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13
Someone might say that we are doing something less radical than that, namely refusing to accept any of the following: (Neg-P2*-1) Two is the least number of grains of sand that are enough to make a heap.
(Neg-P2*-2) Three is the least number of grains of sand that are enough to make a heap

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

This is less radical because it merely involves our refusing to accept, of any particular number, that it is the least number of grains of sand required to make a heap. That falls short of refusing to accept that there
is
such a number. And on some views this distinction is crucial. (In particular it is crucial on a ‘supervaluational’ view: see Fine (
1975
).) Even so I shall continue to assume that we are doing the more radical thing. If in fact we are doing this less radical thing, my argument needs to be modified, but not, I think, abandoned altogether.
14
Cf. also Williams (
1995b
), p. 217.
15
Essentially the same distinction is drawn, using that same terminology, in Harman (
1967
), p. 134. See also Dummett (
1978i
), p. 283.
16
The example is not an arbitrary one. In Deleuze (
2004
), p. 38, Deleuze writes that ‘duration differs from itself.’
17
Cf. also
Ch. 15
, §5: in these terms Nietzsche is rejecting the proposition that God exists, not denying it.
18
Both in this section and elsewhere I have emphasized Wittgenstein’s conservatism. But it is interesting to note two examples of philosophers who can be said to be more or less Wittgensteinian in their outlook, but who are prepared to accept an element of revisionism. The first is Friedrich Waismann: see Waismann (
1959
), §§VII and VIII, helpfully discussed by G.J. Warnock in Warnock (
1969
),
Ch. 10
. The second is P.M.S. Hacker, an ardent defender of Wittgenstein, who acknowledges (without, I think, seeing this as a departure from Wittgenstein) that ‘in practical philosophy there is room for the introduction of novel … concepts and for the remoulding of existing concepts’ (Hacker (
2009
), p. 150, emphasis removed).
19
Cf. also how Nietzsche, in Nietzsche (
1982b
), cited in
Ch. 15
, §7(a), likens himself to Spinoza by specifying ‘five main points of his [Spinoza’s] doctrine’ in which he recognizes himself, each of which is the
rejection
of something. (Walter Kaufmann in his translation has ‘denies’ rather than ‘rejects’, but in terms of the distinction that I drew in the previous section it is certainly rejection, not denial, that is involved here.) See also
Ch. 15
, n. 78, for a reminder of how one of these five points, the rejection of freedom of the will, goes against the non-revisionary grain of P.F. Strawson’s work.
20
I adverted to another relatively simple example in
Ch. 21
, §2(d): the way in which empiricists, in effect if not perhaps by design, introduce their own concepts of derivation and sense experience in order to formulate their empiricism. (See again the reference to Williams (
2006l
) in n. 31 of that discussion.) A fifth relatively simple example, I would contend, is Bernard Williams’ novel use of realism: see Moore (
2007a
), esp. §4. (This is the example to which I referred in the Introduction, n. 39.)
21
Or more strictly, everything finite with which we are acquainted: see
Ch. 2
, §2, for discussion of what ‘nature’ means here.
22
The formalization of theories that Quine envisages presupposes the Fregean account of how declarative sentences function.
23
‘In the form in which he introduced it’ is an important qualification. Bergson’s concept was one of many variations on a theme that had been familiar since at least the time of Aristotle: see e.g. Aristotle’s
Metaphysics
, Bk Θ,
Ch. VI
, and the concept of potentiality introduced therein.
24
See
Ch. 21
, n. 27.
25
See Introduction, n. 41, and the accompanying text: there is a case for saying that
all
concepts are action-guiding.
26
This gives the lie to the contrast that P.M.S. Hacker tries to draw, in the context of the quotation that I gave in n. 18, between ‘theoretical philosophy’, which he clearly takes to include metaphysics, and ‘practical philosophy’ (ibid., pp. 149–150). When Hacker makes provision for innovation in the latter, he also, willy-nilly, makes provision for innovation in metaphysics.
27
See Cohen (
1978
),
Ch. I
.
28
Another interesting if more marginal example is provided by the theory and practice of Derridean deconstruction and their influence on literary criticism (see Culler (
2008
)). This is more marginal for two reasons. First, there is an issue about how far Derridean deconstruction counts as a contribution to metaphysics. Second, the repercussions in this case are less far-reaching than in any of those cited in the main text.
29
Not that this is decisive. One might think, with Hegel, that metaphysics has to achieve what it does through the resolution and
Aufhebung
of opposition. Or one might think, with Dummett, that it has to achieve what it does by following ‘a meandering [path] that twists and turns upon itself’ (Dummett (
2010
), p. 149).
30
Cf. Williams (
2006a
), p. 49.
31
This is related to a wider failure to which metaphysics is prone: the failure, as Bernard Williams puts it in a wonderful passage on these and related matters, ‘[to] listen to what it is saying’ (Williams (
2006n
), §5, in which the quoted phrase occurs on p. 213). This is a failure to which the later Wittgenstein is especially sensitive: cf. the injunction in Wittgenstein (
1967a
), Pt I, §66, not to think, but to look.
32
This is not to deny, what my argument in §2 prevents me from denying, that metaphysics can be hard to distinguish from history – as indeed it can be hard to distinguish from sociology or anthropology. But it can also be hard to distinguish from physics.
33
This is part of the reason why I answer the Creativity Question in the way I do. See Introduction, §6(c).
34
Here I take myself to be in agreement with Bernard Williams, despite an initial appearance to the contrary: see Williams (
2006o
), pp. 182–183. See also the splendid passage in Lovejoy (
1964
), pp. 22–23.
35
Here there is an important difference between metaphysics and other branches of philosophy: see Williams (
2006m
), esp. §7.
36
Wittgenstein (
1967a
), Pt II, §xi, is very relevant here.

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