PRESOCRATIC DIALECTICS

 PRE-SOCRATIC DIALECTICS

ANAXIMANDER, HERACLEITOS, PARMENIDES, ZENO

CONTENTS:

INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

ANAXIMANDER. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

HERACLEITOS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13

PARMENIDES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33

ZENO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

THE ZENONIAN PARADOXES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

LOGOS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53

INTRODUCTION:

The majority of the pre-socratic texts have been delivered to us from other authors, in a fragmentary state, possibly simplified, misinterpreted and rather modified, the way these inferior thinkers understood them or the way they needed them for use in their writings.  So we are obliged, by our turn, to restore their altitude, either revealing their real meaning or supplementing the gaps of their fragmental delivery and simplified interpretation.  This practice though, causes a “dynamical creative violation” of these texts, which have been already violated and misinterpreted by the effort of inferior thinkers to "rationalise" their pre-socratic ambiguity (double-meaning). Modern interpreters should take this responsibility respectfully and if their effort is truly virtuous, will deserve a share of truth.

      This practice is neither new nor paradoxical, because all ambiguous texts include a dynamic characteristic that provokes the interpreter to participate more in this creative process. Yet this is exactly the element that still keeps them alive. These texts provoke the reader, to get from the spectators hall, on the theatre scene, and participate to the action of the drama itself.

      In the present work, the determination of the distinction between "contraposition and contradiction", the "collapsing-composition” evolution process as opposite to the rational differentially and some other key meanings for the distinction between rational formality and dialectics, is often repeated.  Though this is not dialogically elegant, it is necessary because the reader enters in a dialogic process of Contradictive Dialectics, to which is mostly untrained.  Therefore, for better comprehension of the "Contradictive Thinking", these prepositions must be repeated in key positions of the meaning development of this dialogic process until will be completely understood.

                                                                                                                       1

Since the days of Aristotle, rationalism and formal logic have taken in our conscience the position of Logic itself.  That is, rationalism has been innate in the contemporary human personality, so even intending to follow a contradictive dialogic discipline, during this process, unconsciously rolls down to rationalism.  Beside we have seen this behaviour to great thinkers like Hegel and many distinguished marxists.  Indeed, a big part of the european marxists have consciously roll down to a contradictive-contrapositive eclecticism, because they can not clearly distinguish their dialectics from the rational formality. Even more the scientific evolution, having the electronic computer as a basic instrument of research, (which principally is a formal logic tool), and the anti-dialectic behaviour of the former “socialist” countries leaders, had the result Dialectics to be consider as a dialogic “curse”. So all this argument about dialectics would have been vanished, if the quantic aspect for the world, would not "diabolically" matched so mach with the pre-socratic dialectics.

      Nature have showed that it is much more democratic than we believe and we are; there is enough space for both determinism and dialectics; determinism for aristotelian and newtonian objectivity and dialectics for relativity and quantum-mechanics.

    The present work is neither proud of its literature qualities nor of its dialogic formality, also it would not have been written if the Aristotelian gravestone was not still upon the dialectics of the pre-socratic thinkers. This work has the ambition to uncover that gravestone and erect the thinking of the pre-socratic dialectics after two and a half thousand years.  Rationalism, formal logic and objectivity, pushed science and social developments forward, from Aristotle to Newton, but the genesis of Relativity and Quantic Theories, revealed that our world is much more democratic than we believe, and indisputably there is space for more than one and opposite aspects for the same matter.  That is why our world can be rational contrapositive and deterministic objective, but simultaneously could be logically organised as contradictive and anti-deterministic.  So our world obeys simultaneously to the objective rationalism and pre-socratic dialectics.  This dialectics is far from Platonic-Hegelian idealism and christian-judaism metaphysics, being consciously hylozoic-materialistic.

[The persistence of the Greeks to the City (polis), as a phenomenon, is justified from the aspect that the City comes from the prehistoric agricultural settlement, which had high quality aesthetics, ethics and democratic or oligarchic representation spirit. 

    The city was innate to the existence of Greeks, so it was impossible for them to change their way of life and follow another way considered by them inferior. They were imbued by a supreme sense of citizenship, so they could not follow as herd great kings as Egyptians or Persians did.  So they felt, that their cities lived under the shadow of the Persian King “barbarity”, something that played a basic role to the formation and the decisions of these small and scattered “islands” of civilisation].

2

INDICATION:

For the seamless development of this work and to avoid misunderstandings, under the persistence of the idealists we will accept the existence of two dialectic methods:

   A.  The contrapositive one, which accepts that deeply inside the world, and things, the logics-lingual syntax describing them, consist of ultimate and unchangeable series of elements (knowable or not); these elements interact without violating the ultimate limits in between them, composing an operation system of absolute terms. Therefore, these elements composing that absolute ontological and lingual operation system, presuppose since the integration of its functional cycle, to repeat a specific finite series of lingual and ontological functional games for ever. These are its functional limits and  we could name then “synthetic prototypes of the end”. These games, since the absolute terms of this system were set, presuppose simultaneously to be, as ideal, the beginning of that system also, waiting for their utilisation from the operation of this system.

    This represents a closed and teleological world of objectivity, which as a result of its operation, has predetermined limits; these limits finally altogether could be named "world of Ideas".  Only this way a World of Ideas could be logically possible.  

  That prospect, presupposes a world of Ideas existing before Things, together with Things and after Things, composing a contrapositive, teleological, finished, objective, closed, system of a science course, departing from Aristotle and integrating to Newton. The argument “if Ideas exist before or after Things”, has no meaning. The real meaning is about the matter "if world is an open or closed system", "how an open or closed system is logically possible" and what satisfies the thinker who chooses his cognitive ethos and Logic. That Contrapositive Dialectics is a dynamic-differential rationalism, whose differentiability stops in front of the ultimate, unchangeable elements, composing this contrapositive world. 

   B. The other one is the Contradictive Dialectics, which accepts that world and the logics-lingual syntax describing it, is a whole in continuous evolution process; so it is not possible to be composed by an unchangeable, ultimate elements system. According to this aspect, the elements which compose this operating system reacting, inter-extend inside each-other, without leaving any inviolate limits in between them;   so the elements of this system, being self-overpassing, have contradictive nature, containing the whole by their specific evolving way their composition permits. The way of a specific elementary unite contains the whole, is the specific code of the world as it is inscribed differently to every specific elementary unite, until the moment of its own evolutionary integration and formalisation, containing by a complicated and para-centre way, all evolutionary moments and faces of the world instantly.  This ontological aspect, presupposes that world is an open whole, one script, in a continuous evolution, where every elementary unite has the attribute of not repeated (singularity), being the cause and the result of itself, the cause and result of universe. 

 The contrapositive dialectics accepts evolution as a phenomenal, while the contradictive dialectics, accepts evolution process as real.                                                                                                                                                                                                                                                 3

ANAXIMANDER (610-546) AND HERACLEITOS (535-475)

Anaximander and Heracleitos have been described as opposite characters.  Anaximander was a colonial leader. That is, a military leader and scientist (house and boat builder, geometer and mechanic) of Miletus.  He was a multi-talented political personality. 

    These dark ages, when cities were overcrowded, a talented leader departed from the city with a teem of courageous and talented workers-soldiers, to create a settlement for a new colony. These leaders should be friendly and diplomatic to the inhabitants of the new geographic territory, convincing them that they come as friends to establish peacefully their settlement near by them; but they should be brave enough to draw the sword, if something would go wrongly.  So, Anaximander was a philosopher-warrior.   

    Heracleitos, oppositely to him, appears as an antisocial personality being always aggressive against his fellow citizens, whose he consider as being corrupted.  Maybe Anaximander lived in the flourishing Miletus and Heracleitos in the collapsing Efesus.  Anyway both Anaximander and Heracleitos had a great ideological relationship. It is possible that Anaximander was in a broad meaning teacher of Heracleitos or they have coincide in the same ideological aspects from different roads.  Although Heracleitos do not refer to Anaximander, we know that he admired Thales the Milesian, who was teacher and friend of Anaximander.

    Their ideological relation appears in their common aspect about the Collapsing-composition of things, beings and universe, wherefrom their contradiction nature derives.

   This which makes Heracleitos different from his previous dialectic thinkers, is the meaning of Logos,  which is the logics-lingual contradictive syntax of nature and beings. Logos is the contradictive speech and logic.  This contradictive speech (logos) is a kind of contradictive dialectic formality. The roots though of the world and beings as a collapsing-composition aspect, derives from Anaximanders prepositions about Evolution and Infinite. According to Anaximander Infinite is a continuous alternation of birth and death, (Genesis and Collapse) result of beings, in an evolving process. 

4

THE FRAGMENTS OF ANAXIMANDER

Simplicius  physics  24, 13

     ἕν καὶ κινούμενον καὶ ἄπειρον. . . . 

     ἀρχή τὲ καὶ στοιχεῖον τῶν ὄντων τὸ ἄπειρον. . .

     τὴν εἰς ἄλληλα μεταβολήν τῶν τεττάρων στοιχείων

     οὗτος οὐκ ἠξίωσεν ἕν τι τούτων ὑποκεἰμενον ποιήσαι,

     ἀλλά τι ἄλλον παρά ταῦτα.

     οὗτος δὲ οὐκ ἀλλοιωμένου τοῦ στοιχείου τὴν γένεσιν ποιεῖ,

     αλλ᾽ἀποκρινομένων τῶν ἐναντίων διὰ τῆς ἀϊδίου κινήσεως

universe is one, moving and infinite. . . 

small and great, first and last element of universe is infinite...

during the transformation of the four elements of nature (earth, water, fire and air)

Anaximander did not accept any of them as generative, but something else. He cannot accept that Genesis occurs from the modification of these elements, but from the dialogue of the opposites and the eternal motion.

Aristotle physics A4 187a 20

    οἱ δ᾽ ἐκ τοῦ ἑνὸς τὰς ἐναντιότητας ἐκκρίνεσθαι ὥσπερ

    Ἀναξίμανδρός φησι καὶ ὅσοι γ᾽ἕν καὶ πολλά φασίν εἶναι.

Anaximander and all them who believe that One and Many act reversely, declared that the oppositions are innate in beings and emanate from them.

Hippolyte Air. Eleg. 16 1-7

   οὗτος άρχή τῶν ὄντων ἔφη φύσιν τινὰ τοῦ ἀπείρου,

   ἐξ᾽ἧς γίγνεσθαι τούς οὐρανούς καὶ τὸν ἐν αὐτοῖς κόσμον.

   ταύτην ἀΐδιον εἶναι καὶ ἀγήρω καὶ πάντας τοὺς κόσμους 

   περιέχειν.  λέγει δὲ χρόνον ὡς ὡρισμένης τῆς γενέσεως

   καὶ τῆς ούσίας καὶ τῆς φθορᾶς. . . . . . . . . . . . .

   οὗτος μὲν ἀρχήν καὶ στοιχεῖον εἴρηκε τῶν ὄντων τὸ ἄπειρον,

   πρῶτος τοὔνομα καλέσας τῆς ἀρχῆς.

   πρὸς δὲ τούτῳ κίνησιν ἀΐδιον εἶναι, ἐν ᾗ συμβαίνει

   γίγνεσθαι τοὺς οὐρανούς.

Anaximander declared that beings are under the authority of some kind of infinite, where from skies and worlds are born.  This is eternal and ageless and comprises all the worlds.  For that reason, Time is related and gets meaning from the birth and death of the related materials. . .    He determined, that both authority and element of things, is infinite and he is the first to use this word for that meaning.  He also declared that infinite is the eternal motion, in which occurs the universal evolution process.

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Comment: According to Anaximander universe do not consist of two worlds, that is, the material one and the ideal one, but it is a Whole, a unity in infinitival evolution process. He also rejects the existence of unchangeable ultimate elements, which composing universe, do not violate the limits in-between them. He proposed the “unity and interaction of the opposites” (one basic principal of dialectics), which gives birth to the eternal motion.   According to him, universe coincides with infinite and infinite coincides with the eternal evolution process; Time is related to the alternation of the birth and death of beings, therefore Time coincides to the Evolution process.  This way Being, Time, Space, Motion and Infinite, coincide to the Universal Evolution process. Yet, according to him: this to be utilised, a dialogue is presupposed, where the opposites interact without leaving any inviolated limits in-between them, composing contradictive unities. For that reason, the dialogue of the opposites in every contradictive unity, violating the limits of the specific contradictive unity, can “travel” far away, and so expands to the universe.  Therefor, every contradictive event departing from the dialogue with itself, passes to the dialogue with the near by existing contradictive unities, after that to the farther and finally to the universe itself, which is the faraway Other self, the ultimate cause of the contradictive event changing. Through this dialogue, the contradictive event changes continuously, changing simultaneously the other contradictive events composing this dialogue. That’s why the contradictive elementary units have a “collapse-composing-evolutionary” nature, containing potentially an integrated face of the Whole.  This way infinite is not only the quantitative authority as a whole, but simultaneously it is the qualitative small ultimate evolving finite element.

Hermeias  Phil. 10

   ἀρχὴν εἶναι τὴν ἀΐδιον κίνησιν καὶ ταύτῃ τὰ μέν γεννᾶσθαι τὰ δὲ  φθείρεσθαι.

The eternal motion is the Universal authority, where beings simultaneously born and die.

(Universe consists from the continuous beings collapsing-composition and this is the Motion as Evolution and as living essence).

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Aetius p. t. ares. 

    Ἀναξιμανδρός φησι τῶν ὄντων ἀρχὴν εἶναι τὸ ἄπειρον.

    ἐκ γὰρ τούτου πάντα γίγνεσθαι καὶ  εἰς τοῦτο πάντα φθείρεσθαι…

    ἁμαρτάνει δὲ οὗτος μὴ λέγων τί ἐστι τὸ ἄπειρον,

    πότερον ἀήρ ἐστι  ἢ ὕδωρ  ἢ γῆ  ἢ τι ἄλλον.

    ἁμαρτάνει οὖν τὴν μὲν ὕλην ἀποφαινόμενος,  τὸ δὲ ποιοῦν αἴτιον 

    ἀναιρῶν. τὸ γὰρ ἄπειρον οὐδὲν ἄλλο ἢ ὕλη ἐστίν.

    Οὐ δύναται δὲ ἡ ὕλη εἶναι ἐνέργεια,  ἐὰν μὴ τὸ ποιοῦν ὑποκέηται.

Anaximander claimed that infinite dominates all beings, since all of them are born from this and die returning again to this…Yet he mistakes, not saying what the infinite material is composed of (air, water or anything else). He speaks about infinite, but do not refer to the cause of its existence;  Infinite cannot be anything else but material. Because material cannot exist, if has not infinite inside, to give energy and life.

Aristotle physics γ. 7 207b 3

   Ὡς ὕλη τὸ ἄπειρον ἐστίν αἴτιον καὶ ὃτι τὸ μὲν εἶναι αὐτῷ στέρησις,

   τὸ δὲ  καθ᾽αὐτό  ὑποκείμενον τὸ συνεχές  καὶ αισθητόν.

   φαίνονται δὲ καὶ οἱ ἄλλοι πάντες ὡς ὕλη χρώμενοι τῷ ἀπείρῳ   

   διὸ καὶ ἄτοπον τὸ περιέχειν ποιεῖν αὐτὸ ἀλλά μὴ περιεχόμενον.

Infinite, as material, is the cause and though it seems to be something different than material, it is exactly the same to that; and all them who claim that it is necessary material to coincide with infinite, accept that it is absurd infinite to give birth to material, to contain it, and not to be contained by material.

Comment: According to pre-socratics infinite is not only a quantitive characteristic of material, but coinciding with the evolution process, from one hand is the authority as quantitive Mega, on the other hand, is contained to material as a collapsing-composition genetic elementary essence: that is, as “contradictive elementary unite”.     

    In the previous fragment where Hippolyte referred to Time, Anaximander claimed that: τὸν δὲ χρόνον ὡς ὡρισμένης τῆς γενέσεως καὶ τῆς ούσίας καὶ τῆς φθορᾶς. . (Time is related and gets meaning from the birth and death of the beings, Time refers to).  Anaximander connects the relativity of time, to the alternation of birth and death of beings, thus with the eternal evolution process and this way with infinite.

Aetius  V 19. 4

   Ἀναξίμανδρος  ἔφασκεν  ἐν ὑγρῷ γεννηθῆναι τὰ πρῶτα ζῷα

   φλοιοῖς περιεχόμενα ἀκανθώδεσι, προβαινούσης δὲ τῆς ἡλικίας

   ἀποβαίνειν ἐπὶ τὸ ξηρότερον καὶ τοῦ φλοιοῦ περιρρηγνυμένου,

   ἐπ᾽ὀλίγον χρόνον μεταβιῶνται.

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Anaximander claimed, that the first animals, at the beginning, were born in between fishes in wet (watery) environment, having thorny scales and when the environment became dryer, they threw away the scales and adapted themselves to a new environment.

Ploutarch Symp.  VIII 8,4 

    Ἀναξίμανδρος ἀποφαίνεται ἐν ἰχθύσι ἐγγενέσθαι πρώτον τοὺς 

    ἀνθρώπους καὶ τραφέντες ὥσπερ οἱ γαλαῖοι καὶ γενομένους  

    ἱκανοὺς ἑαυτοὺς βοηθεῖν, ἐκβῆναι τίνικαῦτα καὶ γῆς λαβέσθαι.

Anaximander claimed, that human beings were born in between fishes and they were fed like them, but when they became capable they came out to earth.

Comment:Anaximander claimed, that the contradiction of beings and infinite, has as a result the evolution of species.  That we conclude from his fragments about infinite we will see next.

    The “Evolution Theory” of Darwin is an elegant and blameless work of art, as a result of observations and infallible conclusions, the preposition of Anaximander in frond of that “pales”, if we do not consider that his aspect was proposed 2500 thousand years ago. The Anaximander’s aspect reached to as fragmentary and formed the way other writers understood his aspect and proposed rather misunderstood and simplified. Yet his aspect departing from the evolution of beings, describes the contradictive nature of beings and universe, proposing an other logic (dialectics), that fits to the Evolution Theory, which about, i believe, Darwin did not care.

Simplicius physics 1121, 5

    Οἱ μὲν γὰρ ἀπείρους τῷ πλήθει τοὺς κόσμους ὑποθέμενοι ὡς οἱ 

    περὶ Ἀναξίμανδρον καὶ Λεύκιππον καὶ Δημόκριτον καὶ ὕστερον οἱ 

    περὶ Ἐπίκουρον γινομένους αυτούς καὶ φθειρομένους ὑπέθετον  

    ἐπ᾽ ἄπειρον, ἄλλων μὲν ἀεὶ γινομένων ἄλλων δὲ φθειρομένων καὶ 

    τὴν κίνησιν ἀΐδιον ἔλεγον.   Ἄνευ γὰρ κινήσεως οὐκ ἔστι γένεσις ἤ 

     φθορά.

    I consider correct: ἄνευ γὰρ γενέσεως καὶ φθοράς οὐκ ἕστι κίνησις.

    Instead of “without movement there is not genesis or death” .  I accept: “without

    genesis and death, there is not motion”.

The people around Anaximander, Leykippos and, Demokritos and the later around Epicurus, believed and accept that worlds born and die infinitely, and this is what they consider to be motion, because without alternation of birth and death there is not real motion.

Comment: From the information we have about the aspect of Anaximander, “material is innate with motion, infinite, evolution, space and time”, we 

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conclude that: Motion is the continuous change, that is, the alternation of birth and death of beings, which compose eternal evolution and infinite. Material could not be alive (being in a continuous evolution), if infinite did not exist potentially in every finite elementary unit to energise it.  Though formal infinite is a meaning that contains material, Anaximander who was the first who defined the meaning of Infinite, believed that Material and every elementary unit contain infinite potentially; because, Infinite to be the authority and generative great (Mega), should simultaneously the elementary units composing it, being evolutionary to be infinite also; Thus, the elementary unite should be potentially infinite, containing a face of the Whole.     Because “infinite and evolution”, “vacuum and fulness”, “time and space”, and “beings” are innate each-other, composing a unity in motion as “the essence itself”, all events and things are specifications of Motion as Essence; therefore he did not consider Things to be the Essence, and Motion to be attribute of Things, but the opposite.

On the contrary, Rational Objectivity and determinism cannot accept Material, Infinite, Evolution and Being (Εἶναι) to be an Essence Itself, all these are considered to be categories of thinking.  According to determinism and objectivity: Material always exists as a finite specific event; and Infinite exists as a quantitative accumulation of elementary units, which do not exist as a Whole-Essence; and Evolution exists only as phenomenal attribute of the Idea. Even more: Time exists as duration of the finished, specific, objective things or finished specific objective system of things. Determinism therefore, neither can accept or determine the “Being Itself” as a specific Essence, nor as a “meaning itself” (something which has been an object of much argument, but no one achieved to accomplish it satisfactorily).  Therefore the opinion of Anaximander about infinite: that “every body and elementary unit is infinite, because worlds end their limits are infinite”, made Aristotle to wonder rather ironically. Heracleitos and Zeno though agreed with Anaximander.  Heracleitos believes that everything is in a state of collapsing-composition process, because other “under-elements”, passing inside things, make them this way to exist. These “under-elementary” units simultaneously collapse-composing by the passage of other deeper level “under-elements” of the world and so on infinitely. Therefore nothing really has absolutely specific limits, expanding this way to universe, being potentially infinite.

     Zeno claimed that: nothing can contain an ultimate, elementary, specific part (atom). According to him an ultimate part of a material tending to zero, simultaneously tends to infinite, (being simultaneously infinite and zero). This is the “Contradictive Elementary Unite”, the “Being as the Potential Level of Universe”, having all faces and none simultaneously, the “Contradiction itself” and finally the “Material itself”. Without this aspect of elementary unit, no one can be dialectic. Only this way Being, Infinite, Motion Evolution, Space and Time would compose a unity (One Essence), which can be described and spoken by the Dialectic Logos.

     Because Aristotle looked the world from an other and different point of view, did not inform us the way Anaximander accepts the meaning of infinite. All the kinds of infinite he proposed, do not mach with the Anaximandrian way, except the one that makes him to wonder ironically.

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Aristotle physics γ 4 203b 6 

   ἅπαντα γὰρ ἢ ἀρχή ἢ ἐξ᾽ ἀρχῆς, τοῦ δὲ ἀπείρου οὐκ ἔστιν ἀρχή,

   εἴη γὰρ ἂν αὐτοῦ πέρας. ἔτι δ’ἀγένητον καὶ ἄφθαρτον ὡς ἀρχή  

   οὖσα, τὸτε γὰρ γενόμενο ἀνάγκη τέλος λαβεῖν καὶ τελευτή πάσης 

   ἐστὶ φθορᾶς. διὸ καθάπερ λέγομεν, οὐ ταύτης ἀρχή, ἀλλ᾽αὐτή τῶν 

   ἄλλων εἶναι δοκεῖ καὶ περιέχειν πάντα καὶ πάντα κυβερνᾶν ὥς 

   φασιν ὅσοι μὴ ποιοῦσι παρὰ τὸ ἄπειρον ἄλλας αἰτίας, οἶον νοῦν ἢ 

   φιλίαν.  καὶ τοῦτ᾽εἶναι τὸ θεῖον,  ἀθάνατον γὰρ καὶ ἀνώλεθρον, ὥς 

   φησιν  Ἀναξίμανδρος καὶ οἱ πλεῖστοι τῶν φυσιολόγων. τοῦ δὲ τὶ

   εἶναι ἄπειρον ἡ πίστις ἐκ πέντε μάλιστ᾽ ἄν συμβαίνοι σκοποῦσιν

Everything has a beginning in something else; or it is a beginning of something else. Infinite have neither a beginning nor end, being immortal and not born. Everything which borns is necessary to have an end as a result of decay. Nothing has an authority on infinite. Infinite contains everything being the authority of all. This is claimed by all them who do not accept any other cause of the world, as Eros or Nous (universal mind) but Infinite. So as Anaximander and the other physical philosophers claimed: because infinite is immortal and undistracted, is divine. Therefore they believed that infinite could be conceivable by five ways: (I notice that this basic way of infinite comprehension do not agree with the opinion of Anaximander, who assimilates infinite to evolution process. He did not accept, infinite and evolution to be immortal and unborn, but in eternal death and birth alternation).

Aristotle physics Γ 4 203 b 6

    Ὥς φησιν Ἀναξίμανδρος  καὶ πλεῖστοι τῶν φυσιολόγων, τοῦ δὲ 

    εἶναι τι ἄπειρον, ἡ πίστις ἐν πέντε μάλιστ᾽ἄν συμβαίνει σκοποῦσιν:

    ἐκ τοῦ τε χρόνου (οὗτος γὰρ ἄπειρος). καὶ ἐκ τοῖς μεγέθεσι 

    διαιρέσεως χρῶνται γὰρ οι μαθηματικοί τῷ ἀπεἰρῳ. ἔτι τῷ οὕτως 

    ἂν μόνως μὴ ὑπολείπειν γένενεσιν καὶ φθοράν, εἰ ἄπειρον εἴη ὅθεν 

    ἀφαιρεῖται τὸ γινόμενον. ἔτι τῷ τὸ πεπερασμένον ἀεὶ πρός τι 

    περαίνειν ανάγκην ἕτερον πρὸς ἕτερον. μάλιστα δὲ καὶ 

    κυριώτατον ὅ τὴν κοινήν ποιεῖ ἀπορίαν πᾶσιν, διὰ γὰρ τὸ ἐν τῇ 

    νοήσει μὴ ὑπολείπειν καὶ ὁ ἀριθμός δοκεῖ ἄπειρος εἶναι καὶ τὰ 

    μαθηματικά μεγέθη καὶ τὸ ἔξω τοῦ οὐρανοῦ ἀπείρου δ᾽ ὄντος τοῦ 

    ἔξω και σῶμα ἄπειρον εἶναι δοκεῖ καὶ οἱ κόσμοι.

10

Anaximander and the most of the physiologists believe that infinite is conceivable by the following five ways: A. By the time which is infinite. B. By the divisibility of mathematic sizes. C. Because only that way can exist the continuous alternation of birth and death of things.  D. Because every finite thing, touches another one and that endlessly.  E. But most important, which causes confusion to anyone who dispose common sense and would be able to understand the infinite of mathematical sizes, or the infinite expanse of the sky toward outside, is that since universe is infinite, everything is infinite and the worlds are infinite.

Comment:

Α. According to Anaximander, the relation of time and infinite, do not exist in the continuous and eternal expanse of time but in the contradictive nature of time.

     Pre-socratics believed that yesterday do not exist, tomorrow do not exist, only now exists. “Now” is the zero edge of the fading present, between past and future, which eternally Exists-NotExisting, being contradictive and that’s why infinite.

B.  Infinite as a result of continuous mathematic sizes division, is a typical and poor way to be understood. The rational and objective mathematic way leads to the conclusion that, the more something is divided the smaller becomes and this to infinite. Pre-socratics believed that dividing something, this, by one hand gets smaller, but on the other hand  gets bigger, because of the empty spaces, which are created by that process. So tending the division to zero size, simultaneously tends to infinite and zero relation. 

    The mathematic division of Aristotle is typically objective, while the pre-socratic is contradictive.

C. The continuous alternation of birth and death of the events and things is the cause of infinite and not the infinite cause of the continuous alternation of their life and death.

D.  This is the most typical and poor way of understanding the infinite, something which has nothing to do with the pre-socratics.

      My opinion is that pre-socratics rather agree to the fifth way about infinite, for which Aristotle wonders ironically: since universe is evolutionary infinite, every finite thing is evolutionary infinite and the worlds are infinite.

Aristotle often undervalues pre-socratics as primordial, simplifying their aspects. His four prepositions about infinite do not agree with the way Anaximander really accepts infinite. Anaximander departing from his aspect about the “collapsing-composition” of things, nature and evolution, and his opinion that time is related and gets a meaning from the alternation of genesis and death of the specific things, expands the contradictive nature of infinite to the ultimate unite, which composes the universe.  Therefore, according to him, infinite is not simply an accumulation of things, but a generating evolving process that composes-collapsing by elementary unites, which by their turn, collaps-composing eternally and this way containing infinite dynamically and potentially. So that is the meaning of “Infinite is authority and element of things”; because infinite comprises quantitatively everything as Mega, but it is comprised qualitatively by every-thing as elementary. So, according to him, all elements and things are potentially infinite because of their evolving nature.

                                                                                                                     11

    According to Anaximander, Heracleitos and Zeno, every specific material, thing or event, performs a dialogue which begins internally with itself, continuous with the nearly environment things, after to the faraway things and finally to the universe itself, which is the Other the opposite self which makes the thing to change. The limits of a thing depart deeply inside from itself, without leaving any element or space inviolate, and travelling far away out of that to universe, once they return to the thing they departed, changing it continuously and changing its limits also.  Therefore every element, event or thing, do not have absolutely specific limits, being in a continuous dialogue with universe and for that reason to infinite, being infinite itself.

    For the pre-socratics the meanings of infinitesimal big and small, coincide to the meaning of the Ether. That ether has nothing to do with the neutral ether of the 19th century European scientists which was rejected by the Michelson-Morley experiment; The “Miletian Ether” was the level of the potential existence of our world, the nude contradiction. The contemporary physics with the possible instantaneous interactions of sub-quantic elements, brings back the meaning of the “Miletian Ether” as a genetive cause of the elementary unites. (Infinite as “authority and element of the world”, as “Contradiction itself”,  as the simultaneously “instantaneous and immobile”, “zero and infinite”, “all faces and none specific”).  The existence of that potential universal level of the world, is somehow accepted by Heisenberg as the under quantic level of the world. 

   The ancient ancestors of our scientists, used to see the world by an opposite way. According to them motion was not an attribute of things, but things were attributes of Motion Itself. 

   That aspect was vanished by Aristotle, who claimed that motion is an attribute of things and there is not anything, as Motion and Infinite to be a specific material. So after the acceptance of the aristotelian formal logic and objectivity in the medieval monasteries, the aspects of the pre-socratics were forgotten. 

According to the Dionysian worship, everything is mask over a mask; the last mask is that of Dionysos. Behind exists Mystis the nurser of Dionysos- Bacchus, the empty face, the presence into the absence, the dithyramb, the simultaneously passing by two opposite doors, “the door of birth and the door of death”. That is the “Contradiction Nude”, the level of the world’s potentiality.

12

THE FRAGMENTS OF HERACLEITOS

Sextos  to the mathematicians VII 132    

1.  τοῦ δὲ λόγου τοῦδ᾽ἐόντος, ἀεὶ ἀξύνετοι γίνονται ἄνθρωποι,

    καὶ πρόσθεν ἢ ἀκοῦσαι καὶ ἀκούσαντες τὸ πρῶτον

    γινομένων γὰρ πάντων κατὰ τὸν λόγον τόνδε,

    ἀπείροισιν ἐοίκασι πειρώμενοι καὶ ἐπέων καὶ ἔργων τοιούτων,

    ὁκοίων ἐγὼ διηγεῦμαι κατά φύσιν διαιρέων ἕκαστον καὶ φράζων 

    ὅκως ἔχει. τοὺς δὲ ἀνθρώπους λανθάνει  ὁκόσα  ἐγερθέντες  

    ποιοῦσιν, ὅκωσπερ ὁκόσα εὕδοντες ἐπιλανθάνονται.

Since Logos (contradictive speech, dialectics) exists always, people do not feel it even if they have been informed about it. Although every-thing is done according to Logos, they seem participating-not participating, to the way things exist and be spoken, which I analyse and name them the way exactly are. So people seem to sleep when they are awaken and to alert when they are sleeping.

Comment: Heracleitos, guides us in the first steps of his logical path. Logos is Logic, Language and Essence, therefore it is innate to Being. (Essence can be perceived and be said only by Logos, which is the Dialectic Logic). Although Logos exists everywhere,  man can not feel it and although they have been conscious about its existence, have not the sense of it; like fishes do not feel water and young people do not feel youth. I am conscious of the changing process inside me, but i do not feel it, being present-absent.

KLEMES.  ΣΤΡΩΜΑΤΕΙΣ V 116

34.   ἀξύνετοι ἀκούσαντες κωφοῖσιν ἐοίκασι φάτις αὐτοῖσιν μαρτυρεῖ παρεόντας ἀπεῖναι.

People who listen to something and they do not feel it, look like deaf, being present-absent.

Comment: Though am absolutely convinced that inside me exist celluloses and atoms, i never feel them.

ΜΑRCUS ΑΝTOΝΙΝUS,  IV 46

72.  ᾧ μάλιστα διηνεκῶς ὁμιλοῦσι,  λόγῳ τούτῳ διαφέρονται,

       καὶ οἷς καθ᾽ ἡμέραν ἐγκυροῦσι,  ταῦτα αὐτοῖς ξένα φαίνεται.

Human beings,  commune immediately and continuously with Logos  and because of that, evolve changing and though everyday confirm that, they do not feel it.

                                                                                                                 13

Comment: All beings commune to Logos and since Logos as contradictive, it is the cause of their movement and modification. So everything agreeing to Logos, differs from itself; it confirms-refusing its identity, being contradictive. Because all beings have Logos in common, being contradictive, they agree to that, differing each-other; therefore they have their own particularity.

PLOTIN  ΕΝΝΕΑΔΕΣ  IV 8,  1.

84.  μεταβάλλον ἀναπαύεται καὶ κάματός ἐστι τοῖς αὐτοῖς μοχθεῖν καὶ ἄρχεσθαι.

Change and modification is the real state of things inactivity and state of rest.  So achieving immobility is the Action to dominate motion.

Comment: Negation and affirmation is simultaneously change and motion.  The moving one either “Is-BeingNot” momentary in the same position or changing position, is different from itself. (Different but a similar one).  So the eternal motion of the world is its normal state of rest, since stability needs action and labor to be accomplished. “Change”, being innate to the nature of world, needs “no change” to be accomplished, but the achievement of stability demands a “change”. 

HIPPOLYTE  IX 9

51. Οὐ ξυνιᾶσιν ὅκως διαφερόμενον ἑαυτῷ ὁμολογέει, παλίντροπος ἁρμονίη, ὅκωσπερ τόξου καὶ           λύρης.

People do not understand, that something differing, agrees to itself; this is a contradictive harmony like bow and lyre.

Comment: The Changing One agrees-disagreeing to itself, verifies-falsifying itself. This is the contradictive harmony, like the one of the string organ and the bow does. The strings of the music organ give separate sound and different notes, but the bow produces a harmonic confluence of all these; therefore the contradictive harmony of particularity and unity is created. Yet, we need a language to speak this evolving world. Heracleitos proposed Logos, the contradictive speech, (dialectics). Heracleitos speaks consciously this language, setting its terms and the first term is “διαφερόμενον ἑαυτῷ ὁμολογέει”; “The changing one (the differing one) agrees to it self”, (it verifies-falsifying itself). This is the contradictive identity.

STOVAIOS,   ΑΝΘΟΛΟΓΙΟΝ Ι   179.

114. ξύν νόῳ λέγοντας ἰσχυρίζεσθαι χρὴ τῷ ξυνῷ πάντων,

        ὅκωσπερ νόμῳ πόλις καὶ πολὺ ἰσχυροτέρως. τρέφονται γὰρ  

       πάντες οἱ ἀνθρώπειοι νόμοι ὑπὸ ἑνὸς τοῦ θείου. κρατεῖ γὰρ 

       τοσοῦτον ὁκόσον ἐθέλει καὶ ἐξαρκεῖ πᾶσι καὶ περιγίγνεται.

14

The logical people need Logos, which is common to everything, much more than the city need of lows, because all lows are based on one, which is divine. That has its own will;  it dominates and leads being inside everything, but simultaneously encloses containing them.

Comment: We see Heracleitos and we will see later Parmenides, to present, first of all, the legality of their logical terms, something we evade taking it as granted nowadays.   So many intellectuals choose one or the other logical process unconsciously, since “they cary it in the luggages” of their intellectual belongings. However this could create antinomies, surprising the unconscious user.   Scientists nowadays, believe that the world is in a continuous change and the evolving process of nature is not phenomenal but real; However because they cary in their small suitcase their formal logic, oppose to Logos, (the common low of the divine nature). Maybe they invested everything in formal logic, maybe they are more Aristotelian than Aristotle or they are so poor and that’s all they possess. All these great scientists working in their very precious laboratories and their accelerators, “have reached the turtle and as Achilles did, they cannot leave it behind”, because they afraid that will make a “logical mistake”.  On the contrary to them, their pre-socratic grand fathers, only with their logic, had reached to conclusions, which still stimulate and fertilise our mind.  They have ready for us the logic to approach the world and we only have to take it.

SEXTOS,  VII  133.

2.  Διὸ δεῖ ἕπεσθαι τῷ, τοῦ λόγου δ᾽ἐόντος ξυνοῦ, ζώουσιν οἱ πολλοί 

     ὡς ἰδίαν ἔχοντες φρόνησιν.      

Because Logos is commune and everything follows it, that is why everyone has his own particularity.

Comment: The particularity of the individuals is legal, because it derives from Logos which is the contradictive common element in everyone. Differentiability derives from contradiction, which is common attribute to everything.

KLEMES, ΣΤΡΩΜΑΤΕΙΣ V 116.

32. Ἕν σοφόν μοῦνον λέγεσθαι, οὐκ ἐθέλει καὶ ἐθέλει ζηνός ὄνομα.

This One, which is wisdom, may and may not be named a god.

Comment: 

―This one, Logos, which is wisdom, can only be spoken this way and do not care if it is named god or not.

―Logos, which is wisdom, is spoken in a contradictive way and do not have the conscience of its divinity. 

―Logos, God and Nature is a unity and coincides in the contradictive speech, the dialectic logic.  If there is a god, only this way could be and although everything is born from this one, being contained from, it also contains that.  

―This One (Logos) has no conscience of its divinity, just like man, who though participates to Logos, never has a feeling of that.

         Human knows but do not feel, Nature feels but do not know.

                                                                                                                    15

KLEMES,  ΣΤΡΩΜΑΤΕΙΣ V 60.

 30.   κόσμον τόνδε τὸν αὐτὸν ἀπάντων οὔτε τις θεῶν οὔτε ἀνθρώπων 

         ἐποίησεν, ἀλλά ἦν καὶ ἔστιν καὶ ἔσται πῦρ ἀείζωον, ἁπτόμενον 

         μέτρα καὶ ἀποσβεννύμενον μέτρα

This world, which is the same for everyone, was not created by god or man; it was, it is and it will be eternal fire burning up and down in balance (Metron).

Comment: Because the world is a result of itself and because everything communes with it, the world is the same for everyone; That is why everything participates to Logos and all men commune with Logic.

     The problem of objectivity and common-logic approach to the world, is not new.  Always philosophical theories needed to legitimate the value of their logic principals.  The base up on Heracleitos establishes his dialectic logic is Logos, while Parmenides establishes his rationalism up on the Ἐὀν (the Being, the Existing one). Eon and Logos look similar because both creators accepted that Existence (Essence), Logic and Language coincide to that; they differ though in the meaning of their Logic and consequently to their logic-lingual syntax. Heracleitos accepts Nature to be contradictive, thus he accepts a contradictive logic-lingual syntax;  on the contrary Parmenides do not to accept Nature to be contradictive but contrapositive, so he proposes an ortho-rational Logic-lingual syntax.

     Plato, instead of Logos or Eon accepted the World of Ideas; he claimed that man to have valuable correlations for reliable comparative logical proceedings, should participate to a “World of Ideas”.

     The world of Heracleitos was the eternal fire, burning up and down in Metron (meter, balance). The word “Metron” is a loaded meaning, as much as Logos is.  Contradiction always presupposes a Meter of the contradictive balance of the contradictive “legs” of which the world, the elements or the event consists. The Meter is the specific character of the contradictive elements relation which compose occasionally a fainting Identity; that is because Identity communes to the world’s eternal evolution process, is continuously  overpassed.  That is,  Metron  (Meter) is  the dynamic balance composing an Identity in a continuous change; Identity being contradictive, Exists―NotExisting, being dithyrambic, (passing through two opposite doors simultaneously).

16

PLUTARCH,  ΠΕΡΙ ΤΟΥ ΕΙ ΤΟΥ ΕΝ ΔΕΛΦΟΙΣ 388 Ε  

90.    πυρός τε ἀνταμοιβή τὰ πάντα καὶ πῦρ ἀπάντων, 

         ὅκωσπερ χρυσοῦ χρήματα καὶ χρημάτων χρυσός.

Everything transforms to fire and fire to everything, just as gold to merchandises and merchandises to gold.

Comment: Logos, Metron, Contradiction, are actualised to Fire. Fire is a primordial form of Energy (this has been pointed also by Heisenberg).  Nowadays it’s commonly accepted that every-thing transforms to Energy and Energy to every-thing. this was formulated mathematically by Einstein, with the equation ε=mc². Dialectics accept that a specific quantitative accumulation could give a new quality; we also know that all material objects emit-receiving energy in order to exist.  Energy and mass, do not have absolute dinstinct limits. Nothing can exist by itself, everything correlates to something else; if something overpasses the relating Metron being by it-self, disappears as It-self and reappears in Other relation, as Different, expressed by another Metron.

HERACLEITOS ΑΛΛΗΓΟΡΙΑΙ 24.

49a    ποταμοῖς τοῖς αὐτοῖς ἐμβαίνομέν τε καὶ οὐκ ἐμβαίνομεν, εἶμεν τὲ καὶ οὐκ εἶμεν.         

In the same river we enter and not enter, as we are and we are not.

PLUTARCH, ΠΕΡΙ ΤΟΥ ΕΙ ΤΟΥ ΕΝ ΔΕΛΦΟΙΣ 392β.

 91.    ποταμῷ γὰρ οὐκ ἔστιν έμβῆναι δὶς τῷ αὐτῷ, οὐδὲ τῆς αυτῆς οὐσίας ἅψασθαι κατ᾽ἕξιν, 

          ἀλλ’ὀξύτητι καὶ τάχει μεταβολῆς,  σκίδνησι καὶ πάλιν συνάγει  καὶ πρόσεισι καὶ ἄπεισι 

          (μᾶλλον δὲ  οὐδὲ πάλιν οὐδ᾽ὕστερον, ἀλλ᾽ἅμα συνίσταται καὶ ἀπολείπει).

We neither enter in the same river twice, nor we touch the same material again, since everything changes rapidly and violently, departs-returning, spreads-gathering, collapses-composing.(not again or after but simultaneously).

Comment: A perfect description of the contradictive identity; this also could give as an idea about the wave-particle existence or the energy emit-receiving of the objects or the field-object relation. The example of the river could easily be understood: the water passing by, makes the river continuously other; for the solid materials though there is a question. 

    Popper tries to explain: “the pots get rusted, the woods get rotten, the stones  break  to pieces,  everything  changes  during  the  time passing;  but Heracleitos claims: everything “collapses-composing” and Plutarch points out: “simultaneously”. Popper and Aristotle, simplify the pre-socratic aspects. Pre-socratics were much more sophisticated and complicated than we believed. 

  According to them: an object exists, because Fire fundamental elements, passing from a position, compose this object; these fire fundamental elements (pyridia as they called them), could be accepted nowadays as “quanta of energy”, since pre-socratics believed that “all things transform to fire and fire to everything”.  

                                                                                                                                                           17

HIPPOLYTE  IV 10.

59.    γναφείῳ ὁδὸς εὐθεῖα καὶ σκολιή  μία ἐστὶ καὶ ἡ αὐτή.

         (ἡ τοῦ ὀργάνου τοῦ καλουμένου κοχλίου έν τῷ γναφείῳ περιστροφὴ 

         εὐθεῖα καὶ σκολιή,  ἄνω  γὰρ ὁμοῦ καὶ κύκλῳ περιέχεται).

In the turning lathe (spiral, way) rectilinear course, is a result of rotation (helicoid way).

Comment: If we combine this fragment with fragments 12, 91 and 103, we find out the way Heracleitos accepts motion: A. Objects-events consist by the elementary energy units  passage-antipassage (fire elements, quanta or “pyridia”) in a specific position. These elements departing from the objects position make a multi-dimensional journey to the Universe and return back to the departure position. The course of these elements is considered multi-dimensional, because they depart-returning continuously after the verification contact with every other object they meet in their journey. The composition of an object by this multi-dimensional process, consists of an unconstrained number of “circular” fire elements depart-returning (from the position of departure to the position of the arriving). Since the universe of Heracleitos is not closed but open and infinite, the course of the departure-returning elements do not accomplish a perfect cycle, but a thick elliptic-helicoid course; so every time the departing elements return, do not verify the object exactly in its former position, but a little farther, composing this way the course of the object motion. The motion of an object and the object are contradictive, because they are the results of the depart-returning elements and the collapsing-composition way these elements perform traveling to universe. These returning, verify-falsifying both object and position, during their composition. Motion this way, coincides with the collapsing-composition evolving process of beings, which are continuously theirSelves-beingOthers, being similar and not similar to their-selves, and continuously to Another Place.

Hegel claimed that motion is contradictive because, not only the moving one is here now and somewhere else later, but because the moving one is at the same time here and not here.  Heracleitos would answer to him that motion is not really a removal of an identical object from place to place, but an evolving process where the identity of the moving one collapses-composing and therefore it is always different; so he would insist that: the moving object being different in a every different position, really neither deserves to move, nor to have speed.

18

ARISTOTLE,  ΠΕΡΙ  ΚΟΣΜΟΥ  396b 7

10.   συνάψιες ὅλα καὶ οὐχ ὅλα ξυμφερόμενον διαφερόμενον 

        συνᾷδον διᾷδον καὶ ἐκ πάντων ἕν καὶ  ἐξ᾽ ἑνός πάντα.

Everything is “complex, not being complex”, “composes-decomposing”, “agrees to itself, disagreeing” simultaneously; plethora derives from the unique and unique from the plethora.

ARIAN DIDYMOS  κατά  ΕΥΣΕΒΙΟΝ Ε.Π. XV 20.

12.   ποταμοῖσι τοῖσιν αὐτοῖσιν εμβαίνουσιν ἕτερα καὶ ἕτερα ὕδατα 

        ἐπιρρεῖ καὶ ψυχαὶ ἀπὸ τῶν ὑγρῶν ἀναθυμιῶνται.

In the same river continuously, other waters enter and other go out; they are evaporated also. 

Comment: An event is not only modified by the passing through elements, but the elements are modified by the event also. (The inter-reaction principle of dialectics).

PORPHYRIOS είς Ξ. 200

103.   ξυνὸν γὰρ ἀρχὴ καὶ πέρας (ἐπὶ κύκλου περιφερίας).

Beginning and end is a common place (in the cycle periphery).

Comment: This fragment reminds Parmenides: ξυνὸν δὲ μοί ἐστιν ὁππόθεν ἄρξομαι τόθι γὰρ πάλιν ἱξομαι αὖθις  (i believe that we return to the point we depart once).  Parmenides believed that world’s evolution process is finite and phenomenal, thus world is a spherical-closed system;  on the contrary, Heracleitos accepts the world as an open and infinite system. So the part of the fragment “in the cycle periphery”,  seems to be an explicative adaptation of Porphyrios. To my opinion this adaptation doesn’t match to the Heracleitian spirit. This should rather be: “every end is at the same time a beginning”; because, every-thing being contradictive is dithyrambic; it passes simultaneously and continuously by two opposite doors; the door of birth and the door of death, the door of the beginning and the door of the end, etc. 

HIPPOLYTE ΙΧ 9.

53.    πόλεμος πατὴρ πάντων ἐστι.

ORIGENES,  Α‘Α  ΕΛ”Ο’ VI 42.

80.    εἰδέναι δὲ χρὴ τὸν πόλεμον εἶναι ξυνὸν καὶ δίκην 

         ἔριν καὶ γινόμενα πάντα κατ᾽ ἔριν καὶ χρεώμενα. 

War is the father of every-thing. We must know that war is common element of every-thing and every-where; Dike is Eris. Everything is a result of quarrel and necessity.

Comment: War exists every-where, being the struggle of the opposites inside beings and overflows out of them when it is necessary.  (Justice is quarrel and fighting).

                                                                                                                 19

KLEMES,  ΣΤΡΩΜΑΤΕΙΣ  IV 16.

24.    ἀρηιφάτους θεοὶ τιμῶσι καὶ ἄνθρωποι.

Gods and men honour the ones who obey to the demands of Ares. 

KLEMES,  ΣΤΡΩΜΑΤΕΙΣ  50.

25.    μόροι γὰρ μέζονες μέζονας μοίρας λαγχάνουσι.

The more dead they are the greater honours they enjoy

PLUTARCH, ΣΥΜΠΟΣΙΑΚΩΝ ΠΡΟΒΛΗΜΑΤΩΝ Γ644F.

96.    νέκυες γὰρ κοπρίων ἐκβλητότεροι.

Dead are of less worth than excrements

ΓΝΩΜΟΛΟΓΙΟΝ,  VATIC. 743

132.   τιμαί θεοὺς καὶ ἀνθρώπους καταδουλοῦνται.

The honours enslave men and gods.

Comment: The tradition to honour everyone who’s only characteristic is to be dead, has no meaning; on the contrary, dead heroes must be honoured by following their example. 

    Formal and Typical process though, is suitable to them who “the more dead they are, the more honourable should be”.

HIPPOLYTE  ΙΧ 10.

62.    ἀθάνατοι θνητοί, θνητοὶ ἀθάνατοι, ζῶντες τῶν ἐκείνων 

         θάνατον, τῶν δὲ ἐκείνων βίον τεθνεῶτες.

We are mortal-immortal, we live our death and we die our life.

Comment:We are in a state of collapsing-composition. We live-dying every our moment.  That is the contradiction of existence (the Dithyramb).

PLUTARCH, ΠΕΡΙ ΔΕΙΣΙΔΑΙΜΟΝΙΑΣ 166C.

89.    τοῖς ἐγρηγορόσιν,  ἕνα καὶ κοινὸν κόσμον εἶναι,  

         τῶν δὲ  κοιμωμένων ἕκαστος εἰς ἴδιον ἀποστρέφεσθαι.

The awaken people participate to the common world of all other people, the sleeping ones turn to their own world.

Comment: Literally that is so; but deeper, awaken people are the clever ones, who participate in the social and political proceedings. More clever though, are the people who perceive this common world by means of the Logos.

20

HIPPOLYTE,  ΕΛΕΓΧΟΣ ΙΧ 9.

50. οὐκ ἐμοῦ ἀλλὰ τοῦ λόγου ἀκούσαντας ὁμολογεῖν σοφόν ἐστιν ἓν  πάντα εἶναι. 

According to Logos, we must agree that every-thing coincides to the Unity. The Unity, dialectically is not an accumulation of objects or materials, but an interacting-evolving Whole, as living Essence.

DIGENES THE LAERTIAN,  ΙΧ 1.

41.   ἕν τὸ σοφόν,  ἐπίστασθαι  γνώμην,  ὁτέη ἐκυβέρνησε πάντα διὰ  πάντων.    

Wisdom is to understand Logos. The one which rules everything through the others.

Comment: The One is accomplished by plethora and plethora by one. One and plethora being in a continuous dialogue and interchange, compose a Unity (whole). This One is Logos, that is the eternally evolving motion, (the contradiction mechanism of existence),   which governs everything through the others.

[The Ἐόν (the Existing One) of Parmenides, oppositely to his claim, cannot exist as a whole. This is the sum of the immortal elements, light and darkness*, whose limits being inviolable, are complementary to each other. There is an antinomy there: Thought Parmenides vanishes “Not-Being” from the correct thinking, the darkness, which is the not existing of light (No-Light), continuous to exist as Something inviolable. He has climbed up on the platform of rationalism, by a contradictive ladder and since he did not need it anymore, he threw it away, forgetting it].

   *The Parmenidian rational reply to the Heracleitian dialectics, will be presented after the presentation of the pre-socratic dialectics.

     At the Heracletian way of thinking, darkness and light compose a contradictive unity, where the opposites extend interacting, but do not leave any inviolable limits in between each-other. On the contrary Parmenides believes that the dialogue of the opposites, light and darkness elements, (photons and “scotons”) do not violate their ultimate limits; this way the evolving process, as it was conceived by Parmenides, was contra-positive and phenomenal. Thus since the terms of the evolutional system have been set, all the “games”, which represent its final limits, are ideally from the beginning, waiting to be utilised from the system’s operation. For that reason the phenomenal process must always be finite and no one is able to say, “if terms or limits are before or after. So the limits could be named “synthetic prototypes of the end”.  This way another antinomy of rationalism rises again in the mater of “time consequence”. These prototypes compose a closed system, being a sum of many ideal ultimate elements, returning this way to the Ideas of Plato.  The Ideas being eternal, are away from a beginning or an end, being simultaneously departure and destination and because they dispose this character, exist all together, without time and space consequence.     Ideas as elements of logic, being the Things Their-Selves of the rational logic process aren’t objective, the way determinism needs badly, creating this way rational antinomies.  That has being revealed by Plato in his dialogue “Parmenides”. It seems that except of Parmenides himself, in his poem “About Nature”, no one else of ancient philosophers, accepted rationalism as infallible logical instrument, but as a conventional one.  

                                                                                                                     21

DIOGENES THE LAERTIAN IX 1

40.  πολυμαθίη νόον ἔχειν οὐ διδάσκει,  ἡσίοδον γὰρ ἄν ἐδίδαξε καὶ  

       πυθαγόρην αὖτίς τε καὶ ξενοφάνεά τε καὶ ἑκαταῖον.

Polymathy, (erudition-scholastic learning), can teach no one. Because it would have taught Pythagoras, Xenophanes and Ecataeos.

DIOGENES THE LAERTIAN VIII 6 

129.  πυθαγόρης μνησιάρχου ἱστορίην ἤσκησεν ἀνθρώπων μάλιστα 

         πάντων καὶ ἐκλεξάμενος ταύτας τὰς συγγραφάς ἐποιήσατο 

         ἑαυτοῦ σοφίην πολυμαθίην κακοτεχνίην.

Pythagoras studied hard, gathered and learned almost everything other people wrote and finally he succeeded “polymathy” and “kakotechnia”.

Comment: Polymathy is rejected by Heracleitos, being the knowledge ethos of accepting a world consisted by many positive ideal or material elements. This presupposes a closed, finite and phenomenal world, which cannot give birth to the New and this is the reason of “kakotechnia” (gives bad birth, dead birth).  It leads properly around the past, but when it concerns about the new and the future it is a bad adviser. 

    As we noticed before any system consisting of absolute and unchangeable elements, is closed; that’s why its function produces a specific number of predetermined games which will be repeated for ever, being a “kakotechnia”.

PLUTARCH TO KOLOTES 1118C.

101.  ἐδιζησάμην ἐμεωυτόν.

I looked into myself, i analyse myself.

Comment: The word “Ἐδιζησάμην” (i search) derives from the word “Δίζως”.  Δίζως was the god Πὰν (Pan), who was man and animal having double and contradictive nature.  So the most inside we ender to ourselves, the farther we travel out to universe. 

    Identity, according to Heracleitos, consists of contradictive elementary units fighting their-selves and each-other.   According to contradictive logic an elementary unit tending to zero, simultaneously tends to infinite; that is why the deeper we enter inside ourselves, the most far away we travel out, to universe. 

22

DIOGENES THE LAERTIAN IX 7 

45.    ψυχῆς πείρατα ἰὼν οὐκ ἂν ἐξεύροιο πᾶσαν ἐπιπορευόμενος 

         ὁδόν,  οὕτω βαθὺν λόγον ἔχει.

The limits of human soul are so deeply inside, that we cannot find it. 

(It is impossible to reach the depth of something which expands to infinite).

Comment: Human soul is the Heracleitian Logos of “the great in to the small”, of “zero to infinite”, of “immediate to immobile”. The great dives into the small and the small expands to the great, then human elements tending to zero simultaneously tend to infinite. The Element Dialectically is dithyrambic, passing two opposite doors at the same time.

Psyche (human soul) for the pre-socratic thinkers, is the ultimate contradiction structure of every specific being; that includes a face of the whole from the point of view of the specific being. Soul tending to the ultimately small tends simultaneously to infinite. The soul dialectically could nowadays be DNA.

PLUTARCH, KORIOLAN 22 

85.    θυμῷ μάχεσθαι χαλεπόν,  ὅ γάρ ἄν θέλῃ ψυχῆς ὠνεῖται.

It is very hard to fight against our desires, because it exchanges everything with our soul.

Comment: It is hard to improve ourselves, because we must change our character, our soul, and “ψυχῆς πείρατα ἱὼν ούκ ἂν έξεύροιο”, we cannot find the limits of our soul.

     To improve ourselves, we must fight our hereditary mechanism, our DNA, which is bottomless, but at the same time, this is our main ally.

STOVAIOS, ANTHOLOGY I  178

115.     ψυχῆς ἐστι λόγος ἑαυτὸν αὔξων.

Our soul is the dynamic meter of self evolution.

Comment: Our soul can be improved only by itself and this can be accomplished by the dynamic balance of the inner and small, to the faraway and big. This balance is the ultimate contradictive elementary mechanism, the DNA.        To my opinion only this one could be named “soul”.

ORIGENIS AGAINT KELSOS VI 12.

78.     ἦθος ἀνθρώπειον μὲν οὐκ ἔχει γνώμας, θεῖον δὲ ἔχει.

Human behaviour is unexpected, while divine is expected.

Comment: The human being, who created his gods, can expect their behaviour, but the behaviour of human being, which is the result of the bottomless world evolution process, is unpredictable.

                                                                                                                    23

HIPPOLYTE  IX 9 

52.     αἰὼν παῖς ἐστι παίζων πεττεύων,  παιδός  ἡ βασιληίη.

Time is a child playing the “pessoi” game; That is the kingdom of the child.

Comment: “Pessoi” was a both luck and skill game. Men played it using strategy and logic, being outside and observing objectively the game. The child plays with passion being inside the game.  Child playing, stops to be itself, traveling into the Other (the game). The worth of the game is that child overpasses itself, being in another reality. 

The kingdom of the child is where time exists only Now. Time being only Now overpasses itself being contradictive: Past does not exist, Future also, only Present exists being the changing edge of the fading Now.  A zero edge between past and future being eternal in its nihility. This is the nude contradiction. Therefore world is always only Now, being continuously Different. If every-thing differs a little, the world as a whole is in a continuous explosion of difference and simultaneously, being immediate is always back to its former position.

The Heracletian contradictive approach for all events of nature, does not leave any doubt that accepts a world where opposites are in a continuous inter-action each-other, as Time and Space also do.  Anaximander claimed the Time is related to the birth and death of beings; and Zeno with his paradoxes, revealed the relativity of Space, Time, Motion and Beings.  He also claimed the relativity of Small and Big, Immediate and Immobile.

    Relativity wasn’t revolutionary approach these days but consecrative one. 

Greeks of the prehistoric and archaic period, believed that world was born from the unity of Rea and Cronos.  Rea could mean the universal flow of the primordial life and Cronos could mean Chronos  (Χρόνος-Time, ὡρό-νος, Ουρανός-sky,);  Cronos gives birth to the limits, the periods (the seasons), the Hours (ὧραι).  Cronos rotating gives Rea the meaning or space and their relation is the universal dance, which is the Existence as space-time unity, the contradictive relation of flow and rotation (rhythm); these, as opposites, fighting each-other, give simultaneously birth (identity) to each-other. This unity-relation is Life itself (Zeus), who transforms the Space to Flow and the Time to Rhythm, the time to duration and space to extension.

DIOGENES THE LAERTIAN   ΙΧ 2

42.     τόν τε ὅμηρον ἄξιον ἐκ τῶν ἀγώνων έκβάλλεσθαι καὶ 

          ῥαπίζεσθαι καὶ ἀρχίλοχον ὁμοίως.

Homer and Archilochos should be rejected from the triumphant of festivals.

24

Comment: Heracleitos loved poetry, because his aphorisms are at least poetic. His opposition to Homer and to Archilichos, was not aesthetic but ideological: Heracleitos being Ionian and for this reason Pelasgean and aristocrat, was inspired by the tragic spirit. 

     After the Thera volcano eruption, the volcanic wave over-flowed and drown all the Pelasgean cities located near by the sea. Then Achaeans, the mountaineer shepherds, came as conquerors of the devastation, imposed their semi-barbarity.  Homeric poems narrated their live and “glory”.   

     Heracleitos believed that homeric stories, being the Bible of the Greeks, divinised violence, infamy and nonsense; According to Heracleitos, the Homeric stories, where a negative examples to follow.

     Archilochos, according to Heracletos, was arrogant, hubristic and immoral; he was a hired soldier. The shield was not sacred for him; the battle was not a sacrifice; it was not a sacred theatre; he was a butcher, a slaughterer.  The reason for the hired soldier to fight was money or loot.

     What impression would have made to Heracleitos, the verses of Archilochos where: “He threw away his shield during a battle and he would find another better”. The battle for Heracleitos was a horrible, but sacred action, like the sacrifice of the bull. The child is  sacred, the victim is sacred; the dead fighiter-victim has been purified and deserves a decent burial. The winner is bloody, profane and to be purified he must fertilise the blood to civilisation. Moreover the verse of Archilochos, where, “He can lead dithyramb, the sweet song of Dionysos, fulminated in his head by wine”. was hubristic to the Bacchic spirit. ―A drunkard butcher, as a leading priest of tragedy―.  For Heracletos the drunkard is not ecstatic to be in the state of “Bacchia”. 

 PLUTARCH, KORIOLANOS 38 86. 

86.     ἀπιστίῃ διαφυγγάνει μὴ γιγνώσκεσθαι.

Infidelity disinclines from ignorance.

―doubt leads to knowledge

KLEMES  STROMATEIS III 24   

18.    ἐάν μὴ ἔλπηται ἀνέλπιστον οὐκ ἐξευρήσει, ἀνεξερεύνητον ἐὸν καὶ ἄπορον.

Without hope, hopeless cannot be discovered

HIPPOLITE IX 38

55.     ὅσων ὄψις ἀκοὴ μάθησις, ταῦτα ἐγώ προτιμέω.

I prefer as elements of knowledge these i listen and i see.

I believe to the worth of experience.

ARISTOTLE  ABOUT SENSES 443a 23 

7.      εἰ πάντα τὰ ὄντα καπνὸς γένοιτο, ῥῖνες ἄν διαγνοῖεν.

If everything was made of smoke, we would investigate by our nose.

 Experience is not enough.                                                                                                                  

                                                                                                                                          25

POLYVIOS  XII 27 

101α.     ὀφθαλμοί γὰρ τῶν ὤτων ἀκριβέστεροι μάρτυρες.

Eyes are more accurate witnesses than ears.

I prefer these i see than these others tell me.

I believe to the worth of experience.

SEXTOS VII 126 

107.      κακοὶ μάρτυρες ἀνθρώποισιν ὀφθαλμοί καὶ ὦτα βαρβάρους ψυχὰς ἐχόντων.

The eyes and ears of them who have barbarous soul are not reliable (not good evidence).

Comment: Barbarity is not to know how to see and how to listen. Civilisation is the ability to approach and elaborate experience rationally.  

   Heracleitos believed, that experience must be evaluated by Logos.  Barbarians know very well to accept things as identical to themselves, but they do not know to approach the world in its differential and contradictive way. This kind of approach and analysis is far from barbarity. 

KLEMENS TO STROMATEIS V 60.

 29.     αἰρεῦνται γὰρ ἓν ἀντί ἀπάντων οἱ ἄριστοι, κλέος ἀέναον 

           θνητόν, οἱ δὲ πολλοὶ κεκόρηνται ὅκωσπερ κτήνεα.

The best thinkers instead of searching for Many things, look for the One (Logos), which is the glamour of dying (fainting) knowledge.   The majority of the people are satisfied as animals (to these they come to immediate contact).

Comment: Logos is eternally dying, because its content changes continuously. It exists being Always Other.  Moreover, because of its continuous changing, being One, seems at the same time, to be Many.

THEOFRASTOS  METAPHYSICS 7a.

124.     ὥσπερ σάρμα εἰκῆ κεχυμένων ὁ κάλλιστος κόσμος.

The beautiful world looks like rubbish thrown here and there.

Comment: Hazard and necessity; Hazardous deeply inside has a secret-hidden multi-dimensional reason very difficultly traced; so “the hidden harmony is better from the obvious one”;  but if someone has barbarian eyes, it is obvious that he cannot trace it.

26

DIOGENES THE LAERTIAN  IX 73

47.      μὴ εἰκῆ περὶ τῶν μεγίστων συμβαλλώμεθα.

We must not deal thoughtlessly with the very great and important things

Comment: Let’s deal with the small and everyday things, because these dynamically and potentially, contain the great.

MARCUS ANTONINUS IV 46. 

74.      οὐ δεῖ ὡς παῖδας τοκεώνων.

We must not follow blindly the steps of our family ancestors.

(We must violate tradition to accomplish the New, regardless how dangerous it is).

Comment: Heracleitos is presented as a conservative oligarchic aristocrat. In reality though, he was a revolutionary mind and true democrat; he was in a critical position against the “democrats” who demolish democracy in order to “save” it.  Oppositely to them, his friend Hermodoros, who was banished as oligarchic, by these “democrats”, wrote laws for the democratic Rome. Moreover, Heracleitos convinced the Tyrann Melagonas to resign.  He also did not accept the invitation to visit Great King Dario. 

DIOGENES THE LAERTIAN IX 2 

44.     μάχεσθαι χρὴ τὸν δῆμον ὑπὲρ τοῦ νόμου ὅκωσπερ τείχεος.

Citizens must fight for their lows as much as they fight for the city fortress (for social justice and for liberty).

Comment: Lows are abolished by the tyranny and oligarchy, since the walls of the city by the Persians, who usually were allies of oligarchs.

CLEMES TO STROMATEIS V 116 

33.     νόμος καὶ βουλῇ πείθεσθαι ἑνός.

We must obey the law and the will of the one (Logos)

(Logos is the contradictive Meter of every specific event)

DIOGENES THE LAERTIAN  IX 1 

43.     ὕβριν χρὴ σβεννύναι μᾶλλον ἣ πυρκαϊήν.

It is more urgent to fight against hubris, than conflagration of the city.

Comment: the arrogance of pseudo-democrats is more dangerous than conflagration. The result of fire can be overpassed by hard work, the result of political arrogance can be overpassed by blood, violence and unforgotten hate.

CLEMES,  STROMATEIS III 14 

20. γενόμενοι ζώειν ἐθέλουσι μόρους τ᾽ἔχειν μᾶλλον δὲ ἀναπαύεσθαι

      καὶ παῖδας καταλείπουσι μόρους γενέσθαι.

They are born and intending to live doing nothing, receive death; and they give birth to children, leading them in the same death process of doing nothing.

                                                                                                                    27

STOVAIOS ANTHOLOGY IV 40 

119.      ἦθος ἀνθρώπῳ δαίμων.

God for every man is his own ethos (his character).

Comment: According to Heracleitos, god is neither the kind creator nor the zealot punisher; it is the contradictive elements, whice compose the human character in a contradictive Metron (human Logos). This is the contradictive multi-dimensional recording of the evolving universe inside the human biological hereditary mechanism; this mechanism, being contradictive, gives to any person the ability to have free will.  The choice to create his own character, is for any man, his god

ORIGENIS AGAINST CELSOS  VI 12.  

12.  ἀνὴρ νήπιος ἤκουσε πρὸς δαίμονος ὅκωσπερ  παῖς  πρὸς ἀνδρός.

The immature man obeys to his daemon like the child obeys to man.

Comment: Heracleitian Daemon, is the force of living nature inside every man; Man, being born, has that element uninfluenced by the social process, being his vital impulsion; When he cultivates this natural internal force though, integrates it to maturity and ethos.

HIPPOLYTE IX 10 

60.  ὁδὸς ἄνω κάτω μία καὶ ὡυτή.

Uphill road and downhill road is one and the same.

(the unity of the opposites).

ARISTOTLE METEOROLOGY 335 a 13 

6.    ἥλιος οὐ μόνον νέος εφ᾽ἡμέρῃ ἐστίν, ἀλλ᾽ἀεί νέος καθάπερ 

       ἡράκλειτός φησι. 

The sun is not only everyday new, but as Heracletos claimed, always new.

Comment: Xenophanes claimed that sun is every day new: “τὸν δὲ ἥλιον, ἐκ μικρῶν πυριδίων ἀθροιζομένων γίνεσθαι, καθ᾽ἑκάστην ἡμέραν”.  (the sun is composed by small fire elements, photons, gathering every morning and scatter every night).  On the contrary Heracleitos claimed that “the sun is always new”. This difference reveals a deeper opposition between them:  Xenophanes accepts evolution, but being phenomenal; according to him: the world, deeply inside, do not change. It consist of unchangeable, not known-unspeakable (άρρητα) elements. These are the terms of a closed predetermined, finite, phenomenal and deterministic system. This way the Sun rising from chaos, is composed every day from the same (πυρίδια-pyridia) photons, being new but absolutely similar to the one it was before (because according to him the world eternally repeated, being a closed system). On the contrary, Heracletos believed that evolution is real and the sun always composes-collapsing, being a little different and in an other position always.

28

THEMISTIOS LOGOI  5 69 

123.      φύσης κρύπτεσθαι φιλεῖ.

Nature likes to be hidden.

HIPPOLYTE IX 9

54.       ἀρμονίη ἀφανής φανερῆς κρείττων.

Hidden harmony is higher than the obvious one.

Comment: The world being multi-dimensional, has many levels of reality, covered by the obvious surface; yet, at the hidden bottomless part of the world, exists the higher, the contradictive harmony. 

Experimental criticism observes the world “by barbarian eyes”, “as rubbish scattered accidentally, hear and there”; the “beautiful world” though, can be revealed only by the  Logos of Heracleitos.

PLUTARCH   ABOUT PYTHIA 397 . . . 404 D

92.    σίβυλλα μαινομένῳ στόματι ἀγέλαστα καὶ ἀκαλλώπιστα καὶ 

         ἀμύριστα φθεγγομένη χιλίων ἐτῶν ἐξικνεῖται τῇ φωνῇ διὰ τὸν θεόν.

         93.    ὁ ἄναξ, οὗ τὸ μαντεῖόν ἐστι τὸ ἐν δελφοῖς, οὔτε λέγει οὔτε κρύπτει ἀλλὰ  σημαίνει.

Sibyl inelegant, uncared in furious and frenzy mouth, vocalises the spells of the Delphian God in a sacred madness;  this speech being launched into the future for a thousand years, neither hides, nor reveals, but it means.

Comment: God is the Logos of nature, the Dionysian dithyramb; The contrdictive one, therefore it steps simultaneously on both sides of thinking: negation and affirmation. Logos (the contradictive speech) travels for 2500 years; its destination is quantum-mechanics.

PLUTARCH, ΕΙ ΠΡΕΣΒΥΤΕΡῼ ΠΟΛΙΤΕΥΤΕΟΝ 787C.

97.      κύνες γὰρ καταβαΰζουσιν ὧν ἂν μὴ γινώσκωσι.

Dogs bark those, they do not know.

(Lao-Tsu:  Scholastics and sceptics listening a great truth shall laugh; if not, maybe it is not a great truth.

KLEMES, STROMATEIS II 29

17.      οὐ γὰρ φρονέουσι τοιαῦτα πολλοί ὁκόσοι ἐγκυρεῦσιν, οὐδὲ 

           μαθόντες γινώσκουσιν, ἑαυτοῖσι δὲ δοκέουσι. 

The people who search, thinking philosophically, are not learners, but users their own mind.

  Comment: This work of mine has the ambition to fill a gap on logic, which tractati about Heracleitos have left behind. The majority of them do not differ each-other. As Heracleitos said in fragment 17: “there are not many researchers thinking the way i propose; no one really knows something learning from others.  Someone to know must use his own mind”.     “The students of the students reproduce the already known”.                                                                                                                  

                                                                                                                                                             29CLEMES, STROMATEIS II 24

19.       ἀκοῦσαι οὐκ  ἐπιστάμενοι οὐδ᾽εἰπεῖν.

Scholars (learners), really know nothing and have nothing to say.

Knowledge and research is a dynamic process, a journey into the unknown. The unknown cannot be taught but can only be discovered.

CLEMES PROTREPTIKOS 34 

15.      εἰ μὴ γὰρ διονύσῳ πομπήν ἐποιοῦντο καὶ ὕμνεον ᾆσμα 

           αἰδοίοισιν, ἀναιδέστατα εἴργαστ᾽ἄν,  ὡυτὸς δὲ ἀίδης καὶ 

           διόνυσος, ὅτεῳ μαίνονται καὶ ληναΐζουσιν.

If the fallic ceremony was not for the sake of Dionysos, would be an impudent behaviour;  Ades is Dionysos himself, for whom they are frenzy and proceed in their furious orgies.

Comment: Heraclitos points out the decay of the Dionysian spirit at his days: the participants were forgetting that “dithyramb” is the simultaneous passing through two opposite doors, the door of life and the door of death; the worship of Dionysos-Bacchus, who is the spirit of life and fertilisation, is simultaneously the worship of Ades (death).

    Tragedy is the joyful-sorrow; So the participants of the bacchic ceremonies should not foolishly transformed it to a joyful-happiness.  On the contrary to them, Dithyramb must point out the contradiction of the tragic event and to find the Metron of happiness and sorrow (the Logos).

Could Heracleitos be alive nowadays?    

When Niels Bohr was named knight by the king of Denmark, to be honoured for his achievements in science, the symbol he chose for his escutcheon was the Parmenidian and oriental one of the unity of the opposites.      contraria complementa sunt (opposites are complementary)

According to scientists who accept that quantum-mecanics give sufficient description of the quantic situation, the quantic objects do not have dynamic attributes before measurement,  being in a state of potentiality;  the dynamicattributes of these objects are utilised during their measurement and observation. Moreover these scientists claim that during the action of measurement, the measurement instrument, the object to be measured and the observer, compose a quantic unity. They also claim, that all this process take place in an under-quantic world of potentiality, relating to a superluminal speed and an indeterminate and not objective behaviour to the experimental process.  Moreover, some scientists suspect the existence of some instantaneous inter-reactions in this territory. For this reason, determinists consider quantum-mecanics, for the time being, to be inadequate for the quantic objects description, believing that some hidden parameters are missing. 

Though Bohr was aware of the Einstein’s indication that: “quantic theory accepts silently the existence of instantaneous interactions”, proposed complementarity as a kind of evasion to the previous indication.  

30

 If there is an instantaneous process in quantic world, this world should be of a contradictive nature and not appositive as complementarity indicates. Complementary and appositive approach, presuppose that deeply inside the existence, the opposites should be really independed and the observed object identity, to be absolute and not conventional; in this case interactions could be superluminal but not instantaneous. On the contrary the contradictive approach at this level of potentiality, accepts the existence of instantaneous interactions and therefore opposites to inter-expend each-other, without leaving any margin of independence between them or existence of an absolute identity. We also see that in this field of scientific antagonism, the so called anti-determinsits, make a good effort,  to leave an open door for determinism to pass in the future. On the other hand, determinists overpass Einsteins objections, accepting superluminal sub-quantic inter-actions, along with the hidden parameters, which are invisible because only quantic (photon) proceedings we are able to see. There are also some scientists extremely anti-determinists moving violently to mysticism; they believe that the limits of human logic are terminated there, and science must accept its weakness to explain completely the quantic events and consequently the world.

    As for the traditional determinism let us see what Einstein, who places himself to the side of determinism, has declared in the interview given to John S. Birek at 1930:  “our course is predetermined by components we do not control. Especially by mysterious glands by which nature does distill its authentic essence of life,  our inner secretions. . . .I am determinist and i do not believe the existence of real free will...” The great scientist and humanist was Parmenidian, Aristotelian and Kartesian; therefore according to him, regardless what he insists, the world should be closed, accomplished and predetermined. N. Bohr does not accept determinism; his choice though of the complementarity symbol, as the ultimate shelter of truth, indicates an unconscious Parmenidian conception; it’s obvious that Bohr do not accept a contradictive nature of the world and therefore does dot accept dialectics. 

                                                                                                                     31

 Modern scientists have invest all their existence to rationalism and formal logic being more aristotelian than Aristotle; they are not so revolutionary to reject their formal logic research behaviour and at its position to put another one.  That’s why Heracleitos has something new to say: According to him, world is of a contradictive nature, motion is the essence and things are its attributes; Logos is the way world is and could be said; the principle of Identity is contradictive and self-overpassing; the principle of causality is amphi-coursial (both-way) and the chain of ration infinitely dimensional. Time, Space and Motion, Complete and Vacant, Great and Small, and evolution process, get other faces which need another logical approach: the Heracletic Dialectics.

PARMENIDES (515-440)  AND ZENO (490-430)

The limits of thinking are between Parmenidian rationalism and Heracleitian Dialectics.  It is said that Zeno was friend, student and follower of Parmenides; that is the reason doxographs interpret his prepositions under the Parmenidian logical terms; This way Zeno seems as a strange paradoxologist. If we accept him as a dialectic thinker though, his paradoxical syndrome vanishes. Aristotle refers to him as the father of dialectics, but it is possible this would be a negative characterisation of assimilation to sophistry.  In the present tractatus Zeno is considered as one of the great workers of dialectics, together with Anaximander and Heracleitos.  It is sure that all archaic physical philosophers were dialectic, but i distinguish those three, because they don’t make any burying to formal rationality logic against dialectics.

Plato, in his dialogue “Parmenides”, presents him to be very different than Permenides we discover in his own ontological poem “About Nature”.  That is an enigma we will never be able to solve. It is possible that Parmenides wrote this poem when he was young (that’s why the Muse cals him “κοῦρον”-young man) and maybe later he changed his aspects. Although doxographs present Zeno as follower of Parmenides, it’s obvious that  the Platonic “Parmenides”, rather follows the Zeno’s aspects. Maybe Plato did not present the characters of his dialogues, absolutely as they were, but violated their personalities and their ideas for the sake of his needs; never the less, though the result of his work was rather magnificent. Even Socrates presented by Plato is very different, from the one presented by his other student and follower Xenophon. It is also strange, that neither Plato nor Aristotle mentioned the offer of Parmenides to rationalism, formal logic and determinism. I also believe that Zeno was misunderstood by the doxographs, 

who consider him to be a follower of Parmenides.  To my opinion, Zeno’s aspects were firstly against the Parmenian about “not existence of real motion”.  The doxographs, being writers of very lower worth, were not been able to understand the tractati of genius thinkers they referred to, simplified them (of love, hate or ignorance) for the use in their writings. I could imagine the demonic Zeno to be the intellectual dog of some one, even if hi would be the magnificent Parmenides.

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THE PARMENIDIAN RATIONAL REPLY TO THE HERACLEITIAN DIALECTICS

(Parmenides considers contradiction synonymous to inconsistency and falsehood)

Fragment 1, στ. 24-32

   ὦ κοῦρ᾽ἀθανάτοισι συνάορος ἡνιόχοισιν,

   ἵπποις ταί σε φέρουσιν ἱκάνων ἡμέτερον δῶ,

   χαῖρ᾽, ἐπεὶ οὔτι σε μοῖρα κακὴ προὔπεμπε νέεσθαι

   τήνδ᾽ ὁδόν (ἧ γὰρ ἀπ᾽ἀνθρώπων ἐκτὸς πάτου ἐστίν),

   ἀλλὰ θέμις τε δίκη τε. χρεὼ δὲ σε πάντα πυθέσθαι

   ἠμὲν ἀληθείης εὐκυκλέος ἀτρεμὲς ἦτορ

   ἠδὲ βροτῶν δόξας, ταῖς ούκ ἔνι πίστις άληθής.

   ἀλλ᾽ ἔμπης καὶ ταῦτα μαθήσεαι, ώς δοκοῦντα

   χρῆν δοκίμως εἶναι διὰ παντὸς πάντα περῶντα_

Young man, whom immortal charioteers brought to my dome, be pleased, because it was not an ill fate to bring you here; far from the footsteps of men, along with the path of Themis and Dike (Legality and Justice, logic and ratio). It is necessary for you to know both ways of thinking; not only the way of the solid spirit of Truth, but also about the beliefs of the mortals, which no one can depend on. You must also know about them, because you should be experienced of all the ways of thinking.

Fragment 2

   εἰ δ᾽ ἄγ᾽ἐγὼν ἐρέω, κομίσαι δὲ σὺ μῦθον ἀκούσας,

   αἵπερ ὁδοὶ μοῦναι διζήσιος* εἱσι νοῆσαι,

   ἡ μὲν, ὅπως ἔστιν τε καὶ οὐκ ἔστι, μὴ εἶναι,

   πειθοῦς** ἐστι κέλευθος (ἀληθείῃ γὰρ ὀπηδεῖ),***

   ἡ δ᾽ ὡς οὐκ ἔστιν, τε καὶ ὡς χρεῶν ἐστι, μὴ εἶναι,

   τὴν δή τοι φράζω παναπευθέα ἔμμεν ἀταρπόν_

   οὔτε γὰρ ἂν γνοίης τὸ γε μὴ ἐόν (οὐ γὰρ ἀνυστόν)

   οὔτε φράσαις.

Now pay careful attention to what a have to tell you: There are two contradictory-inconsistent ways of thinking and open to doubt. The first one is that nothing can Be-NotBeing; this is the road of persuasion, out of which truth leaks away (it follows closely but is not the truth itself). The other way is the one of “Not-Being”; This road of thinking is obliged, not to exist. I strongly dissuade you from this path, because “Not-Being”, cannot be sensed, cannot be known and cannot be spoken.

  LIDDELL AND SCOTT  dictionary

δίζω: i am in a state of doubt,  δίζημαι: i search, i look for

δίζησις: research, δίζως: the one having double nature

διζήσιος (my conclusion): the doubtful in research, the contradictory one

Πείθω: persuade, convince with deceptive wards, with supplication, corrupt with money

ὀπηδεῖ, ὀπήδέω: ὀπή: hole, δέω: i am obliged. (my conclusion): i am obliged to act according the existence of a hole,  to leak away through a hole, to follow splitting away by a hole.                                

                                                                                                                                        33

Comment: Up to the times of Parmenides, the “identity” of things was believed to be contradictive; everything was accepted in a dynamic way, at least by the Physiologists (the philosophers whose work was associated with Nature). They felt that objects and generally reality, would be events of a Universal Essence, which was accepted as Motion Itself and as Evolution of Nature.  They believed that everything exists in a continuous change and modification, being self-refuting and for this reason contradictive.

     Parmenides, by one hand, eradicates Not-Being from thinking; thus with one stroke of pen, he proposes the two principles of the rational critic thinking and of the formal logic.

A.  Nothing can Be-Not Being (The formal rationality principle of Not-Contradiction).

B.  Everything can only Be. Not Being cannot exist. (This preposition in relation to the first one gives the formal rationality principle of Identity). Everything not associating with “Not-Being”, can only “Be” Itself.

Fragment 3

   τὸ γὰρ αὐτό νοεῖν ἐστίν τε καὶ εἶναι

Intellect (Logic) and Being coincide. 

Comment: Since Thinking and Being coincide, nothing can escape from logic, so we are able to have infallible logical conclusions. (That reminds “cogito ergo sum” of Cartesius and “logical is real and the real is logical” of Hegel)

Fragment 4

   λεῦσσε δ᾽ὁμῶς ἀπεόντα νόῳ παρεόντα βεβαίως_

   οὐ γὰρ ἀποτμήξει τὸ ἐὸν τοῦ ἐόντος ἔχεσθαι

   οὔτε σκιδνάμενον πάντῃ πάντως κατὰ κόσμον

   οὔτε συνιστάμενον.

(Since Intellect and Being coincide) we are able to enlighten by means of logic, from the present situation, as well as an absent one; because the Existing One cannot be separated from any kind of existence (Intellect from Being), whether regarding world as a whole or as an accumulation of separate specific objects.

34

Comment: He stresses, that the logical principles he proposes for the deductive process (going from the known situation by means of logic to the unknown), apply both to the whole and to the specific objects as well. So Logic is a reliable instrument for correct thinking.

Fragment 5 

   ξυνὸν δέ μοί ἐστι, ὁππόθεν ἄρξομαι τόθι γὰρ πάλιν ἵξομαι αὖθις.

I believe that if we depart from a point, once we will return again there.

Comment: The world is accomplished, finished and therefore it’s a closed system; so nothing can escape from Intellect. (Therefore Intellect and Being coincide).

Fragment 6 verses 1-2

   χρὴ τὸ λέγειν τε νοεῖν τ᾽ἐόν ἔμμαινε,  ἔστι γὰρ εἶναι,  μηδὲν οὐκ ἔστιν, τὰ σ᾽ἐγὼ φράζεσθαι ἄνωγα.

  It’s necessary for Speech, Thought and Being to coincide; for only “Being” exists, “Not- Being” does not exist;  This is how i advice you to think.

Fragment 6 verses 3-9

   πρώτης γὰρ σ᾽ἀφ᾽ὁδοῦ ταύτης διζήσιος <εἴργω>

   αὐτὰρ ἔπειτ᾽ἀπὸ τῆς, ἣν δὴ βροτοί εἰδότες οὐδὲν

   πλάττονται δίκρανοι, ἀμηχανίη γὰρ ἐν αὐτῶν

   στήθεσιν ἰθύνει πλαγκτόν νόον. οἱ δὲ φοροῦνται 

   κωφοί ὁμῶς τυφλοί τε, τεθηπότες´ἄκριτα φῦλα                                                                                                                                                                                                                                                                 οἷς τὸ πέλειν* τε καὶ οὐκ,  εἶναι ταὐτὸν νενόμισται 

   κοὐ ταὐτόν,  πάντων δὲ παλίντροπός ἐστι κέλευθος.

(Referring to the first of the two contradictive paths of thinking in fragment 2 verse 3): I disincline you from the first path of contradictive thinking, because mortals learn nothing from this one; they become indecisive, double minded, because perplexity in their chest deranges their mind. They behave as deaf, blind and lost, with no judgement; They doubt comparative verification certainty, because for them it Has-NotHaving any value, since they believe that everything has simultaneously an opposite way to exist.

Comment: Parmenides after the Identity and Non-Contradiction principals, proposes  the certainty  of the  comparative  verification  process;     because according to him, only this way we could go from the present and actual, to absent and hypothetic, having valuable analytic deduction and synthetic induction.

                                                                                                                     35

Comparative process:

If A is similar to B and B similar to C, then A is Similar to C.    Synthesis.

If A is similar to B and B is different to C, then  A is different to C.   Analysis.

Fragment 7

   οὐ γὰρ μήποτε τοῦτο δαμῇ, εἶναι μὴ ἐόντα_

   ἀλλὰ σὺ τῆσδ᾽ἀφ᾽ ὁδοῦ διζήσιος εἶργε νόημα,

   μηδὲ σ᾽ἔθος πολύπειρον ὁδὸν κατά τήνδε βιάσθω

   νωμᾶν ἄσκοπον ὄμμα και ἠχήεσαν ἀκουήν

   καὶ γλῶσσαν, κρῖναι δὲ λόγῳ πολύδηριν ἔλεγχον

   ἐξ  ἐμέθεν ρηθέντα

   (The word τοῦτο i translate as identity).

Because  “Identity” never will be forced to “Be-NotBeing”; so you must be away from the contradictive path of thinking and not be lured away by the habitual and usual activity; but judge everything by the way i have taught you (the well tested logical way). 

Fragment 8 verses 1-18

      μόνος δ᾽ἔτι μῦθος ὁδοῖο

      λείπεται ὠς ἔστιν, ταύτῃ δ᾽ἐπὶ σήματα ἔασι 

      πολλὰ μάλ᾽, ὠς ἀγένητον καὶ ἀνώλεθρόν ἐστιν,

      οὗλον, μουνογενές τε καὶ ἀτρεμές οὐδ᾽ἀτέλεστον, 

5    οὐδέ ποτ᾽ἧν οὐδ᾽ἐσταί, ἐπεί νῦν ἐστιν ὁμοῦ πάν

      ἕν, συνεχές,  τίνα γὰρ γένναν διζήσεαι αὑτοῦ; 

      πῇ πόθεν αὐξηθέν;  οὕτ᾽ ἐκ τοῦ μὴ ἐόντος ἐάσσω

      φάσθαι σ᾽οὐδέ νοεῖν, οὐ γὰρ φατόν ούδὲ νοητόν

      ἔστιν ὅπως οὐκ ἔστι.  τί δ᾽ἄν μιν καὶ χρέος ὦρσεν  

10  ὕστερον ἣ πρόσθεν τοῦ μηδενός ἀρξάμενον φῦν;

      οὕτως ἣ πάνπαν πελἐναι χρεών ἐστιν ἢ οὐχί

      οὔτε ποτ᾽ἐκ μὴ ἐόντος ἐφήσει πίστιος ἰσχὺς

      γίγνεσθαί τι πάρ᾽αὐτό.  τοῦ εἴνεκεν οὔτε γίγνεσθαι

      οὔτ᾽ ὄλλυσθαι ἀνῆκε δίκη χαλάσασα πέδῃσιν             

15  ἀλλ᾽ ἔχει. ἡ δὲ κρίσις περὶ τούτων ἐν τῷδ᾽ἐστιν,

      ἔστιν ἢ οὐν ἔστιν.  κέκριται δ᾽οὗν ὥσπερ ἀνάγκη 

      τὴν μὲν ἐᾶν ἀνόητον ἀνώνυμον, οὐ γὰρ ἀληθής

      ἔστιν ὁδός.  τὴν δ᾽ ὥστε πέλειν καὶ ἐτήτυμον* εἶναι.

The only way of thinking, we can speak about, remains the way of Being. There are many signposts to talk about “Being”: “Being” does not die, so there is not any birth to that; it is immortal, unique, finite, motionless, never was or will be, because it is always Now, One-continuous. What kind of birth could we seek in it? from where to where could it move or expand? No one indeed could understand or speak about Not Being, because does not exist and does not be sensed. Nothing can force to exist something before or after Zero. So either everything must coincide with the “Existing Whole” or with “Nothing”, (not existing). Therefore from “Not-Being” we cannot expect nothing to be born;  Thus there is not real evolution or absolute wast away (destruction), because logic demands it. For this reason, every judgement must lie within these boundaries: “Not-Being” or “Being”. The first one is fault, anonymous, meaningless, not a path of thinking, since the other, is the correct one, the path of comparative certainty, because every similar should rationally exist in a family group.

 LIDDEL & SCOTT * ἐτήτυμον εἶναι: To belong in the same family tomb 

   πέλειν καὶ ἐτήτυμον εἶναι: the similar belongs in the same family group

36

 Fragment 8 verses 35-40

35 οὐ γὰρ ἄνευ τοῦ ἐόντος,  ἐν ᾧ πεφατισμένον ἐστίν,

    εὑρήσεις τὸ νοεῖν.  οὐδὲν γὰρ ἦν ἔστιν ἢ ἔσται

    ἄλλο παρέξ τοῦ ἐόντος,  ἐπεὶ τὸ γε μοῖρ᾽ἐπέδησεν

    οὖλον ἀκίνητον τ᾽ἔμεναι,  τῷ πάντ᾽ὄνομα ἔσται

    ὅσσα βροτοί κατέθεντο πεποιθότες εἶναι ἀληθῆ,

40 γίγνεσθαι τε καὶ ὄλλυσθαι,  εἶναι τε καὶ οὐχί,

    καὶ τόπον ἀλλάσσειν διὰ τε χρόα φανόν ἀμείβειν.

    αὐτάρ ἐπεὶ πεῖρας πύματον, τετελεσμένον ἐστὶ

    πάντοθεν εὐκύκλου σφαίρης ἐναλίγκιον ὄγκῳ

    μεσσόθεν ἰσοπαλὲς πάντῃ…..

You cannot find intellect elsewhere but in Being, because it is recorded there. Nothing else but “Being” was exist, exist or will exist, because Being is an immobile Whole. Everything else are names, the mortals give to it, believing that evolving birth or destructive death process,“Being-NotBeing” and any kind of motion or modification, really exists. Since this one is finite, limited, absolutely spheric and fully balanced…

Fragment 8 verses 50-61

50    ἐν τῷ σοὶ παύω πιστόν λόγον ἠδὲ νόημα,

        ἀμφὶς ἀληθείης δόξας ἀπὸ τοῦδε βροτείας

        μάνθανε κόσμον,  ἐμῶν ἐπέων,  ἀπατηλόν ἀκούων.

        μορφάς γὰρ κατέθετο δύο γνώμας ὀνομάζειν,

        τῶν μίαν οὐ χρεών ἐστιν, ἐν ᾧ πεπλανημένοι εἰσίν.

55    τ᾽ἄντια ἐκρίνατο δέμας καὶ σήματ᾽ἔθεντο

        χωρὶς ἀπ᾽ ἀλλήλων,  τῇ μὲν φλογός αἰθέριον πῦρ,

        ἤπιον ὄν,  μέγ᾽ ἐλαφρόν,  ἑαυτῷ πάντοσε τωὐτόν,

        τῷ δ᾽ἑτέρῳ μὴ τωὐτόν,  ἀτὰρ κἀκεῖνο κατ᾽αυτό

        τἀντία, νύκτ᾽ἀδαῇ,  πυκινὸν δέμας ἐμβριθές τε.

60    τὸν σοι ἐγώ διάκοσμον ἐοικότα πάντα φατίζω,

        ὡς οὐ μὴ ποτέ τίς σε βροτῶν γνώμη παρελάσῃ. 

                                                                                                                    37

Now i will stop speaking about the meaning of truth and i will speak about the mortal world of the ambiguous and doubtful truth: They believe that everything has two ways to exist, one is not enough for them; exactly there is where they are wrong.  They claim that opposites are united, while, at the same time, they set limits in-between them.  They believe that the ethereal flame of fire is always the same to itself and simultaneously, different. They consider everything to be against itself, being in deep confusion and darkness. I speak to you about the phenomenal world, the surface of cosmos, the decorative one, so you will never be deceived by the mortal thinking. . .

Comment: Parmenides objects consciously and clearly against the Heracletian dialectic contradictive logic, setting other terms, which reject the existence of “Not-Being” and this way, consider any contradictive concept, which “Is―Not Being” erroneous, because it contains, even partially , the “Not-Being”.

Fragment 9

    αὐτὰρ ἐπεὶ πάντα φαός καὶ νὺξ, ὀνόμασται

    καὶ τὰ κατὰ σφετέρας δυνάμεις ἐπὶ τοῖσί τε καὶ τοῖς,

    πᾶν πλέον ἐστὶν ὁμοῦ φάεος καὶ νυκτός ἀφάντου 

    ἰσων ἀμφοτέρων ἐπεὶ οὐδετέρῳ μετά μηδέν. 

Since all things became of light and darkness and by their own forces took different forms, everything remaining beyond these, is equally balanced of light and darkness ultimate remained elements, because vacant cannot exist. 

Comment: Parmenides accepted a closed universe, composed of light and darkness. Because of that and because “Not-Being” cannot exist, according to him, vacant also cannot exist; there should be an absolute balance of equal light to equal darkness remaining.  If something of these could be more than the other, vacant space should exist and this way the door of zero (the vacant as nothing) opens to the existence and all his balanced system should collapse, being contradictive. 

Fragment 1 verses 9-14

    ἡλιάδες κοῦραι προλιποῦσαι δώματα νυκτός

    εἰς φαός ὠσάμεναι κράτων ἄπο χερσὶ καλύπτρας.

    ἔνθα πύλαι νυκτός καὶ ἤματός εἰσι κελεύθων

    καὶ σφὰς ὑπέρθυρον ἀμφίς ἔχει λάινος οὐδός_

    αὐταὶ δ᾽αἰθέριαι πλῆνται μεγάλοισι θυρέτροις_

    τῶν δὲ δίκη πολύποινος ἔχει κληῖδας ἀμοιβούς.

…I was brought there by the daughters of the Sun . . . . . . .

…in front of a double door, where Dike (Ratio) holds a mutually suitable key; wherefrom the road of light and darkness departs and the synthesis of the world begins.

38

Comment: Parmenides claimed that he followed a new logical road: the rational one. As a beginning he accepted the self-evident, that “only Being exists”. So any acceptance of Not-Being as existing, is the contradiction itself.  He proposed a way of thinking, that rejects Not-Being, (not existing), in all its steps, considering contradiction which is innate to evolution and daily life, as phenomenal (not real).  According to him, the world should be accepted as a closed system, thus rationalism can be an infallible organ of intellect and this way nothing can escape from intellect and logic; therefore “Being”, “Intellect” and “Speech” coincide. This way logic (avoiding the error of Not-Being) can give the reliable and accurate method of the comparative proceedings.  

      We see, on one hand, rationalism and determinism to rise up, as a conscious practice and on the other hand, we see a conscious opposition against dialectics of Heracleitos.

It was when the Greek world was coming out of tragic practice as a way of life, which by the Pythagoreans was considered to be Barbarity.  It is known that Pythagoras and his followers, never consumed flesh; so they considered tragedy profane, since basic process of tragedy, was the slaughter of the bull, the flesh-eating and in some Bacchic ceremonies the raw flesh eating.

     I believe that in this spot, rises the first opposition of Heracleitos to the Pythagorean spirit.  Heracleitos was conservative, fallowing the tradition of the tragic, the, Dionysian-Bacchic spirit. These times the Dionysian spirit, started to decline, becoming a gathering of formality proceedings and superstitions (like these the Comparative Anthropology realises in primitive societies nowadays).

    Heracleitos makes an effort for a tragic spirit redefinition; on the one hand fights against the Pythagorean novelty and on the other hand, against the inner decay of the tragic thinking.  He wants to give to tragic spirit a scientific face, as a counter-weight answer to the rationalism of Pythagoras and Xenophanes.  It seems that his answer was effective, so Parmenides takes the responsibility to counter reply.

    To the possible opinion of Pythagoras about the existence of many ultimate elements (πολυμάθεια), Heracleitos proposes Logos; that is a contradictive elementary unite, which always changes Being-Other-Similar to Itself (this is approximately the same in surface, but it has an inner continuous change, which overpassing a modification grade, changes even the  surface).   This One,  is big and small,  one and many,  zero and infinite, self-overpassing.  Parmenides cannot accept that. The One of Parmenides (the EON, the existing one), is finite, motionless, unchangeable, indestructible, immortal, with no Past or Future, because it is always Now Present.  On one hand, there is the immortal world, where vacancy and Not-Being does not exist, thus it’s motionless and eternal, obeying to the demands of objective rationalism; on the other hand, there is the mortal world, the perishable, the phenomenal one. For this phenomenal world, exists the appositive dialectic logic, reinforced with dynamic analytic and synthetic rational proceedings.  This dialectics rejects contradiction as untrue, and the dialogue of its elements to reach till the limits of its opposites, but never violate them; this dialectics accepts the whole as complementary in regard to the opposites it contains. As we noticed, in the Heracleitian contradictive dialectics, the dialogue of the opposites violates their limits, inter-acting each-other, without living any space inviolable between the. So the opposites expand inside each-other, without leaving any unviolated margins of independence between them and traveling away to the universe, return back verifying, their dynamic contrariety).

                                                                                                                     39

Parmenides conclusion about a closed universe, has a similarity with Einsteins opinion for “a moving straightly and normally object”: Einstein claims that “once it will return to the spot it had departed”. Parmenides: [ὁππόθεν ἄρξωμαι τόθι γὰρ πάλιν ἵξομαι αὖθις]:  The moving one will return to the place of its departure

Logic and speech is recorded in Being; that’s why man is the place where “Being”, “Intellect” and “Speech” coincide and since the whole is recorded inside man, he is able to understand and to know everything; this is his substance and recorded knowledge also. This way Parmenides opinions are related to Plato’s Ideas; According to Plato we know and understand, because we commune to the World of Ideas. According to the idealists, Ideas are the real existing world, which is the “Ἐόν”, the “Being” of Parmenides. Parmenides is also related to Aristotle in rationalism and the logic formality. We can also see his relationship to the determinism and the emblematic extract of Descart: “cogito ergo sum”, (I think so I exist). “Intellect and Being coincide”. We could talk about the influence of Parmenides to Hegel. They are connected with the meaning of “Being-Itself” and the “phenomenal dialectic process of the Ideas” and at last we could also point out the relation of Parmenidian “a priori recording of logic and speech, in human being” with the Kantian “a priori knowledge potentiality” .

    So Plato with his Ideas follows the path of the “πεφατισμένον”, (the a priori inspirited, ―the recorded in the -EON-, the “Existing-one”, the “Being”), the solid truth reflected to the mind. The Ideas of Plato are the terms and the ultimate limits of the accomplished game of the closed world, which Aristotle wants to revert. “The Ideas”, he said “do not exist before the world, but after, reflecting its process”; he also said “ everything has inside its “Εντελέχεια”, (the terms of its final perfection, being recorded in relation to its Tέλος -end”).    To my opinion, Εντελέχεια brings again back from the end (the result) to the beginning of the game, (the cause), the Ideas of Plato. It is known that the terms of operation of a closed and finished system, which have been put at the beginning of its process, presuppose the limits of the end of this game.  That is to say, since the terms of the closed system have been set, the process of this system will reproduce a specific series of its prerecorded games and the related number of these final games, which could be named “synthetic prototypes of the end”. In closed systems, the terms and the limits, are a couple where the one presuppose absolutely the other. Yet nothing forbids us, this “synthetic prototypes of the end” to name “Ideas”. If we accept the existence of Ideas, we must also accept, that Ideas do not evolve being eternal, so do not really obey to any time coherence, being of simultaneous beginning and end.

  There is an intellectual line departing from Pythagoras, goes to Xenophanes, to Parmenides, to Plato, to Aristotle, to Kant, to Hegel, to Heidegger, etc…. whose theories are complementary to each-other.

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The logical man of 21 century should see again the prepositions of Parmenides. There are many opinions we have accepted mechanically, not knowing their origin and their real meaning. For example, Rationality as an instrument of verification and production of infallible meditations, presupposes closed systems and finite Universe. Determinism should once and for all, reject infinite. As a mathematician said: “Infinite is the ultimate shelter of insanity”. We see many thinkers to splash dabbling in between roads of intellect, which do not compromise each-other, creating impassable logical situations.

ZENO (490-430)   THE FRAGMENTS:

Simplicios   physics, 140, 34 

     εἰ μὴ ἔχοι μέγεθος τὸ ὄν,  οὐδ᾽ἃν εἴη,  εἰ δ´ἔστιν ἀνάγκη ἕκαστον 

     μέγεθός τι ἔχειν καὶ πάχος καὶ καὶ ἀπέχειν αὐτοῦ τὸ ἕτερον ἀπὸ 

     τοῦ ἑτέρου καὶ περὶ τοῦ προύχοντος ὁ αὐτὸς λόγος,  καὶ γὰρ 

     ἐκεῖνο ἕξει μέγεθος καὶ προέξει αὐτοῦ τι, ὅμοιον δὴ τοῦτο.  ἄπαξ 

     τε εἰπεῖν καὶ ἀεὶ λέγειν. οὐδὲν γὰρ αὐτοῦ τοιοῦτον ἔσχατον ἔσται. 

     οὔτε ἕτερον προς ἕτερον οὐκ ἔσται. οὕτως εἰ πολλά ἐστιν, 

     ἀνάγκη αὐτὰ μικρά τε εἶναι καὶ μεγάλα, μικρά μὲν ὥστε μὴ ἔχειν  

     μέγεθος,  μεγάλα δ’ὥστε ἄπειρα εἶναι.

To exist something, must have a size and a distance from an other; The same we could say about the space in between. I will say this once and for ever: It is impossible to exist an ultimate part of something or an ultimate part of space between two things; moreover nothing can exist regardless to any other. So if there are many things, it is necessary these to be simultaneously small and big; so small, to have no size, so big to have infinite size.

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Comment: Zeno, in this fragment, with the relativity of big and small, reveals a new unite, different than the Eon (existing) of Parmenides. As we referred to this, the Eon of Parmenides has an appositive nature, accepting the inviolable ultimate elements, of Light and Darkness (photons and darkons). These are the separate ultimate parts, which interact not violating the limits in between them. “αὐτὰρ ἐπειδὴ πάντα φαὸς καὶ νὺξ ὀνόμασται καὶ κατὰ τὰς σφετέρας δυνάμεις ἐπὶ τοῖσι τε καὶ τοῖς, πᾶν πλέον ἐστίν ὁμοῦ φάεος καὶ νυκτός ἀφάντου ἴσων ἀμφοτέρων, ἐπεὶ οὐδετέρῳ μετά μηδἐν”. (everything was composed from light and darkness and by their own forces and hard struggle took their form; whatever remains of them finally, is equal light and darkness, because after them zero cannot exist).

     To my opinion, the meaning of this fragment is that darkness and light to intermix, should be separate elements till an ultimate size (atoms).  The teacher of Parmenides, Xenophanes, named these ultimate size quantities of light (“pyridia”), which today we call them photons; Parmenides proposed the existence of ultimate elements of darkness also.  Empedocles, an other follower of Xenophanes, according to Aristotle, accepted that light travels from sun to earth as elementary luminal particles, but we cannot notice them because of their high speed: Ἐμπεδοκλῆς φησιν ἀφικνεῖσθαι πρότερον τὸ ἀπό τοῦ ἡλίου φῶς εἰς τὸ μεταξὺ πρὶν πρὸς τὴν ὄψιν ἢ ἐπὶ τὴν γῆν.…Ἐμπεδοκλῆς ἔλεγεν ἀπορρέον τὸ φῶς σῶμα ὃν ἐκ τοῦ φωτίζοντος σώματος, γίνεσθαι πρῶτον ἐν τῷ μεταξύ τόπῳ τῆς γῆς καὶ τοῦ ουρανοῦ, εἶτα ἀφικνεῖσθαι πρὸς ἠμᾶς, λανθάνει δὲ τὴν τοιαύτην αὐτοῦ κίνησιν διὰ τὴν ταχυτῆτα.

     On the contrary Zeno, in his aspect mentioned by Simplicius, cleared out that he did not accept any ultimate part for any material or space in between opposites. (being this way against the Atomic Theory of Leykippos and later of Democritos). The ultimate unit of Zeno matches with a contradictive ultimate unite of Heracleitos. That unit is at the same time, zero and infinite, instantaneous and motionless, being the ultimate level of our world; that is, the contradiction itself and level of universal potentiality, (containing all forms and no one simultaneously).

DIOGENES  IV 72 

    τὸ κινούμενον οὔτ᾽ἐν ᾧ ἔστι τόπῳ κινεῖται οὔτ᾽ἐν ᾧ μὴ ἔστι.

The moving one, neither moves at the position it is, nor at the position it is not.

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Comment: Hegel claimed that “the moving one does not move, because one moment is in one position and next moment in another position, but because this Is-BeingNot at the same moment in the same position” and he pointed out that “motion is a contradiction”. 

      It seems that the contradiction of motion occupied the mind of many thinkers since antiquity; that’s why Zeno speaks about a moving one, which does not move!  It seems that some “Hegel” of his days, approached motion as a contradiction of removal and not as a changing essence.  Zeno puts the mater to another base: motion for Zeno and Heracleitos, coincides to the evolving process and changing, which is the genetic cause of Beings. According to them Motion is the Evolving Essence of which all things or events are attributes. So the moving object, from position A to position B, being an Other object similar to the former one, do not really dispose a constant identity.  Motion, according to them, is not an unchanged identity removal, of from position to position, but a continuous changing or a renovation of its substance.  An object, according to Heracleitos, being in a collapsing-composition and destructing-construction process, is similar to itself but always other, so it does not deserve to move on space, but to move inside itself (for that reason the moving one do not really have speed also).  The speed, rather concerns, the change of the one form the other.

SIMPLICIUS PHYS. 562, 3. 

    εἰ ἔστιν τόπος, ἔν τινι ἔσται,  πᾶν γὰρ ὄν ἔν τινι,  τὸ δὲ ἔν τινι καὶ ἐν τόπῳ ἔσται ἄρα καὶ ὁ τόπος ἐν 

     τόπῳ,  καὶ τοῦτο ἐπ᾽ἄπειρον,  οὐκ ἄρα ἔστιν ὁ τόπος.   

If space exists, exists somewhere; because everything exists somewhere; And this “somewhere” exists in a place, therefore it is a place into a place and all this infinitely. So there is not really the Place.

Comment: In the previous chapters we presume, that Zeno accepts the Heracleitian aspect that “time as duration cannot exist, because everything is in a state of a collapsing-composition being continuously Other”, thus Time is always Now.  We also see that Zeno doubts our certainty for the space as expanse and as a supporting base, up on the removing process of an object occurs.  According to them: an object really moves only in the space contained inside itself; this space is also contradictive because continuously changes.  Space itself ultimately exists between two limits: the infinite big and the infinite small, as it is presented to the fragment mentioned by Simplicius (physics 140, 34).  There time and space as Them-Selves cannot exist but coincide to the contradiction itself, which compose a Time-Space continuity, where time and space can not be clearly separate.   The values of time and space in that unity, are modified in relation of many factors and the point of view of the specific situation is seen.

                                                                                                                                       43

Interpreting the fragments of Simplicius (physics 140,34) and Diogenes ( IV 72) referring to Zeno, we realise that by dividing a specific size (of time or space) we have as a result a relativity of “One and Many”, “Small and Great”, “Continuity and Separation”, “Zero and Infinite”. This relativity we referred to, coincides with the contradictive ultimate level of the world, (the level of potentiality), proposed by Zeno.  

In the fragment (physics 562, 3) where Simplicius refers to Zeno’s aspect about  space, Zeno follows the opposite way: he expands a specific and finite space to an infinite one by adding more and more spaces to a place. This way, a specific and finite space situation, reveals its relativity to the infinite and simultaneously zero contradictive space situation.  

 For Heracleitos and Zeno, (from a different aspect), space and time is only now.  The meaning of “Now”, being contradictive, leads to the relation of the space-time continuity also: Yesterday doesn’t exist;  tomorrow doesn’t exist; only Now exists Always but being Always Other. “Now” is the zero edge of the fainting present. In this situation, the smaller time duration responds to a greater space expanse and oppositely.

 Addition and deduction, multiplication and division, in the dialectics of these thinkers, cannot be separate each-other, being always related: anything getting smaller, gets bigger by another way, at the same time. Anything, being continuously divided, tends to zero and this way, tends simultaneously to infinite; (dividing something in smaller parts, is getting bigger, because of the more empty spaces existing in between the parts).

If we summarise all these we spoke about, having in mind the way these thinkers  conceived the world’s evolution process, we should come to that conclusion: world exists by two opposite ways, which do not refute, but integrate each-other:

 A. World always exists as a specific object, being unique; everyone of these specific objects is inter-determined with all the other specific objects of the world, which are its limits. This inter-determination is accomplished by a “quantitive inter-action relating scale” beginning from the “inter-action” of the specific object with itself, passing to the inter-action with the near by objects, gradually to inter-actions with objects of the farther environment and at the end to the Universe Itself, which is the eternally other-self, its Universal Anti-Logous, that forces the specific one to be always other.  So the specific object itself, is an infinite event, since we cannot absolutely determine, were its limits begin and were they end, being the result of the world evolving process.  This way pre-socratics believed that any specific object, is potentially infinite.     The specific one characterised as small, has a continuous dialogue to its surrounding objects of environment and by receiving something from all the others and giving something to them, participates also this way to the great, the infinite.

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B. The world exists as the universality of all these inter-determinations, being simultaneously unique and always different. If we accept that, everything changes continuously; so Whole is always a continuous explosion of change and simultaneously return in its former position.  This infinite universality, exists always as Other, being the contradictive Self.

The world is terminated by two infinite ways:  The first one is the great (mega), having all characters and simultaneously none, (being the potentiality and contradiction itself).   The second one is the small (micro), being the way Zeno had terminated: as the contradictive unite, (the simultaneously “instantaneous and immobile”, “zero and infinite”); and as Anaximander claimed, “the ruler and element of beings”.  This way mega and micro compose a contradictive elementary unite, where mega dives into micro, being the cause of its existence, and micro expands far away to mega (the universe), being its cause also;  so this unity composes-collapsing, expands-gathering.

This universality is an instant-infinite continuity of all separate specific inter-determinations, being at the same time their integration to a new and higher specification of Motion as Essence (the Evolution as Essence).   These thinkers consider Motion to be the Essence and objects to be its specific characteristics. Objects are a result of the motional contexture, that involves in the object and forcing this to be always different (another). So the event, as an identity, do not deserve to move because it composes-collapsing, being this way, always and continuously another identity.

 Aristotle though, with one stroke of the pen, reversed this concept about motion: Physics 200b31-201α3. τὸ γὰρ κινητικόν, κινητικόν τοῦ κινητοῦ καὶ το κινητόν,  κινητόν ὑπὸ τοῦ κινητικοῦ.  οὐκ ἔστι δὲ κίνησις παρὰ τὰ πράγματα.  μεταβάλλει γὰρ ἀεὶ τὸ μεταβάλλον ἣ κατ᾽οὐσίαν ἣ κατὰ ποσὸν ἣ κατὰ ποιὸν ἣ κατὰ τόπον, κοινὸν δ᾽ἐπὶ οὐδὲν ἔστι λαβεῖν  ὡς φαμέν,…..ὥστ᾽ οὐδὲ μεταβολή οὐθενός ἔσται παρὰ τᾶ εἰρημένα, μηδενός γε παρὰ τα εἰρημένα.

[The mobile one is moved by the moving one and the moving one moves the mobile, there is not any other kind of motion related to the objects. The modifier, modifies always the modified in essence, in frorm, in quantity, or in position; so no motion or modification can exist out of these we have spoken about].

Now let’s see again motion the way Heracleιtos did: All objects of the world are events like the river, but instead to be accomplished by the water flowing, they are accomplished by “fire” elementary units passing-antipassing  inside  the  events;  these  elementary  units,  departing from an event, travel to universe and returning from universe make the event to be in a “compose-collapsing”, “spread-gathering”, “depart-arriving”, “Being-NotBeing” state simultaneously.  That can be logically realised by the following way: According to the Heracleitian fragment 59 (Hyppolyte IV 10) “the strait course is a result of rotation, like it is done in the turning lathe instrument”. “Pyridia”, as they named the photons or the quanta of energy, passing by the position of an event, depart to universe and return simultaneously from that; this way they accomplish the event in the specific position. 

                                                                                                                    45

     Since the universe of Zeno, Anaximander and Heracleitos “Is-BeingNot” infinite, the departure-returning of the traveling elements, is neither a vanishing corse to infinite, nor a perfect closed circular course, but a thick spiroid-helicoid one.  Thus every departure of these under-elementary units to universe and their arrival to the former position verify-falsifying “pyridion” in a collapsing-composition form; this way the “pyridion”, cannot be accomplished exactly in the same position but a little farther, so the “pyridion” moves.  Thus the removal of a “pyridion” (photon-quantum of energy), is a result of an internal motional contexture, coinciding with its evolving process.

    The (quantic) particles of Heracleitos, are followed by a wave of infinite complexity of flowing-antiflowing under-events, which also compose-decomposing-depart-arriving, by their own way of complexity, giving to us the idea of the dynamic field.  The micro-particles, according to the opinion of Heracletos, are dynes (whirlpools) of emit-receiving quanta of energy (ἀεἰζωον πῦρ); they exist-moving or move-existing.

    A pyridion, in the state of rest, moves straightly and normally with the speed of light, (300.000 kilometres a second). The under-events which compose-collapsing that pyridion (photon) cover, simultaneously, inconceivable greater distances to coincide with the course of the pyridion; consequently, the related continuation, of the under-events (under-level elements), which respond to the consequence of their collapsing-composition, expand to infinite.

     The quantum of energy, “according to the opinion of these thinkers”, reacts with Universe by unconstrained ways, so that it is not only the Universe that gives birth to quantum, but at the same time, quantum returns its depth, playing a generative role, giving birth to the Universe. Universe dives into the quantum, while quantum simultaneously expands to universe.

    The event sends messages verifying universe and universe also sends messages verifying the event in respond. These messages compose scales of departure-returning, beginning from the message of the event to itself, continuously there are messages responding to the environment near by, after to the farther one and finally to the universe,  which is the opposite self.   The message  responding to itself, never departs, because  it is the one that responds at the same time to universe (to infinite), which never returns, (the “infinite and zero”, the “instantaneous and immobile”, the potential ultimate level of the world, proposed by Zeno). (For more information about this “contradictive unit and the evolving process” which could follow this preposition, the reader could be informed in my work “Logic Action and Language” publ. by Dodoni at 1994 or to thodoroskavasis.blogspot.com to “Dialectic Thinking”

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THE PARADOXES

Zeno proposed four paradoxes of motion:

   A. An arrow to reach the target, must firstly reach the half distance from the bow to the target, but before it must reach the half of the distance it has already covered (the half of the half) and afterwards fallowing this process infinitely, the arrow should be stopped.

   B. An arrow to reach the target, must firstly reach the half distance from the bow to the target, and after that, it must reach the half of the rest distance (the half of the half), and this process infinitely. So the arrow never reaches the target.

   C. The arrow launches to hit a moving target. Whenever the arrow is faster and reaches the target, this has been always a little farther and this process infinitely. So the arrow never reaches the moving target.

These three paradoxes reveal the antinomies of the objective conception, motion, space and time are accepted by rationalism and especially by formal logic. I believe, these have been proposed by Zeno as an argument against the aspects of his friend and teacher Parmenides.  Moreover, he intended to point out “time and space relativity”, the “identity principle uncertainty” and the way motion should be accepted. To my opinion, his paradoxal prepositions can only be explained by an Heracleitian logic approach:  If we accept that beings exist in collapsing-composition evolving process, the meaning of time and space, cannot be conceived by the objective rationality and common sense, as it has been formed until nowadays by the Aristotelian formal logic and Newtonian determinism.      Zeno indicates that the meanings of time and space in the “field” of a contradictive world and therefore motion and speed, should be reconsidered.  Time should neither be anymore the abstract meaning of Duration Itself (the duration as Ideal) nor the duration of an object in space; and space should neither be the meaning of the Expanse Itself (as Ideal), nor as the expanse of an object in space. The Zenonian and the Heracletian preposition matches more to relativity and quantic view of existence.  According to them, during the collapsing-composition process of the elementary unites, composing physical systems, Time is the repetition frequency of the under-events elementary units, which passing from an event, accomplish it;  and Space is the wave-length of the under-events passing-antipassing process consisting that.      From this point of view, Zeno’s imaginary arrow, being in a state of collapsing-composition, is a quantic event consisting of a flow-antiflow of sub-elementary events process in position, which always changes.  Since this “flow-antiflow” relation is “the frequency” and “the wave length” relation of the arrow, which could be accepted as a time-space event, (being in the state of a collapsing-composition), do not deserve to move as itself and to have a speed of its own, because it is always Other (it is continuously a different identity). Thus the speed in this case, is the speed of transformation of one identity to other.

                                                                                                                             47

  Now let’s see the paradoxes from an other view: that is, how the arrow would imaginary accomplish the meeting with the target: 

      a. According to the second paradox, the arrow launches from the bow to a target in space. Due to the continuous division of the remaining course of the moving arrow infinitely in the middle, this accelerates-retarding; it retards having the same speed and overpassing continuously smaller distances, so to maintain its speed should accelerate.  At the moment the distance of the moving arrow to target tends to zero, the length of the arrow tends to infinite (because the bow, the arrow and the target compose a unity). The exact moment that arrow touches the target, there is the unity of Space-Time relation. This unity represents the immobile and instantaneous. The unity of bow, arrow and target composes a situation where the following relations could occur: For the bow to touch the target with the arrow, either the arrow becomes of infinite size and the distance between arrow and target becomes of zero size, or the parts of the arrow become of infinite number and the length of every part of the arrow of zero size. In this case we either have infinite wave length of arrow pieces and zero frequency of their repetition rhythm, or we have zero wave length and infinite frequency. (That is, from the point of view of the contradictive element of Zeno). The arrow during its course, being in a collapsing-composition relation, appears as length and frequency relation. “The more wave length and less frequency” or oppositely, “the more frequency and less wave length”.

      b.  Suppose again that the arrow is launched tending to a target in space. The “intention” of the arrow is to be in a straight and normal course to the target; the divisions of its course in the middle though, deviates imaginary the arrow from its course to the target, due to space rotation. The arrow to catch up the deviations must accelerate, but though its course straightens up, always looses something, being unable to accomplish the absolute straightness. In order the arrow to straighten its course absolutely and hit the target, its speed should be instantaneous and at this very moment immobile  simultaneously. (The moving one during the instantaneous motion, exists simultaneously at the departure position and the destination. Over-more the moving one has been expanded to infinite  diving simultaneously in to zero. It s an explosion of changing and instantaneous return back to its old position).

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     c. Now let’s see this matter differently: the arrow tends to the target, but due to the rotation of space, it deviates from its course; this as a result of the curvedness of its course, it will be forced to accomplish many cycles of departure-arrival and after a long time, it will return at the position of departure.  That will have the fallowing results:

     1. If universe is a closed system, the arrow integrating its “cycle” verifies it self from its opposite side.  From this side of view, the target is its opposite self.  

     2. If universe is an open system, the arrow returns once at the position it departed, but never exactly there, it verifies-falsifying the target, which is the opposite self of the arrow.  The arrow to verify exactly the target, (its opposite self), should make unconstrained departing-arrivals and in every arrival it touches the target differently. Thus the verification of the arrow-target, departing from the minimum one, passes by all the grades of verification-falsification, ending to the greatest one, which is the greatest verification and the smallest falsification.  The arrow at the point of smallest verification has not departed yet, being just itself, while at the greatest verification the arrow verifies the target absolutely, but in an other position, (so it falsifies it absolutely).  Both absolute verification and absolute falsification compose a unity tending to the infinite and zero relation.    Finally, the arrow departs-returning, making a thick helicoid-spiral course of unconstrained verifying-falsifying “junctions” and once it will meat the target; then the bow, the arrow and the target, will be a contradictive unity.  The speed of the arrow will be instantaneous and immobile and the size of the arrow will be infinite and zero at the same time (one unique infinite or infinite zero part sizes).

    This is, the motion of a specific object in a full developed of a collapsing-composition evolution process, the way Anaximander, Heracleitos and Zeno could imaginary inspire us;  According to these thinkers, the changing position of objects is a result of the wave and frequency relation of their collapsing-composition function. Their compactness is fluid, being in a continuous division of small parts, which in the moment of the crash, are of zero and infinite size at the same time. This way, we come back to Zeno’s principal, about the ultimate unit which tending to zero parts, becomes simultaneous of zero and infinite size. Only this way an object keeping its identity could really accomplish motion from an A to B point, other-else the collapsing-composition object, moving from point A and arriving to point B, is an object of an other identity, so it never accomplishes this course.

    D. It is said that the forth paradox of Zeno has been brought to us in confusion.  I will use the Aristotle’s evidence in Phys. Z 9 239 b 33:                                                                            

     περί τῶν ἐν σταδίῳ κινουμένων ἐξ ἐναντίας ἴσων ὄγκων παρ᾽ἴσους,           

     τῶν μὲν ἀπὸ τοῦ τέλους τοῦ σταδίου τῶν δὲ ἀπὸ τοῦ μέσου ἴσῳ 

     τάχει ἐν ᾧ συμβαίνειν, οἴεται,  ἴσον εἶναι  χρόνον τῷ διπλασίῳ τὸν ἥμισυν.

“When objects of the same size move oppositely in a stadium, some departing from the end and directing to the starting point of the stadium and others departing from the middle of the stadium directing to the end, though they move with the same speed, (Zeno claims) that the moving oppositely objects cover double distance than the others”.

The object directing from the finish to the starting point of the stadium, has to cover double distance than the object directing from the middle to the finish. If these two objects move the way of the “infinitialy in the middle division of their course”, they will reach to the end of their course, almost at the same time, having always a very small difference (tending to zero), that will be fading as the bodies tend to reach in their destination. (This continuously fading difference of the moving objects, which though, always exists, is a walking up on the Calculus). 

Now let’s change a little this mental experiment, and put the one object to be directed from the start of the stadium, to the finish and the other from the middle of the stadium to the finish, in the same line and having the same speed and same direction.  Following again the dividing of the course process in the middle, the objects reach to their destination almost together (with a small fading difference tensing to zero, as the objects approach to their destination); though they have the same speed, the second has covered all the distance in between the two objects, pushing the first one to the finish.

Let’s see now the motion of the One object, measuring its course from the beginning A of  its size and simultaneously measuring its course from its end B:  Following the same ”in the middle division” process of motion and measuring the distance of the object from point A to the finish, and at the same time from point B to the finish, the more the body reaches its destination, the smaller the object becomes. The –A to B– distance of the object, gets smaller because the points A and B tends to reach to the finish together (for the reason we have pointed previously).

    This paradox has been proposed by the contemporary science differently: Lorenz proved mathematically that the moving object modifies its length toward its direction; something which relativity theory has stepped on to be constructed.

Let’s summarise again all these proceedings together: The arrow according to the first paradox “intends” to depart for the target but it cannot do so, returning back at the same time; so instead of that, it rotates around it self;  according to the second paradox the arrow departs but due to the space rotation, its course deviates being cut in small pieces; so its straight course has been curve; and according to the last paradox, its length gets smaller to the direction and during its motion. 

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All this means that we have a moving straightly and normally object, whose course is curve, it has a spin and its length shortens toward its motion direction; it accelerates-retarding and the very moment of crashing to its target, it is instantaneous and immobile, zero and infinite.  

[The “fiction” i made to this last paradox, is not arbitrary; due to the different evidences of the forth paradox, in which we see, sizes of bodies, spaces and directions, to be pointed out, with sometimes no evident purpose; I get a rationally tactful aptitude to play with the size and the space using the spirit of Zeno]

THE  TRAIN OF EINSTEIN AND THE ARROW OF ZENO

The train of Einstein is an imaginary train that moves up on a rail-way of many million miles; its speed is very near to the speed of light. The clocks of the stations and the watches of a passenger and his friend, waiting for him at the station, have been adjusted at the same time. When the train arrives, the watch of the passenger will be behind from the watch of his friend. The length of the moving train according to the people in the station, will be shorter than the length of the train according to the passengers;  the doors of the train arriving to the station, according to the passengers, open simultaneously, but according to the people in the station, open with a retarding consequence each-other.

    Einstein’s train of and Zeno’s arrow, have things in common. This train cannot overpass the speed of light, because approaching it, on the one hand slows down, on the other hand accelerates, and just the moment it accomplishes the speed of light, stops because its mass is infinite. This reminds the cutting of the Zeno’s arrow course infinitely in the middle. This arrow thought it moves straightly and normally, because of the cutting of its course in the middle should accelerate to straighten the deviation cuts of its course; so approaching the target it retards, because of the infinitely cut in the middle of its course and tending to approach the target, it will stop (as we have pointed out before, then it will be of instantaneous and immobile speed).   Einstein would claim that these paradoxes happen because the speed of light is not over passable, while Zeno would claim that paradoxes happen because motion really is not the way we understand it: according to Zeno, motion occurs inside the evolving object, which by its collapse-composing process is always of another similar to itself but of other identity.

Einstein would say, that the target of Zeno’s arrow is the speed of light.  The arrow tending to reach the speed of light, has a deviation cut returning to its state of rest (the in between cutting spaces are the retarding situations) and simultaneously accelerates again to straighten its course and catch up the speed of light. So the arrow accelerates-retarding, because the cuts of its course become smaller but more and its mass tends to infinite. 

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     Zeno would say that the paradoxa of relativity, appearing in the train of Einstein, would never exist, if we would have realise that neither this we call speed really does exist, nor this we call time and space as formal exist.  At the mental experiment of the Einstein’s train, Zeno’s concept would be this way: Objects, events and beings taking place in this train, are collapsing-compositions of different evolving procedings, which we crowed them together illegally in the same mental place, though they belong else-where. We place quantic collapsing-compositve events in the objectivity and the formal rationality game, though they belongs in a contradictive-dialectic logical discipline. That is, we place the quantic events in the space and time of newtonian objectivity, though the belong to the quantic reality. These collapsing-composition events, being continuously different (other), do not dispose constant identity to have time-duration or space-expanse; the duration and expanse of these events could operate in a phenomenal frame of determinism, but when the situation is boundary, as in the “speed of light”, paradoxical events appear. Even more, a photon cannot have a speed, because although it is similar to itself, cannot keep its identity, being continuously another event.  

    The system of light could be rationalised differently: Everything that takes place in the train mental experiment of Einstein, is not an object anymore but a luminal-contexture-motion-event (a quantic one). This exists in an other level of nature, existing under of the world’s objectivity. There, Time is Frequency and Space is Wave Functions.  Everything in that world, is of quantic wave functions and frequency relations.

   We, erroneously, put the meaning of time-duration together with the meaning of frequency in the same mental and lingual game, thought they belong to another one.  (If the reader payed attention to the way Heracletos and Zeno perceive motion, will agree that my previous preposition is not excessive).

PROCLOS  Plato “Parmenides” 127d,   694,  23

      εἰ πολλὰ τὰ ὄντα τὸ αὐτὸ ὄν ὅμοιὸν ἐστι καὶ ἀνόμοιον

If there is plethora of beings any being is similar and not similar to itself.

The mental content of this claim could be seen in the dialogue “Parmenides” of Plato:  Plato presents in that dialogue young Socrates to argue with Zeno for the content  of this claim.   Zeno challenged  Parmenides  to develop the concept and the mental dimensions this claim could take.

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   Plato in this dialogue presents Parmenides to reveals the antinomies of formal rationalism, arguing against his own opinions.  Plato in this work as a Greek, presents the legality of the opposite, as an antipode to his opinions, for an integrated approach to the art of thinking. This Platonic fictional dialogue turns even against the Ideas of Plato, and the aspects of Parmenides himself, expressed in his poem “About Nature”.  So the prepositions of this work would rather agree to Zeno’s concept, being friendly to the Heracleitian aspects.

     The Parmenidian “not oscillated soul of the solid truth” of formal rationality, which we referred in the part about “Parmenides”, is opposite to the Heracleitian contradiction.    Plato in that dialogue presents Parmenides to revoke his own prepositions about thinking, passing to the opposite side.  It could be possible, this Platonic dialogue, is the starting point of the Hegelian Science of Logic. It’s possible the relation of the Hegelian logic to the Heracleitian dialectics, is ruther accidental.

All this argument came to us in fragmental state and it would be buried, if the European scholars would not rise it up again from its grave. Maybe, the arguments of modern philosophers, seem to be different than these of antiquity, but only the phraseology changes; finally they return to the same inquires.  Modern thinking, has been based on the “previous”Parmenidian rationalism and the Aristotelian formal logic, looking for positive supports to go forward, without “if and maybe”, “Being and Not-Being”.  This was not bad at all;  we were accustomed to have specific and concrete results from the scientific activity, while determinism was considered to be the science itself.  In the area of micro and macro though, rationalism and determinism undergo and suffer. These cannot describe quantic reality efficiently. Formal logic, the so necessary one, for objective measurements and the comparative process in this area, where the objects identity to them-selfs suffer or abolish, cannot operate, because everything “Is-Itself, Being Other” simultaneously, “they are similar and not similar to them selves at the same time”. 

      Heracletos, as Sibyl, “χιλίων ἐτῶν ἐξικνεῖται τῇ φωνῇ”, he launches his voice to the future. There have passed 2500 years but his voice has not reach to its destination. Nowadays “we neither know to listen, nor to speak” and “everyone has turned to his own world”, despising the Logos of Heracletos;  the Heracletian Dialectic Logic.

LOGOS

Thought we have referred adequately to the meaning of Logos, we should see this matter again, because it is very loaded: Essence, according to Parmenides, being innate to thinking and logic is recorded in every being.  Thus Parmenides and Heracleitos agree that universal unity coincides to Logos and therefore Logos is simultaneously Essence, Meaning and Speech; though they both typically agree to that, they differ in their Logic and the way consequently accept these three meanings. 

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 According to Parmenides, logic and speech is inscribed in the human being; that gives to the human the ability by thinking and logic, to know, to have intuition, imagination and make valid meditations. And because everything is in-scripted in human by mention and logic, everything could be perceived and be described by speech.  This also is the reason, man could commune with the whole, the Ἐόν (the really and eternally existing one), which is finite and not evolving. So according to Parmenides, though we see the world changing, deeply inside it is constant.  The evolving and contradictive world we see, is phenomenal; therefore to think correctly and to be able by thinking to reach to the truth, we must put away from logic the “Not-Being” and contradiction, because as “Being-NotBeing” contains the error of NotBeing also. So it is necessary to use only the “Being” in our thinking, thus whatever exists and every contradictive meaning appearing in logic, should be rejected.  Parmenidian rationalism is appositive permitting a dialogue of elements, which do not violate their limits, accepting objectivity and the existence of ultimate immortal and unchangeable elements. On the contrary, Heracleitos accepts that evolution is the essence itself, that logic should be the contradictive Dialectics and speech should coincide with Logos.  The heracleitian Logos firstly is the contradictive speech coinciding to the contradictive thinking and to the evolving Nature. Thus Logos is itself simultaneously Essence, Speech and Logic.

     Xenophanes said that everything in its very depth is incomprehensible; that is to say, world consists of a plethora inconceivable elements, which are ἄρρητα (not possibly to be spoken); these are the “things themselves”, the ultimate identities and finally the Ideas.  Xenophanes and Parmenides, accept that world is spherical and perfectly causative (out of hazard). On the contrary Heracleitos do not accept the existence of the ἄρρητα; according to him, whatever exists is “Essence-Logic-speech”; thus Logos-dialectics is expressed as a contradictive speech.  Everything real, should find a way to be and be said contradictively (as Logos does). The acceptance of Many unchangeable and ultimate elements or Ideas, razes continuously unanswered inquires and antinomies. The language of the eternal principles can not say the world as it is. That’s why Hercleitos pointed out “that he said everything as they are”. The problem of what language is the most suitable to speak the world as it is, has occupied intensely the philosophical and scientific cycles, from antiquity till today (as ideologic and philosophic movements, from Kant to Hegel and to Marx, form Hume to Russell to Wittgenstein and to Carnap). This discussion began from Heracletos and Parmenides and it seems that it will continue, as long as determinism will be abolished by quantum-mechanics, which looks out for a new logics-linguial syntax to speak the quantic reality.

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      My opinion is that mathematics have not been discovered for practical, but for  onto-logics-philosophical reasons. Human beings felt the necessity to find divine languages and to speak languages which are the world itself.  Inquiries as “what is the language of truth”, “the value of logic and experience”, which modern philosophy presents as a new, are the most primordial. 

   The conscious logics-mathematic rational language, was organised up on the presupposition of many principles existence (Pythagorean πολυμάθεια) and the conscious rational logic of Xenophanes and Parmenides.  This language to be spoken should include a series of inviolable terms (the principles), which have not enough underground of logical covering. The effort of positivists to create a language, which would rejects metaphysics from meditation, being based on determinism cannot avoid, but to walk around the steps of Pythagoras, Xenophanes and Parmenides; but this cannot really reject the ontological metaphysics of the basic principles of that logic. These will always have a small lack of reliability, when the shadow of very small, very big and infinite falls up on them. Their basic presupposition is to occur in closed systems, thus in a finite universe, something all rationalists after centuries of rational use, have forgot about.  They accept evolution but abolish it unconsciously by accepting determinism.

     Logos of Heracletos do not need to answer to that kind of inquires, but only to say how this language possibly exists.  Dialectics is the dithyrambic language and appears as the contradictive concernment of science.

    Pythagorean world, according to Heracleitos, is the one of “many eternal ultimate elements”, while his own is the world of the one evolving process, as really nature exists;  Parmenides is placed in between; he wants the world of unity, accepting the logic of plentitude; he confuses us.  The Parmenidian Ἐόν, is the really existing, the “Absolutely Being”, so the “Not-Being” by definition cannot exist.  According to Parmenides, logic to be able to lead to truth, has the duty to step only upon the “Being”; According to him, the contradictive logic of “Being-Not Being”, deals with the mortal world, the phenomenal one.   Zeno probably raised his objections to the aspects of his teacher Parmenides, since the Zeno’s “existing-one”, was not at all ἀτρεμές (un-oscillated), not finite, but contradictive. The reference of Plato to the opinions of Parmenides in his homonymous dialogue, rather matches to the opinions of Zeno; Plato would be awarded of that, but maybe Zeno, “the student”, had convince his teacher Parmenides for the opposite; When Parmenides wrote his poem “About Nature”, he was very young, since Muse “called” him in his poem “κοῦρος” (young man).

We will never certainly know, what happened in the magic journey of the pre-socratic thinking, because whatever remained to us is dust and fragments from burned libraries. 

      The Christians “saved” the world from the “Grecian blasphemy” of infidelity:

“ἀπιστίῃ διαφυγγάνει μὴ γιγνώσκεσθαι”― “Unbelief and doubt dissuades from ignorance”. 

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Faith generates fanaticism;  Determinism generates the inflexible thinking;  Mysticism steps on faith and rational formality; The Mysticist climbs skilfully the lather of rationalism, accepting a series of principles, as any formal rational system does;  when he reaches at the hight of his arrogance, throws away the lather and forgets about it, not needing it any more.

The triptych of rationalism, fanaticism, that is to say “the absolute truth” and mysticism, open the road to the barbarity of absolute-despotism. Doubt generates research, dialectics and the democracy of the equal participation of civilians.

Dialectics, doubt and democracy, are civilisation and all together are the spirit of tragedy; that is, the simultaneous passing from two opposite doors, the door of birth and the door death.