The Evolution of Modern Metaphysics: Making Sense of Things (53 page)

2
He dissociated his work from what he called metaphysics in
The Basic Laws
, Introduction, p. 18. See also Dummett (
1981b
), pp. 428ff.

3
See e.g. Williamson (
2007
),
Ch. 1
.

4
Perhaps I should say, ‘who demonstrated afresh …’. For what he demonstrated, at least in broad terms, was hardly unknown to medieval thinkers.

5
The phrase ‘linguistic turn’ seems to be due to Gustav Bergmann, in Bergmann (
1964
), p. 3. See again Williamson (
2007
), pp. 10ff.

6
Cf. my comments about post-Cartesian philosophy and post-Kantian philosophy in
Ch. 2
, §6, and
Ch. 5
, §1, respectively. For a further indication of Dummett’s views on this matter, see Dummett (
1993a
), esp. Chs 2, 13, and 14. For further discussion of these views, see
Ch. 14
, esp. §1.

7
For especially fierce opposition, see Baker and Hacker (
1984
). For an interesting and compelling attempt to provide a corrective, see Skorupski (
1984
), §II.

It is also of course moot whether, if there has been such a revolution, it has pointed philosophy in the right direction. Dummett, who believes that it has, frankly admits that all he has to offer to anyone who is sceptical about this is ‘the banal reply which any prophet has to make to any sceptic: time will tell’ (Dummett (
1978m
), p. 458).

8
There is much in Part Three that makes better sense in relation to it: see e.g.
Ch. 17
, §4; Ch. 20, §3; and
Ch. 21
, §4.

9
See
Begriffsschrift
, Preface, pp. 5–6, and ‘Insights’, pp. 323–324/p. 272. (Inventing this formal language was a principal component in his founding contemporary formal logic: see
Begriffsschrift
, Preface, p. 7.)

10
Cf. Diamond (
1991a
), §IV; (
1991b
); and (
1991d
).

11
In distinguishing between non-radical conceptual innovation and radical conceptual innovation I only mean to register a distinction of degree; the spatial metaphor should not be taken to indicate otherwise. Roughly, the degree in question is the degree of independence that the new concepts enjoy with respect to old concepts. The least radical conceptual innovation consists merely in combining old concepts to form new ones. As Frege emphasized in §88, he was interested in conceptual innovation that was more radical than
that
, for he was interested in conceptual innovation that was ‘fruitful’, in a way in which the combining of old concepts never could be. Nevertheless, to revert to my spatial metaphor, what he was interested in still involved drawing boundaries over, around, and within those that had already been drawn. It did not involve drawing boundaries in new regions altogether. For further discussion, see Moore (2003a), pp. 121–124. (I there introduce a shift of metaphor, to one of fineness of grain. In many ways this is a more appropriate metaphor, though it infelicitously downplays the difference between the conceptual innovation that Frege was interested in and that which I am now calling radical; see p. 123.)

12
Particularly noteworthy is Arnauld and Nicol (
1996
), which is commonly known as the
Port-Royal Logic
and which was written during the seventeenth century. This was a logic textbook that incorporated a good deal of semantics.

13
See esp.
Ch. 10
, §2, and
Ch. 12
, §§4 and 5.

14
A non-logical object is anything whose existence is not guaranteed by logic alone. What would be an example of the opposite, a logical object? If Frege is right (see below), any of the natural numbers 0, 1, 2, ….

15
Why putative? Well, for this to be a genuine example requires, among other things, that the concept of being logical be a logical concept. It is not obvious that it is, though I think Frege would have said it is; see further below.

16
In the terms of
Ch. 5
, §8, we could also say that it is a concept that can be exercised in sense-making of the thinnest kind.

17
Cf. Aristotle,
Metaphysics
, Bk Γ,
Ch. 3
. 1005a19–24.

18
See Kant (
1998
), A242/B300, and Kant (
2002a
), §10.

19
Frege likewise agrees with Kant that the truths of geometry can be known
a priori
. It is a further matter, however, whether he sees this combination of features in quite the same way as Kant, and in particular whether he sees it as supplying grounds for transcendental idealism; for extensive discussion, see Dummett (
1991f
), esp. §7.

20
Cf. Dummett (
1991a
), pp. 45–46. I am greatly indebted to Dummett’s discussion of these matters: see esp. ibid., Chs 3 and 4.

21
In §88 he notes some obscurities and other infelicities in what Kant himself proffered: see
Ch. 5
, §3, esp. n. 16.

22
The two procedures are in effect the same if (1) analysis is just a matter of applying suitable definitions, (2) absurdity is the violation of a primitive logical law, and (3) a truth can be proved by
reductio ad absurdum
. Concerning (1), see §88. Concerning (2), see
Ch. 3
, n. 33, and
Ch. 5
, §3, esp. n. 17. (Leibniz may in fact have had a broader notion of absurdity than this, and Kant, for whom the only absurdity was contradiction, a narrower one.) Concerning (3), see
Ch. 14
, §§2 and 3, esp. n. 47.

23
There is also an issue about whether Frege understands the term ‘object’ in the same way as Kant (see §89; and see Potter (
2000
), pp. 65–66). Frege understands the term in a way that is extremely broad; see further §7. Kant, arguably, understands it in a way that is much narrower; see e.g. Kant (
1998
), B137.

24
Frege reflects on this contrast in §§12 and 89, and in various other places. For discussion, see Dummett (
1991f
), esp. §5.

25
Note that Kant’s own term for logic is ‘general logic’. He contrasts this with ‘transcendental logic’, the study of how our
a priori
concepts relate to intuition (Kant (
1998
), A57/B81–82 and A154/B193ff.).

26
It is in this change of focus, from how we perceive things to how we talk about them, that Michael Dummett thinks we see the very first example of the linguistic turn in philosophy (see §1). He describes the short paragraph in which Frege explains his strategy, i.e. §62, as ‘arguably the most pregnant philosophical paragraph ever written’ (Dummett (
1991a
), p. 111). Here, as before, there is an issue about whether Dummett is guilty of overstatement. Here, as before, there is something of undeniable significance to which he is nonetheless drawing our attention.

27
Beware a significant terminological complication. I talk about ‘properties’ where Frege, though he also sometimes talks about ‘properties’ (e.g. §53 and ‘Concept and Object’, pp. 189–190/pp. 201–202), typically talks about ‘concepts’. I avoid the latter term because I have already been using it in a very different, essentially Kantian way to mean something more like an instrument of thought. To anticipate material from §§4 and 7 below, what I call ‘concepts’ are sense-like; what I, and Frege sometimes, call ‘properties’, and what Frege typically calls ‘concepts’, are the
Bedeutungen
of predicates. This means that the latter are very coarsely individuated. If whatever has a heart also has a kidney, and vice versa, then the property of having a heart is the same as the property of having a kidney. For discussion, see Diamond (
1991d
), p. 118. For a profound problem afflicting this use of ‘property’, from which for the time being I shall prescind, see §7(b).

28
For an argument that we need say no more than Frege has said already, see Wright (
1983
), pp. 113–117. For a rejoinder, see Dummett (
1991a
), pp. 159–162.

Note: in Cartesian terms, Frege’s demand is not just for a clear idea of what we are talking about; it is for a (clear and)
distinct
idea of what we are talking about (see
Ch. 1
, §3).

29
I believe that this reflects his own attitude later in his career when he is confronted with a similar problem; see Moore and Rein (
1986
), esp. n. 19. It is true that if we confine attention to sentences of arithmetic, there is a danger that we shall make it harder for ourselves, if not impossible, to explain the applicability of arithmetic. But that is not part of the current project. A much more serious danger, as far as the current project is concerned, is that we shall invoke definitions that depend on synthetic truths not expressible in arithmetical language.

30
Beware the terminological discrepancies. As I have already noted (n. 27) Frege typically talks of ‘concepts’ where I talk of ‘properties’. But he also talks of ‘extensions of concepts’ where I talk of ‘sets’.

31
Cf. Benacerraf (
1983
). These remarks perhaps do insufficient justice to a certain intuitive appeal that Frege’s definition has. It is noteworthy, for instance, that Bertrand Russell independently arrived at something very similar (Russell (
1992c
)). But other definitions have some intuitive appeal too. See e.g. David Lewis (
1991
), §§4.5 and 4.6, where Lewis motivates an identification of numbers with quite different sets. Cf. also Quine (
1960
), p. 263.

32
Cf. Dummett (
1991a
), p. 159.

33
See Williamson (
2007
),
Ch. 4
, for further problems with this natural thought.

34
Cf. Dummett (
1991a
), pp. 33–35. For Dummett’s own contribution to the discussion, see ibid.,
Ch. 12
, esp. pp. 152–153, where he provides a suggestion about what makes a definition admissible. See also David Wiggins’ fascinating contribution to the discussion in Wiggins (
2007
).

35
‘
Bedeutung
’ is usually translated as ‘meaning’. But Frege is using the word in a technical way. Translators often register this by translating it as ‘reference’. I have decided to leave the word untranslated.

36
Or rather, more strictly, he holds this for expressions of all logically significant types, where by a logically significant type is meant roughly a type that needs to be recognized in the characterization of what follows logically from what else. This excludes words or expressions used syncategorematically, such as ‘of’ in ‘16 is the square of 4,’ or ‘the weather’ in ‘She is under the weather.’ Here and hereafter in this chapter I shall restrict attention to expressions of logically significant types.

37
Sometimes he calls them
proper names
. But, once again, he is using language in a technical way, and ‘proper name’, even more than ‘name’, suggests a category much narrower than he has in mind.

38
The material that follows draws especially on ‘Sense and
Bedeutung
’, ‘Letter to Jourdain’, and ‘Thought’.

39
Nor, as Frege once thought (
Begriffsschrift
, §8), does it state a truth about the two names involved. Frege begins ‘Sense and
Bedeutung
’ by retracting this view. However, he fails to note one of the most serious objections to the view, namely that it creates an infinite regress. For
what
truth is stated about the two names involved, on this view? That they are used to refer to
the same thing
. (For further discussion of Frege’s retraction of this view, somewhat opposed to what I have just said, see Makin (
2000
),
Ch. 4
, §IV.)

40
‘
Bedeutungen
’ is the plural of ‘
Bedeutung
’.

41
That a name’s sense contains the mode of presentation of its
Bedeutung
has led to an interesting exegetical debate. Some commentators claim that it follows from this that a name can never have a sense without also having a
Bedeutung
, and they cite textual evidence that this is Frege’s own view. Other commentators claim that no such thing follows, and they cite textual evidence that it is
not
Frege’s own view. See e.g. respectively Evans (
1982
),
Ch. 1
, §6, and Dummett (
1981a
),
Ch. 6
, §4. One thing seems clear and is acknowledged on all sides: Frege thinks that something is awry when a name lacks a
Bedeutung
, as e.g. ‘Father Christmas’ does, and that such a thing cannot be tolerated in a formal language constructed for scientific or mathematical purposes (its happening at all is another defect of natural language). See e.g. ‘Function and Concept’, p. 141/pp. 19–20; ‘Letter to Husserl’, p. 150/p. 98; ‘Sense and
Bedeutung
’, pp. 163–164/pp. 40–41; and ‘Comments’, p. 178/pp. 133–134.