Friday, May 17, 2013

Part 03 of 29. The DIALECTICA MANIFESTO. The Enigma of the Platonic Dialectic.



Full Title:  Part 03 of 29 --

The Dialectica Manifesto

 

Dialectical Ideography and 

 

the Mission of F.E.D.




Dear Readers,

I am, together with F.E.D. Secretary-General Hermes de Nemores, and F.E.D. Public Liaison Officer Aoristos Dyosphainthos, organizing to develop a new, expanded edition of the F.E.D. introductory documents, for publication in book form, under a new title --

The Dialectica Manifesto:  Dialectical Ideography and the Mission of Foundation Encyclopedia Dialectica [F.E.D.]

-- and under the authorship of the entire Foundation collective.

Below is the third installment of a 29-part presentation of this introductory material, which the F.E.D. General Council has authorized for serialization via this blog over the coming months, as we develop the material.

I plan to inter-mix these installments with other blog-entries, including the planned additional F.E.D. Vignettes, other F.E.D.  news, my own blog-essays, etc.

Links to the earlier versions of these introductory documents are given below.


Unlike the typical blog-entry, this series will attempt to deliver an introduction to the Foundation worldview as a totality, in a connected account, making explicit many of the interconnexions among the parts.

Enjoy!!!
Regards,









 

Part 03 of 29 --

The Dialectica Manifesto

 

Dialectical Ideography and 

 

the Mission of F.E.D.

 

 

 

 

The Enigma of the Platonic Dialectic.

 
The following extracts provide an overview of the difficulties confronting modern scholars of Plato in deciphering the unified meaning of the Platonic dialectic / the Platonic ‹‹arithmoi eidetikoi››.
 
Prior to the insights of Jacob Klein, Denise Schmandt-Besserat, and others regarding ancient arithmetic, and the integration of those insights in the work of Karl Seldon and Sophya St. Germain, no such unified meaning had been recovered.

We learn, for instance, in J. O. Urmson’s The Greek Philosophical Vocabulary, in the entry for the Greek word ‹‹arithmos›› — which is translated, in this entry, simply as number — of the ‘‘‘psychohistorical’’’ fact that the ancient Greek concept of number differed markedly from – and was, in some ways, ‘ideo-ontologically’ shrunken with respect to — our own.  

However, in another way, that ancient conception was ‘ideo-ontologically’ expansive relative to the modern one, in that it included a concept of nonaddible, and therefore apparently of qualitativequalitatively heterogeneousnumbers:

Zero was unknown as a number, and one also was not counted as a number, the first number being the duas — two. [J. O. Urmson, The Greek Philosophical Vocabulary, Duckworth & Co., Ltd. [London: 1990], pp. 31-32]."


We also learn of a key — “obscure” — distinction in Plato’s “unwritten doctrines”, between Plato’s concept of ‘dianoiac’ “mathematical numbers”, the ‹‹arithmoi monadikoi››, versus his dialectical ‘‘‘idea-numbers’’’, the ‹‹arithmoi eidetikoi›:


"From the Pythagoreans … — who consider number to be the first principle — number played a great role in metaphysics, especially in Plato’s unwritten doctrines, involving obscure distinctions of e.g. ‹‹sumblêtoi›› and ‹‹asumblêtoi›› — addible and non-addiblenumbers. [Urmson, ibid., emphasis added by F.E.D.]."


Thus it appears that Plato too, with the Pythagoreans, considered ‘“number”’ to be the “first principle”.

But Plato ‘‘‘also’’’ considered the Forms, the ‹‹eide›› — the «ιδεαs» — to be the “first principle”.

However, these ‘‘‘two’’’ considerations, for Plato, constituted no contradiction.

The «ιδεαs» or ‹‹eide›› were, for Plato, ‘‘‘numbers’’’ – i.e., ‹‹arithmoi›› — namely, the ‹‹arithmoi eidetikoi››, the very ‹‹arithmoi›› of his ‹‹dialektiké››.


This ‘‘‘idea-number’’’ notion of Plato’s has been replete with all manner of perplexity for modern scholarship:

arithmósnumber (see also arithmos eidetikos and arithmos mathematikos)

…    3.  The most perplexing aspect of ancient number theory is Aristotle’s repeated assertions that Plato taught that the eide were numbers (e.g. Meta. 987b), a position that must be distinguished from 1) the existence of the eide of numbers (see arithmos eidetikos) and 2) the existence of the “mathematicals” as an intermediate grade of being (see mathematika, metaxu).  But nowhere in the dialogues does Plato seem to identify the eide with number.  To meet this difficulty some have postulated a theory of later “esoteric” Platonism known to Aristotle (but see agrapha dogmata), while others have attempted to see the emergence of the eide-arithmos theory described in such passages as Phil. 25a-e, the reduction of physical objects back to geometrical shapes in Tim. 53c-56c (see stoicheion), and the increasing stress on a hierarchy among the Forms (see Soph. 254d and genos, hyperousia), which, according to Theophrastus, Meta. 6b, would suggest the descending series archai (i.e., monas/dyas or peras/apeiron, qq.v.), arithmoi, eide, aistheta.  Still others say that Aristotle either deliberately or unknowingly confused the position of Plato with those of Speusippus and Xenocrates (see mathematika).
  [F. E. Peters, Greek Philosophical terms:  A Historical Lexicon, NYU Press [NY:  1990], pp. 25-26].





In the entry for the Greek word ‹‹dialektiké››, translated, in this same reference, as the English dialectic, we learn the following:


On the testimony of Aristotle dialectic was an invention of Zeno the Eliatic, probably to serve as a support for the hypothetical antinomies of Parmenides ... But what was a species of verbal polemic (what Plato would call “eristic” or disputation...) for the Eliatics was transformed by Plato into a high philosophic method.  The connecting link was undoubtedly the Socratic technique of question and answer in his search for ethical Definitions…, a technique that Plato explicitly describes as dialectical (Crat. 390c). …With the hypostatization of the Socratic definitions as the Platonic eide … the role of dialectic becomes central and is the crown of the ideal curriculum described in the Republic:  after ten years devoted to mathematics the philosopher-to-be will devote the years between thirty and thirty-five to the study of dialectic. …

What is dialectic?  The question is not an easy one since Plato, as usual, thought about it in a variety of ways.  There is the view of the Phaedo and the Republic, which envisions dialectic as a progressively more synoptic ascent, via a series of “positions” (hypotheseis, q.v.; the Theory of Forms is one such in the Phaedo 100b), until an ultimate is reached (Phaedo 101d, Rep. 511e).  In the Republic, where the context of the discussion is confessedly moral, this “unhypothesized principle” is identified with the good-in-itself (auto to agathon; Rep. 532a-b) that subsumes within itself all of the lower hypotheses (ibid., 533c-d) [cf. the Hegelian core concept of dialectic, named by the German word ‹‹aufheben›› — F.E.D.] … If the dialectic of the Phaedo and the Republic may be described as “synoptic” …, that which emerges from the Phaedrus onward is decidedly “diacritic”… it is introduced in Phaedrus 265c-266b (compare Soph. 253d-e) and consists of two different procedures, “collection” (synagogue, q.v.) and “division” (diairesis, q.v.), the latter process being amply illustrated in subsequent dialogues like the Sophist, Politicus, and Philebus.  The earlier dialectic appeared similar to the operations of eros (q.v.) [recall Herbert Marcuse’s comment, in his Reason and Revolution, to the effect that '''eros is the force that binds matter together into ever higher unities'''-- F.E.D.], but here we are transported into an almost Aristotelian world of classification through division; ascent has been replaced by descent.  While it is manifest that we are here still dealing with ontological realities, it is likewise clear that a crucial step has been taken along the road to a conceptual logic.  The term [i.e., the terminus – F.E.D.] of the diairesis is that eidos which stands immediately above the sensible particulars (Soph. 229d), and, while this is “really real” (ontos on) in the Platonic scheme of things, it is significant that the same process ends, in Aristotle, in the atomon eidos, the infima species in a logical descent (De an. II, 414b)…
. [Peters, ibid., pp. 36-37].


Within the kind of ‹‹arithmoi eidetikoi›› structure described in the extract from Jacob Klein’s book, and depicted in the illustrations of the section immediately preceding this one, both the ‘‘‘ascending’’’ and ‘‘‘descending’’’ paths are intrinsic.  Further clues regarding this — supposedly only synchronic / eternal dialectical structure may be gleaned from the entry on ‹‹diairesis›› in the above-sited lexicon, by Peters:

diairesis:  separation, division, distinction

1.  Division, a procedure that did not interest Socrates since the thrust of his enquiry was toward a single eidos (see epagoge), becomes an important feature in the later dialogues where Plato turns his attention to the question of the relationship between eide.  Expressed in terms of Aristotelian logic
diairesis is part of the progress from genus to species; but, as is clear from a key passage in the Parmenides, where he first puts the question (129d-e), Plato did not see it as a conceptual exercise.  The dialectical search of which diairesis is part has as its object the explication of the ontological realities that are grasped by our reflection (logismos).

2.  The pursuit of the interrelated eide begins with an attempt at comprehending a generic form (Phaedrus 265d); this is “collection” (synagoge, q.v.).  It is followed by diairesis, a separation off of the various eide found in the generic eidos, down to the infima species (Soph. 253d-e).  Plato is sparing of details in both the theory and the practice of synagoge, and, while the Sophist and the
Politicus are filled with examples of diairesis, there is relatively little instruction on its methodology. 
We are told, however, that the division is to take place “according to the natural joints” (Phaedrus 265e).  What these are becomes clearer from the Politicus:  they are the differences (diaphorai, q.v.) that separate one species from another in the generic form (Pol. 262a-263b, 285b).

3.  The method of division raises certain serious questions, so serious, indeed, that they might very well shake confidence in the existence of the eide. …  Do the species constitute the genus
or are they derived from it? … . [
Peters, ibid., pp. 34-35].”



Regarding the meaning of this ‘second movement’ ‘sub-method’ of the Platonic dialectical method, termed ‹‹diairesis››, the Urmson source provides the following:

diairien (in past tense, dielein), diairesis:  to divide, division, used in many contexts in Greek as in English.  In philosophy particularly the logical division of a genus into species.  In the Phaedrus and the Sophist Plato speaks of a [F.E.D.:  sub-]method of sunagôgê — collection – and [F.E.D.:  a sub-method of] diairesis — division — as the supreme method of philosophy:  … and, Phaedrus, I myself am a lover of divisions and collections in order to become able to speak and think (Pl. Phaedrus 266b); … — unless one is capable of dividing things and subsuming each thing individually under a single form, one will never become skilled in discussion to the limit of human capacity (Pl. Phaedrus 273d): … — a longstanding laziness about dividing genera into species (Pl. Soph. 267d). [Urmson, ibid., pp. 39-40].”


The “mystery” of the ‘first movement’, and ‘sub-method’, of the dialectical method of discovery, ‹‹synagoge››, is also further addressed in our two sources:

sunagein:  to collect; sunagôgê:  the action of collecting.  Non-technically:  … we shall bring together the brides and the bridegrooms (Pl. Rep. 459e).  Also used as a technical term by Plato, particularly in the Sophist and the Phaedrus, where the contrary of sunagôgê is diairesis, division:  … — I am myself, Phaedrus, a lover of these divisions and collections (Pl. Phaedrus 266b).  Collection appears to be bringing together under a single genus a variety of things which are then to be divided formally into species and sub-species:  … — to survey under one form things that are scattered in many areas (Pl. Phaedrus 265d).  [Urmson, ibid., pp. 158-159].”

synagôgé:  collection

The Platonic type of “induction” (for the more normal type of induction, i.e., a collection of individual instances leading to a universal, see epagoge) that must precede a division (diairesis) and that is a survey of specific forms (eide) that might constitute a genus (Phaedrus 265d, Soph. 253d).  An example is Soph.
226a, and the process is also suggested in Rep. 533c-d, and Laws 626d… . [Peters, ibid., p. 188].”



Parts of the entries under ‹‹eidos›› in the Peters source can serve as a summary of our findings, above, regarding the enigma of the Platonic dialectic:

eídosappearance, constitutive nature, form, type, species, idea

…  12.  At various points in the dialogues Plato seems to grant preeminence to one or other [sic] of the eide.  Thus, both the Good (Rep. 504e-509c) and the Beautiful (Symp. 210a-212b) are thrown into relief, to say nothing of the notorious hypotheses of the One in the Parmenides (137c-142; see hen, hyperousia).   But the problem of the interrelationship, or, as Plato calls it, “combination” or “communion” (koinonia), and, by implication, of the subordination of the eide is not taken up formally until the Sophist.  It is agreed, again on the basis of predication, that some eide will blend with others and some will not, and that it is the task of dialectic to discern the various groupings, particularly through the diacritic method known as diairesis (q.v.; Soph. 253b-e). …  
[
Peters, ibid., p. 49, emphasis added by F.E.D.].”

…  8.  Though the eide are the centerpiece of Platonic metaphysics, nowhere does Plato undertake a proof for their existence; they first appear as a hypothesis (see Phaedo 100b-101d) and remain so, even though subjected to a scathing criticism (Parm. 130a-134e).  They are known, in a variety of methods, by the faculty of reason (nous; Rep. 532a-b, Tim. 51d).  One such early method is that of recollection (anamnesis, q.v.), where the individual soul recalls the eide with which it was in contact before birth (Meno 80d-85b, Phaedo 72c-77d; see palingenesia).  Without the attendant religious connotations is the purely philosophical method of dialektike (q.v.; see Rep. 531d-535a; for its difference from mathematical reasoning, ibid., 510b-511a; from eristic, Phil. 15d-16a).  As it is first described the method has to do with the progress from a hypothesis back to an unhypothesized arché (Phaedo 100a, 101d; Rep. 511b), but in the later dialogues dialektiké appears as a fully articulated methodology comprising “collection” (synagoge, q.v.) followed by a “division” (diairesis, q.v.) that moves, via the diaphorai, from a more comprehensive Form down to the atomon eidos.  Finally, one may approach the eide through eros (q.v.), the desiderative parallel to the earlier form of dialectic (see epistrophe).  [Peters, ibid., pp. 47-48].”



There is also another central Platonian theme — more Heraclitean, less Parmenidean; more diachronic, less synchronic than the others noted above — that forms a part, in our view, of the enigma of the Platonic dialectic:  that of ‹‹autokinesis››, or of self-motion — that of the self-induced motion of a ‘‘‘self’’’, e.g., of an agent, subject-object, or [ev]entity.

Our re-discovery of Plato’s ‘‘‘dialectical arithmetic’’’ emerged in the context, also, of our study of this, the most advanced development of Plato’s thinking, as embodied in his final dialogues, beginning with The Parmenides.
  

In those later dialogues, Plato advances beyond his earlier-asserted, ‘Parmenideanic’ eternal «stasis» of the Forms, or «eide», to embrace a theoretical commitment to the fundamentality of self-change, or «autokinesis», and to the primacy of this “self-derived motion” over other-derived motion”, i.e., over other-induced, externally-induced change:

The dialogues of the Socratic period provide that view of the world usually associated with Plato.  The period of transition and criticism, and the final synthesis, are little noted ...  The Parmenides can be taken as signaling the change.  In this dialogue Socrates is unable to defend his Doctrine of Ideas. ...   Where the Republic and Phaedo stressed the unchanging nature of the soul, the emphasis in the Phaedrus is exactly reversed.  In this dialogue, the soul is the principle of self-motion, and we are told that the soul is always in motion, and what is always in motion is immortal.  The difference now between spirit and matter is not changelessness in contrast with change, but self-motion, the essence of the soul, in contrast with derived motion.  The emphasis on self-motion is continued even in the Laws, Plato's final dialogue. [William L. Riese, Dictionary of Religion and Philosophy: Eastern and Western Thought, Humanities Press, Inc. (New Jersey:  1980), pages 442-443, emphasis added by F.E.D.].”


Is there a connection between the late-Platonic principles of ‹‹autokinesis››, of self-change and self-movement, and the Platonic concept of ‹‹dialektiké››?

Considering the following extracts on ‹‹autokinesis›› from the Platonic dialogues cited in the quote extracted above may help us to advance us in our consideration of this question:

[Phaedrus]:  But that which while imparting motion is itself moved by something else can cease to be in motion, and therefore can cease to live; it is only that which moves itself that never intermits its motion, inasmuch as it cannot abandon its own nature; moreover this self-mover is the source and first principle of motion for all other things that are moved.  Now a first principle cannot come into being, for while anything that comes to be must come to be from a first principle, the latter itself cannot come to be from anything whatsoever; if it did, it would cease any longer to be a first principle.  Furthermore, since it did not come into being, it must be imperishable, for assuredly if a first principle were to be destroyed, nothing could come to be out of it, nor could anything bring the principle itself back into existence, seeing that a first principle is needed for anything to come into being.


The self-mover, then, is the first principle of motion, and it is as impossible that it should be destroyed as that it should come into being; were it otherwise, the whole universe, the whole of that which comes to be, would collapse into immobility, and never find another source of motion to bring it back into being.  [Plato, The Collected Dialogues, E. Hamilton, H. Cairns, editors, Princeton U. Press [Princeton:  1989], Phaedrus, 245c-e, pp. 492-493, italic and bold-italic colored text emphasis added by F.E.D.].”


[Laws]:  When we have one thing making a change in a second, the second, in turn, in a third, and so on – will there ever, in such a series, be a first source of change? Why, how can what is set moving by something other than itself ever be the first of the causes of alteration?  The thing is an impossibility.  But when something which has set itself moving alters a second thing, this second thing still a third, and the motion is thus passed on in course to thousands and tens of thousands of things, will there be any starting point for the whole movement of all, other than the change in the movement which initiated itself?


Suppose all things were to come together and stand still – as most of the party have the hardihood to affirm.  Which of the movements we have specified must be
the first to arise in things?  Why, of course, that which can move itself, there can be no possible previous origination of change by anything else, since, by hypothesis, change was not previously existent in the system.  Consequently, as the source of all motions whatsoever, the first to occur among bodies at rest and the first in rank in moving bodies, the motion which initiates itself we shall pronounce to be necessarily the earliest and mightiest of all changes, while that which is altered by something else and sets something else moving is secondary.  [ibid., Laws, 10.894e-10.895b, pp. 1450, bold-italic, underlined, and colored text emphasis added by F.E.D.].”


The above considerations, then, adumbrate the challenge that Karl Seldon and Sophya St. Germain faced in their project to recover their hypothesized original unity of the Platonic conception of ‹‹dialektiké››, and of its ‹‹arithmoi eidetikoi››, from the enigma of its seemingly disparate doctrines, as portrayed in the extracts above, viz. --


1.    Of ‘‘‘ideas asunaddable’ numbers’’’, and of ‹‹dialektiké›› as an ‘‘‘arithmetic of ideas’’’; the arithmetic of the ‹‹arithmoi eidetikoi››;


2
.   Of ‹‹dialektiké›› as the highest philosophic method, one similar in its operation to that of eros; a synoptic method, a method of ascent,  via a series of “positions”, or “hypotheses”, until an ultimate is reached, that subsumes within itself all of the lower hypotheses;


3.  Of ‹‹dialektiké›› as a diacritic method, a method of descent — of synchronic ‘ideo-systematics’, ‘ideo-taxonomics’, or ‘ideo-meta-genealogy’, for the correct determination of the … «gene», the «species», and the sub-«species» …, etc., of the «eide»… — a method composed of two distinct, opposite procedures, or ‘‘‘orchestral’’’ [dance of discourse] movements; first by one of collectionsynagoge»], into «gene», followed, second, by one of divisiondiairesis»], into “classes” — into «species», sub-«species», …, etc. — of the fundamental «ιδεαV» that, per Plato, undergird this «kosmos», and;


4.   Of ‹‹arché kinesis›› as ‹‹auto kinesis››.


Moreover, this challenge emerged in the context of the effort of Karl Seldon and Sophya St. Germain to discover and advance the theory of diachronic, historical dialectics, and of its calculus —  a theory and a calculus of the auto-kinesic, temporal, ‘‘‘chrono-logical’’’, and, moreover, chronogenic self-speciation of species and self-generation of genera, in a way con-«gene»-ial with their immanently-critiqued version of the more synchronic, ‘‘‘systematic dialectics’’’ that Plato emphasized.

All of these considerations converge in the exposition of the rest of this manifesto and of its next section, entitled:  The Secret of the Historical Dialectic.










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