The Evolution of Modern Metaphysics: Making Sense of Things (29 page)

Moreover, given that there is no agreed procedure for even
trying
to answer these questions, our various attempts to answer them give rise to endless irresoluble controversy. This is why the history of metaphysics stands in such stark contrast to the history of, say, mathematics. Where the latter has been marked by a steady but spectacular accumulation of universally accepted results, the former constitutes a tiresome sequence of false starts and repeated squabbles.
⁸
By the latter stages of the eighteenth century the enthusiasm for indulging in metaphysical disputation has begun to give way to weariness and cynicism. This is partly under the influence of Hume. But it is partly a feature of the
Zeitgeist
, which was ripe for Hume’s intervention. ‘There was a time,’ Kant laments, ‘when metaphysics was called the
queen
of all sciences…. Now … the queen proves despised on all sides’ (Aviii, emphasis in original).

‘Laments’ is the operative word, however. We must now consider the baby. Kant is convinced that there can also be good metaphysics – importantly good metaphysics – of a kind for which Hume is entirely unable to account and, worse, which Hume is forced to reject along with its counterfeit.
⁹
In fact, Kant thinks that Hume’s over-zealous strictures also make trouble for much more quotidian, non-metaphysical ways of thinking that are perfectly innocuous and that therefore need to be understood quite differently from how Hume was forced to understand them. The prime example is causal thinking. We saw in §3 of the previous chapter that Hume’s semantic empiricism forced him to search for the impression from which his idea of a causally necessary connection derived, and how he was led to conclude that the impression was a habitual transition in his own mind from one kind of perception to another. For Kant, the resultant conception
of causation is manifestly inadequate. It accords to the necessity in a causal relation a kind of subjectivity that Kant thinks does it a gross injustice. As a result, Hume fails to make sense even of such mundane judgments as that the sun has melted the butter (e.g. B5;
Prolegomena
, 4:257ff.; and 2nd
Critique
, 5:50–52). But this failure on Hume’s part, as Kant sees it, is still at root a metaphysical failure. This is evidenced by its connection with another failure: the failure properly to secure the metaphysical principle that whatever happens in nature has a cause; call this the Causal Principle. Hume certainly endorsed the Causal Principle (e.g. Hume (
1975a
), p. 82). But he thought that we arrived at it by natural processes of extrapolation from regularities that we had experienced in the past, whereas for Kant that is another injustice, of a piece with the earlier injustice, this time to the
a priori
necessity of the Causal Principle. Kant is convinced that we have the same kind of assurance that this principle holds as we do that 7 + 5 = 12.

Not that he takes the Causal Principle to be what Hume would call a relation of ideas. Kant is quite happy to accredit Hume with having shown that it is not. There is therefore no alternative, in Kant’s view, but radically to rethink Hume’s entire empiricist framework and to reassess his reasons for throwing out the dirty water that he has (quite rightly, of course) thrown out.
¹⁰

What we need, Kant believes, is some
principled
way of distinguishing between what is to be rejected and what is to be saved (
Prolegomena
, 4:255ff.). Not that that is any rebuke to Hume, who certainly provided a principle for effecting this distinction – though the principle that he provided was empirical, so that, even by his own lights, it was vulnerable to the possibility that the human mind would one day start operating in some hitherto unknown way. Kant will provide a principle that is
a priori
, thereby revealing once again how much further than Hume he takes the domain of the
a priori
to extend. But more to the point, he will provide a principle that
differs
from Hume’s, a principle that will allow for some of what Hume’s principle excluded. It will allow for substantive
a priori
necessities in metaphysics, no less than in mathematics. (It will allow, among other things, for itself.) Hence, if Kant’s project is successful, we shall be clear about what we can aspire to in metaphysics, we shall be clear about what we cannot aspire to, and we shall be clear about why the line between these is to be drawn where it is. Metaphysics will have been established as a proper, respectable science.

The first step is to reconsider what might count as a ‘substantive’
a priori
necessity and to ask whether Hume was right
even in his account of mathematics.
¹¹

3. Synthetic
A Priori
Knowledge

Hume held that mathematics consists of relations of ideas. He also held that mathematical relations of ideas can be substantive in a way in which no others can. But this was still only substantiveness of a modest psychological kind. It was due simply to the fact that, granted our limitations, some mathematical relations of ideas are unobvious to us. We cannot acknowledge them except by following a chain of reasoning. And the result of any such chain of reasoning may be quite unexpected.

It is significant that Hume did not exhibit unwavering confidence in this account. It took him a while to come round to the view that it applied, in particular, to geometry.
¹²
Nor did he give a clear or compelling explanation for why mathematical ideas are peculiarly equipped to issue in such substantiveness. All he ventured was the following:

As the component parts of quantity and number are entirely similar, their relations become intricate and involved; and nothing can be more curious … than to trace … their equality or inequality through their different appearances. But as all other ideas are clearly distinct … from each other, we can never advance farther … than to observe this diversity…. (Hume (
1975a
), p. 163)

At the very least this requires elucidation. Hume seemed to be struggling.

The fact is, Kant urges, we need to draw some distinctions which have not yet been drawn. Hume offered us a dichotomy between relations of ideas and matters of fact. Leibniz earlier offered us a dichotomy between truths of reasoning and truths of fact. Whatever the relation was between these two dichotomies, neither on its own was able to bear the weight of a satisfactory account of mathematical necessity. For that purpose, Kant believes, there are two dichotomies that need to be recognized, not one. These are in danger of being conflated – if indeed they have not already been conflated, either by Hume or by Leibniz, or by both.

First, there is the dichotomy between truths that can be known
a priori
and truths that cannot.
¹³
A truth is known
a priori
if it is known ‘absolutely
independently of all experience and even of all impressions of the senses’ (B2–3, two passages combined, emphasis removed).
¹⁴
It is a mark of a truth’s being knowable
a priori
that it is necessary, for ‘experience teaches us … that something is constituted thus and so, but not that it could not be otherwise’ (B3). It is likewise a mark of a truth’s being knowable
a priori
that it is universal, for ‘experience never gives its judgments true or strict… universality’ (B3, emphasis removed). (Kant’s discussion, here and elsewhere, indicates that he understands these ‘marks’ to be both necessary conditions and sufficient conditions.) An example of a truth that is knowable
a priori
is that all aunts are female. An example of a truth that is not knowable
a priori
is that some aunts are younger than some of their siblings’ children.

Second, there is the dichotomy between truths that are analytic and truths that are synthetic. Kant distinguishes between two kinds of judgment rather than two kinds of truth, but I shall assume that the application of his distinction to truths is unproblematical. (Thus a truth can be said to be analytic if it can be the object of an
analytic judgment. Likewise, a truth can be said to be synthetic if it can be the object of a synthetic judgment.)
¹⁵
Very well, when is a judgment analytic, and when synthetic? An affirmative judgment of subject-predicate form is analytic ‘if the predicate
B
belongs to the subject
A
as something that is (covertly) contained in this concept
A
’ (A6/B10); it is synthetic otherwise.
¹⁶
As we saw in
Chapter 3
, §4, Leibniz worked with
a notion that was superficially similar to this notion of an analytic truth, and which he took to embrace
every
truth. But by the time Kant has clarified what he means, in particular by ‘containment’, and by the time he has given various examples, his own notion looks far closer to Leibniz’ notion of a truth of reasoning, which Leibniz took to embrace only some truths of course. Indeed, on what Kant takes to be an equivalent definition of his own notion, an analytic truth is one that can be shown, by a (finite) process of analysis, not to be deniable without violating the principle of contradiction (
Prolegomena
, 4:266–267; cf. A150–153/B189–192 and 3rd
Critique
, 5:197 n.). This is highly reminiscent of Leibniz’ definition of a truth of reasoning.
¹⁷
It is also reminiscent of what Hume said about relations of ideas. It certainly leaves room for analytic truths that are substantive in the modest psychological sense. (See, for example, Kant’s discussion of the conceptual taxonomy that he envisages in
Prolegomena
, 4:325 n.) What really concerns Kant, however, is the much more robust sense in which analytic truths are not substantive. Their discovery never ‘amplifies’ our knowledge (A8/B12). An example of an analytic truth is that all aunts are female. An example of a synthetic truth is that some aunts are younger than some of their siblings’ children.
¹⁸

I have chosen the same two examples as before for the simple reason that the two dichotomies can easily appear to amount to the same thing. It can easily appear that yet another mark of a truth’s being knowable
a priori
is that it is analytic. For that matter, it can easily appear that Kant has found two equivalent characterizations of the single dichotomy which both Leibniz and Hume, each in his different way, was also attempting to characterize. But Kant is adamant that it is not so.

He accepts that an analytic truth is always knowable
a priori
(B11–12). What he denies, crucially, is the converse. This is the real trademark of his view. Kant holds that there is synthetic
a priori
knowledge (knowledge of synthetic
a priori
truths).

His primary example is mathematical knowledge. He believes, as would most philosophers who are prepared to think in these terms, that such knowledge is
a priori
. But he also insists, more controversially, that it is synthetic. He writes:

To be sure, one might initially think that the proposition ‘7 + 5 = 12’ is a merely analytic proposition that follows from the concept of a sum of
seven and five in accordance with the principle of contradiction. Yet if one considers it more closely, one finds that the concept of the sum of 7 and 5 contains nothing more than the unification of both numbers in a single one…. The concept of twelve is by no means already thought merely by thinking of that unification of seven and five, and no matter how long I analyze my concept of such a possible sum I will still not find twelve in it. One must go beyond these concepts, seeking assistance in … one’s five fingers, say, or … five points….

Just as little is any principle of pure geometry analytic. That the straight line between two points is the shortest is a synthetic proposition. For my concept of
the straight
contains nothing of quantity, but only a quality. (B15–16, emphasis in original)

In the geometrical example Kant is interestingly anticipated by Hume, who, in the earlier phase of his thinking, before he came to regard geometry as consisting of relations of ideas, wrote:

’Tis true, mathematicians pretend they give an exact definition of a right [i.e. straight] line, when they say,
it is the shortest way betwixt two points
. But … this is more properly the discovery of one of the properties of a right line, than a just definition of it. For I ask any one, if upon mention of a right line he thinks not immediately on such a particular appearance, and if ’tis not by accident only that he considers this property? A right line can be comprehended alone; but this definition is unintelligible without a comparison with other lines, which we conceive to be more extended. (Hume (
1978a
), pp. 49–50, emphasis in original)

Hume concluded that geometry consists of matters of fact, discoverable only by appeal to experience. He did not see any difficulty with this view until later. On a Kantian conception, his problem was precisely that he had not distinguished between the question whether geometrical truths are analytic, which in his earlier work he in effect recognized that they are not, and the question whether they are
a priori
, which in his later work he in effect recognized that they are.

Another of Kant’s examples is our knowledge of what I earlier called the Causal Principle, that whatever happens in nature has a cause (A9–10/B13). Hume, who took this to be a matter of fact, did not feel the same discomfort with it. But on a Kantian view he should have done.