Platonism

[Cult of Reason]

I asked ComradeRed what Platonism was and "what is bad about it?". He told me to ask Rosa Lichtenstein, so I pose the question here, to her and to anybody else who cares to answer:

What is Platonism? What is bad about it? What is good about it? Etc. etc. etc..

[bezdomni]

It makes things needlessly complicated and pretentious.

[Monty Cantsin]

Originally posted by [email protected] 22 2006, 10:46 PM
I asked ComradeRed what Platonism was and "what is bad about it?". He told me to ask Rosa Lichtenstein, so I pose the question here, to her and to anybody else who cares to answer:

What is Platonism? What is bad about it? What is good about it? Etc. etc. etc..
Depends what you mean, it can simply be the philosophy of Plato and the latter schools of differing interpretations, or I can relate to a theory on the foundation of mathematics. Which views maths similar to the way Plato envisioned his theory of forms, were the idea is abstract and constant.

[ComradeRed]

I was referring to Roger Penrose as a Platonist (which Penrose rather openly admits), and Haraldur asked "Why is that bad?"

Being as lazy as I am, I told him to ask Rosa (who could probably provide a more indepth response than I gave --- "because!" :P).

I was referring to his theory of forms specifically ;)

[black magick hustla]

Originally posted by [email protected] 22 2006, 11:44 PM
It makes things needlessly complicated and pretentious.
like dialectics

BAZING


(dont misinterpret me i love you)

[bezdomni]

Originally posted by Marmot+May 23 2006, 03:58 AM--> (Marmot @ May 23 2006, 03:58 AM)
[email protected] 22 2006, 11:44 PM
It makes things needlessly complicated and pretentious.
like dialectics

BAZING


(dont misinterpret me i love you) [/b]
:lol:

That's why dialthism is better. ;)

[kurt]

I'm not really sure how it relates to mathematics.. but I'll give it a shot I suppose.

Think of a table, perhaps even observe a few different ones for yourself. Although all these "tables" may appear different; some are large, some are small, some are brown, some may be green, you know that they are all tables. Plato would call these "particulars". By this, he would mean that each table you have observes is a "particular" instance of the "universal". The universal is the metaphysical form of the table; it contains all the attributes of what a table is, its "tableness" so to speak.

Basically, the universal is a sort of perfect objective blueprint for particulars. Plato would maintain however, that particulars can never approach the perfection of the universals. Without these universal blueprints, particulars could not exist.

[Rosa Lichtenstein]

CPA:

I think you mean 'dialethism' (or as Graham Priest spells it 'dialetheism'), and since dialethists use modern formal logic to try to show that there are, for example, true 'contradictions' in reality, it is certainly a major advance over the know-nothing approach of most dialecticians. [Whether it is clear(er) or not, you can let me know after you have worked your way through Priest's major work: 'In Contradiction' (2nd edition out last year). I can just about make head or tail of it; I suspect the average DM-fan will be lost before they reach page ten. (This is not to put them down; it is not at all easy to comprehend this highly sophisticated work.)]

But, since dialethists have to alter the rules to get the result they wanted, their theory is just a conventionalist fix, and thus of little significance.

Haraldur, I will outline [i]some of Plato's significant ideas later, and try to say why he personifies everything that materialists are against (at least in philosophy), even if Hegel himself (and thus Lenin and other DM-fans) were Platonists.

[Rosa Lichtenstein]

OK, H, I have just banged this together in my lunch break:

We know next to nothing of Plato’s official Philosophy, since his theoretical work has been lost; all we have are the popularisations of his ideas, written in dialogues.

As far as materialism is concerned, Plato’s theory of knowledge and ontology (the study of what actually exists, or of what is fundamental to ‘reality’) seems to be all that is relevant.

Plato was an aristocrat, whose Ideal society would be one ruled by philosophers (and hence, in his day, as in most days, dominated by members of the ruling-class or their hangers-on). He was part of the aristocratic reaction to the democratic ‘experiment’ in the Athens of the fifth and sixth century BC.

As an important part of this, he sought to undermine popular belief based on empirical knowledge (something that has passed down to us since then as a core idea in most forms of traditional philosophy – including that found in dialectics, where appearances are 'contradicted' by underlying ‘essences’, so you can't trust them). True knowledge for Plato had to be a priori (but he did not use this term!), and based on acquaintance with the 'Forms'.

The connection between his thought and anti-democratic theory since has not been accidental, therefore.

These 'Forms' were supposed to be other-worldly archetypes that captured the essential features of disparate things in material reality. If you want to know what all dogs, for example, have in common, given this traditional approach, you could appeal to features all dogs shared (naturally!), but since no dog itself could embody this universal aspect in its own body (how could it? it is an individual), whatever it is that all dogs share cannot be material. There must therefore be an exemplar that all dogs instantiate that is not of this world, since it can nowhere be found in it.

Now this shaky piece of reasoning (that outlined above, or indeed Plato’s own argument) has been very influential; in fact all alternative theories seem to kick off from there, in agreement with this approach, or in disagreement with its conclusions, but not with the way this ‘puzzle’ is usually posed (which suggests we can attain knowledge of such things by thought alone, whose results cannot be confirmed or disconfirmed by any material means -- all subsequent thinkers strayed not one inch from this fixed idea).

For Plato, the common feature (or Form) of, say, dogs exists in a non-material form somewhere (as do the exemplars of everything else in this world – 'a rather tightly packed heaven' I hear you say (and with the Form of dirt and disease there too, a rather unpleasant place into the bargain)! And, is there [i]really an Ideal Nazi in heaven?).

In that case, true knowledge of anything cannot be had in this world if we rely on our senses, or on fallible opinion. Under scrutiny, Socrates (Plato’s mouthpiece) was able to show (with some rather ‘innovative’ reasoning) that most, if not all, of what we believe is fraught with error (which Socrates was able to reveal by the close dialectical (in the old sense of that word) questioning of his ‘victims’. Genuine knowledge was to be had by recollection, by recalling what we have all known all along (but forgotten), and philosophy aimed to bring this out.

Plato believed we all lived in a heavenly realm before we were born, and in that realm we were all directly acquainted with the Forms (in later Platonists, they came to be identified with divine Ideas, and in Plotinus, they were divine Ideas in self-development, which is where Hegel got this doctrine from). So Plato modelled knowledge analogically: it was like the knowledge each of us had of a friend. We recognise who that friend is by acquaintance (by sight); words later merely help recall to mind what we were already ‘unconsciously’ aware of. So, just as th name of an absent friend helps you recall his/her face, so words can help us recall the Forms (but, only if we are orientated in a suitably respectful manner to the Form of the Good (el supremo) -- why this is so I won't go into now), and help us edge our way to genuine knowldege.

However, this view of knowledge contains a serious logical error: basically Plato conflated propositional knowledge and the sort of personal knowledge we have of individuals with whom we are acquainted (you can actually see him doing this in the 'Theatetus').

Now, the French, for example, have two different words for knowledge, ‘savoir’ and ‘connaitre’, which allow these two forms of knowledge to be distinguished; so Plato confused ‘savoir’ (to know things propositionally) with ‘connaitre’ (to know a friend by sight or reputation). In Old English we used to be able to distinguish these easily, too -- we used to have two verbs: ‘kennen’ (‘connaitre’) and ‘witten’ (‘savoir’); the first appears in that old Yorkshire song ‘Do you ken John Peel?’.

This error has dogged all traditional epistemology (Theory of Knowledge) since, where knowledge is not a feature of social development (as Marxists believe), but a relation between a 'knower' to a 'known' (object), be this an abstract idea, sensation, image, thought, sense datum, qualia (a modern form of sense datum), or fact; and, incidentally, this is where the correspondence theory of truth goes wrong, too. Indeed, this error resurfaces, for example, in Engels’s ‘Ludwig Feuerbach…’, where he asserts that the fundamental problem of all philosophy is the relation of thought to being (i.e., that between an individual, or individuals, and a named entity, i.e., ‘reality/being’).

He should, of course, have said "the fundamental error of all philosophy....", but he didn't, becasue he was a traditional thinker, too.

But, if scientific knowledge is propositional (and socially-conditioned, too), it cannot be a relation between one or many things and anything else.

Propositional knowledge is typically of the form “NN knows that p” where ‘p’ can be replaced by a suitable indicative sentence (or its like). This cannot be relational unless we regard propositions as abstract objects of some sort (thus destroying their nature as propositions – why this is so, I will not enter into here).

So, it would be quite OK to say “I know comrade XYZ”, but not “I know that comrade XYZ”. [Sure, one can say “I know that comrade XYZ did such and such”, but then that is propositional knowledge.] One certainly could not say “I am acquainted with p”; but one can say, “I am acquainted with comrade XYZ”.

So Plato screwed up epistemology from the get-go.

[His logic was none too clever either; if general words can only be given an objective status by turning them all into abstractions (in the lingo, into abstract particulars), then that destroys their generality. This is because such words become the names of these particulars, and names cannot express generality. I try to say why at my site (Essay Three, Part One). You can see an echo of this in my recent set to with ‘Peacenicked’ (in the thread entitled ‘Dialectics explained’; a poor joke at the best of times), who, for some reason, could not get this point.]

In addition, Plato bequeathed to Western thought several unhelpful ideas that still dominate today: one of which has come to be known as Platonism in mathematics (but how far Plato would have agreed with modern mathematical Platonists is a moot point).

This view of mathematics sees mathematicians as discovering truths that were already there in some form for them to find (a bit like Australia was there before even the indigenous Australians ‘found’ it, and long before Captain Cook was heard of). Mathematical truths exist in some form, somewhere (better not ask where), and they force themselves onto us by the sheer force of their ontological necessity (better not ask how). They determine for us whether our mathematics is true or not (so they are more ‘intelligent’, or more powerful, than we are!), and we have no real say in the matter (save we come to see things this way). Mathematical ‘objects’ thus exist prior to and independent of our knowledge of them; mathematics is thus a sort of superscience of this hidden world.

[So, all the numbers we use to count with exist in some form before we count with them, and the decimal expansion of Pi (i.e., 3.14159265…) already exists to ‘infinity’ as you read this.…]

Now this has crippled the interpretation of the nature of mathematical truth for over two thousand years, and it was only when Wittgenstein began to unravel this rat’s nest that we could begin to form a correct view of the nature of mathematics (at least that is how I see things -- why this is so I will not enter into here).

So, Plato is the first seriously important Idealist (and probably the Idealist), in human history. To spin his tales, he had to hold ordinary language, common sense, and the people who invented and used the vernacular in contempt. All subsequent Idealists, in some way or another, copy this approach and borrow from him (including Hegel, Lenin and comrades like CLR James and Raya Dunayevskaya, and in their own small way, Woods and Grant -- but that may be to elevate their ideas way too much).

I hope this helps!

and not just its poor tenth cousin, twenty-five times removed: dialectics.]

[Chrysalis]

Heraldur:

Kurt has given your a good interpretation of "Platonism". We can expand on it, but his is sufficient, I think. Usually invoked as a "criticism" in logic and mathematics, Platonism has also appeared as a critique of some philosophers' conception of morality. So, if Kurt's explanation is fairly easy to understand, deduce from his post why "Platonism" is not regarded a good thing.

It's a good philosophical exercise.

Try to focus on this:

Originally posted by kurt

Basically, the universal is a sort of perfect objective blueprint for particulars. Plato would maintain however, that particulars can never approach the perfection of the universals.

Or Kurt could continue with his exposition.

Good question, btw.

[Cult of Reason]

Penrose seems to claim that without Platonism mathematics would be subjective, and that somehow, if somone else had got there before Newton and Liebnitz, calculus could have been different, but still could not have been changed to another form. This is obviously ridiculous, and there is evidence for that because Libnitz and Newton got Calculus independently.

So, with Platonism not considered, what is there to stop the above happening, where all mathematics is subjective?

[Rosa Lichtenstein]

If mathematics is taught and practised on the basis of publicly observable rules, then it cannot be 'subjective'.

If however it is based on the subjective apprehension of 'objects' in a Platonic realm (as it must be given Penrose's ideas, who has to appeal to an obscure notion, i.e., 'intuition', to ground them), then it cannot be objective.

Objectivity is not conferred on mathematics by an appeal to a hidden world of objects, of mysterious provenance, and even more enigmatic inter-connections, but by the practices we human beings engage in, in the objective material world.

So, Wittgenstein's anti-Platonism is eminently non-subjective. Platonism is hoplessly subjetive.

[Chrysalis]

Originally posted by [email protected] 23 2006, 06:32 AM
I'm not really sure how it relates to mathematics..
Platonism in mathematics is captured in this: Pie is in the sky (it was once my sig.... :wub: )

And Rosa and others have already alluded to this realm or world of numbers where they exist without needing humans to think of them, or their existence is not dependent on us apprehending them. The number "pie" is thought to be, under platonic conception, out there already occupying some realm. All it needed is that we apprehend it. This idea implies that mathematics is discovered, not invented. And if you've already read on the debates in philosophy of math, you'll know that issue is far from settled.

"Platonism", in general, is put forth as an attack against Plato's or platonic idealism: only philosophers can have access to this realm, it seems to say. Which, of course, seems dubious. If Plato can access this world, why can't we? And that's the insinuation.

[Rosa Lichtenstein]

Chrysalis:


All it needed is that we apprehend it.

And how do we do this (with a sort of 'third eye', perhaps)?


And Rosa and others have already alluded to this realm or world of numbers where they exist without needing humans to think of them, or their existence is not dependent on us apprehending them.

[You write as if I am unaware of all this -- it is part of my PhD!]

They can allude all they like, that is their problem. The question is, why shouild we listen to these subjectivist 'theories''? And, where is this realm? La La land?


And if you've already read on the debates in philosophy of math, you'll know that issue is far from settled.

It is if you regard mathematics as a social, not an individual, activity.


If Plato can access this world, why can't we?

And how do you know if he did this (or whether was just telling one of his 'likely stories' again)?

And this seems to suggest that Platonism is opposed to Platonism!


Platonism", in general, is put forth as an attack against Plato's or platonic idealism

[Once again, you seem not to have learnt much from Wittgenstein...]

[Chrysalis]

Rosa:

Until you've actually learned philosophy or understand philosophy I will not discuss with you. I gave you a bit of a credit for getting something right and you criticize my giving you the credit. What the fuck is wrong with you, girl? :lol:

Go back to the cave.

[Rosa Lichtenstein]

Chrysalis:


Until you've actually learned philosophy or understand philosophy I will not discuss with you

You mean: until I agree with you you will not discuss anything with me.

Unfortunately, however, you show worrying signs of having fallen for the ideas of assorted mystics and charlatans, ruling-class hangers on, and their a priori word game/'theories'. You accuse me of 'crudeness'; I accuse you of gullibility.

[Even so, I note you cannot answer my objections, which I suspect is the real reason for your cop out, and not the one you use as a fig-leaf.]

[Bye the way, I have a degree in Philosophy (and another in mathematics), and I am preparing for my PhD in Philosophy; you actually know some of this, so why you are throwing this desperate excuse back at me is puzzling.]