The Evolution of Modern Metaphysics: Making Sense of Things (69 page)

Rudolf Carnap (1891–1970) was the arch logical positivist.
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His own brand of logical positivism is however quite distinctive. It is also highly sophisticated. It has, in addition to the features sketched in the previous section, one other crucial feature. Carnap holds that the most fundamental of all the distinctions with which logical positivists are concerned, the distinction between the true and the false, is only ever operative within a linguistic
framework, where a linguistic framework is understood to be a systematic way of speaking about entities of a given kind and where a systematic way of speaking is in turn understood to be a set of ‘rules for forming statements and for testing, accepting or rejecting them’ (‘Ontology’, p. 208).
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A paradigm would be the set of syntactic and arithmetical rules that allow us to speak about positive integers. The decision whether or not to adopt any given framework is not itself a matter of truth or falsity. It is a matter of the advantages and disadvantages of doing so.

By way of illustration, suppose we ask whether there is any positive integer whose square is exactly twice that of another. Then we are asking a question
within
a particular framework, what Carnap would call an ‘internal’ question (‘Ontology’, p. 206). As it happens the answer is no. And this answer can be determined independently of sense experience: it is an analytic truth, determined by the rules of the framework, that there are no such integers. Now suppose we ask whether we are right to accept the existence of positive integers in the first place. This time we are asking what Carnap would call an ‘external’ question (ibid.). It is a question
about
the relevant framework, whether we are right to adopt it or not. And it takes us beyond the realm of the true and the false. (Not that this makes it an illegitimate question. It is a perfectly legitimate question about how to speak. There may be no
truth
of the matter, but there are important practical issues about the costs and benefits of speaking in this way.)

In summary, Carnap holds the following package of ideas:
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• a linguistic framework comprises rules for speaking about entities of a certain kind

• within the framework there are truths and falsehoods about these entities

• among the truths there are some, the analytic ones, whose truth depends solely on the rules of the framework, and these can be known
a priori

• the rest, the synthetic ones, can be known by suitable appeal to sense experience, and
only
by suitable appeal to sense experience

• the decision whether or not to adopt the framework is a
practical one (it is not itself a matter of truth or falsity).

3. A First (Themed) Retrospective

One way to see Carnap’s place in the evolution of modern metaphysics is by explicitly comparing this package of ideas and its implications for metaphysics with views that we have encountered previously and with views that we shall encounter subsequently. Necessarily, at this stage, I am limited in what I can do by way of the latter. In the next section I shall nevertheless glance ahead. In this section I shall look back. And, in keeping with my cartoon sketch, I shall focus on some of the ways in which Carnap embraces what he can and rejects what he must in order to create a suitably robust,
analytically respectable Humeanism.
¹⁰

(a) Hume

The essential point of comparison with Hume himself is already clear. In the famous final paragraph of his first
Enquiry
(Hume (
1975a
)) Hume urged us to commit to the flames any volume that contains neither ‘abstract reasoning concerning quantity and number’ nor ‘experimental reasoning concerning matter of fact and existence’. In
Philosophy
Carnap quotes this paragraph and adds:

We agree with this view of Hume, which says – translated into our own terminology – that only the propositions of mathematics and empirical science have sense, and that all other propositions are without sense. (p. 36)

There, in a nutshell, is Carnap’s appropriation of Hume’s radical empiricism. It requires no further gloss at this juncture – save to note that what appeared to be a curiously unmotivated restriction in Hume, namely the restriction of the non-empirical to the mathematical (
Ch. 4
, §5), surfaces again here, only this time it appears to be, not merely unmotivated, but in direct opposition to its author’s intent. For the very purpose of the lectures from which Carnap’s quotation is taken is to demonstrate how the propositions that philosophers typically produce, though they are neither empirical nor mathematical, nevertheless have sense (see e.g. Lecture II, §8; and see further §5 below). Or so it seems. In fact the appearances are misleading. There is not really any opposition. As Carnap makes clear elsewhere, he has a broad conception of the mathematical. On that conception, analytic truths belong to ‘the mathematics … of language’ (
Logical Syntax
, p. 284).

There is one respect in which, by pouring Hume’s empiricism into an analytic mould, Carnap appears to consolidate it. He appears to make good Hume’s claim that ‘[all] our thoughts or ideas, however compounded or sublime, … resolve themselves into such simple ideas as were copied from a precedent [impression]’ (Hume (
1975a
), p. 19). We saw little effort on Hume’s part to justify or even to illustrate this claim, one notable exception being his attempt to locate the impression from which the crucial but troublesome idea of a causally necessary connection is copied (
Ch. 4
, §3). In his
Aufbau
Carnap appears to make up this deficiency. He appears to show, with painstaking ingenuity, using all the analytic tools at his disposal, how the various more or less sophisticated ways that we have of making sense of things can be reduced to the simple data of sense experience.
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I say he
appears
to do these things. Not only is there the question of how far he succeeds in his project,
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there is also the question of how far his project can in any case properly be said to be a Humean one. Hume was attempting an experimental science of human nature. He was interested in where our ideas actually come from. Carnap is attempting something that is really quite different, ‘a rational reconstruction of the concepts of all fields of knowledge on the basis of concepts that refer to the immediately given’ (
Aufbau
, p. v).
¹³
And, in keeping with his views about linguistic frameworks, he conceives this as just one of many possible reconstructions.
¹⁴
Still, on both accounts there is a sense (flexible enough to allow for
a priori
knowledge) in which all our sense-making derives from sense experience. And such is the basic empiricism that we find in both Hume and Carnap.

(b) Kant

The crucial break with Kant occurs in Carnap’s rejection of the synthetic
a priori
. (See e.g.
Aufbau
, §106.) Kant’s most compelling examples of the synthetic
a priori
were probably those that he culled from geometry. Yet ironically, it is from geometry that Carnap is able to draw some of the clearest illustrations of his own anti-Kantian stance.

There are mathematically coherent alternatives to the Euclidean geometry that Kant believed constituted a true synthetic
a priori
description of
physical space. These ‘non-Euclidean geometries’ are
non-Euclidean
in that they include principles which, taken at face value, are straightforwardly incompatible with those of Euclidean geometry (e.g. that between two points there can be more than one straight line). They are
geometries
in that they nevertheless share sufficiently many principles with Euclidean geometry, and with one another, to constitute a mathematical family.
¹⁵

The Carnapian view is that there are two equally legitimate ways of construing these different geometries. On one construal, they are themselves linguistic frameworks. This means that the choice between them is not a matter of truth or falsity. Once the choice has been made, however,
then
we can use whichever geometry has been selected to make claims that are true or false. And there are two ways in turn in which we can do this. First, we can articulate the principles that constitute the geometry. These are analytic truths, determined by the rules of the framework. They can be known
a priori
. (This is why I included the qualification ‘taken at face value’ in the previous paragraph. On this construal, no principle of any non-Euclidean geometry is strictly speaking incompatible with any principle of Euclidean geometry. For, strictly speaking, ‘point’, ‘line’, and the rest mean different things in the different contexts. Between any two
Euclidean
points there cannot be more than one straight
Euclidean
line.) Second, we can apply the concepts furnished by the geometry we have selected to make claims about physical reality. If our claims are true, then they are synthetically true, dependent for their truth on what physical reality is actually like. Their truth has to be determined empirically. Now although the original choice of geometry is not itself a matter of truth or falsity, even so one geometry is overwhelmingly the best, from a practical point of view, for making true claims of this second kind. It alone allows for a full and accurate description of physical reality that is not hopelessly unwieldy. And, as it happens, for reasons of which Kant could not have had the least idea, the geometry in question is non-Euclidean.

The second way of construing these different geometries is as rival descriptions of physical space that can be proffered within some other linguistic framework. On this construal the choice between them
is
a matter of truth or falsity. The true one is synthetically true. It is also empirically true. And, as it happens, again for reasons of which Kant could not have had the least idea, it is non-Euclidean. But that last fact is less significant, in this context, than the fact that nothing, on either way of construing these different geometries, is at once true, synthetic, and
a priori
.
¹⁶

Adopting a linguistic framework, whether in connection with geometry or in any other connection, is
somewhat
akin to donning a pair of Kantian spectacles.
¹⁷
It provides a set of concepts for making empirical sense of things. But the very ‘donning’ indicates why this is to be sharply contrasted with anything advocated by Kant himself, whose concern was with native spectacles that could be neither donned nor removed. Furthermore, Kantian spectacles involved intuitions as well as concepts, which is why they were supposed to be themselves sources of synthetic knowledge. Carnap accepts nothing like that. Thus his neo-Humeanism.

(c) Frege
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Like any other analytic philosopher, Carnap inherits a huge amount from Frege – including, of course, the distinction between analytic truths and synthetic truths.
¹⁹
But Carnap differs from Frege in one fundamental respect. He is utterly hostile to Frege’s conception of logic as the study of transcendent objects whose existence and character are independent of us. Frege held that the laws of logic are the laws that govern such objects, specifically thoughts and their truth or falsity. Carnap, by contrast, believes about the laws of logic just what he believes about analytic truths more generally, namely that they are truths fixed by the rules of a linguistic framework that we have adopted. Suppose we accept, what Frege would have said we have no alternative
but
to accept, that, bracketing any senses that lack corresponding
Bedeutungen
, every proposition – or thought, in Frege’s terminology – is either true or false (see e.g. Frege (
1997i
), p. 300/p. 214 in the original German). For Carnap this is just a decision about how to speak. It indicates, or goes part way to indicating, our choice of framework. We could have adopted a framework whereby, not every proposition, but every proposition of this or that kind, is either true or false. Such an alternative would have had some advantages, perhaps, and some disadvantages. A possible advantage is that it would have allowed us to prove fewer things and would therefore have run less risk of allowing us to prove the contraries of claims
we want to make, for instance claims about all truths. A possible disadvantage is that it would have been less user-friendly. But it would not have been either correct or incorrect. It would not have been answerable to anything independent of us – still less to anything transcendent.
²⁰

That even the laws of logic should fall within the ambit of Carnap’s views about linguistic frameworks is a direct consequence of his attempt to combine Humean empiricism with some basic tenets of mainstream analytic philosophy. As we have seen, he is sufficiently Humean to insist that the only sense that we can make of things, except for whatever sense we make of things when we adopt a linguistic framework, is empirical sense (the kind of sense that we cannot make of transcendent things). On the other hand, he is sufficiently immersed in the analytic tradition to resist going all the way with Hume and counting our acceptance of the laws of logic as itself an example of our making empirical sense of anything.
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So he takes the only course that remains for him to take. He counts our acceptance of the laws of logic as an example of our making sense of things by adopting a linguistic framework.
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