Sphaera Parmenidis et illius Interpretatio B.Russelli

　　Parmenides(544-501, B.C.) was one of the most interesting philosophers in ancient times. And his doctrine of "The One"(to hen), which he called "a sphere"(sphaira), has been interpreted in various manners. Because the image of "a sphere", of which he spoke as ungenerated and imperishable, whole, unique, immovable, and complete(n.1), can be explained both in metaphysical way and in logical way. So, the interpretation of his spatial image, which Bertrand Russell(1872-1970) gave in his History of Western Philosophy(1945)(n.2), is ambiguous, i.e. his explanation can be regarded both as metaphysical and as logical. He, of course, seems to be interested in logical analysis of Parmenides' arguments. But, concerning the image of "sphere", it is difficult to realize how Russel thought of it, on account of his too brief expression.

　　Then, in this paper, the author attempts to clarify Russel's interpretation of Parmenides' "sphere," in the following order; ss.2 "sphaira" Parmenidis(Parmenides' "sphaira"), ss.3 Interpretatio B.Russelli(Interpretation of B.Russell), ss.4 Conclusio(Conclusion).

　　The doctrine of Parmenides was given in a poem On Nature(Peri Physeos)(n.3), which he wrote after Heraclitus(Herakleitos), and in conscious opposition to this antecedent. While they say that Heraclitus manitained that everything changes("panta chorei" or "panta rhei")(n.4), Parmenides refuted this changing of all and insisted that nothing changes. It is said that Parmenides thought the senses to be deceptive, and considered that the mortal cannot get the true knowledge(aletheie) without thinking(noein), for he distinguished clearly the thought(noeta) from the senses(aistheta). So, he says,

"leusse d'hoos apeonta nooi pareonta bebaios."
(Behold things which, though absent, are nevertheless
firmly present to the mind.)(n.5)

　　His famopus fragment 3: "......to gar auto noein estin te kai einai"(.....for the same thing can be thought and can exist)(n.6) shows us that the thing that can be thought is significatum and the thought is significans. And his most important principle is, what is called, principium identitatis, as he says,

"che to legein te noein t'eon emmenai. estu gar einai,
meden d'ouk estin."
(It is necessary to say and to think Being;
for there is Being, but nothing is not ......)(n.7)

In addition to this statement, he warns us, saying "ou gar mepote touto damei einai me eonta."(For never shall this be forced: that things that are not exist.)(n.8)

　　Therefore, the true knowledge or truth, which Parmenides argues here, seems to be the following two propositions: The things that are exist, and the things that are not do not exist. Strictly speaking, Being is one, but not plural, for there can be changing or multiplicity if the plural things exist.

　　He presupposes this principle and adds his spatial image to this Being. At the beginning of his fragment 8, he says,

"tautei d'epi semat'easi
polla mal', hos ageneton eon kai anolethron estin
oulon mounogenes te kai atremes ede teleston.
oude pot'en oud'estai, epei nun estin homou pan,
hen, suneches."
(Very many signs sre on this road: that Being is ungenerated
and imperishable, whole, unique, immovable and complete.
Ita was not once nor will it be, since it is now altogether,
one, continuous.)(n.9)

These adjectives in this passage, especially, "oulon"(whole), "teleston"(complete) seem to be in allusion to "Sphere," which he will tell us in the ending of this fragment. Then he says,

"autar epei peiras pumaton, telesmenon esti
pantothen, eukuklou sphaires enalinkion onkoi,
messothen isopales pantei. to gar oute ti meizon
oute ti baioteron pelenai chreon esti tei e tei."
(But since there is a furthest limit, it is every
direction complete; like the body of a well-rounded
sphere, from the middle everywhere of equal strength:
for it need not be somewhat more here or somewhat
less there.)(n.10)

　　Here he is speaking of the One or Being figuratively as "a well-rounded sphere"(eukuklos sphaira). And it shoukd be noticed that he imagines "a sphere from the middle everywhere of equal strength." This image is given expressively in the following line,

"hoi gar pantothen ison, homos en peirasi kurei."
(For from every point it is equal to itself, staying
uniformity in the limits."(n.11)

　　Thus, Parmenides' image of "Sphere" is rather metaphysical or figurative. So the scholars cannot easily consider it as mere illusion of antiquity.

　　But, there are, at least, two or three possible explanations of this image; First, Parmenides speaks the One or Being merely figuratively as "Sphere." Second, he thinks seriously that the universe or cosmos is "Sphere." Thirdly, his real thought is beyond modern scheme of thinking, and the first explanation stands on modern logical point of view, the sencond stands on traditional metaphysical point of view. It is difficult to decide between these two or three opinions.

　　Russel's accounts for Parmenides' "the One" are found in Chapter V of his History of Western Philosophy(n.12), and he describes it in the following passages.

The only true being is 'the One', which is infinite and indivisible. It is not, as in Heraclitus, a union of opposites, since there are no opposites. He apparently thought, for instance, that 'cold' means only 'not hot', and 'dark' means ony 'not light'. 'The One' is not conceived by Parmenides as we conceive God; he seems to think of it as material adn extended, for he speaks of it as a sphere. But it cannot be divided, because the whole of it is present everywhere.(n.13)

　　What Russell here intended by the word 'God' is who exists and is immaterial. But, according to the explanation of Russel, "The One" of Parmenides is material and extended, for it is regarded by him as a sphere. Here Russell seems to think that Parmenides' "Sphere" is the real universe or cosmos in which phenomena occur. He, therefore, seem to belong to the scholars who take the second opinion.

　　Furthermore, he refers to the image of "Sphere", when he gives a short account for Empedocles' cosmology. He says,

Empedocles held that the material world is a shpere; that in the Golden Age Strife was outside and Love inside; then, gradually, Strife entered and Love was expelled, until, at the worst, Strife will be wholly within and Love wholly without the sphere.(n.14)

He considers here Empedocles' "Sphere" as material, too. Empedocles wrote after Parmenides and was influenced by this Eleatic, of course. Therefore, it is reasonable that Russell identified "Sphere" of Empedocles with that of Parmenides, for the former took over the image of "Sphere" from the latter.

　　But, the following passages seem to be contrary tonthe explanation hitherto.

What makes Parmenides historically important is that he invented a form of metaphysical argument that, in one form or another, is to be found in most subsequent metaphysicians down to and including Hegel. He is often said to have invented logic, but what he really invented was metaphysics based on logic.(n.15)

　　Here, in short, Russell says that Parmenides built a kind of metaphysics and he was one of metaphysicians. But his metaphysical arguments stand on logic. Russell, therefore, seems to take both yhe first opinion and the second at a time. Here lies the ambiguity of his interpretation.

　　The image of Parmenides' "Sphere" can be surely considered both as metaphysical and logical. Aristotle, for example, reproached him for being eager for strife or battle(eristikos), i.e. metaphysical, when he should have argued natural things, but not metaphysical(n.16).

　　Thus Parmenides' image of "the One" or "Sphere" can be both maintained and refused from various points of view, which proved us that the doctrine of Parmenides was a esoteric one. Today we can consider his "Sphere" as the real universe or cosmos, which modern scientists explain in their explosion-theory of the universe. Ex quibus considerationibus postest dicere Parmenidis imaginationem "Sphaerae" se extendere ad nostra tempora, verbi gratia, in illius interpretatione B.Russelli.