Ancient Philosophy

The Presocratics – The Eleatics

Primary Sources:

• Parmenides, Zeno of Elea, and Melissus, Fragments from Baird and Kaufmann, Ancient Philosophy, pp. 19-30.
• Zeno of Elea, Additional Fragments (Handout).

Background:

From David Sedley’s Routlegde Online Encyclopedia article on Parmenides:

Parmenides of Elea, a revolutionary and enigmatic Greek philosophical poet, was the earliest defender of Eleatic metaphysics. He argued for the essential homogeneity and changelessness of being, rejecting as spurious the world’s apparent variation over space and time. His one poem, whose first half largely survives, opens with the allegory of an intellectual journey by which Parmenides has succeeded in standing back from the empirical world. He learns, from the mouth of an unnamed goddess, a dramatically new perspective on being. The goddess’s disquisition, which fills the remainder of the poem, is divided into two parts; the Way of Truth and the Way of Seeming.

The Way of Truth is the earliest known passage of sustained argument in Western philosophy. First a purportedly exhaustive choice is offered between two ‘paths’ – that of being, and that of not-being. Next the not-being path is closed off: the predicate expression ‘… is not’ could never be supplied with a subject, since only that-which-is can be spoken of and thought of. Nor, on pain of self-contradiction, can a third path be entertained, one which would conflate being with not-being – despite the fact that just such a path is implicit in the ordinary human acceptance of an empirical world bearing a variety of shifting predicates. All references, open or covert, to not-being must be outlawed. Only ‘… is’ (or perhaps ‘… is… ’) can be coherently said of anything.

The next move is to seek the characteristics of that-which-is. The total exclusion of not-being leaves us with something radically unlike the empirical world. It must lack generation, destruction, change, distinct parts, movement and an asymmetric shape, all of which would require some not-being to occur. That-which-is must, in short, be a changeless and undifferentiated sphere.

In the second part of the poem the goddess offers a cosmology – a physical explanation of the very world which the first half of the poem has banished as incoherent. This is based on a pair of ultimate principles or elements, the one light and fiery, the other heavy and dark. It is presented as conveying the ‘opinions of mortals’. It is deceitful, but the goddess nevertheless recommends learning it, ‘so that no opinion of mortals may outstrip you’.

The motive for the radical split between the two halves of the poem has been much debated in modern times. In antiquity the Way of Truth was taken by some as a challenge to the notion of change, which physics must answer, by others as the statement of a profound metaphysical truth, while the Way of Seeming was widely treated as in some sense Parmenides’ own bona fide physical system.

From Stephen Makin’s Routlegde Online Encyclopedia article on Zeno of Elea:

The Greek philosopher Zeno of Elea was celebrated for his paradoxes. Aristotle called him the ‘founder of dialectic’. He wrote in order to defend the Eleatic metaphysics of his fellow citizen and friend Parmenides, according to whom reality is single, changeless and homogeneous. Zeno’s strength was the production of intriguing arguments which seem to show that apparently straightforward features of the world – most notably plurality and motion – are riddled with contradiction. At the very least he succeeded in establishing that hard thought is required to make sense of plurality and motion. His paradoxes stimulated the atomists, Aristotle and numerous philosophers since to reflect on unity, infinity, continuity and the structure of space and time. Although Zeno wrote a book full of arguments, very few of his actual words have survived. Secondary reports (some from Plato and Aristotle) probably preserve accurately the essence of Zeno’s arguments. Even so, we know only a fraction of the total.

According to Plato the arguments in Zeno’s book were of this form: if there are many things, then the same things are both F and not-F; since the same things cannot be both F and not-F, there cannot be many things. Two instances of this form have been preserved: if there were many things, then the same things would be both limited and unlimited; and the same things would be both large (that is, of infinite size) and small (that is, of no size). Quite how the components of these arguments work is not clear. Things are limited (in number), Zeno says, because they are just so many, rather than more or less, while they are unlimited (in number) because any two of them must have a third between them, which separates them and makes them two. Things are of infinite size because anything that exists must have some size: yet anything that has size is divisible into parts which themselves have some size, so that each and every thing will contain an infinite number of extended parts. On the other hand, each thing has no size: for if there are to be many things there have to be some things which are single, unitary things, and these will have no size since anything with size would be a collection of parts.

Zeno’s arguments concerning motion have a different form. Aristotle reports four arguments. According to the Dichotomy, motion is impossible because in order to cover any distance it is necessary first to cover half the distance, then half the remainder, and so on without limit. The Achilles is a variant of this: the speedy Achilles will never overtake a tortoise once he has allowed it a head start because Achilles has an endless series of tasks to perform, and each time Achilles sets off to catch up with the tortoise it will turn out that, by the time Achilles arrives at where the tortoise was when he set off, the tortoise has moved on slightly. Another argument, the Arrow, purports to show that an arrow apparently in motion is in fact stationary at each instant of its ‘flight’, since at each instant it occupies a region of space equal in size to itself. The Moving Rows describes three rows (or streams) of equal-sized bodies, one stationary and the other two moving at equal speeds in opposite directions. If each body is one meter long, then the time taken for a body to cover two meters equals the time taken for it to cover four meters (since a moving body will pass two stationary bodies while passing four bodies moving in the opposite direction), and that might be thought impossible.

Zeno’s arguments must be resolvable, since the world obviously does contain a plurality of things in motion. There is little agreement, however, on how they should be resolved. Some points can be identified which may have misled Zeno. It is not true, for example, that the sum of an infinite collection of parts, each of which has size, must itself be of an infinite size (it will be false if the parts are of proportionally decreasing size); and something in motion will pass stationary bodies and moving bodies at different velocities. In many other cases, however, there is no general agreement as to the fallacy, if any exists, of Zeno’s argument.

From David Sedly’s Routlegde Online Encyclopedia article on Melissus:

Melissus was a Greek philosopher from the island of Samos. A second-generation representative of Eleatic metaphysics, he published one work, entitled On Nature or On That-Which-Is, which has been partially reconstructed by editors. It defends a version of Parmenides’ monism, but recast with terminology and arguments directly accessible to a readership schooled in the eastern Greek (Ionian) style of physical speculation, as distinct from Parmenides’ western Greek background. Although it is uncertain how important Melissus was to his own contemporaries, his prosaic but clear presentation of Eleatic concepts was more widely adopted by later writers than the enigmatic pronouncements of Parmenides.

Melissus argues that that-which-is is: (1) omnitemporal; (2) infinite in extent; (3) one; (4) homogeneous; (5) changeless, that is, without (a) reordering, (b) pain, (c) grief or (d) motion; (6) indivisible; and (7) bodiless. Here (1) – ‘it always was what it was, and always will be’ – is a departure from Parmenides, who had outlawed past and future in favor of a static present. Likewise (2) contrasts with Parmenides’ defense of spatially finite being. The remaining predicates are consonant with Parmenides, although (5)b–c suggest that the being Melissus has in mind is a living one, presumably a deity – an aspect not brought out by Parmenides. Melissus wrote ‘If there were many things, they ought to be such as I say the One is’ – a remark sometimes thought to have inspired his contemporaries the atomists.

Questions:

• How do the Eleatic Philosophers pose a serious challenge for naturalism?
• How does Parmenides distinguish the Way of Truth (it-is) from the other path (it-is-not)? Why is only the first possible and the second impossible?
• How do Parmenides and Melissus argue that what-is is (a) uncreated, (b) indestructible, (c) perfect or changeless, (d) eternal or timeless, and (e) whole or homogenous?
• According to Irwin, what’s the relationship between speech and thought according to Parmenides?
• How does Zeno of Elea show that if there are many things, then these things are both finite and infinite in number? How does Zeno argue that Achilles can never overtake the tortoise, or even begin to move on the course? Why, according to Zeno, the arrow is stationary during its whole flight? What’s wrong with these arguments?
• According to Melissus, what is neccessary for motion to be possible?

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