, what should we focus on? We could mix the indefinite and the definite, but then it becomes a question of what is the best way to do this. And that "fractally" becomes another indeterminate dyad problem too! Aristotle's four causes are often brought into the picture too.

I suspect that the one and the indefinite dyad is isomorphic to many great metaphysical problems, reveals a ton about epistemology, ethics, politics, language, etc. So if you understand this, you have a cheat sheet for thinking about everything and everybody else. You can read the works of other philosophers like Descartes, Kant Hegel, Peirce, and Heidegger through the lens of this ancient metaphysical problem. I think even Eastern metaphysics might have something to say about it too, like the concepts of yin and yang and the eternal Dao. But I digress.

bump

guess I gotta solve philosophy all by myself...

what's going on in this post from that other thread?
>>20920339
>>and reliance on conceptual abstractions rather then experience then yes I was filitered by the stupidity of his work.
>It's basically the exact opposite if you look at PoS. Hegel is trying to create an experience-based groundwork for "absolute knowing" (hence "phenomology"). His logic is just one part of it. It's all ultimately ridiculous (the idea that even intersubjective consciousness can somehow come to a truth through mutual negation, which is basically turning Plato on his head by saying that the "mixed" and "indefinite" are more definite than the definite), but your post is not quite correct, if anything he is more stupid than you made him sound. He basically repackaged the Platonic idea of dialectic (the discovery of the source of axioms, dianoia) into something both historical and existential, which fails on the original Platonic account, but allegedly fits Kant's conditions of "critical philosophy" and leads to some extremely tenuous idea of truth (truth developing from "experience"). His idea of reason ultimately develops out of this existential basis (ie, the higher arises from the lower), hence why it seems so absurd to people commonly acquainted with the term, and it's also why no one ever feels like they've ever properly "understood" him; it's because at a fundamental level there is nothing to be understood, you (and Hegel) are just messing with the Platonic indefinite dyad. It keeps an apple on a stick in front of you and you keep following it hoping one day you'll be able to take a big bite out of absolute knowing.

>>20926679
>the One
It’s the absolute transcendent cause
>indefinite dyad
It’s the dyad, but before it gives rise to the number 2

you seriously got filtered at such a basic level? Kek, what a retard.

>>20928065
plox dont bring h*gel into discussion of platonic theology. It shows you are a pseud.

Why are Straussians so often read when it should be Whitehead they read?

>>20928498
It's a lot more complex than that, anon.

First of all, what could 2 mean? Could it mean 1 and 0, two distinct qualities? Or that 1 copied itself and made two of itself? Or that 1 created something new, 2, that is distinct from itself? You are making the same mistake that the Pythagoreans did in worshiping number and not realizing that these were mere correspondences in the world given a name and put to some kind of practical use.

Second of all, you ought to say *indeterminate* dyad, not *indefinite* dyad. You risk confusing between the limited (the one, the unit, numbers) and the unlimited (greater-or-less, unmeasurable, quality), which are two categorically distinct ontological categories as explained in Philebus. A great example of this would be rational and irrational numbers: a side of a square of length 1 vs. its diagonal, which can only be approximated between 1 and 2. Only in the mixed category do we have both the unit and the indeterminate dyad, an exhaustive method of proportions that gets one closer and closer to measuring the unmeasurable in terms of number. It's not indefinite: by comporting it to measurement, it now has definition.

Actually, definition, limit, determinate, etc., are all terrible Latin translations of what the Greeks would have called it: peiron and apeiron. Peira means more like "trial, experiment, crossing, goal, etc.", and thus apeiron has a richer meaning than "without end, boundary, etc." that all the Latin words are stuck with. The Greek implies forever ongoing process without any clear destination, something that Latin seems hesitant to directly translate without drawing lines, setting it straight, and giving it an end.

>>20928513
Comparing philosophical thinkers is a great way of demonstrating that you know what you're talking about and have solid philosophical chops.

>>20928565
Hegel was an incredible mistake.

>>20929963
Okay and?

how's his book on the odyssey?

>>20930046
Benardete has tons of books in virtually the same drawn-out, seemingly easy to read but hard to parse style. They end up saying the same permutation of Straussianism anyway. Epicureanism is based, Plato was ironic, religion is fake and gay but it's beautiful and we have to believe in it to survive. Insightful, but I can't be bothered to read them all. Diminishing returns.

bump

/lit/ has been very slow on these kinds of threads lately. strangely summer has been the best time for them.

bump

>>20927315
Thats a lot of words. Could I get a quick rundown?

>>20932248
You either deal with vague, relative qualities, or you can define and measure things for precision. But the latter move doesn't always work, as not all things are rational, and some things are lost in translation, escape definition, etc. It means that the way we interact in the world has this strange "in-between" status of being intelligible, tantalizingly knowable, but also being uncertain and unstable.

>>20926679

>>20932377
>>20927074
>Sayre
>Reale
Here's a good book review that summarizes the debate about the unwritten, esoteric doctrines of Plato.
https://bmcr.brynmawr.edu/1998/1998.07.22/

>>20926679
Isn't it related to Same and Other?

>>20932377
>>20932454
>>20927074

i recommend you to learn portuguese asap
https://libgen.is/book/index.php?md5=0CB31CEEF3EC3F4FF14E8CCA679A30A5

>>20932498
>Pythagorean-Platonic
quick rundown on the book? I thought Plato was ACKSHUALLY more of a Heraclitean than previously thought. Only the Form of the Good is the "eternal" constant that Plato embraces.

>>20932576
>quick rundown on the book
not really possible
i'll just gonna say that its apodictical/axiomatic as it systematizes pythagorism(and of course, platonism) explaining the symbolism and metaphysical doctrine behind the numbers (law of unity, dyad, until ten, and hundreds of possible combinations), check the summary to try to get an idea

>>20932498
>>20932576
>>20932616
oh i forgot there's this site that has some translations
https://marioferreirainenglish.wordpress.com/category/the-wisdom-of-the-eternal-laws/

Straussianism is degenerate garbage

>>20932616
>metaphysical doctrine behind the numbers (law of unity, dyad, until ten, and hundreds of possible combinations)
If you have the time, I'd love to read a recapitulation of Plato's doctrine on number. There's one school of thought that says the indeterminate dyad "generates" number, and I wanted to know what that looked like in practice.

>>20932645
just take a look at the site >>20932626
https://marioferreirainenglish.wordpress.com/2015/01/16/law-of-unity/

it explains the indeterminate dyad

>>20932695
Starting to read it now. But what does it say about irrational numbers like the square root of two?

>>20932695
That's a very cool website. Probably the best primer on Pythagoras. Thanks for sharing.

>>20932711
You gotta read the first 100 pages of Klein's Greek Mathematical Thought

>>20932932
I don't have the time.

>>20926679
It's just the insane ramblings of a broken man. Plato and others were driven mad by the metaphysical work of the Eleatics. So many latter-day philosophers found it impossible to refute the Eleatics, yet intolerable to live within an Eleatic model, so they committed intellectual suicide and left the path of truth. They tried to walk on two paths, when we know from the goddess there is only one. Sad!

>>20932932
Klein never understood Plato's form of number. Arguably, neither did Aristotle.

>>20926693
It’s a complex topic this indeterminate dyad, i’ll write up more in depth later but I’ll say that this idea never was lost in various forms of occultism, for example in Thomas vaughan he perceived the great chain of being as extending upwards to the divine mist/light which is god in absolute simplicity, being the monad, then descending the chain in the middle you have earth, and in the absolute bottom you have the divine darkness, which is perceived as a kind of cold infinitely complex point that has so many layers that it can only be perceived as an infinite-multiplicity which transmutes it into effectively a monad but in verse, we see mystical practice with this point as the kaula chakra in tantra, we see usage of this same point in the seven earth model of Kabbalah. Pic related is a good overview of the doctrine and related conceptions on the platonic agrapha.

>>20934505
Klein wasn't talking about Plato’s"Form of Number"; he was getting back to asking whether the transformation of common Greek arithmetic into modern symbolism distorts the understanding of number.

>>20934658
Wonderful. So, from what I understand, Plato deals with the One, the Good, etc., but he also grappled with the Many to preserve the possibility of multiplicity against the attacks of the Eleatics. The One, the Good, etc., is understood through the form of number. This problem of "the Many" evolved into the Indeterminate Dyad, which he tried to understand through number.

Some of his successors may have even taken the belief further than Plato by trying to use the form of the number to "generate" all numbers, but this may not have been Plato's conception. Aristotle also rejected this as superstition. There are also people who you've described in the archives as erroneously worshiping the "Indeterminate Dyad", but I don't know what that means or why it's wrong.

I also am getting the strong impression that Plato positions himself halfway between the Pythagoreans and the Heracliteans. Most people try to portray Plato as a rigid essentialist, where even "chair-ness" is an idea that exists. This portrayal makes Plato seem like a philosopher who hates Becoming and wants to "lock in" the world into a Great Chain of Being. But this is completely wrong. If you look into Plato's philosophy, he's clearly straddling both schools of thought. Plato should best be understood at the "middle" philosopher.

So, Plato understands the infinite flux, that everything changes, as he was a diehard Heraclitean philosopher in his youth. People miss this completely. But after his encounter with the Eleatics, Plato understood the need to mix the two: everything changes, but the senses are illusory to a great extent too. How does one understand what makes anything intelligible at all? By combining the Heraclitean logos with the Parmenidean Being! Through this marriage, one finally understands what makes anything intelligible at all: gnosis.

Plato calls this special knowledge the "the Fifth" in his Seventh Letter, etc. and "the Form of the Good" in the Republic, comparing it to "seeing" (seeing is believing, I assume). It is the result of an elaborate counting and sorting process, the process of dialectic. One learns new things, participates in new experiences, then relates everything to everything in the hopes of catching a "glimpse" of the ultimate discursive knowledge.

Even the vocabulary Plato chooses to describe the classic "participation in the Forms", methexis (μέθεξις) reflects this Eleatic-Heraclitean mixture. Derived from metaxy, (μετεχω), Plato emphasizes the "middle ground" between earth and the heavens that describes the human condition. Breaking down metaxy into its roots, μέθ (met-, meta-) + ἔχω (exo), we get "succession" of "Being": just look at that Becoming-Being unity!

However, if the FotG is "vision" of "the light", then it appears that Heraclitus slightly edges out over Parmenides. It is a curious analogy to use, as sight is normally reserved for Becoming! What is transcendent seems irrational, too. Strange!

(1/?)

>>20934658
Wonderful. So, from what I understand, Plato deals with the One, the Good, etc., but he also grappled with the Many to preserve the possibility of multiplicity against the attacks of the Eleatics. The One, the Good, etc., is understood through the form of number. This problem of "the Many" evolved into the Indeterminate Dyad, which he tried to understand through number. Some of his successors may have even taken the belief further than Plato by trying to use the form of the number to "generate" all numbers, but this may not have been Plato's conception. Aristotle also rejected this as superstition. There are also people who you've described in the archives as erroneously worshiping the "Indeterminate Dyad", but I don't know what that means or why it's wrong.

I also am getting the strong impression that Plato positions himself halfway between the Pythagoreans and the Heracliteans. Most people try to portray Plato as a rigid essentialist, where even "chair-ness" is an idea that exists. This portrayal makes Plato seem like a philosopher who hates Becoming and wants to "lock in" the world into a Great Chain of Being. But this is completely wrong. If you look into Plato's philosophy, he's clearly straddling both schools of thought. Plato should best be understood at the "middle" philosopher. Plato understands the infinite flux, that everything changes, as he was a diehard Heraclitean philosopher in his youth. People miss this completely. But after his encounter with the Eleatics, Plato understood the need to mix the two: everything changes, but the senses are illusory to a great extent too. How does one understand what makes anything intelligible at all? By combining the Heraclitean logos with the Parmenidean Being! Through this marriage, one finally understands what makes anything intelligible at all: gnosis.

Plato calls this special knowledge the "the Fifth" in his Seventh Letter, etc. and "the Form of the Good" in the Republic, comparing it to "seeing" (seeing is believing, I assume). It is the result of an elaborate counting and sorting process, the process of dialectic. One learns new things, participates in new experiences, then relates everything to everything in the hopes of catching a "glimpse" of the ultimate discursive knowledge. Even the vocabulary Plato chooses to describe the classic "participation in the Forms", methexis (μέθεξις) reflects this Eleatic-Heraclitean mixture. Derived from metaxy, (μετεχω), Plato emphasizes the "middle ground" between earth and the heavens that describes the human condition. Breaking down metaxy into its roots, μέθ (met-, meta-) + ἔχω (exo), we get "succession" of "Being": just look at that Becoming-Being unity!

However, if the FotG is "vision" of "the light", then it appears that Heraclitus slightly edges out over Parmenides. It is a curious analogy to use, as sight is normally reserved for Becoming! What is transcendent seems irrational, too. Strange!

(1/?)

>>20934838
To begin, let's start with the metaphysics, which I think is best explicated in The Republic, Philebus, and Statesman.

First, there is the peiron: the limited, the defined, the absolute, the actual, the rational. There is also an empirical component: peras means "trial, experiment, etc.", something which can be seen for oneself. This can be assigned a number and made intelligible. Plato would have called this "the One" or "the Good." Then there is the apeiron: the unlimited, pure potential, the relative, the chaotic, etc. This cannot be assigned a number: think of the qualities we experience like sound or the irrational numbers that go on forever like the sqrt(2). The "limited" and "the unlimited" are the fundamental yet distinct categories of existence and normally cannot be reconciled.

However, in the phenomenology of Being, there is also the "mixed", the "middle ground" in which we live in. This is essentially like grasping onto the "unlimited", making it "limited", thus making part of the unknown "known." Then, one can move beyond the old "limits" to find new "limits" in a Faustian spirit. Most things in life fall into this category, like music or the weather. This is an exhaustive, infinite process of comprehension, where one gets closer and closer to precision, but never quite reaches it. The unlimited can be measured, meaning assigned number to make it appear limited. But in reality, this mixture is merely "expressible", and its precision is indeterminate. Without any corresponding effort to "exhaust" the infinite and make it as limited as can be, it is pure unlimitedness, hence the term "indeterminate dyad."

In addition to the "mixed" domain, there are causes: think Aristotle's four causes of material, efficient, formal, and final. This is where knowledge begins to mature in its own. Heidegger brilliantly points out that "causes" in Ancient Greek, aitia (αἰτία), had a richer temporal meaning than we explain today. Not only did it mean "cause and effect", but it also meant debt, credit, opportunity, motive (motion, emotion, etc.), interrogation, etc. Through causes, one begins to truly acquire knowledge (episteme), as they can have a complex account what things are and why. If one imagines the "unlimited" as an infinite succession of concentration circles, and the "limited" as each particular circle, the causes are like some kind of "chain" that connects each circle in perpetuity.

(2/?)

>>20930046
It's good, and there's definitely something to it on even a surface reading of the Odyssey that notices the Moly passage and the wordplay between outis and metis. But, in his typical Benardete way, hard to read, and really demands that you have the Homeric poems open so you can trace every observation.

>>20934898
To begin, let's start with the metaphysics, which I think is best explicated in The Republic, Philebus, and Statesman.

First, there is the peiron: the limited, the defined, the absolute, the actual, the rational. There is also an empirical component: peras means "trial, experiment, etc.", something which can be seen for oneself. This can be assigned a number and made intelligible. Plato would have called this "the One" or "the Good." Then there is the apeiron: the unlimited, pure potential, the relative, the chaotic, etc. This cannot be assigned a number: think of the qualities we experience like sound or the irrational numbers that go on forever like the sqrt(2). The "limited" and "the unlimited" are the fundamental yet distinct categories of existence and normally cannot be reconciled.

However, in the phenomenology of Being, there is also the "mixed", the "middle ground" in which we live in. This is essentially like grasping onto the "unlimited", making it "limited", thus making part of the unknown "known." Then, one can move beyond the old "limits" to find new "limits" in a Faustian spirit. Most things in life fall into this category, like music or the weather. This is an exhaustive, infinite process of comprehension, where one gets closer and closer to precision, but never quite reaches it. The unlimited can be measured, meaning assigned number to make it appear limited. But in reality, this mixture is merely "expressible", and its precision is indeterminate. Without any corresponding effort to "exhaust" the infinite and make it as limited as can be, it is pure unlimitedness, hence the term "indeterminate dyad."

In addition to the "mixed" domain, there are causes: think Aristotle's four causes of material, efficient, formal, and final. This is where knowledge begins to mature in its own. Heidegger brilliantly points out that "causes" in Ancient Greek, aitia (αἰτία), had a richer temporal meaning than we explain today. Not only did it mean "cause and effect", but it also meant debt, credit, opportunity, motive (motion, emotion, etc.), interrogation, etc. Through causes, one begins to truly acquire knowledge (episteme), as they can have a complex account what things are and why. If one imagines the "unlimited" as an infinite succession of concentration circles, and the "limited" as each particular circle, the causes are like some kind of "chain" that connects each circle in perpetuity.

(2/?)

>>20934945
Finally, there is gnosis, the Form of the Good, "the Fifth". It is related to nous which grasps the first principles existing everywhere. It is how we can understand anything at all, theoretically or practically. Gnosis is associated with dialectical "completeness" with something of an "extra" mystical quality. Let's first recap by straightening out Platonic terms found across his dialogues:
>BECOMING
>eikasia/imagination/unlimited (maybe image), confirming either old prejudices or encountering new possibilities for investigation
>doxa/belief/limited (maybe name), a stable level of understanding, like common sense, the outer limits of acquired knowledge, potentially unstable due to the complications of life
>BEING
>dianoia/demonstration/mathematics (maybe account/logos), "if this then that" syllogistic reasoning, depends on premises, "true" but only contingently
>noesis/discursion/dialectics (maybe episteme), mixing and matching premises, relating demonstrations to each other, etc.
One climbs up the ladder of the Divided Line, engages in noesis, finds more light, then carries it back down to the realm of Becoming step-by-step. This is continuing cycle. But through a lifetime of theoretical contemplation and practical accomplishment, one eventually achieves the highest noetic state of them all, gnosis, the reason why we can understand anything at all. This grants us the truest vision. Returning to the concentric circles analogy: gnosis would be the initial point of the concentratic circle, with the direction radiating outwards (or perhaps the outermost circle radiating inwards!).

(3/?)

>>20935076
Now, what are those first principles, and how does one grasp them? It seems to be both an intellectual and emotional internalization of Plato's principles of the One and the Indeterminate Dyad. And truest to Plato's style, the metaphysics seems best understood through mathematical analogy: the dimensions of a unit square, the Pythagorean theorem, and the problem of irrational numbers. It is a question of relating what is absolutely measurable, the Unit(y) (the One) to the irrational, uncountable, etc. (the Many). Through exhaustive approximation, one can make the Many intelligible (the Indeterminate Dyad). Pic-related illustrates this best, starting with the dialogue of Meno and the attempt to instruct the slave into "remembering" how to construct a new square that is double the size of the unit square.

To jog your memory, Plato shows in Meno that the slave boy can "remember" the Pythagorean theorem, in that they can point out this diagonal and its relationship to the sides. It is intelligible somehow. But the problem here is that the sides of the unit square are absolute (they are 1, simple!), but its diagonals are not (sqrt(2)). Sqrt(2), as famously demonstrated by some disgruntled followers of Pythagoras, is not a rational number, and its decimals go on forever. So, while we can point out that is a line, and it exists, you can't actually "count" it. Any attempt to give it a "number" will actually come up short, since we will truncate that infinite decimal expansion. This is why Plato tells the slave boy not to try to "count" the line, but rather to just point in its direction. It is somewhere between 1 and 2. That's all we know.

Later in the Platonic dialogues, Plato teams up with the mathematician Theaetetus to refine his understanding of knowledge and to create the foundations of Plato's "mixed" approach to reality. I have to admit that my understanding of the mathematics and its evolution is a bit shaky, but I'll try to give my best account. Theaetetus finds that, while we cannot count the sqrt(2), we can still attempt to understand it geometrically through proportion. Find the next square, and the diagonal becomes 2, an intelligible number. So, we have a pattern where irrational diagonals can be squared into an rational area, a rational area that can be removed of an extra dimension and then turned into a rational line. This is the "mixed" approach that is alluded to by Plato: the "indeterminate dyad" as an exhaustive approximation. And if we continue with the causes step-by-step until the end, we find knowledge, episteme, of the "unlimited."

(4/?)

>>20935076
One consideration to think through carefully is that the Divided Line contains itself in its own account: as an image, itself at the lowest part of the line.

>>20935121
That is the gravity of Plato's approach. He finds an ability to insert "the limited" into the "unlimited", create an approach to mix the two through "expression", then link it all the way to the very end through "causes" to find "knowledge." Through exhaustion, one progressively gets closer and closer to the end of the unlimited, infinity. Theaetetus's geometric means finds its way into Euclid's Elements, is related to Archimedes's methods of exhaustion, and eventually evolves into Newton's "geometric" approach to approximating numbers. If modern reconstructions are to be trusted, then this also related to the Golden Ratio hidden in Plato's work and alluded to in the Lecture of the Good (see pic-related). Sounds like we've found gnosis, no? The Indeterminate Dyad is actually the One, Plato states ecstatically, to the sheer confusion of most of his audience!

Remember, however, knowledge is not an armchair sport: it is indeterminate without going through each step for greater accuracy and seeing for oneself. What we've only found is something that is "expressible" and has a certain direction: a straight path perhaps, but a dauntingly long one nonetheless. To achieve gnosis, we have to travel along the path ourselves. However, can one actually reach infinity if it goes on forever? It seems unlikely, especially given our own mortality. With Zeno's parodoxes, the Wildberger critics of the foundations of mathematics (specifically infinity), and knowledge of our own finitude, we have been brought back to Earth, grounded in perpetuity. As Heidegger alluded to in "The Question Concerning Technology" foundations of modern civilization are grounded in the Cartesian mindset and calculus, but these amount to largely unexplored expressions, not true knowledge. Hegel would claim, against Zeno, "yet the arrow flies." But he hasn't figured it out either.

Whatever this irrational, transcendent, and infinite knowledge is, it seems like some kind of strange pattern that allows us to "skip" to the finish line. Abusing the mathematical analogy further, if the One is 1, and the Unlimited is Sqrt(2), then gnosis is π. I won't even pretend to make sense of that. I'm just throwing ideas out there. But on some deeper level, it seems to make sense. Euler would agree, too. But if you claim understand, you risk imperiling yourself to the same hubris that every other philosopher before you engaged in. Fin.

(5/5)

>>20935134
Absolutely. And the funny thing about eikasia, imagination, is that it is both something that can "lull" one into complacency or "awe" one into wonderment, prompting further questions. You see what you already understand through pistis, and the capacity to see further is dependent on caring to understand more: curiosity. If you're a Pythagorean and you have faith in numbers, you see numbers everywhere. Aristotle would have griped that that was simply mental projection: if you see two, you see two, and it is a mere correspondence. Plato would have looked deeper into the issue, going beyond mere "mimesis" of numbers to try to understand what "number" actually was. And he thought, through number, one could understand everything, even the unlimited, that there was "methexis." Aristotle disagreed, believing that there was only "mimesis" and not of the Pythagorean kind, but it's possible that Aristotle never understood the underlying mathematics behind Plato's Lecture of the Good.

>>20934505
>Arguably, neither did Aristotle.
I would be reluctant to claim the genius philosopher who studied with Plato for decades misunderstood something that we moderns have figured out from a handful of ambiguous dialogues.

>>20935268
Don't take it from me. Take it from Aristotle himself (through a secondhand account of one of this students). See pic-related. Amirthanayagam David also makes the convincing argument that Aristotle was perhaps reacting not to Plato but to his Pythagorean-like students.
>That Aristotle knew about the geometry of means is clear enough, but he must not have been familiar with the interpolation of means in the peculiar configuration of the indeterminate dyad, where means become extremes, which in turn beget means, which then in turn become extremes, while each pair of harmonic and arithmetic means serves as the extremes to the geometric mean in the middle. The notion of relativity embodied in this configuration, involving a process of equalising, and motion towards a fixed object, is more subtle and peculiar than that involved in a simple comparison, or even a static analysis expressed in terms of a mean and extremes. I claim it is this peculiar conception of the relative that Plato raised to the level of a principle, to stand in tandem with the absolute measure connoted by the unit.
>While the Academic metaphysicians may appear to have used these very same principles, right down to the letter of their formulation, it is clear that neither they nor Aristotle grasped their proper function. They have nothing to do with accounting for multiplicity in the universe, or with the generation of numbers. They have everything to do with the measurement of numbers. After Theaetetus, numbers are figured as square or rectangular; they can be compared not only in quantity, but in size, by the length of their square roots, just as after Euclid’s II.14, any rectilinear figures can be compared by the sides of their equivalent squares. While all numbers have either absolutely or relatively measurable rootlengths, not all lengths have countable squares. This is one of the odd new ways that arithmetic and geometry, number and magnitude, become interlinked after Theaetetus’ happy reformulation.
>It is therefore in this context, the context of measurement, that Plato is likely to have distinguished the absolute from the relative, being-in-itself from relative being. Aristotle alludes to just such a distinction, in a passage which once again exemplifies his peculiar mire: he wants to review the Academic theories on the generation
of multiplicity based on certain contrary principles, including principles first conceived by Plato, but conceived in a context where in some cases they weren’t even contraries, and where they had had nothing to do with generating either multiplicity or numbers; he knows the language of Plato’s own articulation of these principles, but doesn’t have the mathematics to interpret the words. In this case, he may even foist his own innovations in usage back on to Plato’s original phrases, just to make sense of them.
https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/2b69b2ce561c611b2fc3cefb8e8bdaec.pdf

>>20935268
Don't take it from me. Take it from Aristotle himself (through a secondhand account of one of this students). See pic-related. Amirthanayagam David also makes the convincing argument that Aristotle was perhaps reacting not to Plato but to his Pythagorean-like students.
>That Aristotle knew about the geometry of means is clear enough, but he must not have been familiar with the interpolation of means in the peculiar configuration of the indeterminate dyad, where means become extremes, which in turn beget means, which then in turn become extremes, while each pair of harmonic and arithmetic means serves as the extremes to the geometric mean in the middle. The notion of relativity embodied in this configuration, involving a process of equalising, and motion towards a fixed object, is more subtle and peculiar than that involved in a simple comparison, or even a static analysis expressed in terms of a mean and extremes. I claim it is this peculiar conception of the relative that Plato raised to the level of a principle, to stand in tandem with the absolute measure connoted by the unit.
>While the Academic metaphysicians may appear to have used these very same principles, right down to the letter of their formulation, it is clear that neither they nor Aristotle grasped their proper function. They have nothing to do with accounting for multiplicity in the universe, or with the generation of numbers. They have everything to do with the measurement of numbers. After Theaetetus, numbers are figured as square or rectangular; they can be compared not only in quantity, but in size, by the length of their square roots, just as after Euclid’s II.14, any rectilinear figures can be compared by the sides of their equivalent squares. While all numbers have either absolutely or relatively measurable rootlengths, not all lengths have countable squares. This is one of the odd new ways that arithmetic and geometry, number and magnitude, become interlinked after Theaetetus’ happy reformulation.
>It is therefore in this context, the context of
measurement, that Plato is likely to have
distinguished the absolute from the relative being-in-itself from relative being. Aristotle alludes to just such a distinction, in a passage which once again exemplifies his peculiar mire: he wants to review the Academic theories on the generation of multiplicity based on certain contrary principles, including principles first conceived by Plato, but conceived in a context where in some cases they weren’t even contraries, and where they had had nothing to do with generating either multiplicity or numbers; he knows the language of Plato’s own articulation of these principles, but doesn’t have the mathematics to interpret the words. In this case, he may even foist his own innovations in usage back on to Plato’s original phrases, just to make sense of them.
Link: (p25-61) https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/2b69b2ce561c611b2fc3cefb8e8bdaec.pdf

>>20935268
Don't take it from me. Take it from Aristotle himself (through a secondhand account of one of this students). See pic-related. Amirthanayagam David also makes the convincing argument that Aristotle was perhaps reacting not to Plato but to his Pythagorean-like students.
>That Aristotle knew about the geometry of means is clear enough, but he must not have been familiar with the interpolation of means in the peculiar configuration of the indeterminate dyad, where means become extremes, which in turn beget means, which then in turn become extremes, while each pair of harmonic and arithmetic means serves as the extremes to the geometric mean in the middle. The notion of relativity embodied in this configuration, involving a process of equalising, and motion towards a fixed object, is more subtle and peculiar than that involved in a simple comparison, or even a static analysis expressed in terms of a mean and extremes. I claim it is this peculiar conception of the relative that Plato raised to the level of a principle, to stand in tandem with the absolute measure connoted by the unit.
>While the Academic metaphysicians may appear to have used these very same principles, right down to the letter of their formulation, it is clear that neither they nor Aristotle grasped their proper function. They have nothing to do with accounting for multiplicity in the universe, or with the generation of numbers. They have everything to do with the measurement of numbers. After Theaetetus, numbers are figured as square or rectangular; they can be compared not only in quantity, but in size, by the length of their square roots, just as after Euclid’s II.14, any rectilinear figures can be compared by the sides of their equivalent squares. While all numbers have either absolutely or relatively measurable rootlengths, not all lengths have countable squares. This is one of the odd new ways that arithmetic and geometry, number and magnitude, become interlinked after Theaetetus’ happy reformulation.
>It is therefore in this context, the context of measurement, that Plato is likely to have distinguished the absolute from the relative being-in itself from relative being. Aristotle alludes to just such a distinction, in a passage which once again exemplifies his peculiar mire: he wants to review the Academic theories on the generation of multiplicity based on certain contrary principles, including principles first conceived by Plato, but conceived in a context where in some cases they weren’t even contraries, and where they had had nothing to do with generating either multiplicity or numbers; he knows the language of Plato’s own articulation of these principles, but doesn’t have the mathematics to interpret the words. In this case, he may even foist his own innovations in usage back on to Plato’s original phrases, just to make sense of them.
link: (p25-61) https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/2b69b2ce561c611b2fc3cefb8e8bdaec.pdf

>>20935268
>>20935396
And Aristotle's thoughts are a bit all over the place in how he rejects the Form of the Good and the concept of the infinite in "space", only to posit that the universe had always been in existence, sneakily reinserting infinity into "time":
>A science is defined by the genus or kind it studies and by a group of specifiable properties which belong to that kind. Secondly, the properties studied within a science are defined in terms of the genus of the science (per se2). Hence, it follows that it will commonly be impossible to prove one thing using a different science. For one would have to prove that a property within one genus applies to a completely different genus. Hence, every science is autonomous. Aristotle makes this claim, however, in the context of his rejection of Plato's view that sciences are subordinate to knowledge of the Good. What he actually claims is much more modest. If one genus comes under another genus, it will be possible, in some cases incumbent, to prove that a property belongs to a genus by using a theorem from another science. In such a case the one science is said to be under (subalternate with) the other science.
>However, since Aristotle believes that the universe has no beginning and is eternal, it follows that in the past there have been an infinite number of days. Hence, his rejection of the actual infinite in the case of magnitude does not seem to extend to the concept of time.
https://plato.stanford.edu/entries/aristotle-mathematics/
So, what Aristotle ends up doing with his fragmentation of the sciences and the rejection of the Form of the Good that allows intelligible change, is constructing an arbitrary "Great Chain of Being", as the Neoplatonics and the Scholastics were wont to do back in the day. If Plato's enumerative method somehow leads to the horrors of technological society, then Aristotle's method seems to lead to permanent stagnation, a snapshot of a particular mode of Being and nothing more. This was obviously unattractive to us as creatures of free will, always tantalized by the constant presence of brighter possibilities shining from over the horizon.

I may even hazard that perhaps the modern world pays little attention to the best metaphysics of both thinkers, instead bringing out their worst features: the enumerative technique of Plato with the crystallized organization of being towards a certain end by Aristotle. And now THAT is a suicidal, all-consuming drive that may cause us to take a minute to ponder our modern predicament.

>>20934789
From another post based on an understanding of Klein that I found helpful (which also explains what the confused followers of Plato were doing with the "generation of numbers" and what Aristotle may have misunderstood as pointed out here: >>20935223):
>The philosophical use was mainly derived from the Pythagoreans who used it to talk about how multiple units of a set of concrete entities "shared in" their common property (number).
>This is why Aristotle criticizes them for being relatively shallow and superficial in describing which things are structured by (i.e. participate, share in) which numbers. Because they'd just find arbitrary numberings and harmonies everywhere and say all those things are alike in deriving from from twoness. But they did not hypostatize "number" in our sense, as an Arabic numeral set up as an "idea" over and against concrete multiplicities. All numbers were for them concrete multiples of things. They didn't have hypostatic numeral-ideas, we do only as a function of later developments.
>All this is in Klein's Greek Mathematical Thought. If you want to understand the Platonic participation concept you need to understand the Greek "natural" ontology he describes in Husserlian phenomenological terms.
I will be reading Klein later for full understanding. But from a glance, it seems that Klein (and Aristotle, and the Pythagoreans) misunderstood Plato's fixation on "number." Specifically, they do not understand the form of the number "one", the unit, its metaphysical relation to the One and the Indeterminate Dyad, and how/why Plato sees it as essential through mathematical analogy. After all, how can "oneness" not be everywhere? How can "oneness" that enables "multiplicity" without permanent, infinite fragmentation be a bad thing? If Plato is the philosopher of unity, then Aristotle is the philosopher of fragmentation, and it's no wonder why Deleuze enjoys calling himself an Aristotelian.

>>20935617
>>20934789
I meant to also emphasize that Plato's solution of mixing number with the apeiron was also a mere "expression", symbolism, e.g. Indeterminate Dyad. It is symbolism whose full meaning appears to have been lost on Aristotle. The symbolism is explained in more detail here:
>>20935121
>>20935198
>>20935396
>>20935450

bump

I have a feeling that space, place, life, extension, and grouping may have a role to play here. I will report back on this thread if it's still up. Unfortunately, it seems as if this topic isn't very interesting for most people, even though I'm almost certain that it is one of the highest peaks in philosophy that one can climb.

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>>20934898
A nuance I think you’re not striking on is that number appears as a kind of, relational existent; as if the One and the dyad were two infinitely vast spheres and these spheres intersected, that intersection point being the numeric world, that numeric world formulating the rest, it’s implied and many commentators such as ficino will tell you plainly that in Parmenides that this dyad for it to be truly the different-in-itself it has to be different-to-itself, and thus must be different from difference, thus even the indefinite dyad is a “kind” of monad, thus it is not a dualism for the essential nature of difference in itself is unity all over again.

>>20934945
You over-fixate on the indeterminate dyad as being the material/mixed, when in actuality the monad and indefinite dyad in themselves are equally distant to this material experienced world, I personally am of the opinion that Plato has a “one-behind-the-one” for his commentators argue this and the related and influenced schools such as Kabbalah have such “one-behind-the-one” schemes which reconcile the two.

To elaborate further, if one wanted to experience the mystical indefinite dyad I believe the tamas based ignorance based mystical modes are best, considered the datura based sadhana of the aghori which both maintain dichotomy and hierarchy but heighten the sense of otherness, heighten the sense of difference, but eventually do this until the sense of self is alienated from, in this eventually you experience the “flip” wherein the hallucinations and illusions show they are illusions, the “not” says “not “ to “not” the double negation occurs, you experience the heart of this difference of this shakti, as good, as monad, one. Usually this ontological position is called cold or dark which is why the descriptions of it in kabbalistic lit speak of the lowest earth as a kind of pitch black world that only the light of the tip of the mezla pierces, why I am explaining this is, either extreme results in knowledge of god whether directly or through identification of ignorance with knowledge, it is this material mixed middle ground world that is ontologically bad, but fixation on either point has various mystical and sorcerous results.

Very good thread.

>>20935396
>>20935450
I'm not sure I entirely get what you're saying. But again, Aristotle studied under Plato for 20 years until Plato's death. It's entirely possible that Aristotle misunderstood Plato on this point, and that this guy 2500 years later working from a group of ambiguous dialogues and some scattered second hand accounts has the correct interpretation, and that we can use our ambiguous source material to judge Plato correctly on this. But I am highly sceptical. We don't even *have* a direct account of Plato's unwritten doctrine. Aristotle did. And if your evidence for Aristotle misinterpreting is that 1) he disagreed with Plato, and 2) Aristotle's own positive theory has problems of its own, well as far as I can see neither of those have any bearing on whether he understood Plato's theory correctly or not. Maybe Aristotle understood perfectly well, but was just wrong. Or Plato was wrong. Or they both were.

(As an aside, I don't know why you say the Great Chain of Being is arbitrary. It's not arbitrary, it's just teleological. Plenty of philosophers have agreed with you and criticised teleology as arbitrary, but Plato uses teleology all the time - in fact he sets up the Form of the Good itself as teleological. I suspect Aristotle's Great Chain of Being is just a different formulation of the same thing.)

OP here, I finished reading another great work. Apparently, Plato may have understood unity as number, while Heidegger argued that Aristotle understood unity as geometry. They may be reconciled as analytic geometry, which is Cartesian in origin. Will write about it if the thread is still up in the morning.

>>20937932
>As an aside, I don't know why you say the Great Chain of Being is arbitrary. It's not arbitrary, it's just teleological. Plenty of philosophers have agreed with you and criticised teleology as arbitrary, but Plato uses teleology all the time - in fact he sets up the Form of the Good itself as teleological. I suspect Aristotle's Great Chain of Being is just a different formulation of the same thing.)
What do you think the Form of the Good is, exactly?

>>20928522
Whitehead should be read more in general.

>>20935121
I think what the incommensurability of the diagonal shows in this example is that "oneness" is not a mathematical unit or line, or anything definite in that sense (as possessing "matter", whether intellectual or otherwise). The hypotenuse of that triangle clearly forms a part of a new, internally commensurable square which is at 45 degrees of and within the greater square (yet the two squares, relative to each other, are not commensurable), which could be made "one" and thereby commensurable insofar as that inner square is taken as the unit definition. It's possible to form infinitely many incommensurable squares within those two squares, by the way, all of which will be incommensurable with each, because the next hypotenuse will have a length of sqrt2(1/2 sqrt2[2] + 1/2 sqrt2[2] ), with the pattern continuing ad infinitum.

>>20935121
>>20938529
It should be clear, but if not, what I mean by "internally commensurable" is this: The inner square has sides of square root of 2, but if we take this as the unit definition, we can either do two things, assign the value as absolutely 1, or use 1 * square root 2. Whichever one we use, when investigating the ratios of the inner square, the outcome is exactly the same as the greater square (if we ignore the addition of sqrt2 and focus on the pure ratios: one and its relationship to the commensurate numbers of the square), except now we have tacked on the "square root of 2" as a coefficient, or in logical terms, we are predicating oneness (1 *) of something which is indeterminate (square root 2) in order to arrive at a definite conclusion about one and what is commensurate with one (we have taken the indefinite as the definite). What is the only commensurate between the inner and outer square? Oneness, insofar as the square root of 2 is one. The square root of 2 is the incommensurate between ones which have twoness predicated of them. To make one relative to one is to make it two. The whole problem turns into a similar issue that I've found in the Parmenides dialogue.

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>>20938529
So, it's a:
>flip
>flop
>flip
>flop
>flip
>flop

Plato's geometric mean is like the aporia in Protagoras. You just switch positions. You don't straighten anything out or get anywhere.

>>20939585
society: ok

>>20939697
Society likes to flip flop too. Except things get really gay when that starts to happen and nothing makes sense anymore.

bump

indeterminate monad

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hump

>>20937932
>Aristotle did.
Are you sure about that? I felt that David's paper was convincing enough to demonstrate that Aristotle didn't understand Plato's intuition regarding the One and the Many. And if you look into Aristotle's work in Nichomachean Ethics, it's almost as if he took Plato's work, formalized it all, but then forgot the punchline when he rejected the Form of the Good, only to have zero substantial content for what nous (intuitive reasoning) is supposed to be about. Plato's wisdom gets reduced to "theoria". What is "theoria", the end of the contemplative life, according to Aristotle? It appears to be some kind of feat of strength, a nimbleness, completeness, and flexibility of mind that one would obtain if they followed Plato's allegory of the cave (see pic-related)... but noticeably missing ONE element. Aristotle does not speak of the "revelatory flash" that one experiences, in Plato's view, after direct acquaintance with the Form of the Good.

>>20937520
>A nuance I think you’re not striking on is that number appears as a kind of, relational existent; as if the One and the dyad were two infinitely vast spheres and these spheres intersected, that intersection point being the numeric world, that numeric world formulating the rest, it’s implied and many commentators such as ficino will tell you plainly that in Parmenides that this dyad for it to be truly the different-in-itself it has to be different-to-itself, and thus must be different from difference, thus even the indefinite dyad is a “kind” of monad, thus it is not a dualism for the essential nature of difference in itself is unity all over again.
Could explain more by what you mean? I'm not sure if I'm following. From what I understand about Plato after Parmenides, Theaetetus, Philebus, etc., is that there ARE two metaphysical categories to consider, the unlimited (irrationality, quality, relativism) and the limited (measurement, quantity, absolutism). The problem is that the unlimited can't be measured without some form of truncation. Yet Plato then begins to formulate an understanding of the indeterminate dyad that shows that number CAN be applied to the unlimited... if one can consider the ability for measurement to be infinitely applied. So there wouldn't be any real difference: it's all One. But without that application, man's measurement, there is no unity. Hence the indeterminate dyad is indeterminate.

While you're here, I'm also going to throw out the consideration that while Plato likely thought of number as unity, Aristotle may have been making the serious and informed rejection of number by believing that arithmetic was reductionist and lacked "direction", and that only geometry was true unity. I can expand on this if you wish later.

bump
Frater Asemlen, I think you would my other threads on mathematics and infinity: >>20944284, >>20939220

>>20934898
>>20934945
>>20935076
>>20935121
>>20935198
Great posts, I'm glad /lit/ still has threads like this one.

>>20945381
Thank you anon. I consider it my job to de-mystify the two greatest philosophers of all time, Plato in 1st place and Aristotle in 2nd place, so that one may be brave enough to follow in the former's footsteps until it we are forced to make the leap of faith into the unknown mysticism. If Plato is to be believed, then not only is the Form of the Good the truest thing there is, the breath-taking understanding of the infinite, but it is something that must be discovered for oneself in order to be believed. In other words, Plato found some kind of "shortcut" for finite creatures to experience infinity. And if not, then perhaps anything goes. Scary.

Furthermore, it is worth trying to understand why Plato was accused by Heidegger of setting the foundations for Descartes's analytic geometry and thus the Cartesian worldview (of mind/body dualism, subject-object distinction, and especially of res extensa, which implies infinite divisibility). As explored in this thread, >>20939220, the Greeks seemed to have had a different understanding of space compared to us, which has been forgotten because we retroactively applied modern concepts to Greek knowledge (e.g. "Euclidean space"). For the Greeks, geometry was seen as a mere mental exercise, a closed system, one step removed ("khora" = divisibility, abstraction, etc.) from the "concrete" world of "place." When Plato told people to know their geometry, for all we know, he was telling people to "steelman" themselves so he could break it down for them with his first principles of the Unit and the Indeterminate Dyad.

So, what is the problem with Plato and his embrace of number? Arithmetic was seen as the realm of the "monad" (unit), which has no orientation other than measurement, is absolute, completely abstract (e.g. what we take space to be, nothingness). In contrast, geometry was seen as the realm of the "stigme" (points), which was abstracted from place. The point, unlike the unit, still has orientation. Returning to Descartes, what is analytic geometry but trying to quantify the unquantifiable, e.g elements of geometry like the sqrt of 2, pi, etc.? And what is that but Plato's indeterminate dyad in action but a form of analytic geometry (e.g. adding number to the unlimited, like quantifying irrational numbers, and seeing that exhaustive process to the end)? This is probably why somebody like Leibniz (remember, monadology, characteristica universalis, his work with the I Ching, etc.) was so fascinated by Plato, too. Both Descartes and Leibniz believed in infinite divisibility, with Leibniz making that argument explicitly that space is infinitely divisible in the Leibniz-Clarke correspondence.

(1/2)

>>20945381
>>20945516
It is also worth noting that Plato hated Democritus and his atomism, seeking to have the latter's works burned. So, maybe it's unfair to accuse Plato of being the harbinger of Cartesian thinking. Or perhaps Plato knew he had no counter, that he had made a mistake from the beginning. Maybe Plato knew that there was a counter, e.g., achieving gnosis, but would otherwise be dangerous if it fell into the wrong hands. Perhaps Plato ought to NOT have been concerned because he knew that writing, like all symbolic language, is directionless without a "cipher" (as much as he complains about the problems of writing in Phaedrus, the Seventh Letter, etc.).

Speaking of Plato's concern about measurement, ambiguity of writing, atomism, etc. I'm also reminded of the problems of "measurement" with Plato's dialogue Protagoras, the sophist who declares that Man is the "measure" of all things (e.g. the only limit). If you remember that dialogue, then you'll notice that Socrates and Protagoras switch positions on virtue by the end. So, if man is truly the measure, then there is no "end" to reach, only an endless cycle of opposites that go on forever. Makes you wonder about the importance of God's existence: only God can measure to the end. But I digress.

All I know is, if Heidegger and Klein are to be trusted, then Aristotle *does* have something on Plato, even if he didn't understand Plato's mathematical basis for the indeterminate dyad, by demonstrating the importance of geometry's "unity." According to Aristotle, who was well-immersed in the Greek conception of "place" (and not space), lines are more than just monads lined up in a row: they are a collection of stigme. They have the same orientation, leading to the emergent property of the line from the points, a unity of the shapes that are preserved from the natural "bodies" of the world that geometry is abstracted from.

The next thing I'm working on is understanding the Early Modern revolution in physics: understanding how classical mechanics "outperforms" Aristotelian "natural motion" (which is much more true than we give it credit for: Galilei's understanding of gravity requires us to abstract "air" out of the picture). Why does Aristotle ignore "inertia"? Because there's no reason to suspect inertia exists in a world filled with "causes" (e.g. friction, collisions, etc.) that will naturally cause all non self-propelled things to come to a rest. Only in abstract space will concepts like inertia even make sense: you can think of Early Modern science as the attempt by man to "dissect" nature.

I suspect that the only way the Cartesian "geometry" even has any sort of connection to the real world is through its application through classical mechanics, which people like Newton made solid use of. But I don't fully understand the ramifications. Just putting this out there for anybody who's curious at how science actually works and how philosophy is deeply connected to it.

(2/2)

>>20945516
>>20945566
If you want a little bit of the intuition behind the problem of "man is the measure" and why I think that God has to be involved, try checking out the classic "coastline paradox" problem. which is also related to the troll physics I posted. The "distance traveled" by man trying to approximate the path by trial and error is potentially infinite when he alone is the measure. The second video is really good at building the intuition, too.
https://www.youtube.com/watch?v=kFjq8PX6F7I
https://www.youtube.com/watch?v=Rv0c7R8brjE

Plato-anon, how do you feel about Plotinus? I've read more of him than Plato and I'm not certain if he perverts anything. So far everything you've said seems to line up with what he says Plato said.

>>20945610
I'm not an expert on the Neoplatonists. I've only read some secondary and tertiary sources on them. Never read the Enneads, but I have read some of Proclus and his commentary on Plato's work. I also like how they tried to reconcile Plato and Aristotle: such an attitude almost ways bears intellectual fruit. Every single time I see a thinker who says "the Neoplatonists are cool", like Schelling or Peirce, I immediately want to take a second look at what they're saying, no matter how dry and analytical their work appears to be. I'm also very partial to Christianity, just to be honest about where I'm coming from, but I like the Christianity of Origen best.

My main impression (take it with a grain of salt) is that the Neoplatonists were too focused on the theoretical underpinnings of Plato's Form of the Good to the point where they were often divorced from what it actually feels like and how to get there. Against Plato's advice, they failed to recognize that "seeing is believing", focusing too much on what the Form of the Good is structured like (something that is supposed to be ineffable anyway according to Plato). So, I see the enterprise as bankrupt from the beginning, unless they believe they're doing Plato better than Plato. I don't see an impulse by Neoplatonists to perform the rigorous dialectic that Plato prescribes in The Republic to escape the allegory of the cave. IIRC, only Plotinus caught a glimpse of "The One": so everybody else must have been like blind people trying to describe an elephant. And who knows if Plotinus wasn't just bullshitting everybody.

I'm also baffled by the Neoplatonic resistance to Christianity, which seems to me in hindsight as a more "Platonic" religion with its (more) unitary theology in contrast to the fragmented Greek pantheon. Christian theologians like St. Augustine were able to easily incorporate Neoplatonism back into Christianity to the point where you can see Platonic reverberations even in thinkers like St. Aquinas, whose concepts of "concupiscence" and "irascibility" as he was interpreting Aristotle (without access to Plato) clearly mirror the Empedoclean (and later Platonic) division of the soul into eros and thumos respectively.

Perhaps this could all be explained with more historical and philosophical research into Neoplatonism, but I digress. One day I may return to Neoplatonism and better digest its history and philosophy. But I don't think it has any urgent value for me right now.

bump

I'm too dumb for this thread. I can hold the pertinent information in my mind while reading some anons' posts, but as soon as I get done it slips away. Those that deal with both metaphysics or philosophy and mathematical concepts I have to re-read two or three times before they click, and they still slip out of my head afterwards. I couldn't explain what I read here to someone else if they asked me to.

>>20946631
No you're not. It's radically simplex:
https://www.youtube.com/watch?v=t9FllcgMBnA

>>20945695
>Never read the Enneads
https://www.youtube.com/watch?v=WmTxCzl2YMY

>>20946631
Ask questions and I'll help you out. There's no such thing as a stupid question if you're trying to learn.

>>20947306
I gotta get to bed, but I'll post my questions tomorrow if the thread is still up.

>>20926679
this nigga named Bernadette LMAO

>>20947464
why can't people spell Benardete's name right? it's like everybody has ADHD these days

>>20945566
>Democritus
Probably was not hated as much by Plato as previously thought. That came from another rumor spoken by one of Aristotle's students, Aristoxenus (same guy who reported on the Lecture of the Good). If you think about it carefully, Plato had many atomistic proclivities.
>https://www.jstor.org/stable/4430143

https://plato.stanford.edu/entries/paradox-zeno/
>The construction of non-standard analysis does however raise a further question about the applicability of analysis to physical space and time: it seems plausible that all physical theories can be formulated in either terms, and so as far as our experience extends both seem equally confirmed. But they cannot both be true of space and time: either space has infinitesimal parts or it doesn’t.

>>20947907
>either space [which exists] has [mathematical abstractions which can't exist as such] or it doesn't have them [mathematical abstractions which can't exist as such].
It boggles my mind that there is still debate over such trivial problems that were already refuted by much older great minds, like Shankara, Aristotle, et al. Even Zeno demonstrated that "infinitesimal part" is a contradictio in adjecto, just as much as "infinite whole" is.

>>20947776
Plato likely didn't hate anyone. But he definitely was not an atomist. The closest he comes to positing atomism is in the Timaeus, where he argues that geometric shapes are the basic building blocks, not simple atoms.

>>20947965
>The closest he comes to positing atomism is in the Timaeus, where he argues that geometric shapes are the basic building blocks, not simple atoms.
What's the difference?

>>20948026
What is the difference between monism and pluralism, or dualism?

>>20948035
Not similar to what’s being argued here.

>>20947907
great Chomsky video
https://www.youtube.com/watch?v=EVFBABFdLXE

>>20948035
the funny thing about this argument is that Democritus admitted that atoms can be, well, incredibly small, or they could be as large as the entire universe
>One
>and the Many
it's all atoms nigga, and it doesn't differ from what Plato argued.
>Epicurus then starts talking about how every atom has weird grooves n shieeeet that make them unique

>>20949430
>Descartes and mechanistic forces
>btfo'd by Newton and occult forces
>contact as we know it is gone
>Descartes as ghost in the machine is wrong, >Descartes was the machine-lover, Newton banished the machine and returned the ghost
>Leibniz has an autistic fit over the return of the ghost without any explanation
>"lol gravity is just God's hand you swarthy German nigga, now seethe"

>>20949489
better summary here:
https://www.youtube.com/watch?v=XGgro7whKSI
>Newton: there are no mechanical bodies

this shit makes you wonder what abstraction really is.

is it a way of peeling away some properties, leaving other properties "exposed", so one can see hidden connections in the world? e.g., a tool for building understanding? or is it a way of getting more and more divorced from reality until one is left either with absolutely nothing (void, abstraction par excellence) or, even more extreme, an unintelligible creation (not even just the "opposite" of reality, just one where every property has been at least slightly tweaked to a random extent)? what does it even mean to perform logical operations on abstract concepts, especially those toward the insane end of the spectrum?

site: https://mathcs.holycross.edu/~little/WinterMathTalk.pdf
>“For the art of mechanics, now so celebrated and admired, was first originated by Eudoxus and Archytas, who embellished geometry with subtleties, and gave to problems incapable of proof by word and diagram, a support derived from mechanical illustrations that were patent to the senses. For instance in solving the problem of finding two mean proportional lines, a necessary requisite for many geometrical figures, both mathematicians had recourse to mechanical arrangements adapting to their purposes certain intermediate portions of curved lines and sections.3 But Plato was incensed at this, and inveighed against them as corrupters and destroyers of the pure excellence of geometry, which thus turned her back upon the incorporeal things of abstract thought and descended to the things of sense, making use, moreover, of objects which required much mean and manual labor. For this reason, mechanics was made entirely distinct from geometry, and ... came to be regarded as one of the military arts.”
So, Plato was described as a purist according to Plutarch. But, in the Republic, Socrates says:
>“[The language of geometers] is most ludicrous, though they cannot help it, for they speak as if they were doing something and as if all their words were directed towards action. For all their talk is of squaring and applying and adding and the like, whereas in fact the real object of the entire study is pure knowledge.”
And Glaucon acknowledges that geometry is great for use in war as well. Socrates does not push back against this, either.

I wonder if what's going on is more of a Cartesian-like mechanical philosophy (Eudoxus, Archimedes, etc.) versus a more "Newtonian" philosophy that Plato may have preferred, one that doesn't make unnecessary ontological assumptions about a world that is necessarily split between the unlimited and the limited.

https://fountainmagazine.com/2011/issue-84-november-december-2011/the-metaphysical-versus-the-modern-sense-of-the-idea-of-infinite
Guenon begins to talk about the unlimited vs. the limited here. He even brings up a new category, the indefinite, which IMO seems like a better way of describing the apeiron than the unlimited. the mixture seems like it'd match the unlimited better.

>>20950042
Building on this, I think unlimited/limited of Philebus has to be a terrible translation. As explained here, >>20939836, "limit" has etymologically strange origins. We think of limits as "straight, hard-set" boundaries, yet if you look at its origins, it "bends" like the roaming contours of hills and valleys. To say that unlimited and apeiron are anything like each other is a mistake: "limit" does not carry the terminating aspect of "peras", only perhaps its experiential, spatial aspect. Perhaps a better way of translating the two in a way that captures the "measurement" aspect of it all is:
>indefinite = apeiron
without precise measurement, relative, boundless, etc. I like to think of this as the realm of qualia, something that has "stretch", has continuity, what we see prior to measurement attempts, etc.
>definite = peras
(“set a limit, bound, end”), unit(y) through a chosen measurement.
>mixed/indeterminate dyad = infinite/unlimited
this is what happens when Plato applies his method of exhaustion to progressively define the indefinite. It also seems like a way of increasingly dividing, then unifying, then dividing the world until one can go no further. The possibilities truly are infinite, with infinite effort. Then one must return to the surface with the principle of unity, or at least the hope that it is all unified, and nothing is left to the void (hence it is indeterminate).

if you're familiar with Peirce, then firstness, secondness, and thirdness vs. indefinite, definite, and infinite/unlimited make a lot of sense here. but Peirce has no understanding of the void, what may lie beyond the indeterminate dyad.

>>20950180
I also think that Peirce has some kind of "indeterminate dyad"-like movement going through his triads, when things move from firstness to thirdness, or from thirdness to firstness (and not in the sense of beginning a new cycle but rather oscillating backwards). Pic-related might be informative, but ultimately a mistaken, analogy. This video's distinction between the "factual dependency" and the "logical dependency" of Peirce's categories illustrates it well: notice the directionality involved.
>https://youtu.be/YNPVefLzJqU?t=614

Aquinas is pretty interesting here. Think about extension, Guenonian distinctions between indefinite and infinite, Cartesian extension and the (perhaps questionable) assumption of continuity, etc.
>This distinction between the singularity and particularity of a form due to its reception in and composition with matter corresponds to a distinction Aquinas makes more generally between extensive and intensive infinity. Extensive infinity pertains to number and quantity, and intensive infinity to quality and perfection.
>In qu. 2, ar. 9 of the De veritate, Aquinas distinguishes between the ordinary use of the term ‘quantity’ to refer to extension, and a metaphysical use of it to refer to degree of perfection. Arguing that “[n]othing prevents something from being infinite in one way and finite in another way,” he posits the heuristic example of an infinite white body. He says that the whiteness of the white body might be called ‘infinite’ because of the infinite extension of the body, “but its quantity per se, that is, its intensive quantity, would nonetheless be finite, and this would like- wise be the case for any form of an infinite body, or every form received in any matter is limited according to the mode of the receiver, and so does not have infinite intension.”8 In short, the infinite white body would be infinitely extended, but not infinitely white.
Citation (on scihub): Tomarchio, J. (2002). Aquinas’s Concept of Infinity. Journal of the History of Philosophy, 40(2), 163–187. doi:10.1353/hph.2002.0040

>>20950579
I'm also reminded of the connection between Peirciant thirdness, habit (which are like laws, but preliminary and not permanent), and Aquinas's hierarchy of laws

>>20928561
The thing that two corresponds to is the indefinite dyad. Plato isnt an empiricist
>Second of all, you ought to say *indeterminate* dyad, not *indefinite* dyad.
No

>>20950753
Indefinite is the apeiron. The indeterminate goes beyond the apeiron in that it tries to define the indefinite in an ever-exhaustive process. It's a subtle, but crucial, difference.

>>20950042
>Guenon
https://www.youtube.com/watch?v=McuTZRBNCXg

>>20950773
You're hair splitting in a way that I think is getting a bit in the way of the convo. The choice between un/limited, in/determinate, and in/definite isn't so crucial here because of the semantic overlap between these words. The safest way to tie down what Plato is after is to just look carefully at how these terms are described in Philebus and Statesman and track the arguments. An argument from definition as everyone's still trying to see what's yet unclear might get in the way of seeing how Plato presents these terms as they first necessarily appear in opinion and are perhaps later transformed in the arguments.

>>20951193
>You're hair splitting in a way that I think is getting a bit in the way of the convo.
It's not hair-splitting. It's an important distinction. If you don't get it, you don't get Philebus. It's that simple.
>The choice between un/limited, in/determinate, and in/definite isn't so crucial here because of the semantic overlap between these words.
The semantic overlap only exists in the English appropriation of those words, not in their etymologies and original use.

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>>20947306
Can you give any pointers for understanding mathematics from a metaphysical point of view? I'm struggling to understand, say, what is meant by asserting that points are monads, or the philosophical implications of the coastal measurement problem, but I think it's because I'm too wrapped up in the hard, empiricist view of numbers and measurement to grasp the mindset I should be approaching it from.

>>20952549
>what is meant by asserting that points are monads
Points are not monads. The word means "one", "unit", or "unique" in Ancient Greek, and it is the substance of arithmetic, the study of arithmos (number). A number is essentially an arbitrary collection of discrete monads. It is a general representation of quantity, abstracted from the real world. Points, in contrast, have all the properties that monads do, but they also have orientation, given that geometry shares a more direct relationship with concrete objects. They have position, direction, etc., which, in unison, allows for an emergent continuity of points in geometric figures.

The main problem Plato is grappling with is trying to reconcile the discrete monads of arithmetic with the continuous points of geometry. Take, for example, the diagonal of a right triangle. If the sides are length 1, then the diagonal is the sqrt(2). This is called an incommensurability problem, because the sides can easily be measured in discrete units, but the sqrt(2) would be an infinitely-long string if we tried to use numbers to represent it too. Most likely, you end up having to truncate the string, making it inaccurate. You could always make it more accurate by measuring more, though, up until you've exhausted infinity. But then again, infinity is impossible. You have to set the cutoff somewhere.
>I think it's because I'm too wrapped up in the hard, empiricist view of numbers and measurement to grasp the mindset I should be approaching it from.
Well, what do you think numbers are? Tell me, and that would be a great start. I can supply the rest of the intuition.

>>20926679
>what exactly is the One and the Indeterminate Dyad?
we will never know for sure, since it's the core apsect of esoteric paltonism, which is completly lost, all we have is speculations and what other people like aristotle wrote about it

Since there's no better place to ask, has anybody read pic related? Is it good?

Or should I read this instead? I only really have time for one.

>>20952671
>Well, what do you think numbers are? Tell me, and that would be a great start. I can supply the rest of the intuition.
Well, to me numbers are expressions of particular arithmetic values. They're representations of actual quantities observable in nature (3 sheep, 50 rocks, 100 million stars, etc) that have been given symbols to make referring to and manipulating them easier.

>>20954077
I agree with you. On one hand, nature is filled with infinite potential for arithmetic groupings, which the Pythagoreans loved to point out. On the other hand, what you want to see is what you get. That's why Aristotle chastised the Pythagoreans for worshiping number. (The debate is also what made it click for me that looking on the bright side of things is 100% a better way to live, kek. Just replace number with attitude.)

However, there is one number that seems to be everywhere. One. Everywhere is one. Don't you think?

>>20954182
>However, there is one number that seems to be everywhere. One. Everywhere is one. Don't you think?
One as in existing in one world, sharing one common attritube of being or existence, or receiving their being from one uncaused cause, yes. If you mean some other way of being one then I don't quite follow.

>>20954488
>?
>One as in existing in one world, sharing one common attritube of being or existence, or receiving their being from one uncaused cause, yes. If you mean some other way of being one then I don't quite follow.
What other ways could I mean?

>>20954490
Well, you said "everywhere" and not "everything" so it seems like you're implying that there are different meanings of "place" or "spacial relation," some of which allow a definition of "everywhere" in which all places are one, unless I had it right initially and there aren't any other meanings to what you said.
Does this make sense?

>>20954705
That makes sense. I see where the ambiguity is. I wonder how I’ll make it more clear (or refine my own understanding). I suppose the whole world, everywhere, is filled with undefined things that can be assorted into groups, numbers, as one wishes. But there is one group that everything seems to belong to.

>>20955275
>But there is one group that everything seems to belong to.
Things that exist? Intelligible things? Things with the potential to exist or to be intelligible? Things that belong to the group that everything belongs to?

>>20955521
>Things that exist? Intelligible things?
I'd say they're both the same thing.
>Things that belong to the group that everything belongs to?
Yes. See above.
>Things with the potential to exist or to be intelligible?
Now THAT is a good question. What do you think is at stake?

Great line of questioning. I need to go back and read some Aristotle, Aquinas, and Early Modern commentaries/refutations of the two. Understanding potential vs. actual, matter vs. form, and their relationship to the four causes, is something I need to work on.

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>>20945516
>If Plato is to be believed, then not only is the Form of the Good the truest thing there is, the breath-taking understanding of the infinite, but it is something that must be discovered for oneself in order to be believed. In other words, Plato found some kind of "shortcut" for finite creatures to experience infinity.
Can you explain this a little more? In what way is it a shortcut?

>>20957717
A finite creature cannot contemplate the infinite without a shortcut, discovering the underlying pattern.

bunmp

@Platoanon are you the One who always comes into clg threads to ask for meanings of Greek words?

>>20958722
yeah

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>>20951230
>The semantic overlap only exists in the English appropriation of those words, not in their etymologies and original use.
But the Greek peras clearly accomodates for "limit", "definite", "determinate", see for example its uses in Meno where they speak of a peras of solid. I don't contest asking about, say, the connotations of gnoskein or eidenai, but what I contest is, like Prodicus, an unwillingness to compromise on English translations that don't even damage the underlying Greek.

It would be like arguing that "virtue" is a bad translation of arete on the basis of a technical definition of arete that appears at the end of a dialogue; it ignores, as an approach the dialectical manner of starting from opinions about virtue and then coming to a deeper understanding that looks different but still addresses the same word. The other risk is making distinctions by argument with English words that don't consistently hold as distinctly as you're arguing. "Limit", "definite", and "determinate" are used by and large as synonyms in philosophy and math. This particular argument doesn't have the same weight as translating mousike as, e.g., "culture" in the Republic and wiping out a dimension of the argument.

>>20951230
>>20959612

Like, all I mean is that this:

>>20950773
>Indefinite is the apeiron. The indeterminate goes beyond the apeiron in that it tries to define the indefinite in an ever-exhaustive process.

Doesn't have a basis in Plato, since, whichever you choose, indefinite or indeterminate, they're just translating apeiras, and there's not any clear reason to take the latter as more inappropriate except by perhaps contrasting with a specific author's use (say, Hegel), and making more out of that difference than is otherwise present.

>>20959612
>But the Greek peras clearly accomodates for "limit", "definite", "determinate" ...
So, why would you waste the effort repeating yourself without bothering to address the etymologies at hand? There are key differences between limit vs. definite, determinate as the Romans knew them: e.g. the latter set has a terminus, "an end." A limit is a mere boundary, having its origin as a reference to the topography of the land. We use limit vs. definite, determinate, etc., interchangeably today, but that's not how it always was. What we've done today is essentially forget the category of the "mixed" from Philebus: the understanding that every "limit" is not the end, and that one can always set a "limit" beyond the "limit." Where is the "terminus" there? You can't find one.

And the million dollar question: if peras can accommodate both "limit" and "definite", "determinate", etc., then why doesn't Plato use it to describe the mixed category? The simple answer is that it's ontologically distinct: it's "mixed." The the question of there being an "end" being uncertain until one travels long enough to reach that "end", with obvious cosmological implications given the nature of infinity. And that's a huge problem: given that "peras" also means:
>trial, experience, etc.
You would essentially be swinging too much to one side or the other. Depending on how far you "measure" is how much you've "undergone a trial": the rest is still "apeiron." If the setup of your terms don't reflect that understanding, then you've missed the argument.

Going back to your original argument, that there is some semantic overlap, I think you have a strong point. But only in the sense that perhaps I wasn't being precise *enough* in my original formulation. The more I explained it, the more I think it makes more sense to refer to it as:
>unlimited (perhaps, instead of indefinite)
>definite (rather than the limited)
>indeterminate
Or something along those lines, to try to have the best compromise between etymology and connotation. The point being, they're not the same thing. And you have take notice when translating from Greek, "bending" the terms appropriately so that the full picture is understood with as *little* semantic overlap as possible.

(1/2)

>>20959612
>>20959864
>see for example its uses in Meno where they speak of a peras of solid.
They use it as an analogy, not the real thing. Geometry is an abstraction from being, once removed. See the following quote:
>In the Physics (II, 2), discussing the scope of natural science, Aristotle examines the mathematical objects of stereon and gramme – solids and lines. Whilst these can be considered as physika, with a surface as peras, the limit of a body (als Grenze eines Körpers), the mathematician con-
siders them purely in themselves. 11 Heidegger suggests that this negative
description of the mathematical in Aristotle – ‘that it is not the peras of
a physikon soma’ – means that ‘the mathematical is not being considered
as a ‘place’ (Ort). Therefore this abstracting, this extraction (Heraussehen)
of the essence of the mathematical from the realm of physikon soma, is
314 STUART ELDEN
essential, but oyden diaphora, it makes no difference (macht das keinen
Unterschied). By this, Aristotle means that the abstracting does not turn
them into something else, but the ‘what’ of the peras is simply taken for
itself.
>https://progressivegeographies.files.wordpress.com/2012/04/the-place-of-geometry.pdf
There's more to the argument, by the way. I highly recommend you check out the article: Klein, Heidegger, and Wachterman all make an appearance. This is also why I emphasize the etymological roots of "limit", as they are functionally similar to "topos."

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>>20959654
>>20959864
>see for example its uses in Meno where they speak of a peras of solid.
They use it as an analogy, not the real thing. Geometry is an abstraction from being, once removed. See the following quote:
>In the Physics (II, 2), discussing the scope of natural science, Aristotle examines the mathematical objects of stereon and gramme – solids and lines. Whilst these can be considered as physika, with a surface as peras, the limit of a body (als Grenze eines Körpers), the mathematician considers them purely in themselves. 11 Heidegger suggests that this negative description of the mathematical in Aristotle – ‘that it is not the peras of a physikon soma’ – means that ‘the mathematical is not being considered as a ‘place’ (Ort). Therefore this abstracting, this extraction (Heraussehen) of the essence of the mathematical from the realm of physikon soma, is essential, but oyden diaphora, it makes no difference (macht das keinen Unterschied). By this, Aristotle means that the abstracting does not turn them into something else, but the ‘what’ of the peras is simply taken for itself.
>https://progressivegeographies.files.wordpress.com/2012/04/the-place-of-geometry.pdf
This is also why I highlight the difference betwee limit and the other "terminating" roads. If you look up the etymology of limit, limes, you'll see that it is derived from a functionally similar background as topos.

(2/2)

>>20959883
between limit and other "terminating" words*

>>20959864
>>20959883
Unless you're Heidegger, the ancient etymologies of the words passed down to us as "limit", "definite", "determinate" aren't relevant. As English words, the three are very often synonyms, but the most ancient etymologies of their Latin forms don't get in the way of present day usage, which would be the only reason to otherwise distinguish them. This would be like saying it's inappropriate for current day speakers to use the word "salary" because they're not paid in salt.

>>20959883
>They use it as an analogy, not the real thing. Geometry is an abstraction from being, once removed.

What? It's not an analogy, it's very clearly used in the sense of "extremities or boundaries of a solid":

>Socrates: Therefore, you could immediately understand what I mean about shape. For I say this about every shape: that at which the solid ends, that is shape; what I could say, in summing it up, is that shape is the limit (peras) of a solid.

This btw is how peras gets used in Euclid.

>>20959654
the indeterminate dyad is the ἀόριστος δύας not ἀπείρος δύας though. It only comes up in Aristotle in reference to the unwritten doctrines while the apeiros peiras distinction is from the Philebos.

>>20960971
We were talking about peras in the Philebus, as per >>20950180. But even granted, that doesn't necessitate hard and fast rules over which English choice fits best, at least in the case under discussion. If one's translating from a dialogue where peras and apeiron and horos and aoristos appear, distinguishing consistently would be important, but except in the case of horos (where it's often used in the narrow sense of "definition" instead of boundary in general), it doesn't really matter which of these three terms are chosen.

>>20960879
>Unless you're Heidegger, the ancient etymologies of the words passed down to us as "limit", "definite", "determinate" aren't relevant.
Yes they are, if you want to have a concrete place of where to begin, how these ideas evolved, and how mistranslations emerged. Personally, Heidegger's style is a great way to begin investigating what classical thinkers actually meant. Now, do you want to argue over language, or do you want to move beyond language to understand the things-in-themselves?
>don't get in the way of present day usage
I don't care about present-day usage, because present-day usage is completely inadequate to communicate the nuances of ancient Greek philosophy. It isn't even adequate to capture the original versions of those words as Romans understood them, either.
>This would be like saying it's inappropriate for current day speakers to use the word "salary" because they're not paid in salt.
If the text was trying to make some point like "salt should be currency because it's a good store of value", then it makes no sense to talk about salary in the general, modern sense where things like fiat currency would confuse our understanding of the ancient point.
>>20961059
Lol, what do you think the ἀόριστος δύας is referring to? It's referring to the "mixed" category in Philebus. Now, do you get it? Are the puzzle pieces coming together in your mind?

At the very least, there has to be three words for three categories:
>word one: qualitative, unbounded, relative. seemingly endless. (apeiros)
>word two: quantitative, measured, arbitrary. has ends, but they're "false." (peiras)
>words one and two should "oppose" each other
>words one and two should reflect cosmological, theological, etc., implications about man's measure vs. the final measure of things
>word three: something that mixes the two and gives at least the impression of an absolute end, but perhaps unreachable due to an infinite process of setting, then overcoming, those measurements (ahoristos)

>>20960922
>What? It's not an analogy, it's very clearly used in the sense of "extremities or boundaries of a solid":
If you go to the Republic, you'll clearly see that mathematics is dianoia, not noesis. It's an analogy, not the real thing.

>>20961188
>Yes they are, if...
None of it is relevant *for talking about what Plato writes about*. To back to what the argument is over, we're discussing whether "limit" and "unlimited" are appropriate translations for peras and apeiron, the specific focus on the Latin etymologies doesn't have any bearing on that issue since there's no necessity to a word's older meaning carrying its earliest possible meanings or connotations. Again, it's like demanding we stop using "salary" because we're not paid in salt. Further, Plato uses arguments from etymology differently than in this case; in Phaedrus and Cratylus, he's either making a speculative connection via similar sounding words, parodying someone who speaks about etymologies (e.g. Euthyphro and Prodicus), or pointing to something subtler over an extended consideration (the relation of the etymologies in Cratylus to Pre-Socraticism). In our present case, if you're quibbling over the English translation of a handful of terms, with a very similar range, pertaining only to what Plato intended to convey.

>I don't care about present-day usage...
Your evidence is what, exactly? And present day usage was relevant because you were defending your choice in favor of one Latin-derived English over another Latin-derived English term because of possibly minute differences between the ancient etymologies of both words, differences that have collapsed in the meantime.

>If the text was...
Sure, but you haven't demonstrated this to be the case with English translations of peras; you list us your impressions of the associations that it and apeiron should convey, but shouldn't arbiter be Plato's text, and an argument derived from looking at how peras and apeiron are discussed whenever they appear?

>Lol, what do you think...
Okay kid, again, we're arguing over a matter of how much one should nitpick a translation. I didn’t bring up the Dyad, just left it at the Limited etc. of Philebus, but if you wanna switch the goalposts of what was originally being argued, have at it. You're not going to persuade me arguing like that, but I'm sure it'll trick someone less attentive.

>>20961194
>If you go to the Republic, you'll clearly see that mathematics is dianoia, not noesis. It's an analogy, not the real thing.
The use of peras in Meno describing shape as the peras of solid is a definition, not an analogy, first off. It seems odd to have to explain that definitions can be of non-mathematical things and that they're not mathematical themselves. Second, per the divided line, math is among intelligibles, i.e. the real beings. The line itself is an analogy, the cave and sun are analogies, mathematical ratios are in a certain way analogies, but using peras to define a mathematical object is not an analogy. You need to stop runnin' and gunnin'.

Did the Guenon fag shit up this thread?

>>20951193
>You're hair splitting in a way that I think is getting a bit in the way of the convo.

Psyopped by the mentally ill guenonfaggot into engaging with his wall of text pilpul. Every thread has to be about guenon now.

>>20961571
>None of it is relevant *for talking about what Plato writes about*.
Yes, clear terminology is fundamental for discussing philosophy well.
>And present day usage was relevant...
... they're not relevant except to point out that their present-day connotations are philosophically fuzzy in a way that their past etymologies weren't. Again, words are placeholders for meaning. Theoretically speaking, as I described earlier, all you need is for apeiron and peiras to be contradiction while capturing the qualitative/quantitative aspect of that, then to have the third category be "mixed" in a way that conveys that there *could* be an end, but the status of it is uncertain. But if you're going to start lining up words, why not stick to the words via what they originally meant through functional use? It's a stylistic concern, but one that gets you inside the mindset of ancient thinkers while doing the appropriate philosophical book-keeping, so there's a ton of practical wisdom to it as well.
>Again, it's like demanding we stop using "salary" because we're not paid in salt.
Nobody is attempting to police your use of salary in everyday life. This is a ridiculous misunderstanding. Use limited, indeterminate, etc., any way you want. I'm just showing you that you can't simply assign words willy-nilly and not lose something in translation.
>an argument derived from looking at how peras and apeiron are discussed whenever they appear?
I've been talking about Philebus this entire time. If you have a problem with my interpretation of Philebus or any other philosophical texts, feel free to call me out, albeit I'll probably get bored quickly because I think you're arguing just to sake to argue to the point of missing the point of Platonic philosophy.
>The use of peras in Meno describing shape as the peras of solid is a definition, not an analogy, first off.
And Socrates in Meno ironically tells the slave boy not to bother enumerating the quantity of the hypotenuse of a unit triangle because, lo-and-behold, it's an irrational number that repeats infinitely, foreshadowing developments in Platonic ontology in Philebus. No definitions are airtight, which is also a repeated theme in Plato's Seventh Letter.
>Second, per the divided line, math is among intelligibles, i.e. the real beings.
They're dianoetic, but they're not noetic in themselves. There's more two the divided line than the difference between the realm of appearances and the realm of forms. Mathematical truths are not "the highest" truth because they're contingent on uncertain premises. And they're certainly not on the level of dialectic, which is the realm of noetic truths.
>but if you wanna switch the goalposts of what was originally being argued, have at it
The whole point of arguing over translations was to preserve nuance.
>You're not going to persuade me arguing like that, but I'm sure it'll trick someone less attentive.
Not my problem. I don't think you're here to be persuaded.

How did Plato die?

>>20926750
Nice, thanks.

>>20927315
Makes sense. I've often thought about this concept without having a name for it.

Mentally ill guenonfaggot thinks Guenon, who flunked out of first year university math, is a good resource on math.

>>20961948
>>20961979
>>20962402
Read the thread, there's a perfectly legitimate (if autistic) discussion going on here.

>>20962402
I've never read Guenon in my life lol. Why do you keep polluting my thread with your schizoposts?

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>>20962068
Literally non-sequitors as responses. Enjoy samefagging your masturbatory thread faggot.

>>20962991
If you think they were non-sequiturs then you ought to see a neurologist. You might have brain damage. Don't pretend like you're an attentive reader around me.

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Doesn't the existence of both a One and an indeterminate dyad imply that Plato's system was ultimately dualist? Or is he implying that the interaction between the two in the intelligible world creates some form of monistic union between the two?

>>20965414
>Or is he implying that the interaction between the two in the intelligible world creates some form of monistic union between the two?
This. Plato was optimistic about the idea that the indeterminate dyad could be reconciled with the right intuition, the Form of the Good. In a way, he was beyond monism or dualism. He was a nondualist.

>>20965414
>>20965617
but I might add that it might be unfair to call him a nondualist because he ultimately sees the world as One, from the microcosm to the macrocosm. But then again, we have the becoming-being split, the indeterminate dyad, the "eidetic analysis" that Benardete describes all the time, etc.

>>20926679
That book is incredible. Plato and the indeterminate dyad is just one sliver of a lot of deep, mind-blowing readings of the classics. Here's a snapshot of Benardete deconstructing the Judio-Claudian dynasty as a "detranscendentalization" of Greco-Roman myths after it reaches its zenith. The Caesars have become God on Earth, there's nothing beyond the universal empire, and it begins to look inwards with great chaos and destruction. Meanwhile, in the periphery of the empire... the last vestige of an alien worldview is being snuffed out, to make way for another way out. Christianity and a kingdom that is "not of this world." (Only to possibly repeat the same problem on a massive scale.)

bump

>>20926679
>early life

>>20932304
Is there some sort of quick rundown to help me understand this?

you can either be a goy or a Jew. be careful if you mix both, it's like dividing by 0

Since Mmmm-moses. Since Moses Mmmm-Mendelsohn.
>mfw ywn be roasted by Leo Strauss