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p (1) Parmenides. Parmenides, a native of Elea, son of Pyres, came from an aristocratic family and took an active part in the political life of his city. His floruit (the age of 40) is put either at 500, or (by Plato) at 475 B.C. He is said to have been a legislator and given Elea some of its laws. Later, under the influence of Pythagorean Ameinias, he abandoned political activity and devoted his life to contemplation. According to Aristotle and Theophrastus, he was the pupil of Xenophanes but tradition holds that he did not become his follower (see Diog. L.IX, 21). Nevertheless, a close affinity between their vie₍ws is obvious: Parmenides, like Xenophanes, focused on the relationship of One Being and the plurality of existing things. Parmenides is known to have written a poem called traditionally On Nature, large extracts of which came down to us from Sextus Empiricus, Simplicius and some other doxographers. The extreme complexity of the extant fragments, particularly the allegoric prologue to his poem, as well as the glaring discrepancies between different manuscripts account for great divergence of opinion regarding the true meaning of Parmenides’s views. In point of fact, the interpretations of his philosophy range between a religious revelation and a purely deductive logical scheme.

p The most ancient doxographic tradition is expressed by Theophrastus in his Physical Opinions, Book I. It claims that Parmenides asserted the eternity of the universe and at the same time sought to explain how it came into being. He maintained that only the One exists, immutable, immovable and spherical, but, catering of the opinions of the mob that believes in change accounted for it by adopting "two principles, fire and earth, one serving as matter, the other as cause and maker" (DK 28 A 7). This passage from Theophrastus quoted by Alexander Aphrodisiensis gives us a glimpse into the problem of two ways of inquiry brought up by Parmenides: one true, and the other false. The first way leads to the apprehension of the one eternal self complete 84 being, the second, to what seems to ignorant mortals.

p The way to truth, according to Parmenides, is "the one that it is and that it is impossible for it not to be" (DK 28 B 2, 9). Here we have in fact the first statement of the logical law of identity in its ontological interpretation. Indeed, having discovered or, rather, guessed a logical law according to which the thought-content of a notion must not change in the course of reasoning. Parmenides draws from it an ontological conclusion. His argument runs as follows: (1) What is, is. (2) What is not, is not. (3) What is cannot come into being from what is not, nor can it perish into what is not as the latter does not exist. (4) Space (void) and time (distinction between past and present) are non-existent. (5) Being is full. (6) Being has no parts, it is indivisible. (7) Being is one, as there is nothing apart from it. (8) Being is complete (hence finite) and perfect. (9) Motion does not exist as there is nowhere for being to move.

p As is evidenced from this abstract scheme of reasoning which claims to solve the philosophical problem of true being, Parmenides conceives “being” as fullness of everything, something like mass filling the universe. Being neither evolves nor dissolves, it is indivisible, continuous, immovable and selfcomplete. It is like a round ball beyond which there is pure nothingness. This is ostensibly very close to the materialist world outlook and Parmenides’s philosophy was sometimes construed as a kind of materialist or its prototype on the grounds that he understood reality as primary motionless corporeal substance extended in space and therefore “ material”’ with nothing existing apart from it.  [84•1 

p Such a view, however, can hardly be accepted. Parmenides contends that "to think is the same as the thought that it is; for you will not find thinking without Being" (B 8, 34) or, even more plainly, that "it is the same thing to think and to be" (B 3). That means that thinking is conceived by him not as a criterion of being, but as being itself. The starting point for Parmenides, the axiom he considered impossible to reject, was not the material world, but the thought of it which he identified with being. The idealist trend in Parmenides’s heritage was therefore at least as much pronounced as the 85 materialist one. The Eleatic school in its genesis paved the way both for Democritus and Plato.

p Contrasting the "way of opinion" to the "way of truth," Parmenides writes:

p “The one, that it is and that it is impossible for it not to be is the path of Persuasion... The other, that it is not, and that it must necessarily not be, that I declare a wholly indiscernible track; for thou couldst not know what is not—that is impossible—nor declare it, for it is the same thing that can be thought and can be... What can be spoken and thought of must be, for it is possible for it to be, but impossible for nothing to be. This I bid thee consider, for this way of inquiry is the first from which I (hold thee back). But also from this one, on which mortals, knowing nothing, wander two-headed; for helplessness in their own breasts guides their erring mind. They are borne along, both deaf and blind, mazed, hordes with no judgement, who believe that to be arid not to be are the same and not the same, and the path of everything is one that turns back upon itself" (B 2, 3-6; B 6).

p Analysis of these quotations shows that Parmenides, in fact, describes three ways: (1) "the way of truth," i.e. the conviction that "it is"; (2) a false way leading nowhere, i.e. the denial of being and the assertion that only non-being exists; (3) a confusion between being and non-being both of which are believed to exist. The third way, in turn, admits of three variants of the relationship of being and non-being: first, being and non-being are the same; this variant is practically equivalent to the second way and can be identified with the “nihilistic” position of Gorgias of Leontini, Parmenides’s younger contemporary; second, being and non-being are the same and not the same; the reference to the "two-headed mortals" who believe that things come into being and perish and that the "path of everything is one that turns back upon itself" clearly points to Heraclitus. Third, there are being and non-being as independent and opposite entities which do not pass into each other. This is the doctrine of the Pythagoreans which underlies the opinion of "ignorant mortals." All other ways are dismissed as unacceptable.

p Proceeding to the world of appearance, Parmenides preserves only one pair of Pythagorean opposites—"light—night (darkness)." To this, however, he adds contraries-borrowed from Anaximenes, namely, the “rare—dense” and the "warm—cold." The antithesis of “warm—cold” cannot but 86 remind one of Alcmaeon. Aristotle says that Parmenides posited hot and cold meaning fire and earth, the former corresponding to being and the latter, to non-being. In his account of appearances Parmenides fully conscious of the impassable gulf between true being and ’the false world of opinion, puts aside the logical incompatibility of being and non-being and brings back the real opposites well known from Ionian physiology. The world of opinion, i.e. of sense experience, is contradictory, but Parmenides does not flinch from it. The way of seeming, false as it is, is the one followed by common mortals who cannot but conceive reality in terms of plurality, changefulness, generation and perishing of things. These properties of the sensuous world can be explained in physical terms, with the help of the above contraries and their combinations, but they can also be dismissed altogether if we embark on the true way of inquiry and go beyond the bounds of sense perceptions to the world conceived only by reason.

p It is worth noting that Parmenides does not follow Xenophanes who regards this world of absolute knowledge as god. Parmenides leaves no room for god in his conception of being and the goddess in the prologue to his poem who instructs him in the ways of scientific inquiry is a literary personage, a tribute to tradition, rather than a deity in the proper sense of the word. As regards the sensuous world as described by, Parmenides, the nearest to his understanding of it comes the Hegelian conception of "objective appearance" implying the need for the seeming, the appearance, since essence can only be grasped by man to the extent to which it reveals itself in phenomena.

p Parmenides did not evidently concern himself with the problem of transition from the world of opinion to the world of truth. This problem was to be formulated and solved at a later stage of philosophical development. It was not Parmenides who discovered the distinction between sensuous and rational knowledge, yet he was the first to realise the full import of contradictions between the evidence of senses and reason and to show that reason can sometimes grasp the truth in defiance of sensual experience.

p Parmenides’s faith in reason and its superiority over senses was so great that he in fact “ontologised” thought and identified it with being regardless of sense data. He rejected unstable, vague and constantly changing evidence of senses as 87 the world of "appearance," “opinion” in favour of the true world of eternal and motionless being which can only be conceived in thought. It was the first step towards objective idealism.

p The cosmological views of Parmenides expounded by him in accordance with the opinions of mortals do not lend themselves to reconstruction within an orderly “physiological” system. The central idea of his cosmology described in detail by Aetius (A 37) consists in the generation of the sensuous world from a mixture of “light” (fire) and “night” (darkness or earth). This description is partly confirmed by fragment B 12. The single world is encompassed by ether beneath which "is ranged that fiery part which we call heaven," then comes what surrounds the earth—a number of circular rings or bands, one inside the other. Some bands are fiery, others are dark, and those between them are filled with fire but partly. "And in the centre of these is the goddess who guides everything; for throughout she rules over cruel Birth and Mating, sending the female to mate with the male, and conversely again the male with the female" (B 12). According to Aetius, Parmenides also called her "steering goddess and keyholder and Justice and Necessity.”

p Parmenides’s "circular bands" are highly reminiscent of the “rings” of Anaximander, particularly when we learn that "the sun and the circle of the Milky Way are exhalations of fire," his central fire reveals a close affinity to Pythagorean Hestia or the goddess of hearth, etc. The origin of life, ’as well as sensation and thinking, was evidently attributed by Parmenides to the interaction of earth and fire (cold and hot): "Thought varies according to whether the hot or the cold prevails, but that which is due to the hot is better and purer" (A 46). Sensation is caused by the similar (A 46). Speaking of the propagation of animals and human beings, Parmenides maintains that women are warmer (evidently, they are better and purer, though he is not quite explicit about the matter) than men; the birth of a male or female depends on which of the parents prevails and on the location of the foetus in the womb: "on the right, boys, on the left, girls..." (B 17).

p (2) Zeno of Elea. Zeno, son of Teleutagoras, was adopted by Parmenides. According to Plato, he was some twenty-five years younger than his foster-father and Apollodorus increases this difference to about forty years. Tradition holds him as a courageous political leader who fell victim in the 88 struggle against an Elean tyrant (the name of the tyrant varies). According to one story, the philosopher who headed a conspiracy against tyranny was seized and put to the torture. However, he did not give away his friends, but defamed the tyrant’s confidants. Being unable to endure the torture, he said he would whisper their names into the tyrant’s ear and, when the tyrant bent to him, Zeno dug his teeth into his enemy’s ear and was killed by his servants. In another version, he bit off his own tongue and spat it into the tyrant’s face, whereupon he was thrown into a large mortar and ground to death.

p According to Diogenes Laertius (IX, 29), "his views are as follows. There are worlds, but there is no empty space. The substance of all things came from hot and cold, and dry and moist, which change into one another. The generation of man proceeds from earth, and the soul is formed by a union of all the foregoing, so blended that,no one element predominates." If Diogenes did not confuse Zeno with somebody else, we have reason to believe that the Elean deemed it necessary to expound not only the "truth," but also the "opinion," as was the case with his teacher Parmenides. Zeno is mainly known through his acute attempts to substantiate Parmenides’s doctrine by the dialectical refutation of his opponents. The method he used was based on the rule of contraries and consisted in adopting his opponent’s position as a premise and showing that it leads to absurdity. Ancient sources ascribe to Zeno forty arguments "against plurality," i.e. in defence of the conception of one being, and five arguments "against motion," in defence of the immobility of reality. These arguments are called “aporias” or insoluble problems. Among the aporias that came down to us some are directed against motion and four against plurality, dealing with the numerical and spatial aspects. They were aimed simultaneously against sensuous knowledge in general.

p In his aporias Zeno investigates the logical structure of the "world of opinion" which is dominated by number and motion and demonstrates by inductive inferences that these concepts are contradictory and should therefore be rejected. In other words, the very fact that the basic conceptions of ancient philosophy, mathematics and everyday consciousness turn out to be contradictory so that contrary conclusions can be drawn from identical premises is regarded by Zeno as sufficient reason for eliminating them from the realm of 89 true knowledge. Zeno’s "negative dialectics" is in fact based on the application of the laws of formal logic to the concept of the unity of reality. We cannot say with certainty who formulated these laws and in what form they were used by the Eleatics, yet there is no doubt that Parmenides consciously applied the laws of identity and non– contradiction, and Zeno also used the law of the excluded middle. His aporias clearly proceed from the assumption that if we have simultaneously A and non-A and if non-A proves contradictory, it is bound to be false and A is bound to be true in accordance with the law of the excluded middle. Such is the logical structure of all Zeno’s aporias irrespective of their content.

p Aporias against the idea of plurality. "If things are Many, they must be both small and great: so small as to have no size, so large as to be infinite" (DK 29 B 1). This conclusion, revealing the self-contradictory nature of the notion of plurality was apparently aimed at the Pythagorean conception of things as consisting of a number of corporeal elements (dots). Zeno’s argument runs like this (Lee, 9 and 10, DK, fragments 1 and 2):

p (a) Infinitely large. If a thing has size and depth, one part of it must be separate from another. [Obviously the parts cannot occupy the same space.] Now one pa-rt of it must be the outer surface, which limits it, and lies beyond the inner part. If it is merely a geometrical surface (i.e. with no depth), it is not a part of a solid body at all, in fact it is nothing, and the object has no limiting surface; but if it has depth (i.e. is a solid body itself), then it too must have an outer part or surface and an inner part, and so on ad infinitum.

p (b) Infinitely small. The only alternative is that the parts of each thing have no magnitude: but an infinite number of parts of no magnitude can never add up to a magnitude.

p Viewed from the quantitative aspect, the same argument runs as follows (Lee, 11; DK, fragment 3)T if there is a plurality, it must contain a finite number of components, because they must be neither more nor less than they are; on the other hand, it must contain an infinite number of components, because if they are separate at all, then, however close together they are, there will always be others between them, and yet others between those, and so on ad infinitum. In other words, a plurality must contain both 90 a finite and an infinite number of components which is absurd.

p Aporias against space and sense perceptions. To dispose of the notion of space, Zeno puts forward the following argument: if a thing occupies a space, this space must be enclosed in another space, and so on ad infinitum. Yet an infinite plurality of spaces is absurd, therefore space does not exist at all.

p To discredit sensation, Zeno uses a somewhat different argument which deals with the relation of part to whole and is known as the "millet seed." Zeno asks his opponent if a single seed makes a sound in falling. If the opponent replies in the affirmative, Zeno asks whether half a seed makes a sound, and so on. To the negative reply he rejoins that there will be no such thing as sound since a sum of zeroes is still zero. In this way he supports Parmenides’s view that senses are not "to be trusted (Lee, 37 and 38; DK A 29).

p The aporias against the notion of plurality testified to a crisis of ancient theoretical knowledge, the first of its kind. Its resolution in mathematics called for a substantive system of general axioms developed by Euclides. In philosophy the problem of being which turned out to be fraught with paradoxes was solved by ancient atomism.

p Aporias against the idea of motion. Zeno’s general argument is very simple: if a thing moves it must move either in the place where it is or in the place where it is not. The latter is impossible (nothing can act or be acted upon where it isn’t), and where a thing is, it must be at rest.’ Hence, "that which moves, moves neither in the place in which it is, nor in that in which it is not" (B 4). His second paradox known as -"The dichotomy" says that an object which moves from one point to another will never reach its destination: it must first pass through half the distance, but before it can do this, it must traverse the half of the half, and so on ad infinitum. It means that motion can neither end nor begin. According to the third aporia known as "Achilles and the tortoise" the fleet-footed Achilles will never overtake a tortoise, because, while he is reaching what in any moment is the tortoise’s starting point, the tortoise will have moved further. As Achilles always must reach first the position previously occupied by the tortoise, he will never be able to catch up with it. In the fourth aporia,known as "The flying arrow" Zeno argues that an arrow ’which appears to be flying 91 is really stationary because at any moment of its flight it must occupy a space equal to itself: it can move neither in its place nor in the place where it is not. The fifth aporia called "The stadium" is as follows. In the stadium there are three rows, each containing an equal number of equal-sized objects arranged initially as follows:

p (a) AAAA

p cecc

p The A row is stationary, the B and C rows begin to move in opposite directions with equal velocity until all three rows are opposite each other:

p (b) AAAA BBBB

p cccc

p The B row has passed half the A row, while the C row has passed the whole of the B row. Now, rows moving with equal velocity must take the same time to pass an equal distance. All the rows are equal, but it takes row C as much time to pass row B, as it takes row B to pass only one half of row A. Hence, half a given time is equal to the whole, which is absurd. This, according to Zeno, again shows that motion is unreal (DK A 28).

p Analysing these puzzles, a modern reader will have no difficulty in solving them. Indeed, the aporias against the notion of plurality are based on the fallacious axiom of the ancients that a sum of an infinite number of magnitudes is bound to be infinite. It is well known to us that there exist infinite convergent series. We can accurately calculate when and in what point of the path Achilles will catch up with the tortoise. Suffice it to recall the elementary psychological notion of the threshold of perception and we shall stop mulling over the "millet seed." Again, the author of the “stadium” puzzle appears very naive indeed in the light of the rule of the composition of velocities... Nevertheless, Zeno’s arguments continue exercising the minds of philosophers, logicians and mathematicians even in our days. Their historical significance consists in that they revealed the difficulties of the formation of scientific concepts of space, time and motion rooted in their dialectical nature and posed the problem of expressing their objective contradictoriness in logical forms.

p It is this contradictoriness alone that Zeno is interested 92 in: he proceeds from the assumption that what is contradictory cannot be thinkable and, consequently, cannot exist. The conclusion is that being can only be conceived as one motionless and immutable reality. The untenability of Zeno’s conclusion is obvious. First, he does not see that the concept of one immutable being involves no less contradictory consequences as was already shown by Plato. Second, Zeno is not aware of the fact that thinking itself is subject to change and genesis, and that therefore what we cannot express in to-day’s concepts will make no problem for the logic of to-morrow. Third, he is still unable to accept the idea of the objective contradictoriness of reality—contradictoriness to him is incompatible with being. Nevertheless, Zeno’s arguments emphasised, though in the negative form, the dialectical nature of motion. The real question that was posed before scientific thought was not whether there is motion, but how to express it in the-logic of concepts.  [92•1 

p (3) Melissus. Melissus of Samos, son of Ithaegenes is known to have been elected admiral during tlie war with Athens and to have defeated the Athenian fleet in 441 B.C. Later, however, Pericles won a victory over the Samians and took the city after a nine-month seige. He rased the city walls, seized the ships and imposed, a heavy indemnity on the citizens. Ancient sources give us no information on Melissus’s further fate.

p As a philosopher, Melissus remained firmly in- the Eleatic tradition and was called a follower of Parmenides. We possess ten fragments of his book On Nature or What Is, two of which being of considerable length. What with the extensive commentaries of the doxographers and the exposition of his teaching in the treatise On Melissus, Xenophanes and Gorgias (MXG) mentioned earlier, we can form a fairly accurate idea of his views. Melissus elaborated the arguments of Parmenides 93 and Zeno in the light of the problems of ancient physiology and the doctrines of his contemporary Empedocles and. possibly Leucippus. A characteristic feature of his arguments consists in that he applied the Parmenidean thesis "what is, is" not only to being as a whole, but also to individual things. Denying plurality and all. sensible objects and properties, Melissus asserts that if they existed, each would be such as it appeared to us at first, and not change nor become different, but each must always be as it is. However, "it seems to us that the hot becomes cold and the cold hot, and the hard soft and the soft hard, and that the living thing dies and comes into being from what is not living, and that all things change, and that what was and what now is are not at all the same, but iron which is hard is worn away by contact with the finger, and gold and stone and whatever seems to be entirely strong (is worn away); and that from water, earth and stone come into being. So that it comes about that we neither see nor know existing things" (B 8 [3]).

p The extension of the law of identity beyond the sphere of abstract being and its application to individual things reveals at once the fallacy of the reasoning whereby the properties of sensible objects are derived from the notions of them, i.e. from thinking. Indeed, so long as we regard the speculative “essence” as something lying beyond " phenomena," we may still attempt to maintain a theory of its basic difference from appearance and contend that essence can only be discerned by reason owing to their contiguity. Yet as soon as we pass to sensible objects and declare them essentially immutable, we challenge elementary common sense and clearly reveal the untenability of the “physical” interpretation of being as motionless and changeless.

p For all his adherence to the Eleatic tradition, Melissus does not blindly follow all its tenets and makes a number of important improvements to the basic conception of being. First, he defines being as infinite (apeiron) both in space and time because it is eternal and immutable and therefore cannot haye either beginning or end. Second, he considers being and its parts (individual objects) motionless in space because there is no emptiness ("for the Empty is Nothing; and so that which is Nothing cannot be" [DK 30 B 7]) and they ₄have nowhere to withdraw to. This argument was evidently directed against the atomistic doctrine which was based on the assumption of void. Melissus thus links reality with space 94 thereby emphasising its material character. Third, Melissus deprives being of anthropomorphic characteristics asserting that it feels neither pain nor grief, and, contrary to Xenophanes, does not see, hear or think... The term God used by Melissus as a synonym of reality has nothing in common with the traditional idea of God in Greek mythology. It is in fact the god of philosophy, the universal concept of the world. Finally, Melissus substantiates and elaborates Parmenides’s implicit principle Ex nihilo nihil fit (out of nothing comes nothing) which placed an extremely important part in Greek philosophy.

p The general trend of Melissus’s thought confined within the framework of Eleaticism suggests an obvious inclination towards materialism. The extant fragments of his book give no evidence for his adherence to the idea of identity of thought and being. His recognition of infinite reality gave Aristotle cause to assert that Melissus, in contrast to Parmenides, spoke of one reality "in relation to matter" (Met. I, 5, 986b), but not in relation to notion. This view was evidently shared by Galen (A 6).

It is interesting that Melissus attacking the idea of plurality opens the way to atomism: "If Things were Many, they would have to be of the same kind as I say the One is" (B 8, 6). Yet this is precisely what the atomists averred: the world consists of a plurality of atoms, each possessing the properties of the Eleatics’s Being—it is one, indivisible, ungenerated and unperishable...

p To conclude, the Eleatics made an important step forward in the philosophical cognition of the world by focusing on reason and thinking. They opened new horizons in philosophy and turned it from cosmological speculations to an examination of the logic of thought. The Eleatics advanced the problem of distinction, even contrast, between being and appearance, essence and phenomena, truth and arbitrary opinion of the mortals. Parmenides and his followers in the fifth century B.C. made a great advance upon the Ionian concept of "existing things" and rose to a much higher level of philosophical generalisation, yet they were still unable to develop a full-fledged abstract notion of being as such in the Platonian sense.

95

p Eleaticism was an important stage in the self– determination of philosophy and had profound and highly contradictory consequences. First, it exploded the initial unity of Greek thought naive in its pristine simplicity but representing the royal road of philosophical development. Second, it put an end to the unity of the ancient world outlook, as much naive and based on direct contemplation. On turning into “Being” nature as unity in diversity became One as opposed to Many: “physis” was divorced from "metaphysis." Third, the living and changing dialectical reality gave way to immutable and motionless metaphysical "being," supranatural and antidialectical, while intuitive comprehension, immediately valid, pictorial and contradictory was superseded by discursive and conclusive reasoning.

This latter circumstance was of enormous importance for philosophical progress. The Eleatics revealed a new world, the world of concepts and ideas, and laid it open for exploration. The paradoxes of ancient thought discovered by them induced the philosophers to focus on their origin—in mathematics, logic, epistemology—and to look more closely into man’s position in the world and society and his attitude to the gods. Contradictions in thought could not be tolerated and the Eleatics’ negative dialectics was bound to bring about a positive dialectics in the shape of the logic and epistemology of Greek classical philosophy. The impact of the Eleatic school, however, was not confined to the field of logic—its doctrines led, on the one hand, to a revival of “physiology” or natural science and, on the other, to the problem of man and society.