Negation in Ancient Greek Philosophy: Parmenides
Domenico Pacitti (1991)
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8. Given the spirit of critical discussion and the relative absence of our doctrinal teaching and specialisation in ancient Greece, it is not so surprising that in the three millennia which have elapsed since the Vedic riddle was first posed, the greatest light has been shed on the problem of negation by Plato. But as this comes in the form of an attempted refutation of Parmenides, we would do well to commence with Parmenides himself.
For the ancients, then, the problem of negation was couched in ontological terms as the problem of nonbeing. To attend to this will throw further light on truth and meaning, which we have observed to be closely linked to the question of the nature of the negative.
Consider the following extracts from the fragments of Parmenides accompanied by my interpretive renderings.
8.1. The argument, then, is sublime in its simplicity: only being is, since nonbeing cannot be. Being is therefore one: the collateral existence of nonbeing would have meant two, from which an infinitude of divisions would then have arisen. Now, since it is the same thing that can be thought and can be, any thought of that which is not will be impossible. For a thought of that which is not will be a thought of nothing, and hence not a thought at all. It follows, moreover, that sameness and difference can have no meaning, since it requires at least two for this to be possible, and that both time and change are illusory, since only ‘is’ is.
It is sometimes objected that the thought of, say, a four-sided triangle would still qualify as a thought even though such entities could not exist. But here we must be careful to distinguish the thought of a given thing in the sense of our actual prehension of it, on the one hand, from the thought that some thing might be the case, on the other.
Thus Parmenides could have answered that while there are such things as triangles and four-sided figures, their combination in the intended sense is nowhere to be found.
The thought that is not the thought of.
Furthermore, we must take care to distinguish that which can be now from that which can be in the future. If there can be no coming into being, no time, no change, then only the former will have sense.
This argument of Parmenides, almost certainly mounted against sophistic relativism and probably against Heraclitus, has been grossly underestimated by almost everyone except Plato. Its seeming weakness lies in its treatment of falsity and negation. For as we have seen, a thought will either be of that which is, in which case it will be a valid thought, or else it will be of that which is not, namely nothing, in which case it will not be a thought at all.
Equally, on this view how can a thought be negative when thought is so closely linked with being and there is no such thing as nonbeing?
Parmenides contrasts ‘Truth’ with ‘belief’: belief is wholly illusory and belongs to the world of sense-perception and therefore of appearance. Thus there can be no question of truth’s immanence in belief, for truth is to be pursued and attained through pure thought, the pure thought of that which is.
It is in this sense that truth is transcendental.
8.2. Utilised by the sophists against Plato, one strand of the Parmenidean argument had taken the following form: If thinking is thinking something, and thinking what is not is not thinking, then by the same token you cannot refute anyone who is thinking what is not, since you would be refuting nothing, which would of course not be refuting at all.
A partial response to this occurs in the Theaetetus between 188c and 189d where Socrates, proceeding “not by this method of knowing and not knowing, but by that of being and not-being,” demonstrates that there is a difference between holding a false opinion and holding an opinion on that which is not, so that an opinion will always be of something which exists. In arriving at a false opinion he misses the object he was aiming at and thus says one thing for another – ἕτερον δὲ ἀνθ᾿ ἑτέρου.
Hence false opinions are, after, all refutable.
However, one wants to say: But an opinion is not a thought. For is it not the case that opinions belong to the world of appearances, while thought belongs to the world of reality, the transcendent world of truth?
Two more aspects of Parmenidean thought caused Plato to revise his early theory of forms as presented in the Phaedo (74-75, 92d & 100c) and Republic (596a & 597c), thus inducing him to write the Parmenides, where:
1. immanence (μετέχειν) and transcendence (μίμησις) are shown to be separately untenable but mutually interdependent;
2. the One (τὸ ἕν) is defined antinomially as one, whole and finite (142d) and many, divided and infinite (144c).
This second point is highly significant for us, as it clearly contradicts and seemingly disproves the Parmenidean position on negation – for Plato convincingly shows that the same thing is describable both as X and as not-X.
Chuang (B), in perceiving that like and unlike could share a common feature which would make them together different from something else, failed to see what Plato saw, namely that there was no contradiction or paradox in the fact that the same thing could both be and not be X.
Plato's Parmenides is seemingly about the One, but in effect it is about being. If we bear in mind that ‘nothing’ in Greek was ‘not one’ (μηδὲν), then it will come as no surprise that the opposite of nothing may be seen to be one. And it is in this sense that ‘one’ can be taken as standing for something, i.e. what there is, as opposed to nothing, i.e. what there is not. But when Plato distinguishes ‘one’ from ‘is’ on the grounds that ‘one one’ and ‘one is’ would otherwise be admissibly interchangeable, we feel like saying: Aren’t you confusing name and meaning here?
Although the modern ‘commonsense’ view typified by Quine (1948) sees it this way, I think that the notion of rightness of assertion to which I have already referred favours Plato, and indeed also Parmenides, on this. What I mean is that from the modern perspective two or more words may be said to name the same thing (just as the same word may be made to name different things on different occasions), but this notion of synonymy or interchangeability seems to me to be a pejoratively modern development arising out of the concept of a certain progressive decadence in the use of language.
The stronger bond that the ancients possessed in respect of being, knowing and saying seems to have a moral rightness about it which has now been lost. And it was this loss of contact with the real on the part of the artists which led Plato, as we know, to condemn art outright in the Republic.
Anselm of Canterbury saw this moral rightness about language so much so that he accorded truth and rightness even to false statements, although to a lesser degree than in the case of true ones:
Disc. [V]era est oratio, etiam cum enuntiat esse quod non est.
Mag. Vera quidem non solet dici, cum significat esse quod non est; veritatem tamen et rectitudinem habet, quia facit quod debet. Sed cum significat esse quod est, dupliciter facit quod debet : quoniam significat et quod accepit significare, et quod facta est.
Truth is absent only in the meaningless, for here language does not signify as it should : there is no rectitudo. Thus Plutus in Dante’s Inferno can only say, “Papè Satàn, papè Satàn aleppe!”
For Anselm truth is therefore graded or scalar as opposed to exclusive with respect to falsehood. A certain rightness of moral judgement will be operative in grading the truth-content of the following sentences where all are strictly speaking true. Thus, in normal circumstances,
/1/ There is no sugar on the table.
will have a greater degree of rightness – and hence of truth – in respect of:
/2/ There are no elephants on the table.
and even more so compared to:
/3/ There are no unicorns on the table.
/4/ Two men are not fencing.
/5/ Two men are not in orbit around Jupiter.
are materially admissible, but /5/ lacks the rightness of judgement of /4/.
Rightness of assertion, rightness of judgement and therefore truth itself, being in this manner scalar, will resist any solely formal application of precise criteria – rather in the manner of the sorites paradox.
If the Parmenides is not always intelligible, it is certainly powerful and unrelenting. Hegel (1807) refers to it as “surely the greatest artistic achievement of the ancient dialectic.”
In this dialogue the first step towards a clarification of the nature of the negative is taken, the nature of the forms is set in better focus and the way is paved for Plato’s final refutation of Parmenides and his fullest exposition of negation in the Sophist.
It is important to see that Plato’s enormous respect for Parmenides and his attack on the Parmenidean position are not incompatible. For as Plato himself puts it, we must not honour a man above the truth – ἀλλ᾿ oὐ γὰρ πρό γε τῆς ἀληθείας – another thing that many moderns find it difficult to understand.
 I therefore agree wholeheartedly with Popper (1969, pp.148-149) when he writes: "The early history of Greek philosophy, especially the history from Thales to Plato, is a splendid story. It is almost too good to be true. In every generation we find at least one new philosophy, one new cosmology of staggering originality and depth. How was this possible? Of course one cannot explain originality or genius. But one can try to throw some light on them. What was the secret of the ancients? I suggest it was a tradition – the tradition of critical discussion." Popper sees the splendour of the ancients as being due also to the fact that theory of knowledge was for them closely linked to cosmology, or as I would put it, because the distinction between ontology (what there is) and epistemology (what we can know about what there is) did not exist in the same way for the ancients as it does for us now. But Popper's conception of cosmology is much wider than the normal conception: "All science is cosmology, I believe, and for me the interest of philosophy, no less than that of science, lies solely in its bold attempt to add to our knowledge of the world, and to the theory of our knowledge of the world" (op.cit., p.136). Thus for Popper both philosophy and science lose interest "when they become specialisms and cease to see, and to wonder at, the riddles of our world" (op. cit., p.136).
 The philosophical arguments put forward in Parmenides' poem, On Nature, are not always easy to follow and are subject to much debate. My renderings are interpretive in that they make no claim to final linguistic precision or felicity of literary expression. I have considered the following translations of the fragments presented here: Burnet (1930), Mourelatos (1970), Barnes (1982) and Kirk, Raven & Schofield (1983). The classic editions containing comprehensive commentaries are Diels (1897), Untersteiner (1958) and Tarán (1965). See Kahn (1968) for a review of Tarán. But Zeller & Mondolfo (1967) is perhaps the most comprehensive of all and contains the best bibliography. The present extracts from Parmenides correspond to Diels & Krantz (1960) – DK – as follows: Parmenides1 = DK B2 (complete); Parmenides2 = DK B6 (lines 1-2); Parmenides3 = DK B7 (lines 1-2); Parmenides4 = DK B8 (lines 34-36); Parmenides5 = DK B8 (lines 12-21).
 Barnes (1982, pp.174-175) gives a 28-stage formalisation of Parmenides' argument: (∀x) (∀y) (Sxy → -Ey), where 'Sxy' abbreviates 'x studies y' as opposed to 'x thinks of y'. I find this transformation of νοεῖν both unnecessary and misleading. Barnes probably has in mind Mourelatos's (op.cit., p.164) observation that the Greek verb in question "functions in Parmenides not as a psychological but as an epistemic term", expressing a surer apprehension of truth. But Mourelatos rightly rejects such a solution. See von Fritz (1943 & 1946) on the development of νοεῖν in Homer, Hesiod, Xenophanes, Heraclitus and Parmenides. According to von Fritz, νοεῖν in Parmenides becomes thinking in the sense of reasoning, although the general continuity with Homer remains more broadly valid. Provided this is borne in mind I see nothing wrong with the English rendering, 'to think'. On saying and thinking in Parmenides, see Graeser (1977).
 Mourelatos (op.cit, pp.41-73) provides a perceptive analysis of Parmenidean ἐστι, summarising that it is a hybrid between the 'is' of predication and the 'is' of identity." He gives a fairly well-balanced evaluation (pp.51-55) of Calogero's position as put forward in Calogero (1932 & 1935), although I do not agree with his characterisation of Calogero's conception as "metalinguistic", depending as it does on a use/mention distinction which would be anachronistic in the context of the ancients (cf. my note 37 to 4.1., p.20). Nor do I agree with Mourelatos's (pp.53-54) criticism of Calogero's view – in certain respects close to my own – that "for Parmenides reality, truth and language are fused, as they are in much of archaic thought." A similar view to that of Calogero is expressed by Furth (1968). Again, on being and existence in Ancient Greek see Kahn (1973 & 1976). Reinhardt (1916) and Fränkel (1930) stand alongside Calogero as the classic studies of Parmenides. See also the seminal paper by Owen (1960).
 Neglect of this crucial distinction continues to lead many scholars astray. Thus Barnes (op.cit., p.17), having considered the relevant fragments, erroneously concludes: "We can and do think of things that do not exist; we can and do talk of things that do not exist; we can and do study things that do not exist. Such thoughts, such discourses, and such studies are not always fatuous. Parmenides has given us no good reason to rejects those ordinary opinions; and in consequence his metaphysics is based upon a falsehood and defended by a specious argument." Barnes does not dismiss Parmenides' argument: he misses it.
 At the beginning of chapter on "the vagueness of what is not" Mourelatos (op.cit., pp.74-93) takes himself to have understood why Parmenidean being and truth are equivalent, so that what-is "collects the values that go not on the left-hand side, the subject position of speculative predication, but rather those that go on the right-hand side, the predicate position." This reminds me very much of Ramsey's (1927, p.39) formulation that in 'For all p, if he asserts p, p is true', "we see that the propositional function p is true is simply the same as p, as e.g. its value 'Caesar was murdered is true' is the same as 'Caesar was murdered'." What Ramsey and Mourelatos fail to see – but what, I think, Parmenides sees – is that 'Caesar was murdered is true' expresses a higher-order judgement in respect of 'Caesar was murdered'. It is partly in order to avoid this problem that I reject the concept of a truth-functional proposition (cf. pp.21-24 and note 37, D. Pacitti, The Nature of the Negative). Furthermore, Mellor (1990, p.xix) is wrong to see Ramsey as "really only echoing Aristotle" at Metaphysics 1011b, 26-28, for Aristotle's definition gives truth as a mixture of saying with being (cf. my note 43). Notice how in Parmenides4 and Parmenides5 judging, thinking, naming and being are tightly held together for truth. An important link between Parmenides, the Vedic poet and Chuang, it seems to me, emerges at DK B9:
Guthrie (1965, p.57) translates: "Then since all things have been named Light and Night, and the names appropriate to their powers assigned to these and those, everything is full alike of Light and obscure Night, both equal, since there is nothing that shares in neither." Mourelatos (op.cit., p.85) prefers "since nothingness partakes in neither", which seems quite wrong in reifying 'nothing'; Guthrie avoids this by use of the expression "since there is nothing that"; I should have preferred "since no thing partakes of neither" in order to disambiguate completely. Now if no thing partakes of neither light or night, then all things will have to belong to either the one or the other or to both, which is to say that light and night are both things that are. This may reasonably be seen as an admission of cosmic opposites but with the crucial exclusion of being/nonbeing as a valid opposition in this category. Within this perspective the opposite pairs day/night and death/immortality in the Vedic hymn could be understood as accepted symmetrical cosmic opposites inducing the reader to accept such an opposition in the case of being/nonbeing thus rendering the riddle insoluble. The solution is to perceive that only being is, that nonbeing is the result of judgement over being and that the ensuing relationship is consequently asymmetrical. Chuang's symmetrically presented Things are not not-other; things are not not-so (Wu wu fei pi, wu wu fei shih – cf. my note 5 to negation in Ch.2 of the Chuang Tzu) leaves the real world as it is, a world of 'is' and not of 'is not'. Again the symmetrical being/nonbeing relationship is untenable. Heidegger (1957, p.18) interprets Parmenides at DK B3 to be saying essentially, "Das Sein gehört in eine Identität", i.e. that being 'belongs in an identity' (with thinking), on the basis if which he presents an important and penetrating study of identity and difference which, however, turns out to have little to do with Parmenides. I quite agree with Mourelatos (op.cit., p.197) that the "capricious use of terminology in 'hermeneutic' interpretations of the pre-Socratics (by Heidegger and scholars who have been influenced by him) has given a bad name to etymological considerations as such". For a philosopher's insight into Parmenides see Anscombe (1969). On Parmenidean being/nonbeing (in addition to the bibliographical references given in my previous notes) see also the more recent papers by Mourelatos (1976), Gallop (1979) and Swindler (1980). Notwithstanding my disagreements with Anscombe (see for example Domenico Pacitti, The Nature of the Negative, page 78), I have found her work the most stimulating.
 I say 'seemingly' since Parmenides' position remains substantially unaffected: what really is is not what is not but what is. Or to put it differently, 'not' has no place in a first-order description of the world.
 I do not, of course, mean that the Greeks consciously tried to maintain such a bond out of any sense of duty – see Adkins (1960, p.253), who writes: "The Greek moral scene does not provide, and never has provided, even the raw material from which a categorical imperative could be fabricated." Rather, how one ought to live was how one ought to live, which for them was – 'eudaimonically'. How language ought to function was how language ought to function. It is this purposefulness inherent in language that I have in mind.
 Student (S): [A statement] is true even when it states that what-is-not is. Teacher (T): Admittedly, we are not accustomed to call the statement true when it signifies that what-is-not is; nevertheless it has a truth and a correctness because it does what it ought. But when it signifies that what-is is, it does what it ought in two respects: for it signifies (1) what it has received the capability of signifying and (2) what it is designed to signify. The original Latin versions of this and the following passage as they occur in Domenico Pacitti, The Nature of the Negative are from Anselm's Dialogus de veritate (Migne, 1853), ch. 2: "De veritate significationis, et de duabus veritatibus enuntiationis", pp.469-470. The newly added English renderings are by Jasper Hopkins & Herbert Richardson (Hopkins & Richardson 2000). It is worth looking at some of the discussion which leads up to this. One is struck not only by the brilliance of Anselm's thought, but also by the pupil's intelligence: T: Then, does it seem to you that the thing stated is the truth of the statement? S: No. T: Why not? S: Because nothing is true except by participating in truth; and so, the truth of something true is in that true thing. But the thing stated is not in the true statement, and thus must not be called its truth; rather, it must be called the cause of the statement's truth. Therefore, it seems to me that the truth of the statement must be sought only in the statement itself. T: Consider, then, whether the truth you are looking for is either the statement itself or its signification or something in its definition. S: I do not think it is. T: What is your reason? S: Because if the truth of the statement were any of these, then the statement would always be true. For the statement's definition remains the same irrespective of whether what it states is or is not the case. In fact, the statement, its signification, and the other things remain the same. T: Then, as you see it, what is truth in the statement? S: All I know is that when the statement signifies that what-is is, then it is true and truth is in it. T: What is an affirmation designed to do? S: To signify that what-is is. T: Then, this is what an affirmation ought to do? S: Certainly. T: So when an affirmative statement signifies that what-is is, it signifies what it ought to. S: Obviously. T: But when it signifies what it ought to, it signifies rightly, or correctly. S: That's right. T: And when it signifies correctly, its signification is correct. S: No doubt about it. T: Therefore, when it signifies that what-is is, its signification is correct. S: This follows. T: Moreover, when it signifies that what-is is, its signification is true. S: Yes, its signification is both correct and true when it signifies that what-is is. T: So for an affirmation to be correct is the same as for it to be true, namely, for it to signify that what-is is. S: Yes, these are the same. T: Therefore, the affirmation's truth is simply its rightness, or correctness (rectitudo). S: I now see clearly that truth is this rightness.
 The sorites paradox has become central to a deeper understanding of the limits of a purely extensional approach to meaning. Thus Wright (1975) in his interesting paper on the coherence of vague predicates fails to salvage the very notion of a semantic rule through application of his logically weighted "governing view", although he raises interesting questions on the nature of vagueness, ostensive definition and the concept of continuity. Fine (1975) starts out from what seems to me to be the mistaken premise that "vagueness is deficiency of meaning" in an attempt to tighten the true/false/indefinite trichotomy. Logical relations holding among indefinite sentences are hypothesised as "penumbral connections" and the logic of vagueness is discussed, but no reason emerges in favour of the abandonment of classical logic. Sanford (1975) in his study of borderline logic does well to draw a parrallel with morality: "Morally relevant distinctions can be important without being sharp. The distinctions between living and non-living, between person and non-person, and between one who is the same person and one who is not, can all figure in arguments which involve moral principles" (op.cit., p.39). I would go further and suggest that depth of meaning is independent of precision and perhaps even inversely proportionate to precision. Polanyi (1962, p.251) expresses the view that "only words of indeterminate meaning can have a bearing on reality", and that "we must accept the risks of semantic indeterminacy" (cf. the works of Quine already cited). More recently, Unger (1979) in an amusing and insightful challenge to Ayer correctly highlights our habitual reliance on approximation in our normal transactions with the world: a table is still a table even if a few atoms are removed. Through a sorites of decomposition Unger arrives at the fictional nature of his own existence, concluding that the sorites arguments allow us to perceive "the truly thoroughgoing inconsistencies in our available language and thought." See also Haack (1974, pp.109-125) and Priest (1979). If we consider the wider focus of the negative in respect of the affirmative, then it will not be difficult to see the relevance of the question of 'right judgement' and its close connection with 'magnitude of meaning' in the context of the sorites paradox. This may also be observed at the level of literature. For example in Leopardi's poem Infinito, the poem's sublime staticity yet evokes a mounting effort on the part of the judging mind, which can never impose legitimate divisions or discern extensional boundaries for the "interminati spazi", significantly in the plural. On the concept of infinity in early Greek thought, see Mondolfo (1956).
Note: This text is an extract from Domenico Pacitti, The Nature of the Negative: Towards an Understanding of Negation and Negativity. Giardini, Pisa, 1991 (pp.55-63).
In the same series of philosophical readings from the published work of Domenico Pacitti