offer, a reason for believing that a similar charge applies to other commen-

tators simply because they give the concept of a rule a central place in their

account of Wittgenstein™s philosophical designs.

A further step in Cavell™s diagnosis of Kripke™s scepticism looks dif-

ferent, however. For Cavell also contests Kripke™s conception of the rela-

tionship between rule following in mathematical and in nonmathematical

(say, ordinary) cases “ between the cases of addition (and hence quaddition)

and of nonmathematical instances of going on with words. Kripke claims

that the problems he sees arising with addition can also arise in the latter

case: the only difference is that they can be brought out more smoothly

with mathematical examples. To illustrate this, he constructs the concept

˜tabair™, which he tells us applies to anything that is a table not found at the

base of the Eiffel tower, or a chair found there; and he imagines a sceptic

asking us how we know that we do not mean tabair by ˜table™.

Cavell contests Kripke™s sense of similarity: he points out that the scep-

tic™s imputation that the inside and outside of the tower might be included in

the function of a concept amounts to an invitation to imagine an interweav-

ing of our criteria for furniture with a geographical singularity, but without

actually imagining any recognisably human interest to which it might give

expression. As Cavell puts it, ˜in explaining the concept tabair this sceptic

103

Cavell™s Vision of the Normativity of Language

dissociates criteria from the realm of what Wittgenstein calls our ˜natural

reactions™. I suppose one could say that my natural reactions change in the

face of the Eiffel Tower, but would this not owe an account of why this

has happened just to me and in such a way as to produce this concept?™

(CHU, 88) And whatever conviction such an account might elicit, it could

not produce that sense of the meanings of our words receding generally

from our grasp, of the revelation of a universal truth, that Cavell takes as

the touchstone of a genuinely sceptical anxiety.

Cavell™s further implication is that we do not intuitively sense such an

inexplicable complication in our criteria in the case of quaddition; there,

one might say, we have no more (although also, of course, no less) sense of

puzzlement at the idea that the function of a concept parallel to our concepts

of addition might diverge at numbers above 57 (or above 1000) than at any

other point in the series they generate. One might say: the relevance or

purchase of human interests and concerns upon mathematical functions is

not such as to incite demands for an explanation as to why there should be

such a parallel function, or why it should ˜deviate™ precisely as and when

it does; to understand it just is to understand the series it generates, and

hence the derivability of every step within it. Cavell develops this intuition

at length:

I suppose that something that makes a mathematical rule mathematical “

anyway, that makes adding adding “ is that what counts as an instance of

it . . . is, intuitively, settled in advance, that it tells what its ¬rst instance

is, and what the interval is to successive instances, and what the order of

instances is. The rule for addition extends to all its possible applications. (As

does the rule for quaddition “ otherwise it would not rhyme with addition,

I mean it would not be known to us as a mathematical function.) But our

ordinary concepts “ for instance that of a table “ are not thus mathematical

in their application: we do not, intuitively . . . know in advance . . . a right

¬rst instance, or the correct order of instances, or the set interval of their

succession. And sometimes we will not know whether to say an instance

counts as falling under a concept, or to say that it does not count. . . .

To say that concepts of ordinary language do not determine the ¬rst, or

the succession, or the interval of their instances is perhaps to say that the

instances falling under a concept do not form a series. (CHU, 89“90)

For Kripke to think that the sceptical problem he develops so smoothly

from the example of addition can be equally well (if less smoothly) de-

veloped from nonmathematical examples amounts, therefore, to a failure

to appreciate the speci¬city of mathematical concepts and their associated

104 STEPHEN MULHALL

functions; more precisely, it amounts to assuming that ordinary, nonmathe-

matical concepts have associated functions, that they are or can be presented

as having an essentially mathematical structure. This dissociates nonmath-

ematical concepts from their distinctive relationship with our natural reac-

tions and forms of life, and treats mathematical concepts as normative for

the nonmathematical “ as if the latter would lack something if they failed

to manifest those features which, in reality, distinguish mathematical from

nonmmathematical concepts within human forms of life.

Ordinary language will aspire to mathematics as to something sublime; that

it can so aspire is speci¬c to its condition. The idea of ordinary language

as lacking something in its rules is bound up with “ is no more nor less

necessary than “ this aspiration. This is the place at which Wittgenstein

characterizes logic (and I assume the rule for addition is included here) as

˜normative™, as something to which we compare the use of words (section

81) “ to the discredit of words; he takes this further a few sections later

in posing the question, ˜In what sense is logic something sublime?™(section

89). In this role of the normative, the mathematical is not a special case of a

problem that arises for the ordinary; without the mathematical this problem

of the ordinary would not arise. (CHU, 92)

Here, Kripke™s variant of scepticism meets up with that of Pole, and re-

turns us to Wittgenstein™s most fundamental characterization of the scep-

tical impulse against which he sets his face “ the impulse to sublime the

logic of ordinary language, to see its grammar either as having the form

and nature of a calculus, with its distinctive abstractness, universality, and

completeness, or as something to be condemned for failing to do so. And

here we can say that Cavell™s critique of Kripke has more general implica-

tions: for even if most Wittgenstein commentators dissociate themselves

from the precise details of Kripke™s sceptical problem and solution, they

tend not to question the assumption that the example of addition might be

a reliable guide to the nature of rule following in general, and hence to the

nature of Wittgenstein™s conception of grammatical rules. Hence, if Cavell™s

sense of the distinctiveness of the mathematical is accurate, this assumption

might itself justify the charge that those who cleave to it project a sceptical

conception of the grammar of language upon Wittgenstein himself.

However, this conclusion would leave us with a problem. For of course,

the main reason most Wittgenstein commentators have assumed that the

example of addition casts light on the nature of linguistic rules and hence

upon grammar is that the text of the Philosophical Investigations appears to

share that assumption. It takes a mathematical example as normative for the

105

Cavell™s Vision of the Normativity of Language

whole of its discussion of rule following, and that discussion appears to be

designed to give Wittgenstein™s own account of linguistic meaning. Hence,

if Cavell™s charge of scepticism can be made out against Wittgenstein™s com-

mentators, must it not also apply to Wittgenstein himself? Does Cavell™s

conception of criteria and grammar, then, succeed in avoiding a scepti-

cal in¬‚ection from which even the author whose terminology and method

Cavell claims to be inheriting could not entirely free himself? Or is the

Investigations here not so much succumbing to a fantasy as acting one out

for therapeutic purposes? Perhaps Wittgenstein deploys his mathematical

example with so little overt fuss, and yet so quickly after repeatedly warning

us against taking the mathematical as normative for language, so that we

might eventually come to see that our previous readings of him have in

fact betrayed the insights to which they proclaimed allegiance, and hence

to realize the tenacity of the fantasies he opposes, and the real dif¬culty of

properly uprooting them.

CONCLUSION

Philosophy™s impulse to regard logic as normative for the normativity of

words is emblematic of a broader human impulse to regard such norma-

tivity solely as something to which we must impersonally and in¬‚exibly

respond rather than as something for which we are also individually and

unforeseeably responsible. Given the pervasiveness and depth of that im-

pulse, it should not be surprising that many philosophers™ attempts to artic-

ulate and deploy Wittgenstein™s attempts to overcome it in fact give further

expression to it. The impulse might ¬nd expression in misrepresentations

of Wittgenstein™s account of linguistic normativity. Or it might ¬nd ex-

pression in a failure to allow one™s intellectual grasp of that account (with

its emphasis upon the intertwining of agreement in de¬nitions with agree-

ment in judgements, and of both with our natural reactions) properly to

inform one™s deployment of the philosophical method that draws upon that

normativity (perhaps by allowing the stability of a word™s projectiveness

to occlude its tolerance, perhaps by treating one™s interlocutor as a de-

viant pupil rather than as an equal member of the community of speakers).

Stanley Cavell™s work on and after Wittgenstein is uniquely sensitive to