Forms are mathematical objects. Forms are a subset of math. — ArisTootelEs

I don't remember my math teacher saying anything about goodness or justice though.

I don't remember my math teacher saying anything about goodness or justice though. — Apollodorus

I was wondering recently whether this is because our culture has only kept those elements of Platonism which are useful for science and engineering, while discarding the moral and aesthetic principles that Plato apparently thought indispensable to his philosophy. Galileo was greatly influenced by the neo-Platonic revival of the Italian Renaissance - Ficino had translated Plato into Latin - but his philosophy was mainly concerned with those elements which could be brought to bear on the physics and the overall ‘mathematicization of nature’ that marked the advent of modern scientific method.

I’ve been told that Iris Murdoch’s Sovereignty of the Good extols an overall Platonist approach to ethics and aesthetics (and intend to read it). But it is also noted in the article I’ve linked to that Platonism in morals was considered archaic or eccentric at that time. And so it is. That’s why, as I’ve noted earlier in this thread, there is a connection between traditionalist philosophers and reactionary political movements.

My bias against Plato (in particular) begins with interpreting Classical (Orphic?) Platonism in the naturalistic-experiential this-worldly context of the Hellenistic era's (my preferred "schools") Epicureans, Stoics, Pyrrhonians & Kynics. (Re: eidos as immanent ideas derived from physis rather than transcendent (telos) such as either hylomorphic or supersensible "forms".) Platonism is too other-worldly – escapist (e.g. gnostic) – for cultivating ataraxia, aponia & apatheia here and now in this world, and this was so especially during the tumultous centuries after the death of Alexander the Great in the 4th century BCE. Anti-naturalist nihilism (i.e. devaluing of natural existence), as Freddy Z. had philologically diagnosed, is all that Platonism teaches (pace Hadot), or amounts to, which is what made it so facile for Pauline / Nicene Christianity to adapt (repurpose) it – "the Platonism of the masses".

Re the ultimate goal of philosophy, Solomon and Hadot:

I first met @Fooloso4 on another forum in a galaxy far, far away. I've followed him ever since.
In a discussion entitled 'Secular Spirituality' - he impressed with careful replies to my questions:

What is 'Secular Spirituality' ?
Would you agree with the suggestion below that it is 'the ultimate goal of philosophy'?

'According to Robert C. Solomon, an American Professor of Philosophy, "spirituality is coextensive with religion and it is not incompatible with or opposed to science or the scientific outlook. Naturalized spirituality is spirituality without any need for the 'other‐worldly'. Spirituality is one of the goals, perhaps the ultimate goal, of philosophy."

@Fooloso4 wrote:
p1:

I have not read Robert Solomon’s take on this but I offer the following:

Plato’s Socrates famously said that philosophy begins in wonder (greek: thaumazein). Aristotle said:
All begin, as we have said, by wondering that things should be as they are …
(Metaphysics 983a).

Wonder is an spiritual experience. The history of the term ‘spiritual’, however, has led many to understand this is a narrow and confused sense. Spiritual in its etymological meaning had to do with breath, that is, life (cf. respire, expire, aspire). That we live and die and how best to live and die is a matter of wonder. It arises, as Aristotle said, from aporias, that is, from an impasse of our understanding.

A further difficulty we must face is that Aristotle referred to the Metaphysics as a theology. This may lead some to conclude that what Aristotle was up to was something akin to Aquinas without Christ. But Aristotle’s concern was with “being qua being”, the study of the first causes and principles of things. One who has knowledge of such things would properly be wise (sophia) but Aristotle never claims to be wise. He aspires (note the extension of the term) to be wise,but has not overcome the perplexity that gives rise to and guides philosophy.

In religion we find both an emphasis on the unknown and a plurality of answers to the unknown. When Solomon says that “spirituality is coextensive with religion” I take him to mean that it raises some of the same questions and concerns about life, but when he goes on to rejects the “otherworldly” I take him to mean he rejects the appeal to transcendent answers that are found in religion.

p6:

Hadot’s "Philosophy as a Way of Life", "What is Ancient Philosophy", and "The Inner Citadel: The Meditations of Marcus Aurelius" are helpful for seeing philosophy as therapeutic and transformative practice, an aspect of philosophy that has been occluded by a narrow focus on rationality and the idea that truth is impersonal. This is, however, not merely a matter of historical interest. Wittgenstein, for example, was aware of the spiritual, therapeutic, and transformative dimension of philosophy. Frege's dogmatic rejection of psychologism is now no longer universally accepted by analytic philosophers as an obvious truth.

There is a growing acknowledgement that philosophy as abstraction from human being in the service to Truth is fundamentally wrong, that philosophy is essentially grounded in human life. I see this not as a matter of academic versus non-academic philosophy but as a possibility for a correction within academic philosophy.

Works by Princeton professor of philosophy Alexander Nehamas, such as "The Art of Living: Socratic Reflections from Plato to Foucault" and "On Friendship" might be signposts for the direction of academic philosophy, or they might be disregarded as wooly-headed and soft, literature not philosophy, and this too might be seen as a signpost, a sign of philosophy’s inability to self-correct, of its increasing narrowness and irrelevance.

That was just over 3yrs ago. We still seem to be on the same page...
Thanks @Fooloso4. Take care :flower:

Thanks for the Edit:

We also see one way in which Plato is addressing two different types of readers. On the one hand he says that there are independent Forms, but on the other he indicates that things are not quite so simple. We are left to ask about the origin of the Forms. We are also compelled to consider in what way things would be able to "participate" in the Form. Socrates raises the question in the "Second Sailing" section of the Phaedo:...
...Beautiful we mentioned, for I will not insist on the precise nature of the relationship, but that all beautiful things are beautiful by the Beautiful. That, I think, is the safest answer I can give myself or anyone else.” (100e) — Fooloso4

Yes. Thanks for that reminder from your previous thread:
https://thephilosophyforum.com/discussion/10914/platos-phaedo/p1

***

He raises the question of the relationship between things and Forms, but does not insist on the precise nature of that relationship. Why? It he had a coherent argument why wouldn't he present it here or elsewhere? He calls the hypothesis of Forms (100a) simple, naive, and perhaps foolish, and later "safe and ignorant". (105 b)

Now some will try to defend the idea of transcendent Forms with accusations of bias against those who question it, but in that case it would seem that Plato is biased against Plato.] — Fooloso4

So it would seem...

It kind of sounds like you've made a sort of guru out of Fooloso4.

It kind of sounds like you've made a sort of guru out of Fooloso4. — frank

Guru in the sense of a teacher, he is. I haven't made him that though.

Guru in the sense of a teacher, he is. I haven't made him that though. — Amity

I see. You referred to yourself as a follower. Is it more pupil? Or disciple?

:smile:
Neither. I said I followed him but more as a friend from philo forum to philo forum...
Why do you care ?

Neither. I said I followed him but more as a friend from philo forum to philo forum...
Why do you care ? — Amity

Oh, it was just that you said you followed him, and you seemed to quote him repeatedly. You were just looking like a groupie there for a second.

I get there, my friend, but by a less therapeutic, more strenuous, path. My exemplars are philosophical surgeons, not homeopaths – blues folks, not saints or sages. "Wonder" worked for the ancients but, in this disenchanted age, modernist despair initiates thinking against oneself (ourselves) as one (we) engage/s this raw, indigestible, uncertainty ... gratuitous being ... the Absurd. To unlearn misery (i.e. self-immiserating habits) in order to optimize agency – that's (my) "ultimate goal of philosophy".

:death: :flower:

...You were just looking like a groupie there for a second. — frank

Hah.
He should be so lucky :wink:

My preferred - idiosyncratic - notion is 'ecstasy' rather than 'mysticism'; ecstatic practices - what Iris Murdoch calls unselfings - rather than mystical, or spiritual, exercises (i.e. union with (some) 'transcendent' (something)); ego-suspending via everyday living (i.e. encounters (à la Buber) - sleep, play, prayer, meditation, or contemplation via [ ... ] and/or hallucinogens) rather than ego-killing via ritualized ascetics (e.g. monasticism, militarism, etc). Not religious, not spiritual, not mystical - but I am (an) ecstatic.
— 180 Proof

I'm pleased...nay, ecstatic for ya' ! :sparkle:

"Wonder" worked for the ancients but, in this disenchanted age, — 180 Proof

Wonder. Not just for the ancients, though. It might be a disenchanted age but even when dispirited - I feel wonder...and keep wondering...for better or worse...

:up:

Yeah, but without the ancient verities (or certainties) of life, what is there to "wonder" at today? (Philosophically speaking,) we can't step into that same river twice, y'know.

what is there to "wonder" at today? — 180 Proof

Elvis Presley - The Wonder of You (Official Video Starring Kate Moss)
https://www.youtube.com/watch?v=HcesjvyWmvg

:hearts: :broken: :heart:

Wonder. Not just for the ancients, though. It might be a disenchanted age but even when dispirited - I feel wonder...and keep wondering...for better or worse... — Amity

Yes. And your Presley quote is apt: modern philosophers may be playing the disenchanted, but artists are not.

...modern philosophers may be playing the disenchanted, but artists are not. — Olivier5

Perhaps. Not all. 'Some' in both cases.
Individuals work, play, think and express stuff as perceived in any given period.
Music, poetry and philosophy can be as 'one'.

I just looked back at your first post on the 'Deep Songs' thread; a thread I adore :cool:

Here's the same song but different video. What a life story...

Johnny Cash - One (Music Video)
https://www.youtube.com/watch?v=AjJU8gon02k

One
Johnny Cash

Is it getting better
Or do you feel the same?
Will it make it easier on you now
You've got someone to blame?

You said
One love
One life
When it's one need
In the night
One love, we get to share it
It leaves you, baby, if you don't care for it

Did I disappoint you
Or leave a bad taste in your mouth?
You act like you never had love
And you want me to go without

Well it's
Too late
Tonight
To drag the past out
Into the light
We're one, but we're not the same
We get to carry each other
Carry each other
One

Have you come here for forgivness?
Have you come to raise the dead?
Have you come here to play Jesus
To the lepers in your head?

Did I ask too much?
More than a lot?
You gave me nothing, now
It's all I got
We're one, but we're not the same
Well, we hurt each other, and we're doin' it again

You said love is a temple
Love the higher law
Love is a temple
Love the higher law
You ask me to enter
But then you make me crawl
And I can't be holdin' on
To what you've got
When all you've got is hurt

One love
One blood
One life
You've got to do what you should
One life with each other

Sister
Brothers
One life, but we're not the same
We get to carry each other
Carry each other

One
One
One
One

Songwriters: Jerry Chesnut Bono
For non-commercial use only.
Data from: Musixmatch

composer: Adam Clayton, Larry Mullen, Jr., Bono, The Edge
lyricist: Bono — Lyrics: 'One'

:sweat:

I'm in 'love' mode. Make the most of it :wink: :kiss:

I was wondering recently whether this is because our culture has only kept those elements of Platonism which are useful for science and engineering, while discarding the moral and aesthetic principles that Plato apparently thought indispensable to his philosophy. — Wayfarer

This seems to be a plausible cause.

But another possibility I had in mind would be that Plato's Forms are not mathematical objects.

Superb....




......Have you come here to play Jesus
To the lepers in your head?......

But another possibility I had in mind would be that Plato's Forms are not mathematical objects. — Apollodorus

No, they're not, but I think numbers, universals, and the Forms are of the same order - they inhere in the 'formal realm', the domain of pure form, which is not visible to the senses but only to reason - which is a straightforward Platonist view.

See this post on the modern rejection of Platonism in mathematics. Also Augustine on intelligible objects.

It was a widespread practice in ancient asceticism. — Wayfarer

Although knowledge of the history and culture are informative we cannot simply assume that a widespread practice is what the puzzling claim about the practice of dying and being dead is about.

I think you have a determindly secularist reading of Plato. Obviously you will see the way I'm inclined to interepret it as due to my own somewhat spiritual preconceptions./quote]

And yet only one of us is attending to what he wrote while the other looks elsewhere. When Socrates says that death might be nothingness that is not a secular reading. It is more the case that those who have "somewhat spiritual preconceptions" avoid dealing with this.
— Wayfarer

Maybe that's because he doesn't fully understand them. Maybe he is dimly intuiting something profound about the nature of rational intelligence but hasn't been able to really think through all of the implications. — Wayfarer

If this is an admission that he does not have knowledge of the Forms, then I agree. "Dimly intuiting" does not square with the image of the mind itself seeing the Forms themselves. Without knowing the Forms themselves how do you know that this is an intuition and not something imagined?

I am trying to understand what 'the forms' might refer to, in such a way as to allow for the idea that they're real. — Wayfarer

Socrates "second sailing" is of primary importance. He says:

... I thought I must take refuge in discussions and investigate the truth of beings by means of accounts [logoi] (Phaedo 100a)

If knowledge of the Forms is seeing the Forms with the mind, then taking refuge in talk about the truth of beings does not lead to the truth of them but to opinions about them.

:up:

Forms are mathematical objects. — ArisTootelEs

Not according to Plato, or at least not according to anything I have found there. The divided line distinguishes between Forms and mathematical objects.

Aristotle claims that Plato regarded mathematical objects as intermediates, between Forms and sensible things:

Further, apart from both the perceptibles and the Forms are the objects of mathematics, he says, which are intermediate between them, differing from the perceptible ones in being eternal and immovable, and from the Forms in that there are many similar ones, whereas the Form itself in each case is one only. ( Metaphysics 987b14-18)

Superb....

......Have you come here to play Jesus
To the lepers in your head?...... — Olivier5

Yes. Superb... :smile:

I checked on the lyricist. Not Jerry Chesnut as above but Bono:

U2 - One (Official Music Video)

https://www.youtube.com/watch?v=ftjEcrrf7r0

No, they're not, but I think numbers, universals, and the Forms are of the same order - they inhere in the 'formal realm', the domain of pure form, which is not visible to the senses but only to reason - which is a straightforward Platonist view. — Wayfarer

Correct. It is the close proximity of mathematical objects to Forms that tends to lead to the erroneous assumption that they are Forms.

In reality, according to Plato, mathematics is just the preparatory intellectual training that unshackles the soul and enables it to turn away from the shadows and towards the light.

The contemplation of mathematical objects starts off the learning or recollecting process leading to a grasp of the Forms (and can take years before the philosopher is ready for the study of the Forms).

But mathematical objects are not Forms. An ideal triangle is a mathematical object conceived in the mind, but it is not a Form. The Form corresponding to the mathematical object “triangle” is Shape.

1. The Good or the One.

2. Nous or "intellect" proper: World of Forms, e.g. Shape

3. Logistikon, "intellectual" or "thinking" aspect: World of mathematical objects, e.g. ideal triangle.

4. Thymos or "emotional" aspect.

5. Epithymetikon or "sensual aspect".

So, Forms are above mathematical objects.

Of course we could say, for example, that Shape itself is a kind of mathematical concept. However, being above "triangle", it is not the same as the mathematical object, it is more a function constitutive of objects than an object as such.

Forms are also different from universals in that they are prior to the objects, though again, they are close to universals or in the same general direction leading to the light of reality ....

A bit more on Socrates second sailing:

After this, he said, when I had wearied of looking into beings, I thought that I must be careful to avoid the experience of those who watch an eclipse of the sun, for some of them ruin their eyes unless they watch its reflection in water or some such material. A similar thought crossed my mind, and I feared that my soul would be altogether blinded if I looked at things with my eyes and tried to grasp them with each of my senses. (99d)

Rather than looking directly at beings he does something analogous to looking at their reflection in water, in other words, he looks at images created in speech. He blurs the distinction between beings as things seen with the eyes and beings as the Forms. In the Republic he says that the Forms are the beings themselves, the originals of which things seen with the eyes are images, and yet here he says that he would be blinded by looking at beings and so he takes refuge in speech and looks at images, at hypotheticals he posits and calls Forms.

In the Republic he presents:

... an image of our nature in its education and want of education ... (514a)

that culminates with the image of the philosopher seeing the Forms themselves. In the Phaedo he presents an autobiographical account of his own education, that culminates with his hypothesis of Forms. But the culmination of his account is not the culmination of his search. Philosophy remains radically incomplete.

It is this indeterminacy that some find intolerable. They desire that things be fixed and determined and knowable. Plato gives them what they want, stories and images they mistake for the truth.

Without knowing the Forms themselves how do you know that this is an intuition and not something imagined? — Fooloso4

Plato hardly claims the power to grasp absolute truth for himself. Very often, when approaching the territory of final metaphysical ideas, he abandons the style of logical exposition for that of myth or poetry. There is something characteristically unfinished about his thought; he eschews neat systems and his intuitions often jostle one another. By contrast, the works of any commonplace thinker leave an impression of extreme artificiality in their orderly array of premises leading inevitably to the one possible conclusion. That is not -- one reflects -- how the thinker actually arrived at the solution; those neat proofs do not represent the complex processes of his mind in its fumbling quest. Only after he had worked out his thought to its conclusion, did he conceive of the systematic pattern which he sets down in his book. Nor is he really as pleased with the solution as he claims to be; in his mind, the conclusion is rather a tentative answer standing uncertainly against a background of aggressive alternatives impatient to replace it. Now, in Plato's works, we have not the manufactured article, but the real thing; we have the picture of a mind caught in the toils of thinkings we get the concrete process by which he struggled to a conclusion, the hesitation amongst the thousand different standpoints, the doubts and the certainties together. The dialogues are, each one, a drama of ideas; in their totality, they depict the voyage of a mind in which any number of ports are visited before the anchor is finally cast. And at the end, it is as though the ship of thought were unable to stay in the harbor but had to cast anchor outside; for according to Plato the mind must be satisfied with a distant vision of the truth, though it may grasp reality intimately at fleeting intervals. — Rafael Demos, Plato, Selections (Introduction)