The Evolution of Modern Metaphysics: Making Sense of Things (141 page)

On a Wittgensteinian approach, however, we have a way of seeing how (P2) and (P2*) can come apart, or more strictly how accepting (P2) and accepting (P2*) can come apart. How so? Consider what we would be doing if we accepted (P2). On a suitably Wittgensteinian view,
we would be endorsing a rule of application for the concept of a heap
: not to count any number of grains of sand as too few to make a heap unless we also count the next largest number as too few to make a heap (cf.
Ch. 10
, §3). Very well, what are we doing in accepting (P2*)? We are
refusing
to accept the following:

(Neg-P2*) There is a number
n
such that
n
+ 1 is the least number of grains of sand that are enough to make a heap.
¹³

And what would we be doing if we accepted (Neg-P2*)? Again, on a suitably Wittgensteinian view, we would be endorsing a rule of application for the concept of a heap: to recognize that there is such a thing as the least number of grains of sand required to make a heap. Two rules are now in play then.
And there is no reason whatsoever why, having refused to endorse one of them, we should not refuse to endorse the other
. To think that we
must
endorse one or other of these two rules is like thinking that either ‘The opening move shall be a pawn move’ or ‘The opening move shall not be a pawn move’ must be a rule of chess. We can refuse to accept (Neg-P2*), on the grounds that we want the concept of a heap to admit of a certain latitude in its application; and we can refuse to accept (P2), on the grounds that, combined with (P1), it yields (C). (Cf. Wittgenstein (
1978
), Pt V, §13.
¹⁴
)

What it comes to, then, is this. In accepting (P2*) we register our refusal to accept (Neg-P2*). We endorse a kind of second-order rule that precludes our adopting that first-order rule. But this does not commit us to accepting (P2). We can refuse to accept (Neg-P2*)
and
refuse to accept (P2) and thereby avoid paradox.

This is all very well, you may say, but even if we accede to the idea that, on the most natural interpretation of these sentences, accepting them is tantamount to endorsing the rules specified, what about an interpretation of the sentences on which the meaning of the word ‘heap’ is simply taken as given and the sentences are used, in accord with that meaning and perfectly straightforwardly, to say how things are? Will the paradox not then rearise?

Well, but
is
there any such interpretation? We cannot uncritically appeal to ‘the meaning’ of the word ‘heap’, along with some principle of compositional semantics, say, and imagine that we thereby fix what claim somebody would be making in asserting one of these sentences. (Cf. Wittgenstein (
1967a
), Pt I, §350.) True, there are various claims in the offing that someone
might
make; various claims, therefore, that someone asserting one of these sentences might, with more or less violence, be interpreted as making. But none of them, as far as I can see, threatens paradox. For instance, it is unproblematically true that the removal of one grain of sand from a heap makes no readily discernible difference to it. It is unproblematically false that the removal of one grain of sand from a heap makes no difference at all
to it. It is unproblematically true that no number has ever in fact been specified as the minimum number of grains of sand required to make a heap. It may also be unproblematically true that, if grains of sand are laid down one by one, there will be a first point at which you (or I, or both of us, or everyone in a certain group, or a majority of people in that group) are inclined to say that there are enough to make a heap. (Or it may be unproblematically false.) What is not clear, and what would have to be the case for there to be a paradox, is that there is any claim in this vicinity that both looks as if it must be true and looks as if it can be used to derive, by an argument that looks as if it must be valid, a claim that looks as if it must be false.

(b) Dissent

Back to Wittgenstein himself.

My preoccupation with Wittgenstein is not confined to the ways in which he promotes a correct understanding of metaphysics. It extends to the principal way in which, as I see it, he thwarts a correct understanding of metaphysics. His influence concerning the third of the questions from §6 of the Introduction, the Novelty Question, seems to me essentially malign (
Ch. 10
, §6).

I agree that we need to think clearly and carefully about how we make sense of things. But we also need to think clearly and carefully about how
to
make sense of things. And there is no reason why the second of these activities should not be as much a part of sense-making at the highest level of generality as it is lower down. Perhaps there are, even at the highest level, forms of sense-making that are both radically different from any we now have and an improvement on any we now have. Perhaps, unless we deliberately disrupt those we now have, they will atrophy.

And note that the thought that we do well to renounce some of our current forms of sense-making does nothing to impugn the Wittgensteinian thought that, in some sense, the very fact that we have those forms of sense-making ensures their correctness; ensures that they cannot be gainsaid. There is a distinction that is helpful to invoke here, between, as I shall put it,
rejecting
a proposition and
denying
it.
¹⁵
To reject a proposition is to decline to think in such terms: it is to repudiate some or all of the very concepts involved in the proposition. To deny a proposition, by contrast,
is
to think in such terms, but to count the proposition false. On this way of speaking, it is certainly possible to reject a proposition that it is not possible to deny. Suppose, for instance, that it is one of our rules that difference should count as an irreflexive relation. Then
there is no denying
that difference is an
irreflexive relation. If someone appears to deny that difference is an irreflexive relation,
¹⁶
then this only goes to show that he is not really – not properly, not strictly – using
those
concepts. He may proclaim, with complete ingenuousness, and with a clear grasp of what he is doing, ‘Difference is not an irreflexive relation.’ But then either the word ‘difference’ or the word ‘irreflexive’ or some other feature of the sentence has a use in his mouth that is, relative to our rule, non-standard. That, however, may be the very point of his pronouncement. He may be rejecting what he cannot deny. He may be repudiating some of the relevant concepts in favour of others which, though strictly distinct from them, are sufficiently closely related to them for the use of this sentence, in this context, to be the most effective way of introducing them. This is just the kind of thing that I argued was going on when Hegel appeared to deny the law of contradiction (
Ch. 7
, §7).
¹⁷

In any case, to make sense of things in a way that is radically new is not necessarily to renounce any extant way of making sense of things. The new way of making sense of things may be intended to supplement what we have already, not to replace it. Someone might cheerfully accede to the proposition that difference is an irreflexive relation, and even accede to the merits of thinking in such terms, while insisting that there is another sense of difference, of particular importance to philosophy, say, in which we need to acknowledge the existence of that which differs from itself.

However that may be, I firmly believe that Wittgenstein’s conservatism can be divorced from the rest of his account of sense-making. The answers that I have gleaned from that account to the Transcendence Question and the Creativity Question mark out metaphysics as an autonomous exercise whose aim is neither to dig beneath any surface nor to probe beyond any horizon but to ensure that the conceptual instruments that we use to dig and to probe, and to gain an overview of all that we have dug and probed, are fit for purpose. It is not an attempt to achieve insight into anything beyond those instruments, and it answers to no authority but the authority of their serviceability. This can easily seem to entail that the metaphysician, as such, has no business contriving new instruments. In other words, it can easily seem to entail a conservative answer to the Novelty Question. But it does not. Or rather – there is an ambiguity here – it entails such an answer only on one disambiguation of it. The ambiguity resides in the phrase ‘ensure that the instruments we use are fit for purpose’. This phrase can be heard in two ways. It can be heard in such a way that ‘the instruments we use’ has wide scope, in which case the claim is that, given the instruments we use, the aim of metaphysics is to ensure that they are fit for purpose. If it is heard in this
way, then conservatism does indeed beckon. But it can also be heard in such a way that ‘the instruments we use’ has narrow scope, in which case the claim is that the aim of metaphysics is to ensure the following: that we use instruments that are fit for purpose. If it is heard in
this
way, which is the way in which I intend it, then conservatism does not beckon; just the opposite in fact. What beckons is something much more Deleuzian.
¹⁸

4. Creation and Innovation in Metaphysics

Deleuze presents us with a vision of metaphysicians as creators of new concepts (
Ch. 21
, §6). I applaud that. True, Deleuze has his own distinctive understanding of ‘concepts’. When I, as an analytic philosopher, talk about the creation of new concepts, I do not mean quite the same by it as he does. As I tried to make clear in the last chapter, however, Deleuze’s understanding of ‘concepts’ is not
entirely
different from an analytic philosopher’s. In any case, my own view is that metaphysicians can be creative and innovative in a way that includes both what Deleuze understands by the creation of new concepts and what an analytic philosopher would understand by it. Here I revert to the versatility of the term ‘sense-making’: metaphysicians can be creative and innovative
in all forms of sense-making
. They can create new Deleuzian concepts; they can create new concepts of a sort that an analytic philosopher would recognize; they can create new ways of thinking; they can create new ways of evaluating; they can arrive at new truths. And ‘new’ in each of these cases embraces the radically new.

It is worth noting also that they can be innovative without being creative. They can be destructive, subverting extant forms of sense-making. We have witnessed many examples in this enquiry of the innovative power of destruction in metaphysics – from Hume’s empiricist assault on sense-making that is not suitably grounded in sense experience to Derrida’s Heideggerian repudiation of the metaphysics of presence.
¹⁹
There is good reason, and in
particular good Deleuzian reason, for thinking that such destruction counts for nothing except in the context of, or as a prelude to, creation. (A metaphysician needs as it were to earn the right to destroy.) Even so, the fact is that a metaphysician may see grounds for concern about some extant form of sense-making, which he or she therefore wants to subvert, without – yet – having any idea how to plug the gaps that this will leave behind.

But let us now take stock by reconsidering a few of the many striking examples from what has preceded this of metaphysical innovation that has also been creative.

Three relatively simple examples were given in §7 of the Introduction. We saw Lewis connect the ancient problem of universals with the question of what the purpose of physics is, thereby providing a new way of thinking both about universals and about physics. We saw Quine connect tenseless quantification with practical questions concerning the impact of what we do on future generations, thereby providing a new way of articulating the intuitive significance of the distinction between affecting how things will be for those who come later and affecting who comes later. And we saw P.T. Geach introduce a new conception of numerical identity whereby numerical identity is a three-place relation, not a two-place relation: on this conception,
x
can be numerically identical to
y
with respect to kind
K
₁
yet numerically different from
y
with respect to kind
K
₂
.
²⁰

Once the main narrative had begun, wider-ranging and more powerful examples abounded. Right from the outset Descartes provided us with a set of interlocking ideas about the project of making sense of things – the project of arriving at an integrated science of man and nature – that was unprecedented in the extent to which it met all its own explanatory needs. His vision of how we make best sense of things, which could be applied, in particular, to how we arrive at that very vision, served as an important model for subsequent thinkers, however differently they may have conceived the sense-making involved. In particular, it served as a model for the arch-naturalist Quine (
Ch. 1
, §4) and, less remarkably perhaps, because at less chronological or doctrinal distance, for Quine’s forerunner Hume (
Ch. 4
, §4). Neither Quine nor Hume shared Descartes’ foundationalism, however, whereby metaphysics was an independent part of the project on
which the rest of it was to be erected. Nor, relatedly, did either of them share his demand for certainty. It was in trying to meet that demand, and in trying to sustain that foundationalism, that Descartes arrived at one of his other great metaphysical innovations, the idea that man and nature, or more strictly mind and matter, are of two fundamentally different kinds, jointly comprehensible only insofar as the former is conceived as providing a window on to the latter, which is as much as to say only insofar as the former is conceived as successfully making sense of the latter, or as producing correct representations of the latter (
Ch. 1
, §6).