Negation and Meaning
Domenico Pacitti (1991)
5. Thus my tentative framework for a theory of meaning may be summarised as follows:
where judgement has been seen to be operational at each level.
But judgement must also be exercised over all, in that very often one of the three elements will be seen to predominate over the other two. Judgement in the case of emotive depiction has turned out to be the most complex, especially in the case of literary criticism, where suggestive, implicational or connotative criteria may or may not have been intended by the author, and where the confines between subjective and objective construal are indistinct. Somewhat surprisingly, meaning has turned out to be closely associated with truth despite our rejection of a central role for reference in an adequate theory of meaning. In this way apparent problems regarding truth in fiction on the basis of referential criteria turn out to be pseudo-problems.
We are now in a position to resolve – in part for the moment – Wittgenstein's problem as put forth in the epigraph quotation to Understanding Negation, and this on the basis of our criteria 1 and 2 for a theory of meaning: It is not that we can say how things are not, but rather that we can deny the sense of their being in a certain way, i.e. we can make a negative assertion as to their being. For negation is in our judgement of sense and not in sense itself.
It was necessary to sketch a background theory of meaning within which the negative could be fittingly placed. Now that this has been carried out I would like to look more deeply into some of the properties of negation which we have already touched upon, and indeed more deeply into the very nature of the negative.
A sentence such as:
/1/ Nessuno mi dà una mano.
raises the question whether "nessuno" is reified or simply used as a filler word or 'dummy' in order to give form to a sentence which would otherwise lack form. We may speak of form, as opposed to sense, provided the sentence is valid in its transparency:
/2/ Non mi si dà una mano.
/3/ Non mi si dà alcun aiuto.
/4/ Nessun aiuto mi si dà.
/5/ Non mi si dà nessun aiuto.
with simple or double (in the sense of reinforced) negation in accordance with the relevant linguistic structures. But the formal problem might be conceived of as becoming ontological in a sense. Thus in languages which say only:
/6/ ?*Non è venuto alcuno.
where "alcuno" is positive, the negation is quantificatory, and the fact of zero result obtaining from subtraction of the whole from the whole may be seen to be less significant. Furthermore, it is only on the basis of quantification (and subtraction) that it becomes comprehensible why the Greeks used οὐδένες and why Tuscan at the dialect level has 'nessuni'.
The fact that 'nessuno' should be singular only in 'official' language does not appear to be respected in Russian, which often uses the genitive with negation:
/1/ Он не видел дома.
/2/ Он не видел дом.
but only in indefinite contexts, so that /1/ renders the indefinite article construction 'a house' whereas /2/ renders the definite article construction 'the house' through the accusative. Similarly, in Arabic the indefinite and definite noun plus adjective constructions render the indefinite and definite articles respectively, although the adjectives must of course follow the noun. But,
/3/ Он не видел никого.
may be considered in this respect as representing a confluence of the indefinite genitive with the genitive of animacy.
Moreover, such 'quantificatory' negation will vary according to whether it regards the subject or the predicate. Consider in this respect the following sentences:
/1/ Tutte le frittelle riescono col buco.
/2/ Non tutte le frittelle riescono col buco.
/3/ Le frittelle riescono non col buco, ma con la crosta.
/4/ Le frittelle non riescono col buco.
Whereas in /1/ and /2/ the doughnuts have a regular hole, it is not clear how much sense /3/ and /4/ make. To what extent, if any, does it remain legitimate to talk of a doughnut without a hole? Similarly,
/5/ Mi è arrivata una lettera dove non c'era scritto niente.
leaves us wondering what, if anything, makes it a letter.
Thus /3/, /4/ and /5/ lead us to the necessary conclusion that the negation is actually bound to the subject even though it is apparently bound to the predicate.
/1/ Carlo mangia la minestra.
/2/ Carlo non mangia la minestra.
/3/ Carlo non mangia la minestra, ma la carne.
/4/ Non Carlo, ma Luigi mangia la minestra.
/5/ Nessuno mangia la minestra.
/6/ Nessuno mangia la minestra, ma tutti il secondo.
In /1/ the action is positive with respect to the soup; conversely in /2/ it is negative with respect to the soup, but positive with respect to the meal and diners respectively. /5/ and /6/ are negative in regard to the act of eating soup.
Further reflection on the basis of these examples might lead us to perceive that at the substantial (as opposed to linguistic) level the subject cannot normally be negated, whereas the predicate can. That is to say that when a predicate is negated something else of the same kind is expressed, but when a subject is negated it is simply cancelled. Again, consider the following sentences:
/1/ John is bad.
/2/ John is not bad.
/3/ *Not John is bad.
/4/ John is both big and bad.
/5/ John is either big or bad.
/6/ Both John and Carlo are bad.
/7/ Either John or Carlo is bad.
Compatibly with what we have been saying at the substantial level, the predicate of /1/, when negated, yields a new predicate of the same kind in /2/. But that the subject resists negation is shown in /3/. Sentences /4/ and /5/ similarly allow negation of their compound predicates, but not of their subjects, as in /3/. Negatives in /6/ and /7/ respectively are:
/8/ Both John and Carlo are not bad.
/9/ Either John or Carlo is not bad.
But it is important to see that these are not what we would ordinarily call the negatives of /6/ and /7/, which are:
/10/ Not both John and Carlo are bad.
/11/ Neither John nor Carlo is bad.
Thus, while both simple and compound predicates can be negated, it is not the case that both simple and compound subjects can. Even if they could, this would still, of course, leave the original asymmetry unaffected, but the situation turns out to be doubly asymmetrical where we least expect it, with simple subjects resisting negation but compound ones complying.
In this way the negative subject-predicate asymmetry results in a further asymmetry of compoundability.
Strawson (1971) encounters two further asymmetries in his attempt to reconcile the two which we have mentioned. These he refers to as asymmetries "between particulars and general characteristics of particulars in respect of the possession of incompatibility-ranges", and "between particulars and general characteristics of particulars in respect of the possession of sufficient and/or necessary conditions". It is important to understand that Strawson, as he puts it, "appropriates" the terms 'subject' and 'predicate' in a narrowly propositional treatment. His argument, although attractive, is not wholly convincing, but as regards natural language the asymmetries certainly remain unreconciled and probably irreconcilable.
Again the 'commonsense' view of an orderly, symmetrical relation holding between affirmation and negation turns out to be quite unfounded.
5.1. Sometimes we wish to negate only a part of the sense and not the whole of it. In such cases the NEG marker will be seen to attach more closely to a particular element. But this does not mean that the whole sentence will not be negated. Frege (1919) expresses the matter as follows:
"It is incorrect to say: 'Because the negative syllable is combined with part of the sentence, the whole sentence is not negated.' On the contrary: it is by combining the negative syllable with a part of the sentence that we do negate the content of the whole sentence. That is to say: in this way we get a sentence in which there is a thought contradicting the one in the original sentence."
Examples illustrating this would be:
/1/ John is uncertain.
/2/ John is impatient.
/3/ John is abnormal.
/4/ John is disrespectful.
However, I find Frege less helpful in his reluctance to state whether the following sentences are affirmative or negative:
/F1/ Christ is immortal.
/F2/ Christ lives for ever.
/F3/ Christ is not immortal.
/F4/ Christ is mortal.
/F5/ Christ does not live for ever.
Russell (1918) at least supplies an answer here in analysing 'Socrates is dead' as two propositions rolled into one, namely 'Socrates was alive' and 'Socrates is not alive', but then Russell recognised negative propositions and at least the possibility of negative facts.
On my own analysis, where sense is either upheld or denied, the following solutions (S) would obtain:
/S-F1/ I deny + the sense;
/S-F2/ I assert + the sense;
/S-F3/ I deny + the judgement;
/S-F4/ I assert + the sense;
/S-F5/ I deny + the sense.
Let us note in the first place that /S-F3/ does not contradict anything I have said so far on the affirmative or negative assertion of sense, since what is being denied is not sense but judgement, which can itself be construed as a prior denial of a given sense.
In this way the system I am presenting is perfectly capable of accommodating double negatives, i.e. the negative judgement of a negative judgement, as opposed to the negative judgement of a negative sense, which we have disallowed, there being no such thing as negative sense. Moreover, when seen in this light what we have been calling the denial of a denial, or the negative judgement of a negative judgement, does not lead to an infinite regress, nor do two negatives turn out to be identical to an affirmative. For to assert that not-not-something will be a third-order rejection of a second-order denial of a first-order sense. Where we stop will be determined by our adopted position of focus at the appropriate level on the hierarchy of judgement.
But asymmetrically with this, when we attempt to assert a negative judgement affirmatively it turns out to be indistinguishable from normal negative assertion of ordinary sense.
A Fregean account, as indeed every other account I know of, finds itself in difficulty here over the twofold possible construal of positive assertion of negative sense or negative assertion of positive sense.
The additional problem of negative connotation which was evidently worrying Frege, death as the 'negation' of life, would be resolved at the third level of emotive depiction in my own account.
At the linguistic level it is interesting to follow Lyons' (1977) predictably ever-decreasing success in maintaining a strictly binary opposition from explcit gradable and ungradable opposites through morphologically unrelated semi-explicit opposites to the less convincing directional, orthogonal and antipodal opposition and the final breakdown in the non-binary contrasts leading to the excessively weak, transitive relation of hyponymy. Although all the important material is covered by Lyons, no help is offered as to the substantial and fundamental question of the correct construal – in, say, a work of fiction – of data as either firmly positively coloured on the one hand, or negatively coloured on the other. Here again I see no better starting-point than the understanding of the writer's intentions together with the understanding of what the writer himself understands.
Thus the sense that John is certain (XY) may be denied or negated by either:
/1/ John is not certain (X IS NOT Y),
/2/ John is uncertain (X IS NOT-Y),
even if /1/ and /2/ cannot be said to be identical. Moreover, it is not on the grounds of sense or power of signification that they differ, but rather in terms of what we are calling emotive content.
It is of interest at this stage to consider the quantificatory concept of negation which limits judgement, viz.:
/1/ All men are X.
/2/ Not all men are X.
even though the sense is rejected on both occasions. For example, where:
/3/ Gli uomini sono buoni.
could be logically equivalent to:
/4/ Tutti gli uomini sono buoni.
it is certainly not the case that:
/5/ Gli uomini non sono buoni.
is the logical equivalent of:
/6/ Tutti gli uomini non sono buoni.
On the other hand,
/7/ Gli uomini sono buoni, ma capricciosi.
has sense because "buoni" is positive and "capricciosi" negative, whereas:
/8/ Gli uomini sono buoni, ma gentili.
makes sense only where both predicates are positive.
This seems to point to a prior conception of the positive/negative distinction, which is not always expressed at the surface linguistic level.
/9/ Era una giornata buia.
is 'negative' and not equivalent to 'non luminosa', because the litotes concedes something to the thing it negates (or limits), whereas buio, triste, cattivo etc. concede nothing to their opposites. Furthermore, there are cases of negation which arise from contextual conditions, such that,
/10/ John è certo, ma buono.
gives a substantially pejorative meaning to "certo", which does not obtain, for example, in:
/11/ John è certo, ma cauto.
where the net effect is precisely the opposite.
There are, however, more limited cases such as 'mortal'/'immortal', where the exclusion of one necessarily points to the inclusion of the other. Thus in sentences such as:
/12/ The gods are immortal.
/13/ The gods are not mortal.
the first may indicate a particular appreciation of their powers which men do not share, whereas in the second the gods are more obviously opposed to men. Perhaps pragmatic criteria are relevant here, but at any rate litotes may be said to be equal to negation when the probability is exclusion.
Negativity, as opposed to negation, therefore emerges as an a priori of knowledge in respect of which we exercise a range of values. Consequently, quantifiers regard not only numbers or physical objects, but also grades of quality.
Although formal structures may influence genuine understanding at the substantial level, formal negation must not be confused with substantial negation.
Negativity should therefore be distinguished from negation.
In terms of my tentative framework for a theory of meaning, negation will involve the exertion of power of signification (2) over sense (1), or indeed over one or more such previous exertions, whereas negativity will find its place at level 3: emotive depiction.
But negativity is linked to negation in respect of its intensional (as opposed to extensional) and epistemological or judgemental (as opposed to ontological or existential) nature.
5.2. Proximity of the negative sign to a given term ('not-X' as opposed to 'not X') or for that matter sense or proposition ('not-p' as opposed to 'not p') strongly suggests the logically erroneous but fictionally admissible reification of the nonexistent.
Hence we must reject the concept of infinity as a point however great or distant, since it is only sleight of hand which converts 'that which has no end' into 'a that-which-has-no-end'. The mathematical sign for infinity seems to be on a par with all the other algebraic counters in the game, but it is in fact a second-order sign in respect of the rest, containing as it does a negative. The sign standing for infinity does not therefore denote a quantity or a point; rather it supplies an instruction or even a rule: however long you count you will never come to the end of the series.
I conceive of Cantor's smaller and larger infinite and transfinite sets as telling us something of the nature of mathematics and nothing of the nature of the world. Yet the shadowy phantom figure Alice saw on the road and the ambivalence of the Cyclops' promise to eat a verbal Nobody or a flesh-and-blood Odysseus remain fair game for the imagination.
That the nonexistent does not exist and that the unquantifiable cannot be quantified is self-evident; and yet the ever mounting effor of the mind to conceive the inconceivable, to describe the indescribable, will tend towards sublimity. As Kant puts it:
"[T]he satisfaction in the sublime does not so much involve a positive pleasure as admiration or respect, which rather deserves to be called negative pleasure."
Thus the Advaita Vedānta of Shankara is rich in negative predication of reality, expressed in Sanskrit as 'not-X' through the prefixes 'a-' and 'nir-' , i.e. 'not' and 'without' respectively. 'Advaita' (having no duality, unique), 'avidyā' (unknowability, illusion), 'amātra' (without measure, umeasurable), 'nirguṇa' (devoid of all qualities), 'nirviśesha' (without distinguishing properties), culminating in the formula 'neti-neti' (not-thus, not-thus), all act as rungs in a ladder to be discarded on the attainment of the 'One Reality' – Brahman, whereupon language ceases to serve any useful purpose, giving way to silence.
The language of the negative is the language of the sublime, the language of silence, the language of death.
Similarly, but without the self-annihilating process of the jettisoning of reason, C.S. Peirce proceeds through the rigorous channel of propositional logic to rather surpsising conclusions. In an attempt to improve on a weakness in Boole's algebra, Peirce proposed the inclusion sign —<, such that hi —< di means:
"that on occasion i, if the idea h is forced upon the mind, then on the same occasion the idea d is definitely forced upon the mind."
On the basis of the assumption that a —< b —< c means a —< (b —< c) rather than (a —< b) —< c the question arises as to the meaning of the infinite sequence:
a —< a —< a —< a —< a —< a —< a —< a —< a (...)
which turns out to be equivalent to the denial of a, or:
not-a or not-a or not-a or not-a or not-a or not-a or not-a ... .
Thus Peirce concludes:
"[W]ithout the introduction of any other sign, but merely by the idea of an endless sequence, after we already have the idea of a successive sequence, we reach the idea of negation."
Ingenious though Peirce's reasoning undoubtedly is, I am inclined to interpret this as an erroneous piece of overgeneralising 'infinitant negation':
/1/ Socrates est non stultus.
as opposed to 'negative negation',
/2/ Socrates non est stultus.
deriving from the 'not-ill' example of an indefinite verb in Aristotle and Abelard.
Peirce's metaphysical conclusions, however, I find particularly insightful and remarkably consonant with the mystic's negation-death association:
"We start, then, with nothing, pure zero. But this is not the nothing of negation. For 'not' means 'other than', and 'other' is merely a synonym of the ordinal number 'second'. As such it implies a first; while the present pure zero is prior to every first. The nothing of negation is the nothing of death, which comes 'second' to, or after, everything. But this nothing is the nothing of not having been born. There is no individual thing, no compulsion, outward nor inward, no law. It is the germinal nothing, in which the whole universe is involved or foreshadowed. As such, it is absolutely undefined and unlimited possibility – boundless possibility. There is no compulsion and no law. It is boundless freedom.
So of 'potential' being there was in that initial state no lack."
Narcissus beholds his own undistorted image reflected in the clear pool just so long as the finger that points does not touch the surface of the water. Where the negative wants to point, the affirmative wants to touch.
Wittgenstein meant to include the following key to the Tractatus in the preface to that work, although he never did in fact:
"My work consists of two parts: the one presented here plus all that I have not written. And it is precisely this second part that is the important one."
The relation of language to the world cannot itself be directly expressed in language but can, through the help of what is not said, be shown. And so just as the horizon separates the sea off from the sky, or an insect might be imagined to scan the inside of a bottle in order to determine its external form, what is not said will come to give proper form and perspective to what is said.
But if it is true that only what can be said can be said, it is also true that what cannot be said may still be shown, where it will acquire form through that boundary which is supervenient on both what is said and what is unsaid. However, concerning the whole that is constituted by what is said and what is unsaid nothing whatsoever can be said directly.
Wittgenstein thought of the 'higher truths' of religion, ethics and aesthetics as belonging to the second part, as being only indirectly communicable.
I should express this by saying that their 'not' content or, better, negative judgement level is high, and hence their depth of meaning.
In order to see this more clearly consider the opposite case:
/1/ x = x
where the negative content or negative judgement level is zero, and where the expression consequently turns out to be meaningless. Likewise, Peirce's:
/2/ a —< a —< a (...)
must be regarded as meaningless on the same grounds that its disposition to being other than a is nonexistent.
We can now begin to perceive something like a permeation of the positive by the negative, which will increase the level of meaning in direct proportion to negative presence. It is therefore not surprising to find considerable use of the negative in much of the most sublime literature that has ever been written.
 It could be argued that there is a symmetry rather than an asymmetry here, in that both affirmation and negation do something with the sense: where the former upholds, the latter denies. But the asymmetries strike me as being more real. As regards the pseudo-problems in fiction, I have in mind Heintz (1979) and Lewis (1983): If truth is understood referentially or extensionally, then the statement that Sherlock Holmes lived in Baker Street will be true, and the statement that he was a devoted family man will be false. Yet one wants to say that neither is true as they both appear in fiction. Once reference ceases to play a decisive role in truth, the intuitively obvious fact of the truths contained in great works of literature can be better explained and appreciated. The crucial link is judgement. For an over-reaction to the newly rediscovered capacity of literature as purveyor of truth, see Rorty (1982), Davidson (1984) and my criticism of both in Pacitti (1986).
 See note 11 in Understanding Negation.
 The thought of Shankara (788-820) is put forward in a number of commentaries (especially on the principal Upanishads and the Bhagavad Gīitā) and more explicitly in his Vivekacūḍāmaṇi, 'the crest jewel of discrimination', and Aparokshānubhūti, 'the direct perception of the not invisible'. In this way multiplicity, which belongs to the phenomenal world ('māyā'), is dispelled through 'nirvikalpa-samādhi', 'intense contemplation of that which is free of false notion', as expressed in the particularly finely elaborated śloka 357 of the Vivekacūḍāmaṇi:
upādhibhedātsvayameva bhidyate | copādhyapohe svayameva kevalaḥ ||
"The very Self (or better, 'the deep structure of reality') becomes distinguished as a result of the distinction (lit. 'split', with the repetition of √bhid- in both noun and verb) with the false ('variable', 'illusory', occurring initially in both half-verses) and thus with the false pushed away (but lit. 'in pushing away the false'), the very Self is wholly pure." It is important to see that truth is not epistemological but ontological, so that one is said to be in the truth, and not to possess it. It should also be noted that truth is closely related to being at the linguistic level too, viz. 'sat': 'being', and 'satya': 'truth'. Shankara (Aparokshānubhūti, 107-109) speaks of the limits of language and of that absolute silence ('yasmādvāco') where words cannot penetrate. But even the description of the phenomenal world is said to lie beyond the limits of language. The Brihadāraṇyaka Upnanishad (III,.viii.8) had attempted to define the indefinable Absolute in negatives, and this is echoed in Shankara's youthful but nonetheless sublime Daśaślokī, the ten verses which he recited to Govindapāda and which abound in negative definitions: "I am not Earth nor Water nor Fire nor Air nor Space, nor ami I the Senses nor even all of these things together [...]". Sureśvara, perhaps Shankara's closest disciple writes (Pañcīkaraṇa-vārttika, 62) that the supreme state of Vishnu is without affirmation or negation and lies beyond the distinction between name and named. Existence does not become kinowledge here, but rather self-knowledge becomes self-existence. One is reminded of Dionysius the Aeropagite, Maimonides and Aquinas, but in all three cases the 'ontological' approach of a via negationis is counterbalanced by a positive theology or via eminentiae. Radhakrishnan (1937, p.140) tries to link Shankara's idea of the identification of a knower and known with Aristotle's discussion of the nature of the mind in the De Anima. Radhakrishnan probably has in mind Aristotle's remark at the beginning of 431a to the effect that actively operative knowledge is identical with its object. But Aristotle is concerned rather with the perception of form, and his meaning is not Shankara's. Loy (1988) in his useful cross-cultural study of nonduality traces many interesting parallels, but I am still struck more by the differences than by the similarities. In his interesting paper on the reality of negation, Raju (1941) discusses ther systematic and highly logical approach to negation of the Nyāya-Vaiśeshika school of Indian philosophy which was directly opposed to the school of Shankara. Thus for Chandrakanta negation is positive, but only as difference: the 'negative entity' turns out to be only the positive entity perceived from a different perspective. For a recent study of Shankara see Potter (1981). Shankara's commentary on the Bhagavad Gīitā is well dealt with by Sharma (1986, pp.42-105). See also Martin-Dubost (1973). For an account of Rāmānuja's pluralist reaction to Shankara two centuries later see Srinivasachari (1913). See Mayeda (1968) on Advaita perception. Tucci (1957) supplies a good overview of Shankara's position set within the general context of Indian philosophy.
 Peirce (op. cit., 6.217). For more on Peirce's conception of negation see op. cit., 2.378-2.380 for logical vs. metaphysical negation, 2.593-2.600 for a critique of commonly accepted definitions of negation in terms of identity, contradiction and excluded middle, and 3.381-3.384 for an enlargement of the implication notation to accommodate negation.
 "[M]ein Werk bestehe aus zwei Teilen: aus dem, der hier vorliegt, und aus alledem was ich nicht geschrieben habe. Und gerade dieser zweite Teil ist der Wichtige." The quotation is taken from an updated letter to the Austrian publisher Ficker. The complete text is given in Von Wright (1982, pp.82-83).
 See Wittgenstein (1922, 6.41), where the sense of the world is said to lie outside the world itself, and hence any real value outside the sphere of what happens in the world. Compatibly with this, Wittgenstein denied the possibility that there could be propositions of ethics. Not only do I not see why a judgement cannot be factual, but I have previously drawn attention to the greater tendency towards permanence of 'judgemental' truths in respect of 'scientific' truths (cf. Pacitti, 1989, pp.9-10). It seems almost as though the degree of supposed detachment from the world were inversely proportionate to the degree of truth obtaining. Nor does the expression 'outside the world' mean anything to me here.
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.27-40).
In the same series of philosophical readings from the published work of Domenico Pacitti