D.S. CLARKE, JR.

N E G A T I N G T H E S U B J E C T

(Received 14 April, 1982)

The asymmetry of a singular sentence's subject and predicate Geach has

explained in terms of negation. 1 The sentence

(1) It is not the case that John is standing

expresses the same proposition as

(2) John is not standing

in which the predicate is negated. But there is no equivalent form in which

the subject term ' John ' is negated. More generally, with negation sumbolized by a bar over the negated expression, a sentence of the form (Pa) is equivalent to ffa but notPff. Since negation applies only to predicates and not to subjects,

in terms of it they can be distinguished as the basic logical constituents of a sentence. We shall refer to this claim as 'Geach's thesis'. It has been accepted by enough writers in the years intervening since Geach's statement of it to

warrant a closer look.

Studies by linguists on shifts in the focus of a sentence seem to indicate

that the thesis is false. 2 In fact, we use stress in speaking to distinguish two

negative forms of (2). With the stress on 'standing' in the sentence,

(3) John is not STANDING

we have predicate negation of the proper Geachean variety. But with the stress on the proper name in

(4) JOHN is not standing

the negation does indeed seem to apply to the singular subject. Where spoken stress is unavailable, as in writing, we can express this subject negation by 'I t is not John who is standing'. (3), in contrast, could be made explicit by ' I t is not standing which John is doing'. Hence, (2) is not an instance of predicate negation, but is ambiguous between the predicate negation of (3)

PhilosophicalStudies43 (1983) 349-353. 0031-8116/83/0433-0349500.50 Copyright �9 1983 by D. Reidel Publishing Co., Dordrecht, Holland, and Boston, U.S.A.

350 D.S. CLARKE, JR.

and the subject negation of (4). We thus seem to be able to conclude that subjects and predicates are alike in their susceptibility to negation and that

Geach's thesis is false. It might be replied that (3) differs from (4) in a way that restores the

sought-for asymmetry. In asserting (3) the speaker assumes the hearer's familiarity with a reference class of individuals, e.g. John, Peter, Paul, and

Mary, who are at the occasion of utterance standing in the room occupied by the speaker. In stating that it is not John who is standing he or she is, in

effect, implying that some individual of this class other than John is standing. If we let variable x range over individuals of a given reference class, then of a

given individual a to asserts Pa is to imply 3 x(x :~ a A Px). Though in the

form of a negation, (3) thus implies a positive proposition about an indefinitely specified individual.

But this in itself is not sufficient to distinguish (3) from (4). A given

predicate P occupies a position within an incompatibility range of predicates P, Q, R . . . . such that a given individual must be either P or Q or R or ....

Thus, 'standing' might be regarded as occupying a position within a range including 'kneeling', 'sitting', and 'lying'. To assert that it is not standing

which John is doing is to imply that some other predicate within this range

is to be ascribed of him. More generally, if a is a variable for which predicates P, Q, R, ... can be substituted, then to assert Pa is to imply 3 a(a --/=P A aa). There are two types of mistakes a speaker can make in ascribing a predicate P

to an individual a: he can refer to the wrong individual or can ascribe to a

given individual the wrong predicate. Subject negation points out the first mistake, predicate negation the second. To correct the mistakes requires either referring to some other individual or ascribing some other predicate.

Thus, there is in this respect perfect asymmetry between (3) and (4). These considerations show conclusively, I think, that there is a type of

subject negation, and that in this respect at least Geach's thesis is false. They do not show, however, that this is a distinguishable form of logical negation which affects the truth conditions of the sentence in which the negated term occurs. Instead, the contrast between (3) and (4) can be seen to lie solely in their contrasting conversational implicatures. A predicate negation sentence Pa implies.

(5) 3x(x =a)

and, as we nave seen,

N E G A T I N G THE S U B J E C T 351

(6) 3 a(a ~ P A aa).

A subject negation sentence, in contrast, implies (5) as well as

(7) 3 x ( x q : a A P x ) .

But as the implication that distinguishes subject from predicate negation (7)

has no effect on the truth value of a sentence such as (4). I f we suppose that

John happens to be the only one in the room and that (7) is therefore false,

this would seem to have no effect on the sentence's truth value, either by

depriving it of a condition for having a value or by falsifying it. The truth of

the proposition expressed by (4) depends only on whether John is not

standing, not on the presence of someone else who is standing. The truth conditions of (4) are thus exactly the same as for (3).

The truth of (5) on a given occasion is not, as has been frequently noted, a necessary condition for utterances of either negative sentence having

truth values. It is necessary for a hearer to judge the proposition expressed

by an utterance of a singular sentence true or false that he or she be able to

identify the intended referent of its subject. There must be someone or other in the vicinity for the hearer to make the judgment, but it is not necessary

that this be the individual the singular term is true of. Suppose X says ' John is standing', intending by ' John ' to refer to Peter. Then the hearer Y can judge the proposition true or false if he recognizes X's intention and correctly

identifies Peter as the intended referent. I f Peter is in fact standing, then Y can judge the proposition true but use the subject negation (4) to point out X ' s mistake and 'I t is instead Peter who is standing' to correct it. Similar considerations hold for the negation 'John is not standing', either in its

subject or predicate negation forms. To evaluate it requires only that the

intended referent be identifiable, an individual who may not actually be

John. Here, however, the hearer can only judge the proposition true or false

if the intended referent is not John. Though there is no difficulty in principle of constructing a subject negation sentence to point out a mistake in

reference (e.g. ' I t is not John who is not standing'), such a sentence is not normally used because of its complexity.

Stress affects negation in general sentences in even more complex ways. The sentence

(8) All crows are not black

352 D . S . C L A R K E , JR .

has, in fact, three readings:

(9) All crows are not BLACK

(10) All CROWS are not black

and

(11) ALL crows are not black.

(9) can be expressed by 'No crows are black', (10) by ' I t is not crows which

are black', and (11) by ' I t is not the case that all crows are black' or 'Some

crows are not black'. A similar t r ichotomy can be derived by stress placement for the sentence 'Some crows are not black'. (9) and (10) have implications analogous to those for (3) 'and (4), with (9) implying that there is some

other property that all crows have and (10) that there is some other species all of whose members are black.

But, again, this contrast in what is implied does not affect what is asserted by the two sentences and their truth conditions. The standard logical

representation of the predicate negation is Vx(Cx~ -Bx) . (10), in contrast, would seem to be true if and only if all black things are not crows. Whether

or not there is another species whose members are all black seems to have no

effect on this truth value. The representation of ( I0 ) is thus Vx(BxD - Cx). But by contraposition this is logically equivalent to that of (9). As before, the contrast between the two propositions is not a logical contrast between

different propositions, but only between implications irrelevant to truth value.

If negation is unavailable, what is the basis for the asymmetry between subject and predicate? The l ack of a logical contrast between (3) and (4) suggests that it lies in the unique referring role of the subject term, the

fact that it must be used by the speaker to refer to what is assumed to (in some sense) exist. Even where the subject is negated, as for ' I t is not John

who.. . ' , it continues to be used to refer in the standard way to a particular existent individual. It does not, as we have seen, refer to some indefinite individual other than John though it implies there is such an individual. Since there is nothing analogous to this in the functioning of the predicate, asym-

metry is preserved.

Southern Illinois University at Carbondale

N E G A T I N G THE SUBJECT 353

NOTES

i "What distinguishes predicates from subjects, I suggest, is ... that by negating a predicate we can get the negation of the proposition in which it was originally predicated (plainly; there is nothing analogous for subject terms)." P. T. Geach: 1965, 'Assertion', Philosophical Review 74, p. 461. 2 See, for example, R.S. Jackendoff: 1972, Semantic Interpretation in Generative Grammar (Cambridge, Mass.), pp. 254-265. I am grateful to Geoffrey Nathan for having brought this work to my attention.