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Negation and Sense

Domenico Pacitti (1991)

4.1. Consider the following sentences:

/1/ John broke the window.

/2/ The window was broken by John.

/3/ So it was John who broke the window!

/4/ Big bad John broke the window.

/5/ Did John break the window?

/6/ John didn't break the window.

I want to say that what /1/ /4/ assert, what /5/ queries and what /6/ denies is the breaking of a window by John, and that this 'breaking of a window by John' is the thought or proposition or sense expressed in each of the six sentences. We can make this 'sense' even more precise by writing 'at time t' after 'the breaking of a window by John', or 'that John broke the window'', and we could attribute this very same sense to any number of admissible translations of the six sentences across any number of natural languages.

What we are calling 'sense' here is sometimes termed 'meaning', but this is not strictly the case. For, as we shall see, sense is narrower than meaning, being a part of meaning. Thus the same sense may be expressed in sentences with active or passive constructions (1 & 2), sentences which are exclamatory (3), sentences containing affective devices (4), interrogative sentences (5) and, last but not least, sentences containing negatives (6).

The sense of a sentences is therefore something like its essential, kernel content and can helpfully be conceived of in pictorial terms as a reflection of the logical form of reality.

But although sense is objective and characterisable as such, it is often concealed and distorted by natural language. And so when it is objected that the active has primacy over the passive or that the passive expresses certain nuances which the active does not (1 & 2), that (3) belongs to a lower register than (1) and (2), introduces the action differently and has exclamatory force, that (4) adds to the representation of John, that (5) is a question, and that (6) differs from all the rest in that it is the only negative, we shall of course agree that the overall meaning is, to a greater or lesser degree, different from one sentence to the next but, again, we are not at the moment concerned with the overall meaning.

What we are doing is looking through language as it were, in order to perceive that picture, proposition or skeletal logical structure we are calling the sense of the sentence.[1]

The same basic objection sometimes takes another form: that there is no clear distinction between form and content since what is said is in inseparable from how the utterance is made. Not only does this position preclude the very notion of a theory of meaning, but it leaves one wondering how communication is feasible at all.

Another objection is that my tentative fixed point of sense is both too abstract and absolute in a world where, as is often argued in Italy, everything is relative. Here I provide the reminder that relativism is self-refuting: for if everything is relative how can an absolute statement of this supposed relativity come to be? Those who have recourse to Einstein at this point usually have neither read nor understood him.

As for the charges of abstraction, we need only look to the nature of mathematics, set theory or, better, particle physics in order to understand the revived Platonic need for abstract concepts to fill out our system of the world.[2]

Why sense at sentence level rather than at word, paragraph or complete text level? In the case of overall meaning I agree that any one level will at certain times appear more appropriate, more suggestive, more real, but here again we are speaking of sense, not of overall meaning.[3]

However, there are two further objections which I would regard as the only two substantial ones and the answers to which will lead us much deeper into a new and more satisfactory theory of meaning, for the nature of the negative can only be adequately understood within the context of a more general theory of meaning itself. These are (less obviously):

1. How can an interrogative sentence have the same sense as an indicative one?

and (more obviously):

2. How can a negative sentence have the same sense as an affirmative one?

4.2. The first problem here is to see that there is a problem at all. The best exposition, it seems to me, is to be found in Frege's (1919) classic paper on negation:

"But it must already be possible to grasp the sense of the interrogative sentence before answering the question; for otherwise no answer would be possible at all. So that which we can grasp as the sense of the interrogative sentence before answering the question – and only this can properly be called the sense of the interrogative sentence – cannot be thought, if the being of a thought consists in being true. But is it not a truth that the sun is bigger than the moon? And does not the being of a truth just consist in its being true? Must we not therefore recognise after all that the sense of the interrogative sentence:

'Is the sun bigger than the moon?'

is a truth, a thought whose being consists in its being true? No! Truth cannot go along with the sense of an interrogative sentence; that would contradict the very nature of a question. The content of a question is that as to which we must judge. Consequently truth cannot be counted as going along with the content of a question."[4]

Frege, like so many others, considers the sense (or thought or proposition) expressed in a sentence as having a truth value, which then leads him into difficulty with the sense of an interrogative sentence, and this forces him to make an awkward exception within his overall theory.

Likewise in the case of negation (and in that of a hypothetical thought-complex) he is led to admit false thoughts "not indeed as true, but as sometimes indispensable".[5]

My position is that sense is always free of any truth-value. For sense when clothed in the interrogative form is that with respect to which we are invited to make a judgement. And that which invites an assertion which will have some truth value cannot itself have any truth value.

Now what can we say is required for sense to acquire a truth value?

I shall say that what is required is that this sense should be asserted and not merely entertained. For the entertainment or sense of a state of affairs will require what may be termed 'assertion' or 'power of signification', and the judgement involved in such assertion or power of signification in order for it to acquire the status of truth or falsity.

Consequently, truth arises from a correctness or rightness of judgement in respect of any given sense, and herein lies the connection between truth and meaning.

Thus when we come to consider the negative we can see clearly that a given propositional sense is denied rather than asserted, thus acquiring a truth value. For, as was shown at the beginning of this essay, the assertion or negation of any given proposition or thought will be the assertion or negation f that very same sense in each case.

In this way our six sentences express the very same sense, but with different powers of signification, or what Frege calls 'force' ('Kraft').[6]

The following two examples will serve to elucidate this even further:

1. A tape recorder accidentally goes off, emitting the pre-recorded words: "There is no one in this room" and someone passing by outside the room happens to hear these words when the room is in fact empty. Would we be prepared to say this is true?

2. A worm moving over sandy soil traces out the word 'pluit' when it happens to be raining. Are we prepared to say that this is true?

In both cases – no! For the construed sense was not the intended sense. In the first case, even if we assume deictic correctness, the power of signification is no longer credible, whereas in the second it is quite absent. Human intention, human purposefulness, human judgement applied directly to sense is what is required for it to be right to speak of truth. When people speak loosely of truth as correspondence, the fact is often overlooked that this involves a rightness of assertion. Aristotle saw this:

"To say that what is is not, or that what is not is, is false; but to say that what is is, and what is not is not, is true."

where the operative term is 'to say'.[7]

To recapitulate:

1. There is something that is the sense of a sentence and which is sometimes called its propositional sense, its thought or its proposition, and which can in a more concrete manner be considered as any noun clause of the type 'that such-and-such is the case'. This can have no clear truth value in the absence of assertion.

2. Assertion is what endows sense with truth. Assertion may be affirmative or negative: when it is affirmative the sense is upheld, and when it is negative the sense is denied. There can therefore be no such thing as negative sense, since negation always involves a judgement over sense and is consequently of a higher order.

3. Assertion may express sense intentionally or unintentionally. In the latter case it will lack truth.

4. Truth is therefore a rightness of assertion of sense, i.e. the correct employment of the human power of signification, and hence an act of judgement.

5. Furthermore, sense may be considered objective, representing as it does intersubjectively verifiable criteria. But although the same sense may be expressed in interrogative, optative, exclamatory, imperative and indicative sentences – whether affirmative or negative, active or passive – only the indicative have the property of bivalence.

6. Sentences are taken to be the primary bearers of meaning, two aspects of which are sense and mode of signification.

7. The nature of the negative may therefore be adequately understood only within the framework of a theory of meaning.

4.3. A third aspect of meaning – and one which will be extremely important in the creation and appreciation of works of literature – concerns what we might call 'emotive depiction'. By this I mean any suggestive or implicational element that may remain once we have accounted for sense and mode of signification. Thus the sentence (/4/ in paragraph 4.1. above):

Big bad John broke the window.

is the (true or false) assertion of the sense of each of the other five sentences, namely that of 'the breaking of a window by John', but displays an additional type of element in the two adjectives 'big' and 'bad'. I am for the purposes of this exposition avoiding the further complication of proper names. Strictly speaking, the sense is that of the breaking of a window by a person, and to this extent 'John' in all six sentences is itself such an 'additional element'. Similarly, the definite/indefinite article opposition as well as the tense marker are problematic.

Such elements may be suggestive or implicational either intentionally or unintentionally as well as subjectively or objectively. Thus where 'big bad John', or better 'Big Bad John' is a nickname, the intended suggestiveness on the part of the speaker will be minimal or even nil, while it will be considerable where it represents the speaker's own characterisation. In this way the standard American "Have a nice day!" will have considerable emotive content for the Englishman who is unacquainted with the convention, and nothing beyond 'Goodbye' for the American who is so acquainted.

In literary criticism considerable time and effort have gone into attempting to demarcate the boundaries between admissible interpretations on the one hand, and inadmissible ones on the other. If a writer tells us there are rich colours to be seen, shall we imagine two, three, four or more? Will the reader who sees red and purple be more or less accurate than the reader who sees blue and yellow?

I have spoken before of four conditions that would be necessary but not sufficient for 'correct interpretation' as:

1. understanding the words;

2. understanding the writer's intentions;

3. understanding what the writer understands;

4. moral judgement.[8]

My caution over sufficiency reflected the need to accommodate subjectively inspired associations, suggestions and implications, where our aesthetic judgement will guide us in determining what is admissible as against what is inadmissible in respect of interpretation, but where no clear limit, it seems to me, can be drawn in order to separate the one off from the other.

Much of modern literary criticism is unashamedly concerned with the (more or less) systematic extraction of the greatest possible range of 'meanings' or with inexcusably personalised interpretations of a given text. Where one work of art inspires another, this is certainly highly commendable but it is not literary criticism.

That there can be no precise boundary between acceptable and unacceptable subjectively based construals of suggested data or implicational elements in the area of what we are calling 'emotive depiction' does not by any means preclude our ability to judge correctly either way.

4.4. That 'the Evening Star' and 'the Morning Star' have different sense but the same reference, namely Venus, is an important insight due to Frege. The reference of a term will be to an existent object or state of affairs in the world. But sense and meaning can exist independently of reference; for there is both sense and meaning in my speaking of Sirius as the brightest star in the sky and a binary star in the constellation Canis Major, while admitting the possibility that the star itself could have ceased to exist a year ago, since it is at a distance of 8.7 light years from Earth.

Quine (1969 & 1969) has drawn attention convincingly to what he calls inscrutability of reference to which we are led through the rejection of an uncritical mentalism, namely the pairing off of term and reference in the fashion of a museum exhibit and label, which he calls the myth of the museum. The result is an indeterminacy due to inevitable slippage in correspondence between word and object.

That this is over and above the underdetermination of any theory of nature by all possible evidence has been widely misunderstood. Thus for Quine there can be no saying what something is beyond its restatement in a different form. But his conclusion that "both truth and ontology may in a suddenly rather clear and even tolerant sense be said be said to belong to transcendental metaphysics" I find unsatisfactory in the pejorative sense in which Quine intends it. Let me briefly explain why.[9]

Suppose we are standing in the Louvre looking at the Mona Lisa. Are we looking at the portrait of a young woman? Or Leonardo's masterpiece? Or a painting that was completed in 1503? Or is it a frame containing a picture hanging on the wall? Or something that is priceless? Or such-and-such a weight of a number of materials hanging in a museum? Or an exceedingly complex amalgam of atomic and subatomic particles? And so on. There will be an infinitude of mutually incompatible descriptions demonstrating Quine's thesis that to be is to be the value of a variable, that there is no end to what must be an infinite regress of definitions of definitions, that there is, as he puts it, no truth of the matter.

Now what I have been arguing for is the position that truth is a rightness of assertion of sense, thus construing truth on the side of intension rather than extension, so that any indeterminacies or vagaries of reference are less relevant here.

Ontological relativity finds its fixed point in whatever it is that it is relativised to.

The truth of an assertion can be usefully understood as being correlative to an appropriate question or as being the 'right' response in a given set of circumstances, where the rightness of response will reflect a rightness of judgement.

It is in this respect that I share Quine's holism.

Notes

[1] I use the terms 'sense', 'propositional sense', 'proposition' and 'thought' interchangeably throughout. That is because, unlike Frege and Wittgenstein, I do not think sense can have a truth value. Nor do I think there can be negative sense, or negative propositions. In what follows I take myself to have proved both these hypotheses. While bearing in mind these substantial points of divergence, I continue to find Wittgenstein's 'picture' suggestion helpful (Wittgenstein, 1922, 4.12 & 4.121):

4.12 Der Satz kann die gesamte Wirklichkeit darstellen, aber er kann nicht darstellen, was er mit der Wirklichkeit gemein haben muss, um sie darstellen zu können, die logische Form.

Um die logische Form darstellen zu können, müssten wir uns mit dem Satze ausserhalb der Logik aufstellen können, das heisst ausserhalb der Welt.

4.121 Der Satz kann die logische Form nicht darstellen: sie spiegelt sich in ihm.

Was sich in der Sprache spiegelt, kann sie nicht darstellen.

Was sich in der Sprache ausdrückt, können wir nicht durch sie ausdrücken.

Der Satz zeigt die logische Form der Wirklichkeit.

Er weist sie auf.

4.12 Propositions can represent the whole of reality, but they cannot represent what they must have in common with reality in order to be able to represent it –– logical form. In order to be able to represent logical form, we should have to be able to station ourselves outside the world. 4.121. Propositions cannot represent logical form: it is mirrored in them. What finds its reflection in language, language cannot represent. What expresses itself in language, we cannot express by means of language. Propositions show the logical form of reality. They display it. (English translation by D.F. Pears & B.F. McGuinness in Wittgenstein 1922.)

Since Russell, Tarski and Carnap, the concept of 'metalanguage' has gained much ground. The metalanguage/object language distinction actually goes at least as far back as Burleigh's 'suppositio formalis'/'suppositio materialis' distinction, which also separates the notion of use from that of mentioning. Indeed when seen in this light, many of (the early) Wittgenstein's problems are seen to be dissolved rather than solved. But it is my own belief that such 'detachment' or Quinean 'semantic ascent' proves in the last analysis to be illusory. For the way we perceive the world cannot, it seems to me, be clearly or intelligibly separated off from the world itself. Although this interaction shows itself and is reflected in language, nothing can be said about the relation from the outside, as it were: for we would then have to be outside the world. But within language itself, as we shall see, it is useful to distinguish the formal from the substantial, external negation from internal negation. The history of this distinction is well dealt with by Horn (1989, pp.132-144). We begin, then, with 'sense', reflecting as it does our human experience not with the world, but as part of the world. What relation could there then be when all is one? What sense could there then be in seeking the relation between something and itself –– or between something and nothing?

[2] (Necessarily abstract concepts are to be distinguished from (putative) abstract entities. I recognise the former but not the latter. Whereas concepts require human conjunction or participation, entities are altogether independent of such human factors, although admittedly their individuation (by humans) is not likewise independent. See note 16 in Domenico Pacitti, The Nature of the Negative.

[3] Aristotle brings out this difference between sense and meaning, recognising that while truth and falsity may go along with the latter, they do not go along with the former (De Interpretatione, 16b, 27-17a,9).

[4] p.374.

[5] p.377. The gist of Frege's argument is as follows: If 5+4 is greater than 5+3, then 5+40 is greater than 5+30 ('modus ponens'). If 5+30 is not greater than 5+40, then 5+3 is not greater than 5+4. ('modus tollens'). While I do not dispute the legitimacy of 'modus tollens', I fail to see how this has to depend on a 'false thought'. For how could that which is merely entertained thereby have truth or falsity? Surely the rejected hypothetical only has to have sense, and not truth or falsity. Counterfactual conditionals are commonly regarded as being unanalysable ain truth-functional terms on the grounds of the necessary falsehood of the antecedent, but once the antecedent is reconstrued as entertained rather than stated, the counterfactual conditional will derive its truth intensionally from its rightness of assertion. And this will determine its acceptability. See Goodman (1965) and also Katz (1986).

[6] On sense, tone and force see Frege (1892a, 1892b & 1969). see also Dummett (1978, pp.87-144, and 1981, passim).

[7] Metaphysics, 1011b: τὸ μἒν γὰρ λέγειν τὸ ὂν μὴ εἶναι ἢ τὸ μὴ ὂν εἶναι ψεῦδος, τὸ δὲ τὸ ὂν εἶναι καὶ τὸ μὴ  ὂν μὴ εἶναι ἀληθές, ὥστε καὶ ὁ λέγων εἶναι ἢ μὴ ἀληθεύσει ἢ ψεύσεται. Notice how Aristotle goes on to underline this saying how things stand, rather than that they simply stand in a certain way. Compare my "pluit" illustration with Putnam's (1981, p.1) ant example in "Brains in a vat": "An ant is crawling on a patch of sand. As it crawls, it traces a line in the sand. By pure chance the line that it traces curves and recrosses itself in such a way that it ends up looking like a recognizable caricature of Winston Churchill. Has the ant traced a picture of Winston Churchill, a picture that depicts Churchill?"

[8] See Pacitti (1989, pp.1-5). The terms 'understanding' and 'intentions' may be read transparently, but they turn out, of course, to be problematic. For example, in the latter case something may be true under one description and false under another even though the descriptions could be said to be synonymous or equivalent. See Geach (1957), Anscombe (1963) and Davidson (1980). In my use of the expression 'moral judgement', 'moral' does not add anything to judgement but simply stresses an aspect of what is already contained in judgement. See note 9 to Understanding Negation.

[9] For an identification of Quine's two purported indeterminacies as one, see Chomsky (1975). For Quine's re-articulation and re-insistence, see Quine (1975) in his reply to Chomsky. Quine's remarks on truth and ontology are from Quine (1969, p.68). What Quine is doing here essentially is restating his thesis on the circularity or infinite regress attached to the notion of definition. Where he sees there being no way of determining a definitive stopping point, I see such determination arising out of (moral) judgement, namely the very element that modern 'scientistic' thought seeks to eliminate in the interests of truth. See Quine (1951) for the classic exposition.

Cited Works

  • Anscombe, G.E.M. 1963. Intention. Oxford.

  • Aristotle, De Interpretatione.

  • ––– Metaphysics.

  • Chomsky, N. 1975. "Quine's Empirical Assumptions." In Davidson & Hintikka (1975), 53-68.

  • Davidson, D. 1980. Essays on Actions and Events. Oxford.

  • Davidson, D. & J. Hintikka 1975. Words and Objections: Essays on the Work of W.V. Quine. Dordrecht.

  • Dummett, M. 1978. Truth and Other Enigmas. London.

  • Frege, G. 1892a. "Über Sinn und Bedeutung." Zeitschrift für Philosophie und philosophische Kritik, C, 25-30.

  • ––– "Über Begriff und Gegenstand." Vierteljahrsschrift für wissenschaftliche Philosophie, XVI, 192-205.

  • ––– 1919. "Die Verneinung." Beiträge zur Philosophie des deutschen Idealismus, I, 143-157. (Engl. transl. by B.F. McGuinness et al. in B.F. McGuinness (ed.), Gottlob Frege: Collected Papers on Mathematics, Logic, and Philosophy, Oxford, 1984, 373-389.)

  • Geach, P.T. 1957. Mental Acts. London.

  • Goodman, N. 1965. Fact, Fiction, and Forecast. New York.

  • Horn, L.R. 1989. A Natural History of Negation. Chicago.

  • Katz, J. 1986. "Why Intensionalists Ought Not Be Fregeans." In E. LePore (ed.), Truth and Interpretation, Oxford, 1986, 59-81.

  • Pacitti, D.A. 1989. "On the Rightness of Seeing Double in the Opening Pages of Poe's Eureka." Linguistica e letteratura, XIII-XIV, 1-2, 1-17.

  • Putnam, H. 1981. Reason, Truth and History. Cambridge.

  • Quine, W.V. 1951. "Two Dogmas of Empiricism." Philosophical Review, L, 6, 561-601.

  • ––– 1969. Ontological Relativity and Other Essays. Cambridge, Mass.

  • ––– 1975. "Reply to Chomsky." In Davidson & Hintikka (1975), 302-311.

  • Wittgenstein, L. 1922. Tractatus Logico-Philosophicus. London.

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.19-27).

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