Empiricism is the family of theories which in one or another may locate the source or, at very least, the test of contingent knowledge in experience - specifically, in sensory experience. More circumstantially, it is the family of theories which variously require experiential grounds for concepts to have content or applicability, or for expressions in a given language to have sense. In these versions of a formulation, due allowance is made for the thought that the content of perceptual states, suitably construed, are to be considered the occasion or basis for certain kinds of fundamental judgments from which, together with other premises, our less fundamental judgments about the world (or things other than the content of those states of sensitivity themselves) can be inferred.

In a qualified sense of this broadly characterised position, Russell was an empiricist, and his epistemology remained, in that qualified sense, empiricist throughout its development. But he was also critical of certain forms of empiricism, and the focus of his own concerns were such that his aims in formulating epistemological views, and his evolving attempts to realise these aims in detail, are not straightforwardly traditional. The chief reason for this is that his overarching concern was the question of how science is related to subjective experience, beginning (in the work done in 1911–14) with attempts to show how the fundamental concepts of physics can be derived from experience, and ending (in 1948) by shifting attention to the question of the non-empirical features of knowledge-acquisition required for bridging the gap between experience and science.

Russell's theory of descriptions was first published in his 1905 essay, “On Denoting”,which is surely one of the two or three most famous articles in twentieth-century analytic philosophy. It has been described as “a paradigm of philosophy”, and has been employed by many later analytic philosophers, such as Quine, although disputed by others, perhaps most notably Strawson. Writing in 1967, an astute commentator said: “In the forty-five years preceding the publication of Strawson's 'On Referring', Russell's theory was practically immune from criticism. There is not a similar phenomenon in contemporary analytic philosophy”.

What is the theory which has excited such interest and acclaim? To put it briefly and more or less neutrally, it is a method of analyzing definite descriptions, also called singular descriptions, i.e., phrases, in English typically beginning with the word “the”, which pick out or purport to pick out a single (“definite”) object – e.g., “the man who broke the bank at Monte Carlo”, or “the first President of the USA”. Many philosophers who have accepted the theory of definite descriptions, including Russell himself, have also treated some or all proper names in similar fashion. They are taken to be disguised definite descriptions, and then subjected to the same analysis as overt definite descriptions. Definite descriptions may be contrasted with indefinite descriptions, which do not purport to pick out any particular number of objects – e.g., “any President of the USA”. Note that while the two phrases “the even prime number” and “any even prime number” in fact direct our attention to the same object – the number two – the first is a definite description, while the second is an indefinite description.

Bertrand Russell made use of logic as an analytical tool from the start of his philosophical career and early on adopted a metaphysics that can be called “atomism ” in opposition to “monism”. The name “logical atomism” is nevertheless useful for identifying a distinctive combination of metaphysical and logical doctrines characteristic of Russell's work from around 1910 to at least 1925. Russell introduced the name in his series of lectures in 1918 (PLA), so characterising his “philosophical position”and used it again later for the title of a 1924 essay (LA). He describes this philosophy as the combination of a “. . . logical doctrine which seems to me to result from the philosophy of mathematics . . .” and “. . . on the basis of this a certain kind of metaphysic” (PLA, 160). The metaphysics is not simply derivative from his logical theory resulting merely from reading a metaphysical theory off the expressions of a logically perspicuous language. In a passage of the lectures on the notion of complexity Russell describes certain definitions as “. . . preliminary because they start from the complexity of the proposition, which we define psychologically, and proceed to the complexity of the fact, whereas it is quite clear that in an orderly, proper procedure it is the complexity of the fact that you would start from” (PLA, 175). The right way to analyze certain expressions into a logical language would seem to follow from a correct metaphysical analysis of facts rather than leading it.

introduction

The doctrine of Neutral Monism was an avowed part of Russell's metaphysics for only a relatively short period in his amazingly long philosophical career, although it remained an active ingredient for considerably longer. His acceptance of this doctrine was gradual. To a lecture audience in early 1918, when he was in his mid-forties, he declared: “I feel more and more inclined to think that [Neutral Monism] may be true. I feel more and more that the difficulties that occur in regard to it are all of the sort that may be solved by ingenuity” [PLA Papers 8, p. 242]. Shortly afterwards, Russell gave a partial endorsement of the doctrine and then, during the next decade, in major works like The Analysis of Mind, An Outline of Philosophy and The Analysis of Matter, he set about to deepen and refine that endorsement. For more than two decades thereafter, the metaphysical imprint of Neutral Monism remained evident in Russell's major philosophical writings (An Inquiry into Meaning and Truth, Human Knowledge), though he no longer marshalled his views explicitly under its banner. Neutral Monism constitutes, therefore, a major part of Russell's philosophy outside the area of formal logic. Indeed, the doctrine plays a kind of antipodal role in the whole development of his thought, for prior to taking the first steps towards accepting Neutral Monism, Russell had been its most severe critic.

formative themes

To see why Russell regarded Neutral Monism as an important doctrine even when he was its staunch opponent, it is necessary to recall some of the ideals and values which shaped his philosophical outlook from nearly the start of his career and which continued to be active, though in different proportions and with changing interpretations, to the end.

There are three major ideas arising from Russell's work in logic and philosophy of mathematics which he believed to be of philosophical importance for the theory of our knowledge of the physical world. The first was his theory of descriptions; the second, the concept of structure; and the third, the notion of a logical construction. The use of logical constructions in theory of knowledge was most prominent during Russell's phenomenalist period, the period which culminated with Knowledge of the External World. This phase of Russell's thought falls outside the purview of the present work. Logical constructions play an important - but very different - role in his subsequent realism, where they occur mainly in connection with the “interpretation” of the theory of space-time, and where they subserve both metaphysical and epistemological goals. Although we will have occasion to refer to this application of logical constructions toward the very end of the essay, considerations of space prevent us from exploring their use in any detail. Our focus here will be on the second of these ideas - the concept of structure - and the development of Russell's “structuralism.” But before turning to this topic, it will be worthwhile to sketch Russell’s application of his theory of descriptions to theory of knowledge; this application and his structuralism are often discussed together with the result that they are not always as sharply distinguished from one another as they should be.

introduction

A surprising feature of Russell's work in logic is that he began and ended with a theory of types. This chapter begins with a summary of the 1903 theory of types and then proceeds to the much more complex ramified theory of types that emerged from Russell's intense work on the foundations of logic from 1903 to 1907. After discussing the problems connected with the Axiom of Reducibility, the chapter concludes with the simple theory of types, and the later history of type theory, after the demise of the logicist programme.

the 1903 theory of types

Russell’s early theory of types, presented in Appendix B to the Principles of Mathematics, already contains many of the basic features of the mature system given in his fundamental paper of 1908 and in Principia Mathematica. In 1901, Russell had begun writing out the derivation of mathematics from logic, employing the methods of Peano and his school. This led him to examine Cantor’s proof that there is no greatest cardinal number. This result conflicted with his assumption that there is a universal class, having all objects as members, which ought to have the greatest cardinal number. Close analysis of the diagonal argument used in Cantor’s proof led to the discovery of the paradox of the class of all classes that are not members of themselves, now called “Russell’s paradox,” but which Russell called “the Contradiction.”

The logical paradoxes emerged at an awkward moment, when Russell had already written most of the penultimate draft of the Principles. Rather than hold up its publication indefinitely, he took the manuscript of his book to the printer in May 1902 before finding a solution. His initial reaction was that the Contradiction was of a somewhat trivial character, and that it could be avoided by a simple modification of the primitive propositions of logic.

A major component of Russell's philosophical work was the development of a distinctive method of philosophising, which, though he consistently applied it throughout his career, has been largely ignored. This lack of understanding of Russell's method has been a main cause of the still widespread perception that the progress of his philosophy is fragmented and erratic. This chapter will, firstly, outline key characteristics of Russell's method of philosophical analysis and show how this method underpins a number of his best known contributions to philosophy. Secondly, because his philosophical writings from the 1920s onwards have been rather neglected, some of his work of the late 1940s and early 1950s will be discussed to show that it exemplifies the same basic philosophical method. This will have the effect of emphasising the unity and continuity of Russell's philosophy.Finally, defective accounts of Russell’s philosophy in some critical works are traced to misunderstanding of his method of analysis.

russell’s method of philosophical analysis

Throughout his career Russell adhered to a characteristic view of the nature of philosophical analysis according to which it has two parts. Firstly, philosophical analysis proceeds backwards from a body of knowledge to its premisses, and, secondly, it proceeds forwards from the premisses to a reconstruction of the original body of knowledge. Russell often called the first stage of philosophical analysis simply “analysis”, in contrast to the second stage which he called “synthesis” (or, sometimes, “construction”). While the first stage was seen as being the most philosophical, both stages were nonetheless essential to philosophical analysis. It is beyond the scope of this chapter to fully document the claim that Russell consistently adhered to this two-directional view of philosophical analysis throughout his career; however, a consideration of some representative writings of Russell will further clarify his view of philosophical analysis and its implications.

introduction

'I do not myself think very well of what I have said on ethics', wrote Russell in extreme old age (Dear Bertrand Russell, p. 132). And most subsequent philosophers have agreed with him. Either they do not think very well of what he said or they do not think of it at all. Until very recently, Russell hardly rated a mention in most books and bibliographies on twentieth-century ethics. His most anthologised paper on the subject is 'The Elements of Ethics' (1910) in which he expounds, not his own ideas, but the ideas of his colleague and sometime friend, G.E. Moore. Even dedicated Russell fans such as John Slater (Bertrand Russell (1994)) and Anthony Grayling (Russell 1996) are a bit lukewarmabout his theoretical ethics, whilst R.M. Sainsbury in his 'Arguments of the Philosophers' book Russell (1979), is positively dismissive: 'I have left aside his work on moral philosophy, on the grounds that in both its main phases, it is too derivative to justify a discussion of it'. In the first phase, represented by 'The Elements of Ethics' (1910), Sainsbury suggests that Russell's ideas were derived from G.E. Moore, and in the second, represented by Human Society in Ethics and Politics, they were 'close to Hume's, with a dash of emotivism' (Sainsbury 1979, p. x).

introduction

In his 1893 Grundgesetze der Arithmetik Frege sought to demonstrate a thesis which has come to be called Logicism. Frege maintained that there are no uniquely arithmetic intuitions that ground mathematical induction and the foundational principles of arithmetic. Couched within a proper conceptual analysis of cardinal number, arithmetic truths will be seen to be truths of the science of logic. Frege set out a formal system - a characteristica universalis - after Leibniz, whose formation rules and transformation (inference) rules were explicit and, he thought, clearly within the domain of the science of logic. Confident that no nonlogical intuitions could seep into such a tightly articulated system, Frege endeavored to demonstrate logicism by deducing the principle of mathematical induction and foundational theorems for arithmetic.

In his 1903 The Principles of Mathematics, Russell set out a doctrine of Logicism according to which there are no special intuitions unique to the branches of non-applied mathematics. All the truths of non-applied mathematics are truths of the science of logic. Russell embraced this more encompassing form of logicism because, unlike Frege, he accepted the arithmetization of all of non-applied mathematics, including Geometry and Rational Dynamics.

Both Frege and Russell regarded logic as itself a science. Frege refrained from calling it a synthetic a priori science so as to mark his departure from the notion of pure empirical intuition (anschauung) set forth in Kant’s 1781 Critique of Pure Reason. In Frege’s view, Kant’s transcendental argument for a form of pure empirical (aesthetic) intuition that grounds the synthetic a priori truths of arithmetic is unwarranted. Russell concurred, but spoke unabashedly of a purely logical intuition grounding our knowledge of logical truths. Russell wrote that Kant “never doubted for a moment that the propositions of logic are analytic, whereas he rightly perceived that those of mathematics are synthetic . . . It has since appeared that logic is just as synthetic . . .” (POM, p. 457).

It is difficult to over-estimate the extent to which Russell's thought dominated twentieth century analytic philosophy: virtually every strand in its development either originated with him or was transformed by being transmitted through him. Analytic philosophy itself owes its existence more to Russell than to any other philosopher. He was not, of course, its only originator (Frege and Moore, must be acknowledged as well), but he contributed more across its central areas (logic, philosophy of language, epistemology, and metaphysics) than any other single philosopher, and he was certainly its most energetic propagandist. Moreover, as Pigden forcefully argues in his essay in this volume, even in areas such as ethics, where Russell's work has often been thought to be shallow and derivative, Russell has been the source of a number of innovations which might have made the reputation of a lesser philosopher. With Frege and Peano, Russell created modern formal logic and, much more than they, was responsible for bringing it to the attention of philosophers and demonstrating its usefulness in philosophical applications. His work had a profound influence on Carnap and the logical positivists, on Quine, on A.J. Ayer, and in diverse ways on Wittgenstein. Wittgenstein's Tractatus Logico-Philosophicus [1922] was an attempt (ultimately unsustainable) to push to the limit an approach to language which had been suggested, though not actually embraced, by Russell. Wittgenstein's later philosophy was an attempt to make good the defects of the Tractatus by pushing equally far in the opposite direction. The ordinary language philosophers of the middle of the century also reacted strongly against Russell; by the same token, their work would have been inconceivable without him.

introduction

Bertrand Russell and Gottlob Frege are the two giants on whose shoulders analytic philosophy rests. Whilst G. E. Moore and Ludwig Wittgenstein also played a significant role in the emergence of analytic philosophy, it was Russell's and Frege's work on the foundations of mathematics and their development of new techniques of logical analysis that set the agenda, and without both Russell and Frege, Wittgenstein's own philosophy would simply not have evolved.

There are many similarities between Russell and Frege. Both were trained as mathematicians, and although they also studied philosophy, were both drawn seriously into philosophy through concern with the foundations of mathematics. Both wrote early works on geometry, but became increasingly interested in the nature of number. In the works that represent the highpoint of their intellectual achievements, both set out to demonstrate that arithmetic was reducible to logic, a project that required the development of logical theory itself. Both exerted a powerful influence on the young Ludwig Wittgenstein, whose Tractatus Logico-Philosophicus ushered in the second phase of analytic philosophy when the so-called ‘linguistic turn’ was taken. But despite these fundamental similarities in their mathematical background, achievements, and influence, their personal lives, characters, and careers were very different. Frege spent his entire working career (from 1874 to 1918) lecturing in mathematics at the University of Jena, remained a relative recluse, and grew increasingly embittered as he failed to receive the recognition he deserved.

When Russell and Moore entered Trinity College, Cambridge (in 1890 and 1892, respectively), the prevailing philosophies there, and elsewhere in Britain, were forms of idealism: Kant and Hegel were the heroes of the past, and F. H. Bradley of the present. It was chiefly through association with J.M.E. McTaggart, as both a teacher and a friend, that Moore and Russell absorbed idealism and, as Moore was later to put it, became for a time “enthusiastic admirers” of Bradley. But only for a time. It has been said that the beginning of Russell's break with Idealism can be discerned in a paper read to the Apostles on 11 December 1897, in which he argued that “for all purposes which are not purely intellectual, the world of Appearance is the real world - agin McTaggart's notion of getting religion out of philosophy”. Russell himself describes the revolt this way:

The opening sentence of Russell’s three-part article on Meinong, written probably in the first half of 1903, contains a succinct statement of certain elements of the “new philosophy”:

The process of interpreting any great composer from the past whose music remains a vital force on the contemporary scene is, inevitably, multivalent: performers, scholars and composers all make their contributions to preserving that vitality, that presence. Moreover, the activities of scholars and composers, the prime concern of this essay, proliferate to offer further, diverse levels of discourse and response. In the case of scholarship – informed writing about music – there is a whole range of distinct though interacting theories and techniques, from matters of performance practice and the ‘genetic’ studies basic to historical musicology to various, often radically contrasted, types of technical analysis and hermeneutic commentary. The focus of my discussion here is the current state of Debussy interpretation from the formal and hermeneutic perspectives of theory and analysis as well as of composition, for, as will soon be evident, these points on the interpretative chain cannot easily be separated, especially when the thorny topics of Debussy's influence on, or affinity with, other composers become involved.

This is not the place for an account of the thinking and terminology that informed the analytical interpretation of Debussy during the first half of the twentieth century. But it is clear that the issues present-day musicology often addresses – how ‘tonal’ was Debussy's musical language, given its use of whole-tone, pentatonic and octatonic modal elements? how traditional, or organicist, was his attitude to form? How innovative was the expressive ‘tone’ of his music? – can all be found, however informally defined, in earlier years: for example, in Constant Lambert's Music Ho!, first published in 1934.