School of Economic Science
Patterns of Maths in Plato

 
Post new topic   Reply to topic    School of Economic Science - Study Forums Forum Index -> Plato Forum
View previous topic :: View next topic  
Author Message
Richard Wongkew
Guest





PostPosted: Thu Jul 10, 2014 2:39 am    Post subject: Patterns of Maths in Plato Reply with quote

'Plato is boring' - Nietzsche

To all and sundry who would without lamenting the fate of Platonist or Plato, nor with the dedication to meanly denouncing, take to loosening the clutch on what is to be shown inadequate, and so dropped. What glorious luck to those that think new this departure. Whereas that is never attended to by the so-called scientific atheists of this day, nor by any other genre due to the genius of thinking people. But is at best taken for granted and got by authorities and teachers, and so with perilous abandonment of thought.

I propose a dialectical, with the chief meaning, very short form question and answer, discussion, on the subject thus given in your earlier posting, mathematics. In passing I mention your promise to produce a word of Jacob Klein. I want to run through these subjects because the instinct for thinking them is awesomely forgotten in our deceptively informed and mechanical time. It must be brought into practice newly today, as it was in the early part of the last century. Like this we must become somewhat more free to think these matters.

Here my passion is for getting to science, and not to overthrow the philosopher but to come to his completion, so as to face the problem, which you do not yet face.

---

Dialectic according to the questioned content of that which is expressed in this passage and those that preceded it:

Quote:
After completing his homework the small boy goes to his teacher and says – ‘Look, what is this ‘two’? - Have you seen it before?’ – ‘Yes, thousands of times.’ – ‘But how do you know it is the same two?’ - ‘There aren't any others’ explains the teacher’ hoping the lunch bell will intervene and put an end to this worrying conversation.


Preamble: Just as language is with the historicists, primordial to logos, here we find mathematics before this or that mathematical signification. As if a natural mathematical sense precedes the customary allotment of mathematically thought things. 2 old shoes, two writing tablets, 2 dark pools of mud. Why should we attribute this faculty to anything but the phylogenetic inheritance? And so to ‘remembering’ of experience, and not some wild or mystical realm.

---

Q: DO you take it, then, that neither Plato nor any Platonist nor yet any ancient Greek, was, nor could have been, acquainted with the possibility of such an ‘inheritance’? Inheritance of the kind proper to the concepts of the natural sciences: involving acquisition according to the determining of human beings by genetic inheritance in their conditioning, brought through our ancestors who lived in this world, and not in some wild or mystical realm of unalloyed reason given only to this and that initiate of the cult of Plato according to the costs associated with entry to his school, but instead to all by physical conception.
Back to top
Peter Blumsom



Joined: 09 Mar 2007
Posts: 1099
Location: Wembley, London, UK

PostPosted: Thu Jul 10, 2014 6:16 am    Post subject: Reply with quote

Firstly, I need to apologise for my tardiness to all correspondents and in particular to you for not reacting to your last. I do intend to answer all posts but things have been complicated. Do you want me to respond still or shall we put everything into this new thread which has such a promising title to live up to?
...............................

Quote:
<<Here my passion is for getting to science, and not to overthrow the philosopher but to come to his completion, so as to face the problem, which you do not yet face. >>


So you are waiting for the true science to come to you and act on you or are you seeking to seize it - apto - and make it yours? I prefer your former. Now for a problem to be faced it must be brought to bear upon one. So what I do not see I cannot face, even though it has been hurled at me a thousand times. You must unfurl your discus once again – what am I not facing?

Quote:
<<Q: DO you take it, then, that neither Plato nor any Platonist nor yet any ancient Greek, was, nor could have been, acquainted with the possibility of such an ‘inheritance’? Inheritance of the kind proper to the concepts of the natural sciences: involving acquisition according to the determining of human beings by genetic inheritance in their conditioning, brought through our ancestors who lived in this world, and not in some wild or mystical realm of unalloyed reason given only to this and that initiate of the cult of Plato according to the costs associated with entry to his school, but instead to all by physical conception.>>


Are you saying that two-ness (etc.) is part of nature, the way things evolved, and that Plato could not have been aware of what we have discovered now? For instance that the genome complexity proceeds by doubling, (like natural octaves) and that the vertebrates arrived on the scene on the fourth doubling, bringing with them all the intelligent manifestations of that particular ‘octave occurrence’? If you are thinking this way, I think the ancient mathematics was aware that doubling was special. But they were also aware of opposites much more than we in our linear thinking. Doubling/halving were the same thing – the road to from Thebes to Athens the same as the road from Athens to Thebes. They knew, these old ones, that halving the length of a vibrating string raised a pitch though an octave (diapason – interestingly means dia - ‘through'; pason - all’) so they must have known that there is a kind of fundamental holon to an octave. They would (because they were perspicuous) have known that a fundamental numerical event had been aligned to a fundamental psychological event – though they would have have known it in their, not our, way. (We arrogantly think that the only way to know is as we do.) And this would have been a great source of thaumazein, but I have no idea about this flimsy ‘mystical’ you wave about. I've never understood what it means. But we might have a similar genetic wonder in that the complexity of the nature of genes seems to follow (or precede) that same ‘dyadic twoing’ that brings vibrations to the soul. Wonder is not the sole province of metaphysics.

Sorry if I have answered this question in my own way. If I’ve missed the point entirely please simplify it for a bear of little brain who has never known the Plato read by Nietsche.
Back to top
View user's profile Send private message
ThePlatonist DotCom



Joined: 04 Jul 2014
Posts: 23

PostPosted: Thu Jul 10, 2014 1:32 pm    Post subject: Reply with quote

I haven't been following this discussion which seems to started afresh again here, and I can't really figure out what's being debated from what's been posted above.

But I did notice something above that I think's worth pointing out:

Quote:
After completing his homework the small boy goes to his teacher and says – ‘Look, what is this ‘two’? - Have you seen it before?’ – ‘Yes, thousands of times.’ – ‘But how do you know it is the same two?’ - ‘There aren't any others’ explains the teacher’ hoping the lunch bell will intervene and put an end to this worrying conversation.


In this quote the two that the teacher comprehends is the counting concept of two. But Plato of course derided this type of mathematics of the tradesman, he makes very clear that when philosophers talk about "all is number" etc they don't mean everything can be counted or measured along a scale, they are talking about the archetypal conceptual divisions that occur between the one and unlimited etc. So for example, in Plato's Republic he talks about justice having four mathematical parts, so if we find three we have the fourth in what's left, which obviously wouldn't be the case if we were talking counting numbers instead of dialectic numbers. And, for example, in the Philebus he talks about the ordinary thinkers who divide things up into whatever categories come to mind haphazardly, unlike butchers who know how to cut bodies into clear parts at the joints etc.

Thus Plato's Mathematics, whatever it might be, is nothing like the maths we use to count and measure things, so two is not something that can be applied to numbers of old shoes, writing tablets, and dark pools of mud etc. His numbers are "alive", they are more like functions that bits of data. For example, I studied Pure Maths at university, but his maths is nothing like anything i learnt there. Although he draws allegorical parallels between geometry and philosophy, he is in truth living in a completely different world. The link between numbers and concepts obviously begins with this realization: that thinking about ideas wouldn't be possible if there weren't some kind of structure of ideas, so they are not all at sea but somehow logical. So instead of numbers as object markers, we need concept representatives, creating archetypal mathematics.

That makes it tempting to try and hunt down Plato's numbers, but of course as it explains in the last chapter of the Laws, we should start at beginning. We should master "theological arguments" such as the problem of evil, then perhaps knowledge vs opinion, then being and non-being, then the one and many nature of virtue, then definitions of justice and other virtues. For example, courage is very hard to understand, and all those discussions about "fighting in amour" and so forth are hints. So you can't become an expert in the meaning of Plato's numbers without all that. Unlike counting numbers they are not mindless and therefore describable to non-experts and transparent across-disciplines. For example, suppose for the purposes of argument one of our archetypal concepts is "male~female", so that an idea can be split into a male part and a female part, this would be incomprehensible to anyone who does not know what male and female is, yet only a expert who has devoted a lifetime to the study of duality could grasp the concept. Modern psychologists are nowhere near this level, they collect baskets of statistics and point out correlations, but all this is but a shadow of real understanding. So it's not like ordinary mathematics where the rules are no harder to understand than the rules of chess, on the contrary the very starting bricks are extremely elusive and require great wisdom to catch sight of. So it's an infinitely more difficult subject than the ordinary mathematics we learn at school today.
Back to top
View user's profile Send private message
Richard Wongkew
Guest





PostPosted: Mon Jul 14, 2014 1:40 am    Post subject: Reply with quote

Quote:
Quote:
Are you saying that two-ness (etc.) is part of nature, the way things evolved, and that Plato could not have been aware of what we have discovered now? For instance that the genome complexity proceeds by doubling, (like natural octaves) and that the vertebrates arrived on the scene on the fourth doubling, bringing with them all the intelligent manifestations of that particular ‘octave occurrence’? If you are thinking this way, I think the ancient mathematics was aware that doubling was special. But they were also aware of opposites much more than we in our linear thinking. Doubling/halving were the same thing – the road to from Thebes to Athens the same as the road from Athens to Thebes. They knew, these old ones, that halving the length of a vibrating string raised a pitch though an octave (diapason – interestingly means dia - ‘through'; pason - all’) so they must have known that there is a kind of fundamental holon to an octave. They would (because they were perspicuous) have known that a fundamental numerical event had been aligned to a fundamental psychological event – though they would have have known it in their, not our, way. (We arrogantly think that the only way to know is as we do.) And this would have been a great source of thaumazein, but I have no idea about this flimsy ‘mystical’ you wave about. I've never understood what it means. But we might have a similar genetic wonder in that the complexity of the nature of genes seems to follow (or precede) that same ‘dyadic twoing’ that brings vibrations to the soul. Wonder is not the sole province of metaphysics.


Sorry if I have answered this question in my own way. If I’ve missed the point entirely please simplify it for a bear of little brain who has never known the Plato read by Nietsche.



I must begin with a note on the perilous possibility that you are contemplating proceeding by speechifying. It seems to me dialectic demands the opposite of that.

My question is about the knowledge of the science of genetics itself, with its hard laws, as practiced in the universities and research facilities of our own day. Without reference to meaning, or some special inner nature of doubling, outside from the physical causal power implied, as a natural process impelled by physical forces and not by a hidden inner compulsion, as by a telos. Plato may know of some thin content of this science, doubling understood in this or that special and peculiar manner, without knowing of it simply speaking. Simply speaking, can Plato have been acquainted with this science?


----

Quote:
Do you want me to respond still or shall we put everything into this new thread which has such a promising title to live up to?


The other thread is vital because it aims at exhibiting the specific current orientation of ethics, in contradistinction to that orientation known to Plato and Aristotle. We still evade and deviate from our own age, in clinging in speech to positions that are thoroughly shown to be inadequate; this can lead only to boring and impotent talk. Thus we must scrutinize and penetrate those things that only stand as mere talk, discovering how the truly stand with us.

Quote:
‘So you are waiting for the true science to come to you and act on you or are you seeking to seize it - apto - and make it yours? I prefer your former. Now for a problem to be faced it must be brought to bear upon one. So what I do not see I cannot face, even though it has been hurled at me a thousand times. You must unfurl your discus once again – what am I not facing? ‘


I would say you are not facing the character of our (current) thinking (in contradistinction to that of the Greeks), every deviating position is possible, but each position is decisively oriented towards the foundation of the times (whether one is conscious or unconscious of that, as an educated man, indeed, you are in some way aware of what you deviate from, half-heartedly and in self-deception, as you speak of Nietzsche then I will say it, be more cynical with yourself at last looking for the place of your true sympathies as they stand when push comes to shove), and we today are the completion of Plato’s history as a old man is the completion of a life. One can not pick some age, arbitrarily, and hold to it in itself without reference to the current age. Can one really give reference to ‘old ones’, it is perhaps more sensible here to speak of young ones. Who says of the picture of oneself as a toddler, ‘look at that old one’? Is it not rather that since we ourselves are this history, it is we ourselves who are the ‘old ones’. Although, from a deepened view, that takes us beyond the whole breadth of such dichotomies, we have no time.

It would be better to lay all this bare in the dialectic, in curt exchange, with the thinker’s seasoned and ruthless refusal of the long moralizing speech.


--

ThePlatonist DotCom

Yes. Plato, eg in the Republic, wishes to use the opening of the human being in regard to the many regimes (forms of government) in the appearances in order to come to see the simple unity of the eidos. But in this he gives a specific orientation to number even as it is still thought. 1 through the concept of number moves towards infinity, yet there can be no infinity in modernity. All this must be made more clear in the thinking of the dialectic, as that method of working through that comes prior to philosophy, but for us after it and at the same time as it, for we have no time, but, rather, we have reference to the genetic circle into which we are plunged.
Back to top
Peter Blumsom



Joined: 09 Mar 2007
Posts: 1099
Location: Wembley, London, UK

PostPosted: Mon Jul 14, 2014 5:27 am    Post subject: Reply with quote

Quote:
My question is about the knowledge of the science of genetics itself, with its hard laws, as practiced in the universities and research facilities of our own day. Without reference to meaning, or some special inner nature of doubling, outside from the physical causal power implied, as a natural process impelled by physical forces and not by a hidden inner compulsion, as by a telos. Plato may know of some thin content of this science, doubling understood in this or that special and peculiar manner, without knowing of it simply speaking. Simply speaking, can Plato have been acquainted with this science?


My response is simple. I have no idea what is going on in universities regarding genetics and wonder how I have become an interlocutor on this topic, upon which, unless you can make it fascinating to me, I'll pass. TP may have more of an affinity.
Back to top
View user's profile Send private message
Richard Wongkew
Guest





PostPosted: Mon Jul 14, 2014 10:27 pm    Post subject: Reply with quote

This question does not concern the details of what is going on in universities or any technical knowledge about ‘doubling’. We are here concerned only with what I have in a general way mentioned, giving a mere report, so we do not forget, of that which you surely already know as you have even mentioned details. Why refuse to answer? Go on. Are you such a baby you must be kept interested every moment through artificial means?

We will enhance, not lessen, the possibility of breaking through mere talk only if we keep to dialectic, that is the premise of the terse momentum of simple question and answer since Plato’s own time. To go out of the oblivion of prattle and into the presence of being. One must make no concessions to the well known stupidity of entertainments.
Back to top
Peter Blumsom



Joined: 09 Mar 2007
Posts: 1099
Location: Wembley, London, UK

PostPosted: Tue Jul 15, 2014 8:36 pm    Post subject: Reply with quote

Er, sorry, but could you pose the question again? I think it got lost in the ever increasing welter of words. Ask your question clearly, and I will answer it as best as I can. But obey your own edict and keep it terse.
Back to top
View user's profile Send private message
Display posts from previous:   
Post new topic   Reply to topic    School of Economic Science - Study Forums Forum Index -> Plato Forum All times are GMT
Page 1 of 1

 
Jump to:  
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum
You can attach files in this forum
You can download files in this forum
This forum is sponsored by the School of Economic Science for use by its members; members of its branches; members
of affiliated schools worldwide and by all other Internet users interested in the study subjects presented.
Powered by phpBB Copyright © FSES, 2007. All Rights Reserved