The Cambridge Companion to Early Greek Philosophy

by A. A. Long

  Formally, given the chain structure of the reasoning, this is meant to be a new inference from (iv) homogeneity, although the inferential connexion is weak at best. Would the supposition of change really prevent its being “alike,” and hence “one,” in the senses in which these predicates were used in arguments (iv) and (iii) respectively? Much more interesting is the additional ground for changelessness, which derives from predicate (i), “omnitemporal”: any change involves some measure of perishing, and if a thing’s parts are perishable the whole too will perish, given infinite time. If a thing’s parts are severally perishable, it is possible for them all to perish together, and (an implicit anticipation of the Principle of Plenitude?) whatever is possible cannot remain unactualized for ever.

  There follow four arguments against four specific kinds of change (B7.3-10). The first three, against (a) reordering, (b) pain, and (c) grief, are largely a reapplication of the generic argument that change would negate the established predicates (i) “omnitemporal” and (iv) “homogeneous.” But under (b) Melissus adds the consideration that for the One to feel pain would be a diminution of its “power.” This remark falls outside the inferential chain but conveys the important clue that the One is being assimilated to a deity.24 The equation of the primary existent to god is, once again, sufficiently familiar to an audience attuned to the work of Anaximander, Anaximenes, and Heraclitus to be assumed without argument. But it also constitutes a link to Parmenides, whom we found to be conforming to that same tradition when he identified thinking with being.

  The most important argument against a specific form of change is that against motion (B7.7-10), which can be divided up as follows:25

  (v)(d) Motionless

  1. Nor is there anything void. For void is nothing. Well, what is nothing could not very well exist.

  2. Nor does it move. For it cannot give way at any point, but is full. For if there were void, it would give way into the void; but since there is no void, it has nowhere to give way. (There could not be dense and rare. For what is rare cannot be as full as what is dense, but what is rare already thereby becomes emptier than what is dense. And that is the criterion for distinguishing between what is full and what is not full. Hence if something gives way or absorbs, it is not full, but if it neither gives way nor absorbs, it is full.)

  3. [summary] Hence (1) it must be full, if there is no such thing as void; and hence (2) if it is full, it does not move.

  This is the first recorded argument that explicitly makes motion dependent on void (even if the absence of void may already be implicit in Parmenides’ refutation of motion). And Melissus’ rejection of void, as being nothing and therefore nonexistent, is the nearest he comes to the Parmenidean mode of argument through the logic of being and negation. He is not denying an external void into which the One might move. This is hardly necessary, given that the One is infinite in all directions. He is denying any admixture of void that would make it less than totally dense and thus permit motion by compression or redistribution: that is the point of the parenthetical statement in (2).

  There remains the inference from (v)(d) “motionless” to (vi) “indivisible” (B10): division is taken to be a process that involves the motion of the parts being separated. Finally, we come to an inference (B9) that is hard to fit into the continuous chain, being in fact a further derivation from predicate (iii):

  (vii) Bodiless

  Being one, it must not have (a?) body. If it had bulk, it would have parts and no longer be one.

  It is puzzling that the One, having been shown to be totally dense and therefore immobile, should now prove to be incorporeal. In principle it seems likelier that he is denying here that it has a body, with organic parts, and is thereby rejecting an anthropomorphic conception of divinity. Admittedly, however, the reference to “bulk” suggests that corporeality as such should be the target.

  Just as Parmenides had criticized reliance on the senses (B6), so too Melissus, apparently in a separate section of his treatise, turned his ontological conclusions against the senses (B8):

  That then is the strongest evidence that there is just one thing, but the following are further pieces of evidence.

  If there were many things, they must be such as I say the One is. For if there are earth, water, air, fire, iron, gold, living creature and dead, black and white, and the other things people say to be real – if there are these things, and we see and hear correctly, each of them ought to be just as it first seemed to us to be, and not to be changing or becoming different: each of them ought to stay just as it is.

  Yet as it is, we claim that we do see, hear and understand correctly. And it appears to us that the hot becomes cold and the cold hot, the hard soft and the soft hard; that the living creature dies and comes to be out of what is not alive; and that all these things undergo alteration and that what they were and what they are now are not at all alike; that iron, although hard, is worn away by contact with the finger, and so too gold, stone and everything else that is thought to be hard; and that earth and stone come to be out of water.

  Well, these things are inconsistent. We said that there are many everlasting things which have forms and strength, yet it seems to us that everything undergoes alteration and changes from the state we see it in each time. Hence it is clear that we do not see correctly, and that the appearance that this plurality of things exists is incorrect. For they would not be changing if they were real, but each would be such as it appeared. For nothing is more powerful than what is real, whereas if it changes what-is has perished and what-is-not has come to be.

  In this way, then, if there were many things, they would have to be such as the One is.

  What exists must be changeless (predicate (v)). If sense objects existed, they would have to be changeless. But the senses themselves report them as changing. Therefore sense objects are illusory.

  Retrospect

  Earlier traditions in cosmology had investigated the composition of the universe by primarily empirical means, seeking to identify a privileged stuff in the cycle of elemental transformation, and to account for the regularities of its behaviour by assimilation to familiar biological, mechanical, or political models of order. Neither Parmenides nor Melissus attempts to step altogether outside the discipline of cosmology. Staying within it, they question its use of empirical criteria, which had come up with too many competing answers to inspire confidence. Both therefore recommend a new start, an appeal to a priori principles to see how far these may narrow down the possible answers to the cosmologists’ questions. The outcome is shocking: in virtue of its perfect homogeneity over time and space, the universe can possess none of the differentiating features that cosmologists had hitherto made their explananda.

  So far, there is no difference between Parmenides and Melissus, apart from the stylistic differences that typically separate prose from verse. They further share – a natural corollary to their a priori approach – an intense interest in inferential method, although here Melissus goes further in imposing a clearer overall architectonic on his argument. Even the kind of a priori premises to which they appeal may overlap to some extent – for example, considerations of how available space may constrain motion. Yet, it is here that their greatest differences can be located too. Parmenides’ starting points themselves fall outside the physical tradition: the principles of reference and negation, the conditions of thought, and the logical behaviour of the verb “to be.” Melissus’ are the kind of a priori principles – the impossibility of generation ex nihilo, the infinity of space and time – with which his cosmologically attuned audience would already feel comfortable. Melissus can thus be compared to Zeno. Each in his own way undertook to defend Parmenides’ world view to a disbelieving audience by promoting it in that audience’s own terms. Zeno had done so by dialectical appeal to their commonplace assumptions about space and time. Melissus approached the same task by a physicist’s appeal to the principles of current scientific thinking.

  NOTES

>   1 Most of the interpretations proposed in this chapter can also be found in my two articles, “Melissus” and “Parmenides,” in Craig [145].

  2 On the opening of Parmenides’ poem, see Most in this volume, p. 354.

  3 For further treatment of the poem’s introduction, see Lesher in this volume, p. 236.

  4 Archytas DK 47 A24.

  5 Note that whereas Parmenides (see B8.36-38) explicitly rejects time as a self-subsistent entity, he apparently feels no such need in the case of space. In Sedley [409] I argue that even early atomism had no developed conception of self-subsistent space, its void being a space-occupier.

  6 Depending on the emendation adopted for the impossible ateleston, “unbounded”: I shall myself favour “balanced.”

  7 See, among other discussions, Owen [313]; Sorabji [129] ch. 8.

  8 I place a comma at the end of line 11, not the usual period.

  9 Those who resist the thinking-being identity are forced to translate this as, for example, “For the same thing is there for thinking (i.e., as the object of thought) and for being (i.e., as the subject of ‘be’)” – a most tortuous piece of syntax. For a detailed defence of the thinking-being identity, see Long [305].

  10 I thank Tony Long for this observation.

  11 This reading, oude chronos estin ê estai, in 36 is well defended by Coxon [270] on the basis of Simplicius’ report of the text.

  12 To supply what-is as the subject of onomastai is the proposal of M. Burnyeat, “Idealism and Greek philosophy,” PR 91 (1982), 19 n.22, adopted by KRS, 252.

  13 Meizon and baioteron (44–45) mean “larger” and “smaller,” not “more” and “less” as suggested in some modern translations of Parmenides.

  14 Reading rather than in line 1.

  15 For much the same interpretation, see Bodnár [282].

  16 For divergent accounts of Parmenides in this volume, see Graham, p. 165, Lesher, p. 240, and McKirahan, p. 157 n. 15.

  17 Furley [293].

  18 Popper [316].

  19 For further discussion of Parmenides’ handling of human error and cognition, see Lesher and Laks in this volume, pp. 239 and 255.

  20

  (ii) addresses spatial infinity (see especially Reale [277]) has not been generally appreciated in the English-language literature on Melissus, but see KRS, 393-95 for an honourable exception.

  21 Cf. Heraclitus DK 22B30.

  22

  23 The citation is of the paraphrase of Melissus in the pseudo-Aristotelian De Melisso, Xenophane, Gorgia.

  24 For reports that Melissus identified the One with god, see DK 30 A13.

  25 Analysis based on Sedley [409] 178–79.

  RICHARD D. MCKIRAHAN JR.

  7 Zeno

  Much of our little information on Zeno’s life comes from the prologue of Plato’s Parmenides. Most scholars accept Plato’s statement that when Socrates was “very young” (though old enough to engage in philosophical debate) Zeno was forty and Parmenides was sixtyfive (Parm. 127a-b). The setting of the Parmenides is the quadrennial Great Athenaia, and the best guesses for its dramatic date are 454 B.C. when Socrates was 15 and 450 B.C. when he was 19.1 Also, Plato’s statement that “Zeno was of a good height and handsome to see; the story goes that he had been Parmenides’ young lover” (127b) is perfectly possible, though not otherwise attested. Even if the setting of the Parmenides is historically plausible,2 the notorious unreliability of Plato’s reports on earlier philosophers makes it unwise to take much else of what he says on trust. The conversation in the Parmenides certainly did not take place, and we may fairly doubt that Socrates met the philosophers from Elea. Further, Plato indicates that Zeno’s treatise was unknown in Athens prior to the dramatic date of the Parmenides (127c), but he also implies that it was written many years earlier, and he says it had been circulated (apparently soon after its writing) without Zeno’s authorization (128d) – claims that although not actually contradictory are hard to reconcile.3

  Plato declares that the book aimed to defend Parmenides against those who pointed out absurd consequences of Parmenides’ view that there is only one thing. It contained arguments that showed that even greater absurdities follow from the hypothesis of these opponents – “if there are many things” – than from the view they attacked (128c-d). But we need to exercise caution about all this. Indeed, all we know about Zeno confirms that the treatise contained a number of arguments. Possibly the book left the goal of the arguments unclear; Socrates infers its purpose after hearing it through (128a-b). If so, then Plato’s assertions are an interpretation and one that demands close examination.

  In fact, Plato’s interpretation is open to question on several grounds. First and most obvious, although according to Plato the aim of Zeno’s work was “to contend, against all that is said, that things are not many… each of your arguments proves this” (127e), several of the arguments attack not plurality but motion, and others have other targets. Further, the philosophical link asserted to hold between Parmenides and Zeno, that while Parmenides argued positively for a radical monism, Zeno defended this position by arguing against pluralism (128b-c), has been denied. Still worse, some have held that some of Zeno’s arguments actually tell against Parmenides as much as his opponents. Plato’s interpretation is fatally flawed if these charges are true, and all that remains of Zeno is a number of arguments of varying merit, each of which is worth scrutinizing on its own, but which taken together do not add up to anything as a whole.4

  In what follows, I shall resist the current of this interpretation. Granted that Zeno’s importance resides mainly in his individual arguments, granted also that Zeno’s link with Parmenides requires investigating, there still remains much to be said for Plato’s claim that Zeno’s purpose was to repay those who ridiculed Eleatic philosophy in their own coin.

  ZENO’S FIRST PARADOX

  Zeno’s book mentioned by Plato contained forty arguments against plurality.5 It is not always clear what counts as a single Zenonian argument, but on a plausible count about a dozen survive,6 only half of which straightforwardly attack plurality.

  According to Plato, the first argument met this description. It ran as follows: “If things that are are many, they must be both like and unlike, but this is impossible. For unlike things cannot be like, nor can like things be unlike” (Parm. 127e). Plato interprets Zeno as arguing that if things were many they would have impossible attributes, therefore, things are not many. He further interprets this argument as supporting Parmenidean monism.

  I shall take up these issues in reverse order. First, regarding monism, some hold that Parmenides was not in fact a monist,7 so that Plato’s interpretation of Zeno is desperately wrong. I disagree with this interpretation of Parmenides, but as space does not permit, I cannot argue the point here.8 It has also been remarked that monism and pluralism are not the only possible views: rejecting one does not entail accepting the other. A third possible view, that nothing exists, was propounded in the fifth century by Gorgias.9 I find this consideration logically sound but unconvincing. The issue is not whether there are other formal possibilities, but what ideas were current at the time and what were Zeno’s targets. From chronological considerations, Gorgias could hardly have proposed his theory before Zeno wrote his book, and there is no reason to suppose that when Zeno was writing nihilism was in the air. Further, if Zeno’s opponents were “advocates of plurality” (128d), it is sound strategy to prove their view untenable. Once dislodged from it, they will be more amenable to Parmenides’ positive arguments for monism. In fact, Plato makes it clear that Zeno’s arguments do not amount to a proof of monism; when Socrates suggests that they do, Zeno replies that they do not, but only attack pluralism (128b-d).

  Second, Plato reveals that Zeno’s argument is formally incomplete. Zeno said that if (a) things are many, then (b) they are both like and unlike; but (b) is impossible. It is Socrates, not Zeno, who goes on to infer that the impossibility of (b) entails the falsity of (a). This final ste
p is characteristic of the arguments known as reductio ad absurdum and reductio ad impossibile. To prove X false, show that X entails Y, where Y is absurd or impossible; since Y is absurd or impossible, it follows that X is false. Since all the surviving arguments proceed by showing that something absurd or impossible follows from a hypothesis, but not one contains this characteristic move, it has been claimed that Zeno “does not use reductio ad absurdum as a technique for disproof.”10 This claim too though logically correct fails to persuade. Plato makes it abundantly clear that the argument aims to disprove (a). If Zeno does not actually go on to draw the inference that (a) is impossible, the context makes it clear that this is the conclusion to be drawn (what else could be the point of the argument?), and once we see that (b) is impossible, Zeno expects us to reach this conclusion on our own. Rhetorically if not formally, the argument is a reductio.

  Third, Plato does not say how Zeno got from (a) “if things that are are many” to (b) “they must be both like and unlike.” Also, there is no way to know precisely what he means by like and unlike. Furthermore, the reason why (b) is held impossible, namely (c) “unlike things cannot be like, nor can like things be unlike,” can be understood in more than one way. This state of the evidence makes it impossible to reconstruct the argument with any confidence. On one account it went as follows. If there are many things, there are at least two. Pick two of them, A and B. A is unlike B because A differs from B in at least one way (A is different from B, but B is not different from B). Likewise, B is unlike A. But A is like A (since A is not different from A in any way), and B is like B. Therefore, A and B are both like and unlike. If this was Zeno’s reasoning, the argument fails because A and B can be like and unlike in the way indicated; the alleged impossibility would arise only if the same things are both like and unlike the same things in the same respect, at the same time, and so on.11 Zeno may have reached this conclusion validly, but if so, we have no clue how he did.