The Cambridge Companion to Early Greek Philosophy

by A. A. Long

  (2) “Nor is there, or will there be, time11 over and above what-is, since Fate has bound it down to be whole and unmoved” (37-8). I suggest that its being whole (= “the whole?”), and hence spatially all-inclusive, means that there can be no external change to provide the measure of time, while its being unmoved likewise eliminates any internal measure of time.

  (3) “Therefore it [i.e., what-is]12 has been named all the things which mortals have posited, believing them to be real – to cometo-be and to perish, to be and not to be, to change place, and to alter bright color” (38-41). Parmenides here shows why he need not be embarrassed by his earlier premise that whatever can be spoken and thought of must exist (B6.1). That may seem to populate his world with a vast plurality of items – kettles, pigs, rainbows, even hobgoblins. But it now turns out that all of these names reflect inept human attempts to talk about just one thing, namely what-is, since there is nothing else to talk about.

  Monism, then, is preserved. We are now ready for the final description, predicate (d): what-is is spherical. “But since there is an outermost limit, it is complete on all sides, like the mass of a wellrounded ball – equally balanced from the centre on all sides” (42-44). This certainly sounds like a literal geometrical description of its shape. Grammatically, “equally balanced from the centre” is said of what-is itself, not of the ball to which it is compared. Hence, the resort often adopted of taking this to be a comparison to a sphere merely in terms of perfection or uniformity looks unpromising. And it becomes even less promising if we examine the actual argument which follows (44-49):

  For it must not be any larger or smaller here than there. For (1) neither is there what-is-not, which might prevent it reaching the same distance; (2) nor is there any way that what-is could be more than what-is here and less there, since it is all immune to plundering: for equal to itself on all sides, it has equal being within its limits.

  Unless someone can find a plausible metaphorical interpretation of “larger” and “smaller,”13 one that leaves Parmenides with a real argument here, we have little choice but to take them in their literal spatial sense. What-is cannot be larger in one direction than another, that is, be asymmetrical, because nothing could make one radius shorter than another: (1) there is no not-being to foreshorten the radius; (2) there can be no thinning out to create imbalance, since, given its equal being right up to its limits, nothing is missing from it. In short, there could be no explanation for asymmetry, that is, for any shape other than the sphere.

  So ends the Way of Truth. But can what-is really be geometrically spherical, without sacrificing its partlessness? Surely a sphere has distinct parts – segments, hemispheres, and so on? The answer, I think, is not that divisions cannot be imposed (witness the way mortals fragment reality), but that we misconstrue reality if we do impose them. In which case, the importance of its sphericity is that the sphere is the one shape which you can conceive as a single whole without distinction of parts: any asymmetrical shape can be grasped only by distinguishing corners, faces, ends, and the like. And our instructions from the goddess (B4, of uncertain location, but presumably soon after the proem) have been that we should not attempt to impose any spatial distinctions:

  Gaze in thought equally14 upon absent things as firmly present. For thought will not split off that-which-is from clinging to that-which-is, whether scattered everywhere in every way through the world or gathered together.

  Before leaving the Way of Truth, we should consider its argumentative structure. Once the choice of paths was complete, the goddess took us through a series of largely independent proofs demonstrating each of the predicates of what-is. Only once did the conclusion of one proof serve as the premise for another, and that was (B8.27-28) when (a) the rejection of generation and perishing was invoked among the grounds for (c) the denial of motion. Otherwise each proof was selfcontained, its premises either presented as self-evident or relying on one or both Laws. This will provide a key contrast with Melissus’ methodology.

  However, in a puzzling fragment the goddess remarks: “It is all the same to me where I start from; for I shall come back there again” (B5). Coming back to where you started should be the hallmark of the “back-turning” path followed by mortals, and it is hard to see how the arguments of the Way of Truth could be thought to have such a structure. In particular, she could hardly have started other than with the disproof of ”… is not,” and that certainly is not where she ends up again. Some have even thought, for this reason, that the fragment belongs to the Way of Seeming, but its source, Proclus, clearly implies otherwise. A better guess is perhaps that in context “there” referred, not to the arbitrarily chosen starting point, but to what-is. She would then mean, that all arguments, wherever they may start from, will bring you back to being, because ultimately that is the only possible subject of rational discourse.15

  My account is not fully in tune with recent appreciations of Parmenides.16 While English-speaking scholars like Burnet and Cornford made him very much the radical cosmologist I have claimed him to be, a Germanic tradition, fuelled in the twentieth century especially by Heidegger, has recreated him as a pure metaphysician, and G.E.L. Owen, in his seminal “Eleatic questions” (1960), felt obliged to absolve him of the title “cosmologist” in order to boost his credentials as a philosopher. The present chapter, while heavily indebted to these studies, eschews so absolute a choice. Parmenides’ Way of Truth is, to be sure, not a treatise on physics. Nevertheless, it can remain a contribution to the traditional cosmological debate, despite the fact that its methodology pioneers the newly emerging philosophical disciplines of metaphysics and logic. Even its most outlandish metaphysical thesis, the identification of thinking with being, finds, I have argued, a respectable place within the ancient cosmological tradition.

  The Way of Seeming

  We may now turn to “the opinions of mortals.” The goddess sets out, unargued, an analysis of the phenomenal world in terms of two opposite “forms” or elements, called “light” and “night,” the former bright, rare, and fiery, the latter dark, dense, and cold. What followed (now largely lost) set out a cosmology that included a creative goddess, a detailed description of the heavens as a set of concentric bands, an embryology, and a physiology of human cognition.

  But why teach Parmenides all this? From the outset she has declared it untrustworthy (B1.30), and now in embarking on it she describes it as “deceitful,” if “plausible” (B8.52, 60). Yet Parmenides must learn it “in order that no opinion of mortals may outstrip you” (51). On the face of it, she can only mean by this last remark that the cosmology will be the best of its kind, a successful competitor for the cosmological theories currently on offer. Indeed, what followed certainly was competitive: it even contained two major astronomical discoveries – that the Morning Star and Evening Star are identical, and that the moon is illuminated by the sun. But if the Way of Truth is true, cosmology must be false. So why join in the game?

  The answer has something to do with arithmetic. Parmenides’ major predecessors had been material monists, reducing reality to manifestations of one stuff. Parmenides’ own cosmology is equally clearly dualist. So it is scarcely an accident that he moves from one entity in the Way of Truth to two in the Way of Seeming (B8.53-4):

  For they [mortals] have made up their minds to name two forms, of which they should not name one, and that is where they have gone wrong.

  Despite a long-standing controversy about the meaning of this, it seems likeliest to be saying that two, although the minimum for rescuing cosmology, is one too many. Aristotle plausibly suspected that the two elements somehow corresponded to what in the Way of Truth were called what-is and what-is-not. Elemental dualism, that is, is the physical counterpart of mortals’ combination of being with not-being.

  Can we say whether the illicit second element, corresponding to what-is-not, is light or night? Aristotle and Theophrastus took it to be night. But their supposition may be conditioned by the too familiar sym
bolism whereby light represents truth and reality. Modern scholarship17 has shown that this is not Parmenides’ use of light imagery; indeed, in the proem his allegorical journey is from the light into the House of Night. This lends additional credibility to Karl Popper’s proposal that light – the element that, par excellence, informs the senses – is the intruder.18 Parmenides knew, and was perhaps the first to know, that the moon is in reality a solid sphere, its apparent changes of shape an illusion generated by the play of light. This, Popper suggests, may have inspired an analogous account of how the universe, in reality an undifferentiated sphere, is endowed with apparent variability over time and space by the intrusion of a lightlike second element.

  How, then, does the cosmology complement the Way of Truth? Above all by showing how to bridge the gap between truth and cosmic appearance. The entire range of cosmic phenomena can be generated by allowing the intrusion of just one additional item – by starting out with two instead of one. This makes immediate sense of the frequently noticed fact that the detailed descriptions of the cosmos mimic the language of the Way of Truth. For example, in B10 the “encircling heaven” is “bound down by Necessity to hold the limits of the stars,” immediately recalling the description of what-is as held motionless by Necessity in the bonds of a limit (B8.30-31). This tends to confirm that the very same sphere is being first correctly described, then, in the cosmology, incorrectly redescribed.

  On such an interpretation the Way of Seeming does not vindicate phenomena, but it does address the most glaring problem facing anyone ready to entertain Parmenides’ conclusions: how can human experience have got things so catastrophically wrong? Actually, the goddess is telling us, the step from appearance to reality is surprisingly small, a numerical mistake of one.

  This admittedly does not even broach the problem of accounting for human error. According to Parmenides, there are no separate thinking subjects. All thinking is what-is thinking itself. How could it find room to misconceive itself? That is a question on which Parmenides left his interpreters to puzzle.19

  MELISSUS

  Melissus can be dated loosely to the mid- or late-fifth century B.C. In outline, his treatise argued that what exists is (i) omnitemporal; (ii) infinite in extent; (iii) one; (iv) homogeneous; (v) changeless, that is, without (a) reordering, (b) pain, (c) grief, or (d) motion; (vi) indivisible; and (vii) bodiless.

  This methodical defence of a version of Eleatic monism was written in unadorned Ionian prose, worlds away from Parmenides’ highflown poetic obscurities. Thanks to its relative simplicity, its formulations were to be more widely reflected in ancient formulations of Eleaticism than those of Parmenides himself. The conclusions are by and large Parmenidean, but the arguments are not. There is little sign of Parmenides’ most fundamental premise, the rejection of ”… is not.” Furthermore, whereas Parmenides, as we saw, in the main inferred each predicate of what-is by an independent argument, nearly all Melissus’ arguments form a single chain, with each predicate inferred directly from the previous one.

  Melissus is not interested in Parmenides’ highly refined mode of investigation through the logic of being and negation. He writes, I suggest, as an Ionian physicist addressing a like-minded audience, and expounds the Eleatic One with arguments appropriate to Ionian cosmology. The title of his treatise (probably authentic, despite some scholars’ hesitation), Peri physeôs ê peri tou ontos (On nature or on what-is), in effect labels his account as an Eleatic physics. His departures from Parmenides, in permitting himself ordinary temporal language and in postulating a spatially infinite being, are more symptomatic of this project than of intellectual independence.

  For the book’s first two arguments, we have a probably complete text. However, I believe that scholars have failed to locate correctly the division between argument (i), about temporal infinity, and argument (ii), about spatial infinity.20

  (i) “Omnitemporal”

  (DK 30 B1) It always was what it was, and always will be. For if it came to be, it is necessary that before it came to be there [or “it”] was nothing. Well if there [or “it”] was nothing, nothing could ever come to be out of nothing.

  (B2, beginning) Since, then, it did not come to be, it both is and always was and always will be.

  Where Parmenides had started from a highly paradoxical premise, the rejection of ”… is not,” Melissus’ starting premise, the causal thesis that “Nothing could come to be out of nothing,” would hardly cause a stir in his audience. Some such principle or assumption had lain at the root of the ubiquitous early Greek postulation of an everlasting primeval stuff of the universe. The principle, rarely if ever challenged in antiquity, was generally regarded as indubitable. (Comparably to Parmenides, Melissus leaves us to supply the converse principle, “Nothing could perish into nothing” as grounds for future indestructibility. )

  Also unsurprising, especially in an east Greek context,21 is Melissus’ expression of this permanence in terms of omnitemporality, where Parmenides had chosen to collapse past and future into the present. This need not be a significant philosophical disagreement. Melissus may simply see himself as presenting Parmenidean thought in the philosophical idiom which his audience understands.

  (ii) “Infinite in extent”

  (continuing B2) And it has no [spatial] beginning or end, but is infinite. For if it had come to be it would have a [spatial] beginning (for it would have begun the process of coming-to-be at some time) and end (for it would have ended the process of coming-to-be at some time). But since it neither began nor ended [the process], and always was and always will be, it has no [spatial] beginning or end.

  Critics since Aristotle have detected here the fallacious inference: “If p, q: but not-p; therefore not-q.“ But this is probably unfair. Where Parmenides’ arguments had evidently addressed an audience used to the concept of a finite universe, Melissus assumes the opposite, as we might too – that the universe will be infinite unless it can be shown to be otherwise. This again reflects his audience’s background in Ionian physics, where the infinity of the universe, prefigured as early as Anaximander, was by Melissus’ day a feature of Anaxagoras’ cosmology and on its way to becoming a cardinal doctrine of atomism.

  Melissus’ question is: what could have set bounds on that-which-is? If nothing, then it is infinite. The one thing that could have made it finite is a process of generation, which, being temporally bounded, could only have produced a spatially finite being. You cannot create an infinitely large entity, any more than you can build an infinitely long road, given only that any such process must start at some time (and hence somewhere) and stop at some time (and hence somewhere). Since, therefore, argument (i) has already demonstrated that it never came to be, there is nothing to limit it spatially, and it becomes infinite by default.

  Melissus adds, somewhat obscurely, how the spatial infinity of argument (ii) is both inferentially dependent on and parallel to the temporal infinity of argument (i). B2-4 may be continuous, as follows:

  (end of B2) For what is not all would not be able to be always. (B3) But just as it is always, so too it must also always be infinite in magnitude. (B4) Nothing is either omnitemporal or infinite if it has a beginning and end.22

  Melissus’ next move is from (ii) spatial infinity to (iii) unity: “For if there were two, they would not be able to be infinite, but would have boundaries in relation to each other” (B6). This predicate gives Melissus’ entity its name, “the One.” And from (iii) unity, he infers (iv) homogeneity (it is “alike everywhere”), on the ground that anything heterogeneous would thereby be a plurality (MXG 974a12-14).23

  The surface meaning of these two successive inferences is largely unambiguous – a far cry from Parmenides. What remains open to debate is the quality of argument. The Peripatetic Eudemus was perhaps unfair to object that the move from (ii) to (iii) works only for things infinite in all directions, since Melissus clearly does have that kind of infinity in mind in (ii). On the other hand, the only kind of unity that t
he inference can plausibly yield is uniqueness, and mere uniqueness is not incompatible with being a heterogeneous plurality (most of us, for example, believe the universe to have both properties).

  After a brief summary of the results so far (B7.1), there follows a generic argument for the next predicate,

  (v) “changeless”

  And it could neither lose anything nor become larger nor be rearranged, nor does it suffer pain or grief. For if any of these happened to it, it would no longer be one. For if it changes, it is necessary that what-is is not alike, but that what previously was perishes while what-is-not comes to be. So if it were to become changed by a single hair in ten thousand years, it would all perish in the whole of time.