Negation in Ancient Greek Philosophy: Plato, Sophist
Domenico Pacitti (1991)
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8.3. The Sophist aims explicitly to refute Parmenides3. It is here in his final theory of forms that, in addition to the thesis of the intermingling or intercommunion, four forms are shown to run through all the rest: being, one, same and other. Furthermore, recalling our negative-affirmative asymmetries, this intercommunion of forms has been shown convincingly by Ackrill (1957) in his analysis of the occurrence of κοινωνέω and μετέχω to be asymmetrical.
The following important observations emerge:
In the interests of greater clarity I quote key passages in the original Greek which correspond to these five observations respectively. Each passage is followed by my interpretive summary of Plato's arguments as they culminate in respect of each of these five points.
8.4. The first thing to realise here is that for Plato as indeed for Parmenides what we now take to be the legitimate divisions of investigation into the linguistic, the logical and the metaphysical did not exist as such. I have already suggested that this confluence of the three for the Greek thinkers might just as easily be seen as a distinct advantage rather than disadvantage.
Thus Lewis (1977), for example, has attempted to prove that Plato here recognises a fundamental difference between negative identity statements on the one hand, and negative predication statements on the other. Malcolm (1967) had argued that whereas positive predication statements are distinguished from positive identity statements, negative predication is not distinguished from negative identity.
To our modern, more specialist mentality the making of distinctions where someone else has failed to do so is invariably conceived to be something positive, and no doubt it often is but surely it does not always have to be the case. We are seeing that considerable strength of vision may be found in the ancients precisely through a regular lack of clear distinction in what we now term the identifying, existential, veridical and predicative senses of εἶναι.
If I find myself in agreement with Malcolm in this instance, then it is not so much on account of the arguments he has proposed, but rather in view of the following interesting fact: formally speaking, existential quantification is, in the positive sense, quite separate from universal, and hence predicative, quantification.; but, in the negative, existential and universal quantificaton become the same thing. Thus, whereas
/1/ There are F.
is quite different from
/2/ Everything is an F.
this difference no longer holds between
/3/ There are no F.
/4/ Everything is other than F.
which mean exactly the same thing.
A far more difficult question to answer is the extent to which knowledge of something may be correctly attributed to someone when its mode of formulation and presentation by us differs radically from the manner in which the particular thing was understood by the person who supposedly understood the same thing. This makes one wonder exactly what distinctions Lewis saw.
The insight achieved in Plato1 is substantial. But we are at first inclined to wonder why Plato could not simply have said that in order for 'not' to qualify, there must be something there for it to qualify, and that it is therefore the same thing which is either being qualified or not. Or, as I have been reasoning, that the reality remains the same both times, with or without 'not', and that 'not' expresses a judgement.
But we should remember that ontology preceded epistemology for the ancients, and that for Plato the forms had real existence, even more real than our own existence, as it were, since they were conceived to be permanent. Thus in Plato1, rest motion, being, same and other are existent and enduring entities, namely forms, each made up of the totality of constituent instances in the world, and intermingling with one another, although with certain important constraints.
Socrates in Parmenides (129e) is made to express his amazement over the possibility that sameness and difference could combine. Now we see that they can and do.
It may be tempting to construe forms as classes, especially in view of the fact that Plato's 'otherness' form could be seen as the modern null class. This temptation ought to be resisted. As regards the null class, nothing shares in it; as regards the form of 'otherness', everything shares in it, including being. Also, there is no room for nil in Plato's mathematics. As regards the rest of the classes, we can have a class of tall men, but for Plato we would have a form for tallness, one for men and an overlap.
Plato2 shows that the particles μὴ and οὐ do not indicate oppositeness, but rather difference.
Thus 'not tall' will correspond to a point somewhere along the continuum of height, 'not red' somewhere on the cοntinuum of colour, and so on, This means that 'not tall' is quite different from 'not red', etc. C.S. Peirce, as we have seen, distinguished two 'nots': absolute nothing, or pure zero, which comes before creation, and 'the nothing of negation', which comes second to or after everything. There is no place in Plato's metaphysics for the former, but the latter is close to Plato's meaning.
Some scholars have misunderstood this observation on difference as meaning that where 'John is not tall', John partakes of some form other than tallness. But what he partakes of is in fact 'difference-from-tallness'. Bluck (1975) sees this; Kamlah (1963) and Wiggins (1971) both miss it.
So 'not-X' will mean 'partaking of the other of X'. And this is what is meant in Plato3. The fact that not-X is as much a part of being as X itself is brought out in Plato4, while Plato5 stresses that any relation must be between two existents, for if one of them did not exist, nor would the relation exist. Here (258d) Plato takes himself to have refuted Parmenides at Parmenides3.
Quite consistently with what has been said up to this point Plato applies the same criteria to speech (260b). What it comes to is this:
/S1/ John is running.
/S2/ John is not running.
/S3/ "John is running" is false.
Where /S1/ and /S2/ are (separately) true, then what will be expressed in /S2/ is that John partakes of the other of running (or, in 'difference-from-running'). Where /S1/ and /S2/ are (separately) false, we will explain this as a mixture of saying with nonbeing or other, namely that part of other which corresponds to being on the one hand, together with saying on the other. Hence /S3/ may be seen to express the other of being in respect of what is said about John.
In relation to each of the forms, being (τὸ ὂν) is seen as many, and not-being (τὸ μὴ ὂν) infinite (ἄπειρον), confirming an asymmetry between being and nonbeing. Plato is strikingly consistent in maintaining this ontological, rather than epistemological, approach also in the case of language, so that truth turns out to be a mixture of being with saying, and falsehood a mixture of nonbeing with saying. Thus negation in language is to be understood ultimately on the basis of ontological criteria expressed within a coherent metaphysical account which recognises the coexistence of being and nonbeing as real and existent entities, or forms, in the world.
8.5. In a recent study of Plato's response to Parmenides, Pelletier (1990) rightly draws attention to the crucial but much neglected relevance of Plato (and, one would add, of Parmenides and the ancients in general) in the areas of "natural language understanding and knowledge-representation", seeing the entire enterprise of cognitive science itself as the proverbial "series of footnotes to Plato". But I firmly oppose Pelletier's conclusion that Plato may truly be said to have "disposed of Parmenides' Problem".
If I recognise the depth of insight achieved by Plato on negation surely no one else since has shed such important light on the subject I reject his overpopulated universe of forms, and in particular I reject any purported existence accorded to nonbeing. But I do not advocate any reversal of the being-knowing priority. Let me therefore state my own position in regard to the five observations of Plato's which I have already listed:
1. If I agree that the same thing can both be and not be, then that is because 'not' exists in thought and judgement and not in reality: things are, but are judged not.
2. If I agree that nonbeing is not the opposite of being, then that is because there is no such thing or entity as nonbeing for being to be the opposite of. I heartily applaud and endorse the construal of 'not' as 'other than'.
3. When 'nonbeing' is reconstructed as judgement over the existent, then I agree that, in respect of any given thing, that thing may be judged 'not', and that in this case the 'parts of not' correspond to the 'parts of is'.
4. Again, if each part of nonbeing is real and definite, then that is because the so-called 'parts of nonbeing' are the very parts of being, the only thing there is and hence for them to be parts of.
5. I accept the reality of nonbeing when construed as a part of being over which judgement is passed, but I reject it as a form, firstly because I reject all forms as 'entia non grata', and secondly because I reject its existence on an equal footing with being.
I would in addition make the following more technical, but no less crucial, objection: I do not see that Plato distinguishes between:
/1/ X partakes of non-Y.
/2/ X is different from Y.
as ways of expressing
/3/ X is not Y.
I do not think they can be taken to be synonymous, for we learn from Plato1 that participation in otherness does not preclude sameness in respect of being.
If /1/ does not exclude
/4/ X partakes of Y.
then it is difficult to see how X can ever exclude Y on Plato's account.
This difficulty does not occur on my own account, since no exclusion ever takes place at the ontological level, but rather at the judgemental one.
That is to say that no thing excludes one thing from another, since the exclusion will be an act of judgement on the part of a person over a given thing.
Suppose a conjurer opens his hands to the audience in order to reveal that the small object that was previously in his right hand has now disappeared. the fact that we can now say that there is nothing in his hands depends on a prior conception of there having been something there before.
This 'not' does not even require to be uttered: it need only be thought. It is only necessary for the judgement to take place. This demostrates that negation is not even restricted to language.
Moreover, it is not clear to me that Aristotle (Metaphysics 1006a-1009a) succeeds in resolving this problem of the transitivity of the property of incompatibility over X and Y, i.e. that X excludes both 'X is not Y' and 'X is not-Y'. But what I earlier referred to as the difference in 'emotive depiction' between 'X is not Y' and 'X is not-Y' can now, thanks to Plato's theory of 'the parts of otherness', be understood also in terms of the latter's reduction of focus in respect of the former.
Consider the following sentences:
/1/ John is not grateful.
/2/ John is ungrateful.
Sentence /2/ can be seen to reduce the focus of /1/ to the point of a marked implication of more active behaviour on the part of John in /2/ than in /1/.
In the case of nouns it has already been seen that such more focused negation can easily result in reification (cf. my earlier Homer and Lewis Carroll examples). But we should be wary about making rules here, for language can be deceptive. Thus, in the two sentences,
/1/ Nothing convinces me of his guilt.
/2/ No thing convinces me of his guilt.
the very opposite morphological mechanism produces the effect of greater focus. In this way the greater emphasis of /2/ to mean 'no one thing' is achieved through negative morphological detachment as opposed to attachment.
Similarly, there is a total loss of symmetry between the following two replies to the question, "How's John?":
/1/ Not bad!
/2/ Not good!
where the 'negative' implications are totally absent in /1/, and yet weigh heavily in /2/.
Aside from the tricks of art, which are timeless, there strikes me as having been a far stronger isomorphism binding thought, language and reality in the ancients, which is especially evident in the philosophers. The peculiarly modern discoveries (or inventions) of referential inscrutability and indeterminacy would have been anathema to the ancients and this, I think, on mainly moral grounds. For the power of language to refer was originally conceived of as being magical, and this power of reference later came to be seen as a moral one to be respected in our rightness of the use of language.
Much of this moral decadence has been very recent, for Russell (1959) was able to write:
"It was in 1918, as I remarked before, that I first became interested in the definition of 'meaning' and in the relation of language to fact. Until then I had regarded language as 'transparent' and had never examined what makes its relation to the non-linguistic world."
9. The immensity of the tours de force necessary in the Parmenides and Sophist for the admission of nonbeing on a par with being reflects the enormous hold which Parmenides must have exerted over the Greeks. His writing in verse, like the monotheist Xenophanes, reflects divine inspiration and the transcendent powers of thought. Thus it is not he but the goddess who speaks throughout.
The style of Parmenides5 is strikingly reminiscent of the Vedic hymn and may easily be read as a solution to the anonymous poet's riddle. But Parmenides' answer that there is only 'is' and no 'is not' cannot, I think, be understood as meaning that Parmenides wished to reject negative predication outright, as Anscombe (1969) would have it: in the first place, Parmenides himself consistently uses negatives, which would be highly implausible if that was what he wished to outlaw, and secondly, Parmenides' position on the illusory nature of 'opinion' and the nonexistence of what is not is quite incompatible with the use of the negative.
For in Parmenides (Parmenides1, 2 & 4) thought and reality are probably even more closely bound together than in Plato, in that reality, or at least true reality, can be thought, and if 'opinion' is part of what is not, then the result of thinking that is what he calls a non-thought, which must be taken to mean something that is not a true or authentic thought. We find Aristotle (Posterior Analytics 89a) still pondering the problem of how true knowledge and mere opinion could have the same object of reference.
Similarly, Parmenides' convincing rebuttal (Parmenides3) of what is having been produced out of what is not, led Aristotle (De Anima 417a and Metaphysics 1051b) to his theory of potentiality in order to bridge the gap somehow between nonbeing and being.
And this is a radical challenge to the common concept of time: the unreality of past and future which are illusory, the present which is all there is, timeless and eternal.
For Parmenides, then, reason, namely the correct use of thought in contact with reality not the world of appearance but the real world will alone lead to truth.
To the question, 'What is there?', Parmenides answers 'All that there is and nothing that there is not', reminding us of Wittgenstein (1922);
"Die Welt is alles, was der Fall ist."
To the question, 'Is there a way the world is?', Goodman (1978) and Rorty (1982) answer in the negative. Even Quine (1960) is unable to answer this in the affirmative owing to a loss of isomorphism across thought, language and the world: words tied to objects like museum labels attached to the exhibits are 'the myth of the museum'. Our findings in science at both the subatomic and astronomic levels appear to endorse this.
Parmenides' answer to the question is substantially this: 'Yes there is a way the world is, and it is to be sought with the powers of mind and heart combined. But it is transcendent and not to be perceived at the level of opinion, experientially.' If the thought of Aristotle may be compared to a vast pyramid situated squarely on the ground, and the thought of Plato to a great flame reaching up from earth to touch heaven, then that of Parmenides seems to me to be a sort of prism, simple yet shining brilliantly and filtering that which is and nothing that is not.
We feel drawn to Parmenides and to the Greeks, for here the mind is to be found working with the heart, so that the full force of a man's being is to be felt behind every word. And who can teach us this? Will our words be bound to the heart, or will they, like Jacob's, be to deceive?
 I have carefully considered the translations by Fowler (1921) and Taylor (1961), the commentary by Bluck (1975) and the penetrating studies by Anscombe (1966 & 1981a). Crombie's (1963, pp.388-422) metaphysical analysis still contains important insights. Further essential reading on the Sophist since Owen's (1971) paper on Plato and nonbeing includes, besides the works discussed by Owen, Lee (1972) on the parts of otherness, Ferg (1976) on false statement, Ketchum (1978) on participation and predication, Pippin (1979) on a Plato/Wittgenstein comparison in respect of negation and nonbeing, McDowell (1982) on falsehood and nonbeing, and Bostock (1984) on Plato on 'is not'. On the logical structure of the Sophist, see van Fraassen (1969). The text presented here corresponds to that of Fowler (1921) and is based upon the Codex Clarkianus and the Codex Venetus.
 English 'cipher' and 'zero' come from Arabic ﺼﻒ (sifr), 'empty' and 'zero', perhaps a calque of Sanskrit śūnya-, ''empty', but also 'number'. This meaning 'empty' is retained in English at the figurative level.
 Pelletier's study derives its interest more from the breadth of ground covered (systematic groupings of interpretations afforded by previous scholarship through close readings of these interpretations by Pelletier) than from any depth of understanding or fresh philosophical insights, which are wholly lacking. The psychologistic vein I seem to detect would appear to stem from Pelletier's preconceived purpose of construing Plato in terms of cognitive science: "Perhaps cognitive science, as well as philosophy, is a series of footnotes to Plato" (op.cit., p.xxi). In fact, not only is there little of Parmenides in Pelletier's study, but I am not sure that he always keeps the historical figure of Parmenides separate from Plato's Eleatic Stranger. While I appreciate Pelletier's understatement that "Plato was no dummy" (op.cit., p.xxi), I would have preferred that he took Parmenides' argument more seriously and therefore refer him to Anscombe's (1981, p.xi) considered conclusion: "Whitehead's remark about Plato might, somewhat narrowly, be applied to his great predecessor: Subsequent philosophy is footnotes to Parmenides."
 Wittgenstein (op.cit., 1). His following statement "Die Welt ist die Gesamtheit der Tatsachen, nicht der Dinge" (1.1) is more problematic. See Owen (1966) for a perceptive study of Plato and Parmenides on the timeless present. The recognition of sense in the question 'What is time?' is, it seems to me, the mark of a metaphysical turn of mind. Thus, in his attempted refutation of the reality of time, perhaps the greatest attempt in modern times, McTaggart (1927, p.9) mentions Spinoza, Kant and Hegel, who all treat time as unreal.
 I think Parmenides marks the beginning of metaphysics and the light of reason. I wonder if Plato had Parmenides in mind (at DK B9: αὐτὰρ ἐπεὶ δὴ πάντα φάος καὶ νὺξ ὀνόμασται | καὶ τὰ κατὰ σφετέρας δυνάμεις ἐπὶ τοῖσί τε καὶ τοῖς, | πᾶν πλέον ἐστὶν ὁμοῦ φάεος καὶ νυκτὸς ἀφάντου | ἴσων ἀμφοτέρων, ἐπεὶ οὐδετέρῳ μέτα μηδέν.) when he wrote (Sophist, 254a):
And are we not reminded of Dante (Paradiso, 33: 76-90)?
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.63-75).
In the same series of philosophical readings from the published work of Domenico Pacitti