Russell - A Very Short Indroduction (18 page)

of increasingly difficult cases to see whether it accommodates them; or in discussions of the important forensic and metaphysical concept of personal identity, where imaginative ‘survival tests’ are invented to see whether we would count the persons who go into and come out of them as the ‘same person’.

But even more important, in Ryle’s view, is the way Russell introduced into philosophy the discipline of formal logic. ‘It was due to him, as well as, to a lesser degree, to Frege and Whitehead, that some training in post-Aristotelian formal logic came fairly soon to be regarded as a
sine qua non
for the philosopher-to-be’ (ibid. 19). Ryle was well placed to know; he had been instrumental in ensuring that this happened in the Oxford curriculum. And the reason for a training in logic is that it introduces rigour and promises insights of the kind exemplified in Russell’s theories of descriptions and types. Like Quine, Ryle cites the latter as especially important in illustrating how sense might be distinguished from nonsense, thus, in his view, separately influencing the early Wittgenstein and the Logical Positivists.

Vuillemin nominated Russell’s first major attempt to provide mathematics with logical foundations as the crucible of analytic philosophy. This is no doubt correct, in the sense that, in preliminary and sometimes inchoate form, Russell there made his preliminary identification of its main methods and problems. But Quine is also right to say that it is the whole span of Russell’s works, both books and papers, between 1900 and, say, 1930, on which analytic philosophy rests. In some of these places, however, the germs of later work are more immediately obvious. Take for example the second chapter of
Our Knowledge of the External World
, entitled ‘Logic as the Essence of Philosophy’. This chapter is an illustrative document in two ways. First, it is one of the clearest statements of the aims, motivations, and methods of Russell’s style of analysis. Secondly, it contains a sketch of the philosophical project which Wittgenstein adopted in his
Tractatus Logico-Philosophicus
, showing how ideas take seed and develop.

Russell begins the second chapter of
OKEW
by asserting that the problems of philosophy ‘all reduce themselves, in so far as they are genuinely philosophical, to problems of logic’ (
OKEW
42). By this he means that philosophical problems can be clarified and dispelled by application of the techniques of elementary mathematical logic, which ‘enable us to deal easily with more abstract conceptions than mere verbal reasoning can enumerate; they suggest fruitful hypotheses which otherwise could hardly be thought of; and they enable us to see quickly what is the smallest store of materials with which a given logical or scientific edifice can be constructed’ (
OKEW
51). In particular, the theories of perception and knowledge which he goes on to offer in later chapters of
OKEW
are ‘inspired by mathematical logic, and could never have been imagined without it’ (ibid.). What is chiefly in play is the idea that logic enables us to specify the
forms
of facts and the propositions which express them. The paradigm of an analysis that solves a major problem by revealing the form of a proposition is, as ever, the Theory of Descriptions. Even earlier, Russell had employed formal analysis to show that not all propositions are subject-predicate in form, but rather are relational; which by itself, in his view, had refuted idealism and justified the assumption of pluralism.

In discussing relations in chapter 2 of
OKEW
Russell observes that they can only be properly understood if a classification of the logical forms of facts is available. This is where the anticipatory sketch of Wittgenstein’s
Tractatus
occurs. The suggestion is not that Russell learned it from Wittgenstein, who during the two years before Russell wrote this chapter was his pupil in Cambridge; but rather, the other way round: Wittgenstein learned these ideas from Russell. The grounds for this claim are given shortly. First, it is necessary to remind oneself of the argument of Wittgenstein’s
Tractatus
. Using Wittgenstein’s own words and system of numbering rearranged (here to show the structure of the argument), the fundamental theses of the
Tractatus
are:

1. The world is all that is the case.
1.1 The world is the totality of facts, not of things.
2. What is the case – a fact – is the existence of states of affairs.
2.01 A state of affairs (a state of things) is a combination of objects (things).
2.02 Objects are simple.

Parallel to this austere description of the world’s structure is a description of the corresponding structure of thought as expressed in propositions, a relation Wittgenstein calls ‘picturing’.

4. A logical picture of facts is a thought.
3.1 In a proposition a thought finds an expression that can be perceived by the senses.
3.201 In a proposition a thought can be expressed in such a way that the elements of the propositional sign correspond to the objects of the thought.
5. A proposition is a truth-function of elementary propositions.
4.21 The simplest kind of propositions, an elementary proposition, asserts the existence of a state of affairs.

And so on, with increasing detail. It goes without saying that the logical ideas which underlie these theses are of course familiar from earlier work by Russell; but they relate principally to the notion of structure and the means of their analysis, as exemplified m the Theory of Descriptions. Much more striking is the actual content of the views respectively expressed by Wittgenstein in the
Tractatus
and Russell in the second chapter of
OKEW
. In this chapter Russell writes:

The existing world consists of many things with many qualities and relations, A complete description of the existing world would require not

only a catalogue of the things, but also a mention of all their qualities and relations.... when I speak of a ‘fact’, I do not mean one of the simple things in the world; I mean that a certain thing has a certain quality, or that certain things have a certain relation . . . Now a fact, in this sense, is never simple, but always has two or more constituents . . . Given any fact, there is a proposition which expresses the fact, [such a proposition] will he called an atomic proposition, because, as we shall see immediately, there are other propositions into which atomic propositions enter in a way analogous to that in which atoms enter into molecules . . . In order to preserve the parallelism in language as regards facts and propositions, we shall give the name ‘atomic facts’ to the facts we have hitherto been considering.

(
OKEW
60–1, 62)
And so on.

Now Russell’s account here is simply a sketch, and it is informally presented. In the
Tractatus
Wittgenstein sets out his theses in more detail, and in the systematically numbered format which gives it the appearance of rigour, although it is in fact only in part an argument. And Wittgenstein is careful to detach his account of the parallel worldlanguage structures from any epistemological considerations, whereas Russell gives concrete examples of facts, qualities, and relations: an example of an atomic fact is ‘this is red’, of a molecular fact ‘it is Monday and it is raining’.

That the basis of Wittgenstein’s
Tractatus
derives from these ideas of Russell’s can be shown by the fact that the sketch in Russell’s chapter recapitulates a longer account he attempted to give in a manuscript now called
Theory of Knowledge
(this title was conferred on it when it was posthumously reconstructed and published). Russell was engaged on this work during 1913 while Wittgenstein was his pupil. He showed it to Wittgenstein, who criticized its discussions of acquaintance and judgement. ‘Acquaintance’, as described earlier, is Russell’s name for fundamental cognitive relations between a subject and objects of various kinds; ‘judgement’ is a complex relation roughly describable as accepting a proposition as true in virtue of acquaintance with its constituents. We do not know the details of Wittgenstein’s criticisms; when Russell reported them in a letter he said: ‘We were both cross from the heat. I showed him a crucial part of what I had been writing. He said it was all wrong, not realising the difficulties – that he had tried my view and knew it wouldn’t work. I couldn’t understand his objection – in fact be was very inarticulate – but I feel in my bones that he must be right.’ Largely for this reason Russell published only part of the manuscript, and some years later gave up the concept of acquaintance which is central to it. But the basic plan – of molecular propositions analysable into atomic constituents, which express facts parallel in structure, with the relation between facts and propositions underwriting our understanding of the latter – remains in the sketch given in the second chapter of
OKEW
; and it is the skeleton upon which Wittgenstein puts somewhat different flesh in the
Tractatus
.

It is not surprising that Wittgenstein’s views should derive from Russell in this way. Russell was in effect the only philosophical teacher Wittgenstein had, and, with rather few identifiable exceptions, Russell’s work was his principal philosophical reading. His friend David Pinsent wrote in his diary: ‘it is obvious that Wittgenstein is one of Russell’s disciples and owes enormously to him.’ It is clear then that one of the first philosophical offshoots from Russell’s work was Wittgenstein’s
Tractatus
. It can be argued that in complex and, this time, negative ways Russell is one of the chief influences on Wittgenstein’s later philosophy also.

If the catalogue of Russell’s influences included no more than the names already mentioned – Quine, Carnap, the Logical Positivists, Wittgenstein, and Ryle; to which, by his own avowal as in the case of Quine, is to be added that of A. J. Ayer – it would be proof positive of Vuillemin’s claim that Russell is the founder and presiding spirit of twentieth-century analytic philosophy. But there is much more to be said on that score; and there is also the fact that there are those who award the palm elsewhere. Both points merit discussion.

There is unhappily no index to the collection of Russell’s papers edited by R. C. Marsh under the title
Logic and Knowledge
. This collection brings together some of Russell’s most important and consequential essays, most of which, in turn, are required reading for analytic philosophers. They include ‘The Logic of Relations’, ‘On Denoting’, ‘Mathematical Logic as Based on the Theory of Types’, ‘On the Nature of Acquaintance’, ‘The Philosophy of Logical Atomism’, ‘On Propositions: What They Are and How They Mean’, and others. In the absence of an index a close student of these papers is likely to make his own pencil index on the end-papers of his copy of the book. Looking through my own I find references not only to the topics one would expect in a collection of Russell’s work – descriptions, denoting, types, logical fictions, analysis, acquaintance, sense-data, relations, universals, particulars, facts, propositions, and so on – but also a list of what looks like some of analytic philosophy’s special obsessions: propositional attitudes, modality and possible worlds, vagueness, naturalism, truthfunctionality, the nature of mind, verification, truth, existence, meaning, and much more. A very great deal of this comes from Russell himself, and in focus and range his work therefore constitutes a marked change of direction in the history of philosophy. Even the five contemporaries Russell most frequently cites in acknowledgements – and he was extraordinarily generous, indeed overgenerous, in attributing the source of his inspirations to others – namely, Peano, Frege, Whitehead, Moore, and William James, only one is comparable in discussing this kind and (to a lesser degree) range of topics, and that is Frege.

But although Frege influenced Russell, and did brilliant work in the philosophy of mathematics and language, his influence on Russell was less than one might suppose: for Russell did not understand Frege when he first read him, and had to rediscover some of Frege’s views for himself before he grasped their significance; and even then, on certain crucial points such as Frege’s distinction between sense and reference, he did not take Frege’s point and drew a different and less happy distinction of his own. Moreover Frege’s focus, though deeper, was narrower than Russell’s, so Russell’s application of the new ideas in mathematical logic to wider concerns of philosophy was effectively without precedent. The originality of Russell’s contributions is therefore great.

Russell’s influence worked in other ways too. In the third chapter of
OKEW
he approached the problem of accounting for spatial perception by constructing a ‘model hypothesis’ as a possible explanation of how the highly perspectival private spaces experienced by individuals in vision and touch come to be commensurate with the private spaces of others in public space. He did this by setting up a model and then ‘paring away what is superfluous in our hypothesis, leaving a residue which may be regarded as the abstract answer to our problem’ (
OKEW
94). He takes us step by step through a construction showing how to overcome an important apparent discrepancy between the world of sense and the world of physics. A similar technique was adopted later by P. F. Strawson in his book
Individuals
, where he used it in constructing a purely auditory world to explore the concepts of basic particulars and reidentification. And it was used by A. J. Ayer in his
Central Questions of Philosophy
to determine how much in the way of perceptual and conceptual capacities we must grant a perceiver as a basis for his having perceptual experience. There are other examples besides.

One striking feature of Russell’s legacy is that it is almost wholly philosophical rather than logical or mathematical. This fact requires explanation. G. T. Kneebone remarked: ‘For all the inspiration that
Principia Mathematica
has communicated to the logicians and philosophers of the twentieth century, and for all its rich fecundity as a source of concepts and symbolic devices, this great work remains, in the literature of the foundations of mathematics, a lone classic without progeny.’ This assessment is not strictly true; the felicities of logical notation introduced by
Principia
form the basis of what is now standard, and there have been versions of some of
Principia’s
technicalities, for example Quine’s version of type theory. But it is broadly true, and this is what invites comment. Briefly, what might be said is this: during and after the period in which
Principia
was written there was an explosion in mathematical and logical research, which it is fair to say quickly rendered
Principia
obsolete. A variety of logics was formulated, logicfree formalizations of arithmetic were discovered, logic and set-theory both turned out to be relative (that is, developments in various approaches showed that there is no unique or ‘absolute’ logic or set theory), Zermelo-Fraenkel set theory displaced type-theoretic set theory, and Kurt Gödel’s incompleteness theorem, which in essence states that neither mathematics nor logic can be axiomatized, blocks Russell’s logicist hope of explaining the source and justification of mathematical knowledge in logical terms.