The Evolution of Modern Metaphysics: Making Sense of Things (88 page)

BOOK: The Evolution of Modern Metaphysics: Making Sense of Things

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29
But note that it is not difficult to find what appear to be forthright affirmations of a blanket anti-realism in Dummett’s writings. For instance in
Truth and the Past
we find, ‘What is true is what can be known to be true’ (p. 92); in ‘Campbell’, ‘Only what is knowable can be true’ (p. 313); and in ‘Beards’, ‘It makes no sense to speak of a world, or the world, independently of how it is apprehended’ (p. 892; cf.
Thought and Reality
, p. 64). Part of the explanation for this is that Dummett is genuinely wrestling with these problems and has at different times in his career been more or less convinced by the anti-realist proposal. There is further evidence for his lack of a settled view in the Postscript to ‘Truth’, written for its reprinting, where he says, ‘The text of the article espouses a frankly anti-realist position…. I am no longer so unsympathetic to realism’ (p. 24). Similarly, in the Preface to
Thought and Reality
, where he writes, ‘
Chapters 5
–
7
express views I no longer hold. It will naturally be asked why I am publishing them …, if I no longer agree with them…. In [
Truth and the Past
] I … set out a modification of the views I had expressed [here]. All the same, if I was sure that I had improved on my earlier thoughts, why put those earlier thoughts into print? The answer is that I am
not
sure…. [The two books] offer a choice between two possible conceptions of truth, conceptions that I hope I have succeeded in delineating with reasonable clarity’ (p. vii, emphasis in original). (For the record,
Thought and Reality
‘firmly repudiates’ an anti-realism about the past, ‘but the conception of truth that [it proposes] does not make so conciliatory an advance in a realist direction as does that proposed in [
Truth and the Past
]’ (ibid.).)

A final point: in the quotations from both
Truth and the Past
and ‘Campbell’ above Dummett claims that only what is knowable is true. A familiar argument due to F.B. Fitch derives from this the seemingly absurd conclusion that only what is
known
is true: see Fitch (
1963
). Dummett discusses this argument in ‘Victor’s Error’ and ‘Fitch’s Paradox’. An approach to the paradox that I myself find attractive is that of Joseph Melia in Melia (
1991
). What Melia urges, in effect, is that the anti-realist thought is not that only what is knowable is true, but that only what is
settleable
is
true or false
. Fitch’s argument has no bearing on the latter. (Cf. in this connection Schlick (
1959a
), p. 56. As noted in
Ch. 4
, n. 10, logical positivism involves a similar anti-realism, but here at least Schlick formulates it in the latter way. I think this goes some way towards rebutting the objection that Melia is simply changing the subject.)

30
Cf. Dummett’s own (implicit) comparison of these two cases in
Thought and Reality
, p. 79.

31
For an attempt to resist any slide from anti-realism about mathematics to anti-realism in other areas, see McDowell (
1998
); and cf. Green (
2001
), pp. 130–131. For an excellent discussion of the way in which
Frege
III presents a case for anti-realism about mathematics that cannot be generalized, see Sullivan (
2007
). Note, however, that Dummett’s own interest in the anti-realist proposal stems largely from the belief that
some
forceful arguments for anti-realism about mathematics
can
be generalized: see e.g. ‘Intuitionistic Logic’, pp. 226–227, and ‘Autobiography’, p. 18. (This explains why John McDowell, in the essay cited above, represents himself as opposing Dummett.) The irony is that the anti-realist position in the philosophy of mathematics that first attracted Dummett’s attention, that of Brouwer, is based on considerations that are directly opposed to those on which Dummett bases his own anti-realist proposal (as indeed Dummett acknowledges: see ‘Intuitionistic Logic’, p. 226). Brouwer holds that mathematical thoughts are grounded in mathematical experience, conceived as something essentially private, and are therefore not fully communicable: see Brouwer (
1983
).

Finally, for related views in the philosophy of mathematics in Wittgenstein, views with which Dummett’s have some affinity though about which Dummett also has considerable reservations, see e.g. Wittgenstein (
1974a
), Pt II, §§35 and 39, and Wittgenstein (
1978
), Pt V; and for Dummett’s discussion of these views, see ‘Wittgenstein’s Philosophy of Mathematics’.

32
Cf.
Frege
II, pp. 437–438.

33
The first we know to be true. The second we know not to be true. The truth value of the third, at the time of my writing this, we do not know. I shall have more to say about the third statement in the next section.

34
Cf.
Logical Basis
, p. 326, and ‘Allard’, p. 148. (Frege emerges as a realist about arithmetic on this construal.)

35
One interesting version of anti-realism with respect to arithmetic, on this construal, is Hartry Field’s view, to which I adverted in
Ch. 12
, n. 49. On that view, a mathematical statement such as ‘7 + 5 = 12’ is indeed either true or not true, and the apparent singular terms that occur in it are indeed singular terms; but they pick nothing out, because there is nothing for them
to
pick out, numbers being a fiction (Field (
1980
)). This makes ‘7 + 5 = 12’
not
true. Dummett discusses this view in ‘Mathematics’, pp. 433ff.

36
Others are to be found in the literature cited in n. 25.

37
‘Broadly Wittgensteinian’ here is an allusion to such passages as those cited in n. 24. Some care is called for, however. This view of language is often put in the form of a rough slogan, ‘Meaning is use’, which Dummett and others explicitly attribute to Wittgenstein (see e.g. ‘Theory of Meaning (II)’, p. 38). In fact, Wittgenstein himself would not endorse this slogan without serious qualification: cf. Wittgenstein (
1967a
), Pt I, §§43 and 139, and (
1974a
), §29; and see Hacker (
1996
), pp. 244–249. (Mind you, Dummett would not endorse it either, as anything other than the crudest of guidelines. In ‘Gödel’s Theorem’ he writes, ‘The general thesis that the meaning of an expression is to be identified with its use is not … particularly helpful; until it is specified in what terms the use of the expression is to be described, the thesis is merely programmatic’ (p. 188).)

38
Cf. Bernard Williams (
2006o
),
Ch. 7
, where Williams argues that our use of ethical language harbours illusions about the metaphysics of value.

39
Cf. his opposition to Quine mentioned in n. 11. Cf. also ‘Sense and Reference’, pp. 136 ff.

40
Cf.
Logical Basis
, pp. 246ff.;
Origins
, pp. 174–175; and ‘Realism and Anti-Realism’, pp. 477–478.

41
See again n. 16 for material on what such a theory must deliver.

42
This explains why Dummett has no patience for Wittgenstein’s dictum that philosophy ‘leaves mathematics as it is’ (Wittgenstein (
1967a
), Pt I, §124): see
Origins
, pp. 174–175. There is a profound irony, however, which is itself symptomatic of the difficult position in which Wittgenstein found himself, in the fact that Wittgenstein was prepared to question a great deal in our mathematical practices that Dummett finds quite unexceptionable. Thus Dummett shares none of Wittgenstein’s qualms (
Ch. 10
, §5) about our comparing infinite sets in size: see e.g.
Frege
III, pp. 315–316. Cf. also Dummett’s disparaging reference to Wittgenstein’s remarks on Gödel’s theorem in ‘Wittgenstein’s Philosophy of Mathematics’, p. 166. (Wittgenstein’s remarks occur in Wittgenstein (
1978
), Pt I, App. III.)

43
Cf. Fitch’s argument, mentioned in n. 29.

44
Recall the concentric circles of possibility introduced in
Ch. 9
, §4; and the issue addressed in that same section of who ‘we’ are. (For the connection between these, see Moore (
1997a
), p. 138.)

45
Crispin Wright mounts a defence of the extreme version in Wright (
1982
).

46
Bertrand Russell, who mooted something similar, famously declared that the impossibility of performing infinitely many tasks in a finite time was ‘merely medical’ (Russell (1935–1936), pp. 143–144).

47
For an attempt to trace some of the connections between Dummett’s problem and Wittgenstein’s, albeit not quite in those terms, see Moore (
2002c
). For discussions of relations more generally between Dummett and Wittgenstein, distancing the latter from the former, see Hacker (
1986
),
Ch. 11
, §4.

48
Cf. ‘Preface’, p. xxx. In general, proof by
reductio ad absurdum
has no anti-realist warrant.

49
See
Ch. 2
, §6;
Ch. 9
, §6, esp. n. 55; and
Ch. 10
, n. 55. For Dummett’s own views about knowledge of correct linguistic practice, see e.g. ‘Knowledge of a Language’, pp. 94–96. Dummett himself does not talk of ineffable knowledge. But I see no incompatibility between my proposal and what he says.

50
Cf. again the problem to which I drew attention in the Introduction, §6, in connection with the Transcendence Question, and which I mentioned in
Ch. 9
, n. 60, in connection with Wittgenstein.

For a much fuller discussion of the ideas canvassed in the last two paragraphs, see Moore (
1997a
),
Ch. 10
, §4.

51
In
Ch. 9
, §7, I spoke of understanding rather than knowledge, and of propositional sense rather than linguistic sense, but neither difference is important in this context: see e.g.
Ch. 9
, n. 55, and cf. n. 7 in this chapter.

52
Williams is in fact characterizing a view that he finds in the later Wittgenstein rather than Dummettian anti-realism, but his very next sentence, which is annotated with a reference to Dummett’s essay ‘Wittgenstein’s Philosophy of Mathematics’, suggests that he would view the latter in the same terms.

53
For the distinction between transcendental idealism and empirical idealism, see
Ch. 5
, Appendix.

54
This, I believe, is connected to a comment that Dummett makes shortly after the first of the quotations above: ‘We can abandon realism without falling into
subjective
idealism’ (ibid., emphasis added).

55
This is loosely related to the anti-relativist point that Dummett makes in ‘Frege and Kant’, p. 135.

56
I leave it to others to judge how far Dummett is guilty of trying to answer such questions: see e.g. – as well as the relevant material already cited –
Thought and Reality
,
Ch. 1
.

57
See again n. 13.

58
Hawking writes as though he is quoting Wittgenstein, but he gives no reference. To the best of my knowledge Wittgenstein never said this.

59
So does the work of everyone else we have studied in
Part Two
. To pick just one example: there is, in Wittgenstein (
1967a
), Pt I, §§243–317 and 398–421, some of the most profound material ever produced on the relation between mind and body.

60
The expression ‘in metaphysics’ is important here. Dummett is keen to acknowledge both the existence and the importance of radical conceptual innovation in the large: see e.g.
Thought and Reality
, p. 24.

61
There is also incidentally the issue of where Dummett stands with respect to the other two questions. His stance with respect to the Transcendence Question, on one natural interpretation of the question, is clear. One of the main points of his work is to deny that metaphysicians can make sense of what is transcendent (see the previous section). His stance with respect to the Creativity Question is less straightforward. It raises many further fascinating issues which I shall not pursue here.