The Evolution of Modern Metaphysics: Making Sense of Things (54 page)

42
For extremely helpful accounts of Frege’s distinction, and discussion of it, see Dummett (
1981a
), esp. Chs 5 and 6; Evans (
1982
),
Ch. 1
; and Bell (
1984
).

43
For a defence of the view that this is Frege’s own settled account, see Beaney (
1996
).

44
For scepticism about the notion, see esp.
Ch. 12
, §4.

45
This is not the pedantry that it may appear to be, as Frege will later learn to his cost; see §7(a).

46
Frege discusses this paradox in ‘Review’, and there gives the manifestly inadequate response that in order for a definition to be admissible, at least in mathematics, all that is required is that the
definiendum
and the
definiens
have the same
Bedeutung
. For discussion, see Dummett (
1991c
) and (
2010
),
Ch. 12
. The paradox is related to what is often called the paradox of enquiry, which goes back at least as far as Plato: see
Meno
, 80e.

47
Cf. Wiggins (
2007
).

48
Are they? Frege does not appear to have a settled view on the matter. Sometimes he suggests that they are (e.g.
Basic Laws
, §32, and ‘Notes’, pp. 364–365/p. 275); sometimes he suggests that they are not (e.g. ‘Concept and Object’, p. 188/pp. 199–200).

49
Cf. Wright (
2001
), esp. pp. 277–278. Cf. also Dummett’s related discussion of pattern recognition in Dummett (
1991a
), pp. 36ff.; (
1991c
); and (
1991j
), §2. In the light of that discussion it is unclear why Dummett is as hostile as he is in Dummett (
1981a
), pp. 633–634, to the idea of an equivalence relation among linguistic expressions that is intermediate between sharing a sense and sharing a
Bedeutung
.

50
For discussion of this and related issues, see Potter and Smiley (
2001
) and Hale (
2001
).

51
This relates back to the point that I made in n. 45.

52
Bertrand Russell voices this concern in Russell (
1980b
), p. 169.

53
Cf. Dummett (
1981b
), pp. 425–426, and (
1991a
), pp. 192ff.

54
Cf. Dummett (
1993d
), p. 227. Note: Bell’s formulation can be effortlessly applied to the case, if such there be, in which an expression has a sense but no
Bedeutung
; see n. 41.

55
For what is intended by the label ‘Platonic’ here, see Plato’s
Republic
, esp. Bks V–VII.

56
See Dummett (
1991a
), pp. 77–78, and (
1991e
), pp. 117–118: Dummett gives this less extreme objectivity the very appropriate label ‘intersubjectivity’. (See also Dummett (
1991h
). And see Dummett (
2007c
) – a response to Dejnožka (
2007
) – for a retraction on his part concerning the question of whether senses even qualify as objects on Frege’s broad conception of an object. (We shall consider this conception in §7(b).))

57
See respectively ‘Logic’, p. 250/p.160, and Hegel (
1975a
), §IX passim.

58
That distinction is accentuated in Frege. This is a crucial part of his recoil from Hegelian idealism. Dummett is surely right to insist, as he does in the very last sentence of Dummett (
1981a
), that Frege ‘had for idealism not an iota of sympathy’, but surely wrong to claim, as he does on the previous page, that Frege’s work was instrumental in the overthrow of Hegelian idealism. Dummett subsequently retracts this claim. But he does so on the grounds that ‘Hegelianism had little influence at the time when Frege’s creative work began’ (Dummett (
1981b
), p. 497). Others would reject it on diametrically opposed grounds. They would say that Hegelianism had then, and still has, great influence. For further discussion of Frege’s relation to idealism, see Dummett (
1991d
), (
1991e
), and (
1991f
).

59
For something strikingly similar, see Kant (
1992c
), Introduction, §I.

60
For Frege’s notion of actuality, see
Foundations
, §§26 and 85, and
Basic Laws
, Introduction, p. 16. He gives a slightly more relaxed account of the notion in ‘Thought’, pp. 344–345/pp. 76–77. For discussion, see Rein (
1982
).

61
Cf. Diamond (
1991a
), §IV, and Conant (
1991
), pp. 134–137. (For clarification of this use of ‘thin’, see
Ch. 5
, §8.)

62
In
Ch. 14
we shall see how Dummett nevertheless tries to relate them.

63
This reflects an interesting difference, not only between Frege and Hegel, but also between Frege and most contemporary logicians (in the analytic tradition). For Frege, laws of logic are truths about truth. He would exclude the proposition that, if there is life on Mars, then either there is life on Mars or there is life on Jupiter, on the grounds that that is a proposition about life, Mars, and Jupiter (it is not composed exclusively of logical concepts). That proposition is at most the result of
applying
a law of logic. Logicians nowadays do not typically see laws of logic as truths at all, or, if they do, they do not see them as truths with their own distinctive subject matter. They see them as (schematic) principles determining which combinations of truth, about whatsoever subject matter, are possible. This gives them back a certain scope that they lack in Frege’s eyes. The proposition that, if there is life on Mars, then either there is life on Mars or there is life on Jupiter may not count for these logicians as a logical
law
, but it does count as a logical
truth
, arrived at not by application of a logical law, as on Frege’s view, but by interpretation or instantiation of one. The difference is clearly marked when Frege says that ‘logic is not concerned with how thoughts, regardless of truth value, follow from thoughts’ (‘Comments’, p. 178/p. 133). A contemporary logician would be inclined to say that that is precisely what logic is concerned with. (Cf. Hacker (
2001a
), pp. 200–201.)

64
Cf. Diamond (
1991d
), p. 118.

65
The two examples are not isolated. In ‘Insights’ Frege similarly struggles with the concept of truth, the subject matter of logic. (Cf. Wittgenstein (
1961
), 4.063. Cf. also ‘Thought’, pp. 333–334/p. 66, n. D.)

66
Recall that properties are very coarsely individuated (see n. 27). The property of being a gospel
is
the property of belonging to the set {Matthew, Mark, Luke, John}.

67
This problem was communicated to Frege by Bertrand Russell (Russell (
1980a
)) shortly after Frege had published the first volume of his
Basic Laws
and while the second volume was in press. (
Basic Laws
was the book in which Frege attempted a detailed formal execution of his project. There was also originally intended to be a third volume.

– The problem is clearly related, incidentally, to the result that no barber can shave all and only the men in his village who do not shave themselves, likewise due to Russell, which I mentioned in
Ch. 4
, §5.) Frege was devastated: see ‘Letter to Russell’. He struggled unsuccessfully to find a solution to the problem. Eventually, he concluded, ‘My efforts to become clear about what is meant by number have resulted in failure’ (entry for 23.3.1924 in ‘Diary Entries’, p. 263). He resorted to the Kantian view that arithmetical truths are synthetic
a priori
: see ‘Knowledge of Mathematics’ and ‘Numbers’.

Note: the similarity between the way in which Frege takes sets to be assigned to properties and the way in which he takes numbers to be assigned to properties explains my remark in n. 45.

68
See the material in the previous note.

69
In
Basic Laws
he counts declarative sentences themselves as a kind of name (§26). But that is immaterial for current purposes.

70
But not, given Dummett’s retraction mentioned in parentheses in n. 56, the sense of the expression ‘the number of gospels’. If not, then that seems to me to be yet another problem for Frege.

71
It is interesting to note that Husserl likewise uses the term ‘object’ (‘
Gegenstand
’ in the original German) in this very broad way: see Husserl (
1981a
), p. 13.

72
Frege takes them to be functions whose values are always truth values (see e.g. ‘Function and Concept’, pp. 138–139/pp. 15–16). But that merely postpones the question, at least as intended here; for what
exactly
are functions?

73
This is a point that is as old as Plato: see his
Sophist
, 261c6–262e2. See also Plutarch (
1976
), Question X, esp. 1011c.

– Note that the previous problem concerning the set of non-self-membered sets in fact provides another reason why properties had better not be objects: if they were, they would behave just as sets do on Frege’s inconsistent conception.

74
Elsewhere Frege seems to have a better grasp of the muddle, though he by no means completely extricates himself from it: see ‘Comments’, esp. pp. 174ff./pp. 130ff. For discussion, see Dummett (
1981a
), pp. 211ff.; Wiggins (
1984
); and Wright (
1998
).

Note that the problems afflicting talk of properties arise not only when the predicate ‘… is a property’ is used overtly, but also when it is used covertly, as in the name ‘the property of being a horse’. If the property of being a horse is not a property, what business do we have calling it ‘the
property
of being a horse’?

75
See e.g. Wittgenstein (
1961
), 4.12–4.1213 and 6.5–7. And see §8 of the next chapter.

76
See e.g. Kant (
1998
), A129–130 and B141–142. Cf. Bell (
2001
).

77
Cf. his comment in ‘Comments’, p. 175/p. 130: ‘[Properties] cannot stand in the same relation as objects. It would not be false, but impossible to think of them as doing so.’

78
Cf. the very last paragraph of ‘Concept and Object’. Cf. also the suggestion about Spinoza’s third kind of knowledge in
Ch. 2
, §6; and about Kant’s insights into what it is to make sense of things in
Ch. 5
, §10. I am indebted in this paragraph to Diamond: see Diamond (
1991a
), §IV; (
1991b
); and (
1991d
).

79
Before we leave Frege it is worth considering how his work bears on the three questions that I posed in §6 of the Introduction. It does not bear on them directly of course; Frege is not a meta-metaphysician. But we have seen, in Frege, elements of transcendence-friendliness (§6), conservatism (§1), and Platonism (§6), which mean that it would be at least Fregean in spirit to return the following three answers: we are, in practising metaphysics, (1) free to make sense of transcendent things, (2) constrained to make sense of things in broadly the same way as we already do (notwithstanding my disclaimer in §1), and (3) engaged in an exercise that is fundamentally one of discovery. In other words, it would be at least Fregean in spirit to give precisely the opposite of my own three verdicts.

Chapter 9 The Early Wittgenstein The Possibility, Scope, and Limits of Sense; or, Sense, Senselessness, and Nonsense

1. Why Two Wittgensteins?

Ludwig Wittgenstein (1889–1951) famously produced two masterpieces, both enormously influential, but strikingly different from each other in style, approach, and even, it seems, doctrine: first the
Tractatus
,
¹
in his youth, and later the
Investigations
, towards the end of his life, having in the interim been through a long period of philosophical inactivity. It is commonplace, in fact, to refer to ‘the early Wittgenstein’ and ‘the later Wittgenstein’ as if to two different thinkers. It is something I myself shall do, and I shall accord a separate chapter to each.