The Evolution of Modern Metaphysics: Making Sense of Things (66 page)

Let us return to the example of transfinite mathematics. Wittgenstein insists that ‘philosophy may in no way interfere with the actual use of language,’ and, in particular, that ‘it … leaves mathematics as it is’ (§124).
⁶¹
Yet we have also seen him prepared to challenge what mathematicians say. This of course reflects the very point that we have just been considering. Wittgenstein is prepared to challenge what mathematicians say because he sees a distinction between what they say
when making mathematical sense
and what they say otherwise. What they say otherwise, in other words what they say when they are not engaged in legitimate mathematics, is not in any sense sacrosanct. Mathematicians are no more immune to the confusions of bad philosophy than anyone else. Moreover – and this again reflects the point that we have just been considering – they may very well import their confusions back into their discipline. Consider, for example, early work on the calculus.
⁶²
Some revisionists would even cite their (mathematicians’) use of classical logic as an example.
⁶³
Wittgenstein himself would cite transfinite mathematics.

On what grounds? Well, on several. Most notably, there is the fact that transfinite mathematics involves drawing distinctions of size between infinite sets. In particular, the set of real numbers is said to be bigger than the set of natural numbers – though how much bigger is in turn said to be an unsolved problem.
⁶⁴
Wittgenstein is deeply suspicious, if not of the results themselves, then of how they are couched and of how they are presented.
⁶⁵
He thinks they are couched and presented in such a way as to encourage a ‘realist’ model of mathematics, that is to say a model of the sort that I dubbed in §3 ‘perceptual’ and that we have seen him abjure. Thus in saying that the set of real numbers is bigger than the set of natural numbers, we make ‘the determination of a concept – concept formation – look like a fact of nature’ (
Remarks
, Pt II, §19; cf.
Philosophical Grammar
, p. 287). We talk about these two sets as though we were talking about Mount Everest and Mount McKinley.

But now: Wittgenstein faces the very problem that I have been highlighting. He needs to be clear that what he is castigating are perversions of the relevant mathematical thinking, which have clouded its exposition, and not the mathematical thinking itself, which he knows he has no business as a philosopher castigating. And there is reason to think that he does not manage it. He writes, ‘One pretends to compare the “set” of real numbers in magnitude with that of [natural] numbers…. I believe, and hope, that a
future generation will laugh at this hocus pocus’ (
Remarks
, Pt II, §22). But this invites precisely the same impatient retort as he himself might give if misplaced philosophical scruples cast doubt on a more homespun measuring technique: ‘One
pretends
no such thing. One does it.’ ‘Comparing sets in size’ may or may not be the most felicitous description of what mathematicians do,
⁶⁶
but that
is
what they do, and that
is
, for better or worse, its description. Both here and elsewhere there is something almost paranoiac about Wittgenstein’s horror of what he finds on the pens and in the mouths of mathematicians; and often, in spite of himself, he allows this to become a horror of the mathematics. The upshot is that he treats as ‘metaphysical’ what can surely, quite properly, be treated as ‘everyday’.
⁶⁷

6. Taking Words Away from Their Everyday to a Metaphysical Use?

This problem, though serious for Wittgenstein, still does not bring us to what I take to be the most fundamental objection to his views. As a preliminary to seeing what that objection is, let us reflect on the conservatism that attends philosophy as he conceives it.

This conservatism is perfectly illustrated in what we have just been witnessing. When mathematicians extend the concept of one thing’s being bigger than another, to embrace what they have established concerning infinite sets, Wittgenstein recoils. And when they introduce a new concept, that of an infinite cardinal, designed to measure how big any given infinite set is and thereby to effect relevant comparisons of size, again Wittgenstein recoils. He sees here just the kind of meddling with our concepts that is ripe for, if not constitutive of, philosophical confusion. Such is the conservatism that I have in mind.

The problem identified in the previous section is the problem of knowing when such conservatism is misplaced. Philosophers should have no quarrel with conceptual innovation that subserves sense-making. Their only quarrel should be with conceptual innovation that thwarts it. One thing that surely follows from this is that there can be little or no room for conceptual innovation
in philosophy itself
. Philosophy is an antidote to the confusions that arise from our mishandling our own concepts. Conceptual innovation – the introduction of new concepts, the extension of old concepts to new cases, the fashioning of new links between concepts, whether old or new – can
only ever bring with it the risk of new confusions. Philosophers should be looking to minimize that risk.

I say that there can be
little or
no room for conceptual innovation in philosophy itself. I do not think that it is to be ruled out completely, on Wittgenstein’s conception. Philosophers do after all need to present the grammar of our language as perspicuously as possible, as indeed they need to reflect on what they themselves are doing, and they may find new conceptual resources helpful for these purposes. (Perhaps the concept of a language-game and the concept of a form of life are two cases in point: see §§2 and 4, respectively.) The fact remains that their business is primarily to protect whatever sense-making is already under way, not to indulge in sense-making of their own (i.e. peculiarly of their own). The conservatism identified above may be a natural concomitant of philosophy on this conception. But
philosophical
conservatism is not merely a natural concomitant of it. It is an integral part of it.

One consequence of this is that, if sense-making is construed in such a way that metaphysics is simply good philosophy of the most general kind (see §3), then we have in Wittgenstein an extremely clear answer to the Novelty Question which I posed in §6 of the Introduction, much clearer than that provided by any of the rest of my protagonists: there is
no
scope for us, as practising metaphysicians, to make sense of things in ways that are radically new.
⁶⁸
But this brings us to the objection.
Why not?
Even if our aim is solely to promote our conceptual health, why think, as Wittgenstein seems to think, that the only way in which we can do this is to cure ourselves of conceptual diseases? Perhaps we can also take conceptual exercise. This remark is not as flippant as it sounds. There is a serious point underlying it. And the seriousness of the point extends to the broader issue of what it is that forces us to identify philosophy with the promotion of conceptual health in the first place. In sum: why should we accept Wittgenstein’s conception of philosophy?

We must of course beware of becoming embroiled in a tiresome quibble about how to use the word ‘philosophy’. But there is a point of substance here. It has to do with Wittgenstein’s own celebrated notion of a ‘family-resemblance’ concept, illustrated most famously by the concept of a game. It is remarkable that the same person who writes this:

Consider for example the proceedings that we call ‘games’…. What is common to them all? …
Look and see
whether there is anything common to all…. To repeat: don’t think, but look! …

… The result of this examination is: we see a complicated network of similarities overlapping and criss-crossing: sometimes overall similarities, sometimes similarities of detail.

I can think of no better expression to characterize these similarities than ‘family resemblances’; for the various resemblances between members of a family: build, features, colour of eyes, gait, temperament, etc. etc. overlap and criss-cross in the same way. (§§66 and 67, emphasis in original)

should also write each of these:

Philosophy really
is
‘purely descriptive’. (
Blue Book
, p. 18, emphasis in original)

Philosophy isn’t anything except philosophical problems, the particular individual worries that we call ‘philosophical problems’. (
Philosophical Grammar
, p. 193)

Philosophy may in no way interfere with the actual use of language; it can in the end only describe it….

It leaves everything as it is. (§124)

Philosophy simply puts everything before us, and neither explains nor deduces anything. (§126)

The work of the philosopher consists in assembling reminders for particular purposes. (§127)

Some
philosophy is like that. But all of it? Has Wittgenstein looked and seen?

Admittedly, Wittgenstein has his distinction between good philosophy and bad philosophy. He might say that he has indeed looked and seen. He has looked at what gets classified as philosophy and he has seen that, apart from what he himself endorses, there is only the bad variety. But Wittgenstein’s conception of bad philosophy is as restrictive as his conception of good philosophy.
⁶⁹
We can agree that what he conceives as bad philosophy is bad, and still wonder how much of what gets classified as philosophy is like that. (In particular, we can wonder how much of what we have been looking at in this enquiry is like that.) Wittgenstein is surely in danger of doing what Kant so clearly saw Hume doing: throwing the baby out with the bathwater, to revert once more to that tired old metaphor (
Ch. 4
, §5, and
Ch. 5
, §2).

In my discussion of the Novelty Question in §6 of the Introduction I alluded to the alternative that Wittgenstein so signally fails to countenance: attempting, in philosophical mode, to make maximally general sense of things by supplementing, amending, or replacing the various ways in which
we currently make sense of things, and doing so, moreover, in favour of something radically new. And who is to deny that part of this process might even be to wrench words away from their ‘everyday’ use to new, metaphysical uses, somewhat as mathematicians do with the word ‘bigger’, or as indeed Hegel did with virtually all of the key terms that he used in the presentation of his dialectic (see esp.
Ch. 7
, §7)? Wittgenstein is clearly concerned that we should be in control of our concepts, not they of us. This makes him especially sensitive to the confusions we risk when we start bending our own conceptual rules and allowing our concepts to evolve in this way. But let us not forget that being confused by our own concepts is only one way of being in
their thrall. Being uncritically closed to new ways of making sense of things is another.

There is in any case the question: what is wrong with not being in control of our own concepts? What is wrong with being confused? Obviously, confusion can have bad consequences, dire consequences even. But is it intrinsically bad? Do we have to share Wittgenstein’s abhorrence of it, which, as we saw in §8 of the previous chapter, assumes the form, almost, of an ethical axiom?
⁷⁰
One thing that must certainly be conceded is that, however bad the potential consequences of confusion are, and whatever the status of its own badness is, it can also be a means to valuable ends, as any teacher knows. (I include Wittgenstein: cf. §464.) Perhaps it can be a means to ends that are not only valuable but quite extraordinary, so extraordinary that their value is currently beyond our comprehension. This again relates to my discussion of the Novelty Question, where I alluded to the possibility of our abandoning concepts at the price of our very humanity, a possibility that is all the more significant in view of the reflections in §4 above about who ‘we’ are.

This flurry of questions-cum-suggestions points forwards to ideas that we shall encounter in
Part Three
.
⁷¹
They are not themselves objections to anything in Wittgenstein, although, as I have tried to show, they flow from what I do take to be such an objection, indeed the principal such objection. I think it is in fact a measure of Wittgenstein’s greatness that they do so, and that his work provokes reflection at such a deep level. My aim in the last three sections of this chapter has been to ask questions of Wittgenstein’s work, to challenge it in various ways, and to pit it against alternatives. My aim has precisely
not
been to denigrate it; obviously not. I have wanted to honour it, not to dishonour it.

1
Throughout this chapter I use the following abbreviations for Wittgenstein’s works:
Blue Book
for Wittgenstein (
1969
);
Culture
for Wittgenstein (
1980a
);
Investigations
for Wittgenstein (
1967a
); ‘Logical Form’ for Wittgenstein (
1929
);
Notebooks
for Wittgenstein (
1979a
);
On Certainty
for Wittgenstein (
1974b
);
Philosophical Grammar
for Wittgenstein (
1974a
);
Philosophical Remarks
for Wittgenstein (
1975
); ‘Philosophy’ for Wittgenstein (
2006
);
Remarks
for Wittgenstein (
1978
);
Tractatus
for Wittgenstein (
1961
);
Vienna Circle
for Wittgenstein (
1979b
); and
Zettel
for Wittgenstein (
1967c
). All unaccompanied references are to the
Investigations
, and, where they are section-numbered, to Part I of the
Investigations
. (We do well to remember, incidentally, that only the
Tractatus
, ‘Logical Form’, and Part I of the
Investigations
were written for publication, and, in the case of the last of these, Wittgenstein would no doubt have changed some of it if he had lived to see it published.)