Full Title: Part 02 of 29 --
The Dialectica Manifesto
Dialectical Ideography and
the Mission of F.E.D.
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 second 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.
Part 02 of 29 --
The Dialectica Manifesto
Dialectical Ideography and
the Mission of F.E.D.
The Dialectic According to Plato
We of F.E.D. are embarked upon a project that has bridged, across the abyss of the last Dark Age, the most advanced «problematiques» of the ancient and modern worlds.
This project appropriates the ‘meta-fractal’ self-similarity of those two different, successive scales of «problematique» so as to resume some final and neglected, zenith breakthroughs within the ancient Alexandrian flowering of humanity’s ancient Mediterranean civilization, in relation to what has developed subsequently, and in a way which assimilates, also, the wealth of that subsequent development.
This has led to a rediscovery, in a higher, modernized, and less Parmenidean, more Heraclitean form, of Plato's lost «arithmos eidetikos», his “arithmetic of ideas” -- his ‘ideo-systematic’, ‘ideo-taxonomic’ assemblages of idea-«monads»; his “arithmetic of dialectics”.
This «arithmos» is alluded to in his extant writings, but its full exposition is nowhere to be found in those portions of Plato’s opus which survived the last Dark Age.
It has been ‘psycho-archaeologically’ reassembled in a seminal study, by Jacob Klein, as follows:
“While the numbers with which the arithmetician deals, the arithmoi [assemblages of units — F.E.D.] mathematikoi or monadikoi [abstract, generic, idealized, qualitatively homogeneous “monads” or [idea[ized]] units — F.E.D.] are capable of being counted up, i.e., added, so that, for instance, eight monads [eight abstract idea[ized]-units, unities, or idea-a-toms — F.E.D.] and ten monads make precisely eighteen monads together, the assemblages of eide [of ‘mental seeings’ or mental visions; of “ideaV” — F.E.D.], the “arithmoi eidetikoi” [assemblages, ensembles, ‘‘‘sets’’’, or [sub-]totalities of qualitatively heterogeneous ideas or «eide» — F.E.D.], cannot enter into any “community” with one another [i.e., are ‘non-reductive’, ‘‘‘nonlinear’’’, “non-superpositioning”, “non-additive”, ‘non-addable’ [Plato’s word: «asumbletoi» ], or “non-amalgamative" [cf. Musès] — F.E.D.].”
“Their monads are all of different kind [i.e., are ‘categorially’, ontologically, qualitatively unequal — F.E.D.] and can be brought “together” only “partially”, namely only insofar as they happen to belong to one and the same assemblage, whereas insofar as they are “entirely bounded off” from one another ... they are incapable of being thrown together, in-comparable [incapable of being counted as replications of the same unit[y] or monad; incomparable quantitatively — F.E.D.] ... .”
"The monads which constitute an “eidetic number”, i.e., an assemblage of ideas, are nothing but a conjunction of eide which belong together."
"They belong together because they belong to one and the same eidos [singular form of «eide»: one particular ‘internal / interior seeing’, vision, or «ιδεα» — F.E.D.] of a higher order, namely a “class” or genos [akin to the grouping of multiple species under a single genus in classical ‘‘‘taxonomics’’’ — F.E.D.]."
"But all will together be able to “partake” in this genos (as for instance, “human being”, “horse”, “dog”, etc., partake in “animal”) without “partitioning” it among the (finitely) many eide and without losing their indivisible unity only if the genos itself exhibits the mode of being of an arithmos [singular form of «arithmoi»: a single assemblage of units/«monads» — F.E.D.]."
"Only the arithmos structure with its special koinon [commonality — F.E.D.] character is able to guarantee the essential traits of the community of eide demanded by dialectic; the indivisibility [a-tom-icity or ‘un-cut-ability’ — F.E.D.] of the single “monads” which form the arithmos assemblage, the limitedness of this assemblage of monads as expressed in the joining of many monads into one assemblage, i.e., into one idea, and the untouchable integrity of this higher idea as well."
"What the single eide have “in common” is theirs only in their community and is not something which is to be found “beside” and “outside” ... them. ... ."
"The unity and determinacy of the arithmos assemblage is here rooted in the content of the idea..., that content which the logos [word; rational speech; ratio — F.E.D.] reaches in its characteristic activity of uncovering foundations “analytically”."
"A special kind of [all-of-one-kind, generic-units-based — F.E.D.] number of a particular nature is not needed in this realm, as it was among the dianoetic numbers [the «arithmoi monadikoi» — F.E.D.]..., to provide a foundation for this unity."
"In fact, it is impossible that any kinds of [homogeneous units — F.E.D.] number corresponding to those of the dianoetic realm [the realm of ‘dia-noesis’ or of ‘«dianoia»’, of rigid, radically-dualistic, categorically “either/or” thinking, lacking any capability for the reconciliation, via ‘complex unification’, of opposites, i.e., the realm of ‘pre-/sub-dialectical’ thinking — F.E.D.] should exist here, since each eidetic number is, by virtue of its eidetic character [«eide»-character or idea-nature — F.E.D.], unique in kind [i.e., qualitatively unique/distinct/heterogeneous in comparison to other «eide» — F.E.D.], just as each of its “monads” has not only unity but also uniqueness."
"For each idea is characterized by being always the same and simply singular [therefore additively idempotent — F.E.D.] in contrast to the unlimitedly many homogeneous monads of the realm of mathematical number, which can be rearranged as often as desired into definite numbers. ... ."
"The “pure” mathematical monads are, to be sure, differentiated from the single objects of sense by being outside of change and time, but they are not different in this sense — that they occur in multitudes and are of the same kind (Aristotle, Metaphysics B 6, 1002 b 15 f.: [Mathematical objects] differ not at all in being many and of the same kind...), whereas each eidos is, by contrast, unreproducible [hence modelable by idempotent addition, or ‘non-addability’ — F.E.D.] and truly one (Metaphysics A 6, 987 b 15 ff.: “Mathematical objects differ from objects of sense in being everlasting and unchanged, from the eide, on the other hand, in being many and alike, while an eidos is each by itself one only”...)."
"In consequence, as Aristotle reports (e.g., Metaphysics A 6, 9876 b 14 ff. and N 3, 1090 b 35 f.), there are three kinds of arithmoi: (1) the arithmos eidetikos — idea-number, (2) the arithmos aisthetos — sensible number, (3) and “between”...these, the arithmos mathematikos or monadikos — mathematical and monadic number, which shares with the first its “purity” and “changelessness” [here Aristotle reflects only the early, more ‘Parmenidean’, Plato, not the later, «autokinesis» Plato — F.E.D.] and with the second its manyness and reproducibility."
"Here the “aisthetic” [“sensible” or sensuous — F.E.D.] number represents nothing but the things themselves which happen to be present for aisthesis [sense perception — F.E.D.] in this number."
"The mathematical numbers form an independent domain of objects of study which the dianoia [the faculty of ‘pre-/sub-dialectical thinking’ — F.E.D.] reaches by noting that its own activity finds its exemplary fulfillment in “reckoning [i.e., account-giving] and counting”...."
"The eidetic number, finally, indicates the mode of being of the noeton [that which exists “for” thought; that which thought “beholds”; the object of thought; the idea[l]-object — F.E.D.] as such — it defines the eidos ontologically as a being which has multiple relations to other eide in accordance with their particular nature [i.e., in accord with their content — F.E.D.] and which is nevertheless in itself altogether indivisible."
"The Platonic theory of the arithmoi eidetikoi is known to us in these terms only from the Aristotelian polemic against it (cf., above all, Metaphysics M 6-9).”
[Excerpted from: Jacob Klein; Greek Mathematical Thought and the Origin of Algebra; Dover [New York: 1992]; pages 89-91; bold, italic, underline, and color emphasis, [and square-bracketed parenthetical comments] added by F.E.D.].
Plato may have already embarked upon a dialectically-justified axiomatization of one or more of these three arithmetics, in part, by applying, in particular, a generator that he called the '«aoristos dyas»' [the "indefinite dyad"], circa 380 B.C.E., even prior to Euclid of Alexandria’s axiomatization of geometry, circa 300 B.C.E.:
“Plato seems to have realized the gulf between arithmetic and geometry, and it has been conjectured that he may have tried to bridge it by his concept of number and by the establishment of number upon a firm axiomatic basis similar to that which was built up in the nineteenth century independently of geometry; but we cannot be sure, because these thoughts do not occur in his exoteric writings and were not advanced by his successors."
"If Plato made an attempt to arithmetize mathematics in this sense, he was the last of the ancients to do so, and the problem remained for modern analysis to solve."
"The thought of Aristotle we shall find diametrically opposed to any such conceptions."
"It has been suggested that Plato’s thought was so opposed by the polemic of Aristotle that it was not even mentioned by Euclid."
"Certain it is that in Euclid there is no indication of such a view of the relation of arithmetic to geometry; but the evidence is insufficient to warrant the assertion that, in this connection, it was the authority of Aristotle which held back for two thousand years a transformation which the Academy sought to complete.”
[Carl B. Boyer; The History of the Calculus and its Conceptual Development; Dover (NY: 1949); page 27].
Dialectic is a ‘logic’, or a [‘Qualo-Peanic’ ‘Meta-Peanic’] ‘pattern of what follows from what’, more general than the “formal logic” of content-independent ‘propositional followership’.
Dialectic generalizes about how natural populations, ensembles, systems, [sub-]totalities — both concrete, physical-‘‘‘external’’’ «arithmoi», and ‘‘‘internal’’’, human-conceptual «arithmoi» — change, including, especially, of how they change themselves.
Dialectic is about ‘[allo-]flexion’ or ‘[allo-]flexivity’ — the ‘bending’, or ‘‘‘alteration’’’, of the ‘course of development’ of one ‘[ev]entity’ by the actions of other ‘[ev]entities’.
But Dialectic is also, and especially, about ‘self-re-flexivity’, ‘self-re-fluxivity’, ‘self-dialogue’, ‘self-controversion’, self-activity, self-change, or “self-contra-kinesis” [in summary, about ‘‘‘self-bending’’’: the ‘self-induced’, self-determining ‘‘‘bending’’’ of the ‘course of development’ of an ‘‘‘eventity’’’ as a result of its own, immanent, ‘‘‘inertial’’’, ‘‘‘ballistic’’’, ‘intra-dual’, ‘essence-ial’, ‘self-force’].
Dialectic is the name for the fundamental [and ever self-developing] modus operandi of nature, including that of human[ized] nature, but also including that of pre-human and extra-human nature.
Dialectic is about the subject/verb/object-identical meta-dynamic of ‘quanto-qualitatively’, ‘quanto-ontologically' [self-]changing, [self-]developing, via-‘metafinite’-singularity ‘[self-]bifurcating meta-systems’ or ‘process-entities’ [‘eventities’], manifested in all levels, at all ‘[meta-]scales’, for all ‘‘‘orders’’’ of ‘natural history’, including that part of ‘natural history’ which we call Terran human history, and, by hypothesis, in the history of humanoid species generally, throughout this cosmos [‘human-natur[e-]al history’].
We plan to justify the descriptions of Dialectic, just stated above, throughout the entire course of the rest of this manifesto.
For Plato, «Dialektikê», ‘dialectical thought-technology’, as manifested in his «arithmos eidetikos», names a higher form of human cognition. It is higher than that of «Doxa», mere opinion. It is also higher than that of «Dianoia» or ‘«Dianoesis»’; higher than that which Hegel termed «Verstand», “The Understanding” [cf. Plato].
“Dialectical thought” names a higher stage of human cognitive development, a higher “state” of human [self-]awareness, a higher form of human self-identity, and of ‘‘‘human subject-ivity’’’ -- of human agency -- beyond even those associated with the most advanced possible forms of axiomatic, deductive, mathematical logic, still ‘«dianoetic»’, and partly sub-rational, due to the frequent arbitrariness, authoritarianism, and dogmatism of their unjustified axioms and primitives, as well as due to their categorical rigidity and “either/or” radical dualism --
“...disputation and debate may be taken as a paradigmatic model for the general process of reasoning in the pursuit of truth, thus making the transition from rational controversy to rational inquiry.”
“There is nothing new about this approach.”
“Already the Socrates of Plato’s Theaetetus conceived of inquiring thought as a discussion or dialogue that one carries on with oneself.”
“Charles Saunders Peirce stands prominent among those many subsequent philosophers who held that discursive thought is always dialogical.”
“But Hegel, of course, was the prime exponent of the conception that all genuine knowledge must be developed dialectically. ...”
“These conclusions point in particular towards that aspect of the dialectic which lay at the forefront of Plato’s concern.”
“He insisted upon two fundamental ideas: (1) that a starting point for rational argumentation cannot be merely assumed or postulated, but must itself be justified, and (2) that the modus operandi of such a justification can be dialectical.”
“Plato accordingly mooted the prospect of rising above a reliance on unreasoned first principles.”
“He introduced a special device he called “dialectic” to overcome this dependence upon unquestioned axioms.”
“It is worthwhile to see how he puts [F.E.D.-- this] in his own terms:”
“There remain geometry and those other allied studies which, as we have said, do in some measure apprehend reality; but we observe that they cannot yield anything clearer than a dream-like vision of the real so long as they leave the assumptions they employ unquestioned and can give no account of them.”
“If your premise is something you do not really know and your conclusion and the intermediate steps are a tissue of things you do not really know, your reasoning may be consistent with itself, but how can it ever amount to knowledge? ...”
“So... the method of dialectic is the only one which takes this course, doing away with assumptions. ...”
“Dialectic will stand as the coping-stone of the whole structure; there is no other study that deserves to be put above it.”
“Presumably we are to gain our insight into its nature not so much by way of explanation as by way of example — the example of Plato's own practice in the dialogues.”
[Nicholas Rescher; Dialectics: A Controversy-Oriented Approach to the Theory of Knowledge; SUNY Press (Albany, NY: 1977); pages 46-48; bold, italic, underline, and color emphasis added by F.E.D.].
The procedure of formal proof, of deductively deriving theorems from axioms and postulates, is the exercise of ‘«dianoesis»’ «par excellence».
But the process of discovery, formulation, selection, refinement, and optimization of the individual axioms themselves, and of systems of axioms, resides beyond the «dianoetic» realm.
Formal and mathematical logic provide it with no algorithmic guidance.
That process belongs to the realm of dialectics.