The Evolution of Modern Metaphysics: Making Sense of Things (52 page)

But now: I have said that Frege is not a metaphysician. Why not, on my conception of metaphysics? If logic is ‘the science of the most general laws of truth’ (‘Logic’, p. 228/p. 139), then why is the pursuit of logic not a maximally general attempt to make sense of things?

This relates back to the fundamental difference between Frege and Hegel. (On Hegel’s conception of logic, logic
can
be identified with metaphysics: see §4 of the previous chapter.) The pursuit of logic, for Frege, is a maximally general attempt to make sense not of things, but of sense. I have suggested that metaphysics is bound to be informed by this pursuit (Introduction, §5). But unless everything is constituted by sense – as indeed Hegel, in his own way, thought it was – then the pursuit does not itself have a wide enough scope to be identified with metaphysics.
^62
,
63

Frege attempts to make sense of sense, then. And what he achieves is remarkable. Much of his work is a model of clarity and depth, a paradigm of how to trade in the very sense with which it is concerned. Here again there is room for a comparison with Hegel, at least in this element of reflexivity. Both, insofar as they are successful in their endeavours, make sense of sense not just in what they say about it but in how they display it.
⁶⁴
Nevertheless, the two philosophers can easily seem worlds apart. Frege’s supporters and Hegel’s detractors might well cite the clarity and depth to which I just referred as evidence that they are. There is certainly a great deal
in Hegel that, from Frege’s perspective, will seem not to make any sense at all. The contention, all but explicit in Hegel, that if there is nothing then there is something, namely nothing – if indeed it can be called a contention – seems to rest on precisely the kind of confusion that Frege’s work is designed to eradicate. And the doctrine that we should accept certain contradictions, and can do so provided that we allow what is properly called reason to break the stranglehold of our understanding, would surely elicit from Frege his celebrated cry of censure: ‘Here we have a hitherto unknown type of madness’ (
Basic Laws
, Introduction, p. 14, translation slightly adapted). I tried to show in §7 of the previous chapter that there is more to Hegel’s extravagances than meets the literalistically schooled eye. The fact remains that there is plenty in what meets the literalistically schooled eye to arouse deep aversion.

Still, as we shall see in the next section, not everything in Frege is exactly easy on that eye.

7. Two Problems

In §5 of the Introduction I remarked on the way in which self-consciousness can militate against self-confidence. In this section we shall see two spectacular examples of this, following on from Frege’s attempts to make sense of sense, specifically mathematical sense. One of these examples afflicts the very making of mathematical sense. The other afflicts the attempt to make sense of the making of mathematical sense. The sheer clarity and rigour with which Frege imbues his project are part of the problem. The standards are that much higher; failures to meet them are set in that much sharper relief. By his own lights Frege ends up talking nonsense.
⁶⁵

(a) The Set of Sets That Do Not Belong to Themselves

The first example is very well known. Frege, as we have seen, makes pivotal use of the concept of a set in his project. He understands this concept in such a way that sets correspond one-to-one with properties. To each property there corresponds the set of things that have that property; to each set, the property of belonging to that set.
⁶⁶
Sets, on this conception, do not typically belong to themselves: the set of planets, for example, is not itself a planet. But they do sometimes belong to themselves: the set of sets and the
set of things mentioned in this book are two examples. The problem concerns the set of sets of the former kind, the set of ‘typical’ sets. It is easy to see that this set belongs to itself if and only if it does not, which is a blatant contradiction.
⁶⁷

This contradiction is Frege’s, but it is not his alone. Frege’s conception of a set is an utterly intuitive one. The discovery of this problem was a blow to the entire mathematical community, and mathematical practice, since then, has never quite regained its lost nerve. Though contemporary mathematicians are relatively comfortable once again about using the concept of a set, which of course they now understand differently, they have had to overcome serious uncertainties to get to where they are, and the effect of these uncertainties is still felt.

The contradiction is also a striking instance of how Frege comes to be embroiled in his own conceptual machinery. Still, when he becomes aware of the contradiction, he at least recognizes the need to eradicate it.
⁶⁸
He does not, as Hegel might have done, acquiesce in it. From this point of view the second example is even more striking.

(b) The Property of Being a Horse

To understand the second example we need to reflect a little more on Frege’s semantics. We have already witnessed two linguistic categories that are crucial to this semantics: that of a name; and that of a declarative sentence.
⁶⁹
The category of a name is very broad. It includes any singular noun phrase. And Frege calls whatever a name can be used to refer to an ‘object’. The category of an object is therefore likewise very broad. Frege would count all of the following as objects: my desk, Plato, Bucephalus, the number of
gospels, the expression ‘the number of gospels’, the grammatical structure of the expression ‘the number of gospels’,
⁷⁰
the Big Bang, transcendental idealism, and joy.
⁷¹

When a name is removed from a declarative sentence what results is a predicate. For example, when the name ‘Bucephalus’ is removed from the declarative sentence ‘Bucephalus is a horse’, what results is the predicate ‘… is a horse’. Now predicates, like any other linguistic expressions, have
Bedeutungen
. And the
Bedeutungen
of predicates are what we have been calling properties. Thus the
Bedeutung
of ‘… is a horse’ is the property of being a horse.

Or so it would seem. But what
exactly
are properties?
⁷²
They had better be something of a fundamentally different kind from objects, Frege insists. Otherwise, declarative sentences would in effect just be lists, like ‘Bucephalus, Plato.’ That would mean that they could not be used to express thoughts. They could not be true or false.
⁷³
However, given how broad the category of an object is, it seems impossible to resist the conclusion that properties, so far from being fundamentally different in kind from objects, are themselves objects. For both ‘the property of being a horse’ and, for that matter, ‘the
Bedeutung
of “… is a horse”’ are names. Frege concedes this last point. And indeed, in accord with that, he concedes that the property of being a horse is an object. But he continues to insist that properties and objects are utterly heterogeneous. The only way he can see of accommodating this apparent contradiction is to deny that the property of being a horse is a property (‘Concept and Object’, esp. p. 184/p. 195).

Anyone who thinks that Frege is completely immune to Hegelian excess should pause to reflect on this. The truth is that, by his own high standards, he has got into a hopeless muddle. Indeed, he all but concedes as much. He writes:

I admit that there is a quite peculiar obstacle in the way of an understanding with my reader. By a kind of necessity of language, my expressions, taken literally, sometimes miss my thought; I mention an object, when what I intend is a [property]. I fully realize that in such cases
I was relying upon a reader who would be ready to meet me halfway – who does not begrudge a pinch of salt. (‘Concept and Object’, p. 192/p. 204)

But the problem lies far deeper than this suggests. There is, in a Fregean context, something fundamentally awry with all talk of properties and with all talk of the
Bedeutungen
of predicates – at least pending some explicit account of how not to take such talk at face value.
⁷⁴

Nor is this problem just an inconsequential self-inflicted minutia of one particular semantic theory. Within a generation of Frege’s stumbling into it, Wittgenstein, as we shall see in the next chapter, relates it in a quite extraordinary way to what he calls ‘the problem of life’ and its meaning.
⁷⁵
There are also, for that matter, direct connections with Kant’s transcendental project.
⁷⁶
The fact is, it is a problem that has to do with the very essence of sense-making, the very essence of thought. More particularly, it has to do with what holds the elements of thought together. In Kantian terms (see
Ch. 5
, §4), it has to do with how representation is possible.

At one point Frege himself comments, of a distinction that is relevantly similar to the distinction that he wants to draw between objects and properties, that ‘it is not made arbitrarily, but founded deep in the nature of things’ (‘Function and Concept’, p. 148/p. 31). This suggests that his problem has to do not only with the essence of thought, but with the essence of reality. In a way it does. It is after all couched in terms of the
Bedeutungen
of expressions, in terms of that which determines the truth or falsity of the claims we make, using those expressions, about reality. In another way the suggestion is misleading. What is at stake here is not how thought manages to be, in Cora Diamond’s words, ‘in agreement … with some external thing’ but how it manages to be in agreement ‘with itself’ (Diamond (
1991a
), p. 29). The categories that Frege invokes are intended to reflect requirements that must be met for there to be thought at all. A thought can never be expressed by a mere list of names because there is nothing in a mere list of names to allow for assessment with respect to truth or falsity. And
when Frege attempts to say what holds the elements of thought together and finds himself using expressions which precisely fail to fulfil the function that they are intended to fulfil, he does not express unintended false thoughts about reality; he fails to express any thoughts at all. He fails to make sense.
⁷⁷
Until he says more, and indeed until he retracts some of what he has already said, the predicate ‘… is a property’, as it occurs in his work, simply does not have any authentic meaning. The problem, of course, is that there is no combination of additions and subtractions that will satisfy him. It is as if there are insights that he has achieved into the unity of thought, insights into what it is to make sense of things, which somehow, by their very nature, resist expression; and this too is very pertinent to what will happen in the next chapter.
⁷⁸

8. The Implications for Metaphysics

Ever since Hume helped to demonstrate the importance of reflection on sense, in any attempt to make general sense of things, it was only a question of time before metaphysics would have to reckon with an attempt, of the sort we find in Frege, to provide a decent theory of sense. The rest of
Part Two
will be in large measure a story of how metaphysics in the analytic tradition and, more especially, meta-metaphysics in the analytic tradition come to terms with what Frege bequeaths, both his insights and his aporiae, both his triumphs and his crises.

It is not an easy assimilation. Given the degree of self-consciousness involved, it cannot be. And the aporiae and the crises obviously add to the difficulty. We must wonder whether any attempt to make sense of sense, and therefore, derivatively, any attempt to make sense of how we make sense of things, will, if it has serious theoretical pretensions, merely add to the confusion that it is intended to eliminate. If so, and if there is truth in the recurring suggestion that we cannot make maximally general sense of things without making sense of how we make sense of things, then metaphysics is under renewed threat.

I say ‘under renewed threat’, not ‘doomed’. The qualification ‘if it has serious theoretical pretensions’, in the previous paragraph, was crucial. Perhaps we can make sense of how we make sense of things in a piecemeal, non-systematic way. Perhaps our making sense of how we make sense of things can be a
practical
exercise. (This would make it akin to improving how we
make sense of things, in that it would be manifest
in
how we make sense of things rather than in anything we explicitly say about how we do so.) Perhaps, to echo the point that I made at the end of the previous section, we can achieve insights into how we make sense of things to which we are nevertheless incapable of giving voice. These are all ideas that will resurface at various points throughout
Part Two
. But they will be especially prominent in the next two chapters on Wittgenstein.
⁷⁹

1
See
Begriffsschrift
. Note: throughout this chapter I use the following abbreviations for Frege’s works:
Begriffsschrift
for Frege (
1967
); ‘Comments’ for Frege (
1997d
); ‘Concept and Object’ for Frege (
1997e
); ‘Diary Entries’ for Frege (
1979
); ‘Formal Theories’ for Frege (
1984a
);
Foundations
for Frege (
1980
); ‘Foundations of Geometry’ for Frege (
1984c
); ‘Function and Concept’ for Frege (
1997a
); ‘Insights’ for Frege (
1997k
); ‘Knowledge of Mathematics’ for Frege (
1997n
); ‘Letter to Husserl’ for Frege (
1997b
); ‘Letter to Jourdain’ for Frege (
1997j
); ‘Letter to Russell’ for Frege (
1997h
); ‘Logic’ for Frege (
1997g
); ‘Notes’ for Frege (
1997m
); ‘Numbers’ for Frege (
1997o
); ‘Review’ for Frege (
1997f
); ‘Sense and
Bedeutung
’ for Frege (
1997c
);
The Basic Laws
for Frege (
1964
); and ‘Thought’ for Frege (
1997l
). Page references for all but
Begriffsschrift
, ‘Diary Entries’,
Foundations
, and
The Basic Laws
are in duplicate, first to the translations themselves and then to the original German sources as indicated in their margins. All unaccompanied references are to the
Foundations
.