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Understanding Negation

Domenico Pacitti (1991)

οὐ γὰρ μήποτε τοῦτο δαμῇ εἶναι μὴ ἐόντα.
   That shadow which the picture as it were casts
upon the world: How am I to get an exact grasp of it?
   Here is a deep mystery.
   It is the mystery of negation: This is not how things
are, and yet we can say how things are not.

0. Is it not odd that in saying what is not the case we are at the same time saying something about what is the case? How can this be? For if I say there is no sugar on the table and this is true, have I not contributed something towards a description of the contents of the table, just as I would have done had I said there was sugar on the table and there was? But if we say there is no sugar on the table and there is, or that there is sugar on the table when there isn’t, we shall have said nothing that contributes towards a description of the contents of the table in either case. Thus, we shall say that a negative statement will describe just as an affirmative one, provided they are true.

Falsity must therefore be distinguished from negation. Yet it is not a contradiction to say that negation, when true, is not free of falsity, since the rejected affirmative, embedded proposition contained within the negative will be false. In this way falsity ‘colours’ negation, attaches to it and is even implied by it, though the negation itself is true.[1]

Affirmation, when true, is free of such connections with falsity. But if a negative contains a false affirmative, then clearly a state of affairs is being depicted in order to be rejected, so that we can say that what is being depicted in either case is none other than the same thing. Now, if it is the same thing that is depicted by the negative as by the affirmative, that is to say the same objective reality in the world, then what can be said to correspond to the negative sign?[2] Clearly, nothing. This might be better understood if we add to our existential example a predicative one, such that the opposite propositions of a man throwing stones an a man not throwing stones would be represented by one and the same drawing or mental image of a man throwing stones.[3]

It would seem to follow from this that the affirmative has primacy over the negative here, and that from this point of view what might to many have seemed a naturally symmetrical relationship between negative and affirmative turns out to be decidedly asymmetrical.[4] For we have seen that to both the negative and the affirmative true statements there corresponds the one reality.

1. If, then, nothing in the world corresponds to the ‘not’ of negation, we must enquire into its nature and source.

Since the purpose of the negative sentence is to deny the affirmative proposition it contains, then the act of negation will best be seen as an act of judgement. But could we not equally well say that the affirmative sentence too represents an act of judgement? Indeed: but the important difference is that in each case the negative sentence in question will represent, so to speak, a higher level or second-order judgement in respect of its affirmative counterpart.

Negation thus not only contains the affirmative; it rejects it.[5]

Moreover, this higher level act of judgement will involve movement to an obviously greater degree than its affirmative counterpart, so that it will make sense to talk in terms of (negative) dynamism and (affirmative) staticity. At this point it seems to me that the factor of time must also become involved: whereas the affirmative will in its staticity remain encapsulated within the time expressed by the grammatical tense of its verb, the negative will, in its dynamic path, be forever moving away from a past it has rejected to a present which leaves open to the future a greater field for the imagination.

In this way the negative will be less liable to restrictions of space and time in comparison with the affirmative. Consequently, when we move from this perspective of the mind that judges (negates) to that of the thing or action which is being judged upon (negated), it will not be surprising to find evidence at the morpho-syntactic level of decrease in verbal vitality or dynamism through negation. It is as though there were an inverse proportion existing between the judging mind, on the on the one hand, and the action being judged, on the other, so that the greater the vitality of the verb, the less the activity of judging, and the more intense the activity of judging, the less the dynamicity of the verb.

1.1. It is known that in Classical Greek the durative character of negative imperfects may be shared by the aorist, so that the relative staticity of the verb action is, as it were, frozen by the act of negation. Quite compatibly with this, what I am arguing for is the concomitant dynamism on the part of the judging mind as freezing agent in negative contexts. Thus in the case of the affirmative the action or vitality is in the verb, while in the negative it is in the judging.

It seems to me that the fact of the actual tense employed with the negative is less significant than the fact of interchangeability of tense, namely the imperfect and the aorist in the case of Classical Greek.

The following negatively influenced tense irregularities in Modern Arabic provide further support in this direction:

/1/ To negate the past, the particle lam is used with the imperative: lam yaktub = he did not write.

/2/ To negate the future, the particle lan is used with the subjunctive: lan yaktub = he will not write.

/3/ To negate the present copula, the peculiar verb laysa (is not/are not) is used in the past form but with a present meaning: laysa = he is not.

1.2. What then is the nature of judgement, represented to a higher degree in negative statements than in their corresponding affirmative ones?

Judgement concerns the ability to make distinctions, and therefore the act of indicating perceived relations between two or more concepts. Consider, for example, visual perception. We would not ordinarily say that seeing a vase is an act of judgement but rather a simpler act of perception. Of course, the neuropsychologist will tell us that this apparently simple act of perception is in fact far more complicated than it may appear. Indeed the human visual system has recently been adopted as a useful model in the attempt to gain more fruitful insights into the human language faculty. Here too vision turns out to be highly complex. Yet we would not ordinarily consider it to be such. But when we come to consider the vase picture which can be visually interpreted as being either a white vase in a black background, or else two black facial profiles against a white background, we would naturally begin to speak of judgement.[6]

And that is because judgement assumes or implies the notion of something’s not being the case even though our indication or expression of judgement may just as easily take an affirmative form as a negative one.

However, it would certainly be misleading to see judgement in terms of a this-or-that distinction. Such oversimplifications along the lines of binary oppositions, though attractive to some, are nonetheless perilously inadequate. A continuum with imperceptible transitions from one level to the next would serve as a more appropriate model.

Consider the following example. A man who knows a little about cars stops to admire a beautiful Rolls Royce and expresses his admiration. A second person who himself owns a Rolls Royce notices that the paintwork is not as glossy as on his own car and suspects it may have been resprayed. An insurance expert then points out that there will be other giveaway clues such as the wheel-arches, the boot and other curved and irregularly shaped areas which are very difficult to paint precisely. Finally, the man who actually repainted the car comes along. He tells us about all the other imperfections and minutiae resulting from difficulties encountered, both typical and idiosyncratic of this particular effort. What is happening here is that we are passing from the lowest to the highest of four levels of judgement.

It will be observed that in proportion as we proceed upwards on the scale, the ability to know where to look for ‘negative’ qualities contributes to the refinement and correctness of our judgement. But what if the car had exemplified the ‘perfect paint job’? Would it not have been the case that as none of the four found fault, all four ‘judgements’ were equal and valid? No! For on the same scale the ability to know where to look for faults, even though none were actually found, is what would have graded the four judgements progressively. This seems to me to provide strong support for the hypothesis that the prepositions expressed by counterfactual conditionals can be as real and placed on an equal footing with propositions expressed by non-conditionals, and that they will be as eligible where they reflect or represent soundness of judgement.

To put it another way, the degree of soundness of judgement achieved or expressed will be in direct proportion to the number of places one knows where to look in order to establish the level of competence displayed in whatever it is that one is attempting to judge.

1.3. Could the same thing hold also in the case of aesthetic judgements?

Take, for example, literary appreciation as an instance of aesthetic judgement. It is tempting to construe the hierarchy of levels of appreciation here along the lines of the four responses to the cosmetic merits of a motor car. But first we must emphasise more clearly the distinction – taken for granted so far – between judging or appreciating on the one hand, and giving some sort of account of this judgement or appreciation, on the other. I mean, if a reader who is deeply affected or impressed by, say, a poem he has read expresses himself with no more than a few superlatives and some suitable gestures, or else even in terms of the latter only, i.e. in complete silence (for silence where language is expected is surely a quality space to be interpreted in terms of expression), shall we say he has judged or appreciated to the same extent as another reader who expresses his appreciation more articulately?

I think it should be obvious that there is no reason why there has to be any lesser degree of judgement in either case with respect to the other. It is simply easier for us to evaluate this in the latter case as there is more evidence.

Conversely, one would be suspicious of the presence of any fine judgement on the part of the reader who fails – under questioning, for instance – to communicate in no more than his few superlatives, gestures and significant silence. But it will be instructive to remain with this reader a moment in order to ask ourselves what we would require from him as a minimum to assure us of a level of appreciation, of minimally expressed judgement, which we would be prepared to consider sufficient for us to be able to evaluate his judgement – not the expression of his judgement – on equal terms with an articulately expressed appreciation. I want to suggest that a very limited range of short comments would be enough to convince us one way or the other, and that furthermore the use of negatives would be crucial: “This is well done”; “That is superb”; “This is too long-winded”; “That is less fitting”, etc.[7]

Although the essence of critical appreciation may be detected in the appropriate selection of suitable adjectives from a hierarchical scale, the negative element will, for the sake of completion, have to be present or available even if implicitly, e.g. “This is better than that”, or “This is less beautiful than that”, where the comparative contains an implicit negative, explicit in some languages.

What we have observed here is that not only does (true) negation necessitate judgement, but that (true) judgement necessitates negation.

1.4. It was already apparent from our somewhat primitive motor car example that felt response gave way to less subjective, more discriminatory and discerning judgement as we moved up the hierarchical scale of four. The supposed necessity of the use of exclamatory or declarative terms of ‘appraisal’ became secondary to a more critical response based either on the perception of inadequacies or else on the knowledge of where to look for these inadequacies, whether the latter were in fact present or absent, actual or potential. We then observed that the ensuing explicit or implicit use of the negative was what began to characterise higher judgement.

I maintain, following this ascending progression, that the highest level of real critical judgement will rest on articulated or unarticulated comments of the following sort: “This is right”, “This is not correct”; “This is as it should be”, “That is not as it ought to be”.

Tolstoy wrote:

“He does not write the truth who describes only what happened and what this or that man has done, but he who shows what people do that is right – that is, in accordance with God’s will; and what people do that is wrong – that is, contrary to God’s will.[8]

He saw the connection between truth and art on the one hand, and truth and morality on the other, but was on account of his religious beliefs misled into having to defend the position that any art which does not concern itself with correct or morally just behaviour must fail to qualify as true art.

What I am trying to show is that art will be said to be successful when it describes as it should, and not when it concerns itself with what should be.[9]

Dostoevsky’s great novels represent and describe as they should, but they are certainly not concerned to represent, describe or extol what should be. And the same holds true for the great works of Tolstoy himself. It is a curious fact about the world’s greatest literature that it only rarely describes or represents situations and characters that are as they ought to be, or wholly good. Although this was Gogol’s ultimate purpose in writing Dead Souls, the great unfinished work began to fail when he attempted to portray the morally good. But there have been such rare cases as Dante’s Paradiso, or the character of Falstaff in Shakespeare. But, I repeat, such cases are the exception rather than the rule.

It will be the critic’s task to point out, both at the particular as well as at the more general level, when and how any given thing is represented or described as it should be or otherwise.

That this requires enormous experience and aesthetic sensitivity as well as felicity of linguistic expression is unfortunately demonstrable in the lack of serious critical literature in the modern period. Moreover, it does not seem to me that much modern criticism is overly concerned with such values, either because they are unnecessary or else perhaps because they are too difficult to attain. Speed and specialisation as well as easily perceptible conformity to a ‘school of thought’ are the prerequisites of professionalized criticism, insofar as the results may be reasonably termed criticism at all. This turns out to be largely a question of power. We in the West shirk at the very idea of dictatorship and totalitarian thought control, and yet our own institutions are not so far removed from this in their promoting and rewarding of uncritical conformity to power and in their suppressing and penalising of those who represent any sort of challenge to this. Must the spirit of sincerity in a free quest for truth be frustrated by the obligation to keep senseless taboos and renounce truth and honesty?

Tolstoy went on to say in the same essay:

“And so he who looks down at his feet will not know the truth, but he who discerns by the sun which way to go.”

In the present climate we seem to have lost sight of the sun: too many clouds stand in the way. Will we have long to wait for them to move on?

1.5. Thus it is fundamentally right, I believe, to conceive of the ascendant consciousness of higher human judgement as directly proportional to the rise in its capacity for negative perception. I therefore agree with Whitehead (1929) when he says that negative perception constitutes a higher form of consciousness, being closely linked to prehension of the eternal (in time) and consequently the infinite (in space):

“The general case of conscious perception is the negative perception, namely, ‘perceiving this tone as not grey’. The ‘grey’ then has ingression in its full character of a conceptual novelty, illustrating a alternative. In the positive case, 'perceiving this stone as grey', the grey has ingression in its character of a possible novelty, but in fact by its conformity emphasising the dative grey, blindly felt. Consciousness is the feeling of negation: in the perception of 'the stone as grey', such feeling is in barest germ; in the perception of 'the stone as not grey', such feeling is in full development. Thus the negative perception is the triumph of consciousness. It finally rises to the peak of free imagination, in which the conceptual novelties search through a universe in which they are not datively exemplified".[10]

It is important to understand the force of "datively exemplified" as referring to exemplification in that specific combination as opposed to separately, since there are such things as stones, the colour grey, and even grey stones on other occasions. In this way the following sentences,

/1/ This stone is grey.


/2/ This stone is not grey.

incorporate existent objects (stones) and existent properties (colour), so that in each case perception is of a stone. In /1/ the colour grey is also perceived, whereas in /2/ another (unnamed) colour is perceived and the colour grey envisaged and rejected. and it is this envisaging and rejecting in negation which involves movement or dynamicity as well as imagination.

Now obviously it is the existent which is denied, for how are we to deny the nonexistent, when we first have to mention that which is not in order to deny it? Yet, in addition to saying of something existent that it is not, we may sometimes wish to say of something nonexistent that it is not, e.g.:

/3/ There are no unicorns.

Whereas /3/ would in this respect be distinguished from /2/, it comes as a surprise to find that they share the same logical structure, namely:

/4/   (x) ~Fx.

Admittedly, /3/ may be expressed existentially as well as quantificationally, viz.:

/5/   ~(x) Fx,

but it appears somehow anomalous that the predicate variable (F) should be made to range over nonexistent properties, or that the individual variable (x) should be made to range over nonexistent objects. Hence,

/6/   (x) (F) ~Fx, or (F) (x) ~Fx

in a sense represents a contradiction in terms, giving:

/7/   Nec ~(x) (F) ~Fx, or Nec ~(F) (x) ~Fx


/8/   Nec (x) (F) Fx, or Nec (F) (x) Fx.[11]

'Unicorn' ought not to be seen as an ordinary variable, but rather as a second-order expression or condensed 'atomic' proposition, so that what /3/ really comes down to is:

/9/   ~(p is true) → ~p.

What is therefore being rejected is neither the existent nor the nonexistent, but rather a (mistaken) judgement over the existent, since there is nothing else for it to be a judgement over.

Although this distinction between the rejection of a (first-order) variable and the rejection of a (second-order) prior judgement would appear to be a crucial one, Whitehead fails to make this clear.

Furthermore, I disagree with him when he tells us that consciousness is "how we feel the affirmation-negation contrast", and that "affirmation involves its contrast with negation, and negation involves its contrast with affirmation".[12] For here, and elsewhere, he seems to me to lapse into a neatly symmetrical Hegelian solution of binary opposites, while it is my purpose to maintain a decidedly asymmetrical relationship between the negative and the affirmative.

The road is now fairly clear for an investigation into the connections between negation and the sublime, negation and mysticism, and the nature of the negative in metaphysical terms, but first I want to take a closer look at the more strictly linguistic properties of the negative in respect of asymmetry.


[1] Furthermore, the falsehood of a false statement is closely associated with the truth of a negative statement. Thus,

/1/  There is sugar on the table. (F)


/2/  There is no sugar on the table. (T)

both come down to the same thing. It is not therefore surprising that the affirmative/negative and true/false distinctions are often unintentionally conflated by even the best minds. Aristotle, for example, gets it right in the Categories (13b) and De Interpretatione (18b), but slips in the Metaphysics (1027b). In his comprehensive historical manual on negation, Horn (1989) lists Frege (1919), Austin (1950), Quine (1951a) and Geach (1972) as having explained the erroneous identification of negation and falsity in terms of a confusion of language and metalanguage (p.58).

[2] As I understand ‘statement’ to have assertoric force, I refrain from using the term in this and the preceding sentence, since there is, of course, no need for it to have been asserted, but merely proposed or entertained. Geach (1965, pp.449-453) sees this problem, rightly quoting Strawson (1952, p.88) as having missed it.

[3] Existential sentences should therefore be distinguished from action sentences in the negative. Subtraction is more appropriate in the former – hence the dynamicity of judgement over the static (state of affairs). Freezing is more appropriate in the latter – hence the paradoxically freezing effect on the part of the dynamicity of judgement over the already dynamic (verb of action). This can be seen to produce a temporal relaxation in the verb of action undergoing negation, as is shown in 1.1. Lumsden (1988) attempts to clarify the relationship between the structure of existential sentences and their meaning. Their syntactic structure emerges as complex, semantic restrictions turn out to be relevant and interesting properties are revealed at the pragmatic level. For a criticism of Lumsden on analytic grounds see Milsark (1990). See also Milsark (1977).

[4] Horn (1989) gives a comprehensive account of affirmative/negative asymmetry on the basis of the following theses which would be upheld in proportion to the degree of entrenchment of the asymmetricalist: affirmation is prior to negation logically, ontologically, epistemologically and psychologically; affirmation is simple, essential and objective, while negation is complex, eliminable and subjective; whereas the affirmative sentence describes a fact about the world, the negative sentence describes a fact about the affirmative; the affirmative sentence is worth more in respect of the negative (pp.45-6). Aquinas (1496) is seen as “an early champion” of the asymmetry thesis (p.47), and the following classic quotation from the translation by Oesterle (1962, p.64) is given: “The affirmative enunciation is prior to the negative for three reasons … With respect to vocal sound, affirmative enunciation is prior to negative because it is simpler, for the negative enunciation adds a negative particle to the affirmative. With respect to thought, the affirmative enunciation, which signifies composition by the intellect, is prior to the negative, which signifies division … With respect to the thing, the affirmative enunciation, which signifies ‘to be’, is prior to the negative, which signifies ‘not to be’, as the having of something is naturally prior to the privation of it.” For a survey of the situation at the psycholinguistic level see Horn (op. cit., pp.154-184). Givón (1978), Wason (1972) and Volterra & Antonucci (1979) are among those considered. See also Horn’s pages on markedness and the asymmetry thesis (pp.184-203).

[5] Freud (1925) too finds negation to be essentially rejection of that which is, for there is no such thing as a ‘no’ in the unconscious (p.15). Thus the patient’s repudiation of the fact that the person in the dream is not the mother should be interpreted to mean that it is, after all, his mother. But Freud, I think, sees an essentially symmetrical relationship between positive and negative in terms of what he calls a ‘polarity of judgement’ which, he says, “scheint der Gegensätzlichkeit der beiden von uns angenommenen Triebgruppen zu entsprechen. Die Bejahung – als Ersatz der Vereinigung – gehört dem Eros an, die Verneinung – Nachfolge der Ausstossung – dem Destruktionstrieb“.

[6] Relationships between the human visual system and language continue to throw light on the role of extralinguistic elements in linguistic definition as well as on the nature of the language faculty itself. Chomsky (1988, P.160) writes: "The human visual system observes certain principles, just as the language faculty does. One of these, recently discovered, is a certain 'rigidity principle'. Under a wide range of conditions the eye-brain interprets the phenomena presented to it as rigid objects in motion. Thus, if I were to have in my hands a plane figure, say in the shape of a circle, and were to present it to you perpendicular to the line of sight, you would see a circular figure rotating. The visual information reaching your eye is consistent with the conclusion that what you saw was a plane figure shrinking and changing its shape until it becomes a line and disappears. But under a wide range of conditions, what you will 'see' is a rigid plane figure rotating. The eye-brain imposes this interpretation on what it sees, because of the way it is constructed. In this case the physiology of the matter is understood to some degree as well." Caplan (1987) in his textbook on aphasiology and neurolinguistics introduces concepts from neurology, aphasiology, psychology and linguistics, observing (p.x) that there is a distinct lack of any attempt to devise and make use of different frameworks in neurolinguistics. Jackendoff (1983) in his study of the cognitive foundations of semantics concludes that semantic structure is identical with conceptual structure (see especially pp.95-108). See also Jackendoff (1987). Recent work on visual cognition may be found in Osherson et al (1990) with papers on computational theories of low-level vision (pp.5-40), higher-level vision (pp.41-72), mental imagery (pp.73-98) and vision as relating to belief and knowledge (pp.129-148), by Yuille & Ullman, Biederman, Kosslyn, Spelke and Dretske respectively. Gregory (1977) remains essential reading on the psychology of seeing (see especially pp.9-14 on perceptual decision, and pp.133-162 on illusions).

[7] This dissociation of genuine appreciation from the mode of expression of appreciation is far from Croce (1902), for whom every true intuition is also expression, the expressive power being an accurate measure of response since language is the very medium of such aesthetic expression. On this question see Langer (1953, ch.20: "Expressiveness"). My own view is much closer in spirit and substance to Wittgenstein (1966, pp.1-40).

[8] Tolstoy (1887, p.35). This and the following Tolstoy quote are my own translations.

[9] It is the morality within this 'should' which links aesthetics to ethics.

[10] Whitehead (1929, p.161).

[11] Anscombe (1969, p.5) disagrees that objects or properties are, in fact, mentioned at all in the employment of quantifiers binding property variables to object variables. This anticipates my treatment of Parmenides and Plato, as indeed of the Vedic and Chinese texts (5.3 ff.). The paradox of negative existentials is also presented by Apostel (1972, p.211), and seems to lead naturally to the question of the admission or nonadmission of negative acts. Ryle (1973), in my view correctly, opposes their existence, seeing them as having more to do with saying than doing. Brand (1971), on the other hand, admits them in terms of a Carnapian action language. The classic encounter is that between Demos (1917, p.189), who opposes the negative fact, and Russell (1918, pp.213-4), who supports them. But Russell was inconsistent here, writing much later that the world could be described without the use of the word 'not' (1948, p.520). Gale (1976) does well to distinguish negative events from negative facts, excluding the former while admitting the latter. I think this is because facts are more obviously language-dependent than events. More recently Vermazen (1985) has attempted to reintroduce negative acts among acts, but Davidson (1985) rightly raises the problems of the correct point at which to insert the negative sign in the sentence: "There was no eating of a persimmon by me", and the related point of intention as a non-truth functional sentential operator. But Davidson does seem to allow the existence of at least some negative acts. The problem seems to me to hinge on the concept of existence: if what is can be completely separated from what we can know about what there is, then there can be no negative acts or events. But sometimes epistemological criteria might be said to constitute in themselves an ontology. Thus Eccles (1977), referring in turn to Eccles (1970), Popper (1972) and Popper & Eccles (1976), presents three worlds (p.193): World 1 is the world of physical objects and states, World 2 is the world of states of consciousness, and World 3 is the world of knowledge in an objective sense. Furthermore, there is said to be a special interaction across these 'worlds'. The explanatory power and intuitive acceptability of this model are considerable. For example, language itself and the entire concept of (essentially linguistic) meaning would be understood as having an existence at the World 3 level on an equal footing with the physical objects of World 1. On this view there would be no great difficulty in accommodating negative events or acts as existent entities, no less shadowy or real than positive acts or events. But again, in spite of the convincing attempts of Quine to admit abstract entities on a par with physical entities in order to fill out our system of the world, and in spite of the more recent discoveries in science of particles too small to be seen even in principle since they are smaller than any light wave, I find Eccles and Popper's model difficult to accept: the pull of physical objects as the only really existent ones is too strong. Moreover, Ockham's parsimony must be respected. There is only one world.

[12] Whitehead (op.cit., p.243).

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  • Volterra, V. & F. Antonucci 1979. "Negation in Child Language: A Pragmatic Study." In E. Ochs & B. Schieffelin (eds.), Developmental Pragmatics, New York, 1979, 281-303.

  • Yuille, A.L. & S. Ullman 1990. "Computational Theories of Low-Level Vision." In Osherson et al. (1990), 5-39.

  • Wason, P.C. 1972. "In Real Life Negatives are False." Logique et Analyse, XV, 17-38.

  • Whitehead, A.N. 1929. Process and Reality. D.R Griffin & D.W. Sherburne (eds.). New York & London.

  • Wittgenstein, L. 1966. Lectures and Conversations on Aesthetics, Psychology and Religious Belief, C. Barrett (ed.), Oxford.

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.1-11).

In the same series of philosophical readings from the published work of Domenico Pacitti