Philosophical work of Bertrand Russell

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The philosophical work of Bertrand Russell is wide ranging and covers many fields of philosophy.

Main article: Bertrand Russell

Contents 1 Analytic philosophy 2 Logic and philosophy of mathematics 3 Philosophy of language 4 Logical Atomism 5 Epistemology 6 Philosophy of science 7 Ethics 8 Religion and theology 9 References

[edit] Analytic philosophy

Russell is generally recognised as one of the founders of analytic philosophy, even of its several branches. At the beginning of the 20th century, alongside G. E. Moore, Russell was largely responsible for the British "revolt against Idealism," a philosophy greatly influenced by G. W. F. Hegel and his British apostle, F. H. Bradley.^[1] This revolt was echoed 30 years later in Vienna by the logical positivists' "revolt against metaphysics". Russell was particularly critical of a doctrine he ascribed to idealism and coherentism, which he dubbed the doctrine of internal relations; this, Russell suggested, held that in order to know any particular thing, we must know all of its relations. Based on this Russell attempted to show that it would make space, time, science and the concept of number not fully intelligible. Russell's logical work with Whitehead continued this project.^[2]

Russell and Moore strove to eliminate what they saw as meaningless and incoherent assertions in philosophy. They sought clarity and precision in argument by the use of exact language and by breaking down philosophical propositions into their simplest grammatical components. Russell, in particular, saw formal logic and science as the principal tools of the philosopher. Indeed, unlike most philosophers who preceded him and his early contemporaries, Russell did not believe there was a separate method for philosophy. He believed that the main task of the philosopher was to illuminate the most general propositions about the world and to eliminate confusion. In particular, he wanted to end what he saw as the excesses of metaphysics. Russell adopted William of Ockham's principle against multiplying unnecessary entities, Occam's Razor, as a central part of the method of analysis.^[3]

[edit] Logic and philosophy of mathematics

Russell had great influence on modern mathematical logic. The American philosopher and logician Willard Quine said Russell's work represented the greatest influence on his own work.^[4][5]

Russell's first mathematical book, An Essay on the Foundations of Geometry, was published in 1897. This work was heavily influenced by Immanuel Kant. Russell soon realized that the conception it laid out would have made Albert Einstein's schema of space-time impossible, which he understood to be superior to his own system. Thenceforth, he rejected the entire Kantian program as it related to mathematics and geometry, and he maintained that his own earliest work on the subject was nearly without value.^[6]

Interested in the definition of number, Russell studied the work of George Boole, Georg Cantor, and Augustus De Morgan, while materials in the Bertrand Russell Archives at McMaster University include notes of his reading in algebraic logic by Charles S. Peirce and Ernst Schröder.^[7] He became convinced that the foundations of mathematics were to be found in logic, and following Gottlob Frege took an logicist approach in which logic was in turn based upon set theory. In 1900 he attended the first International Congress of Philosophy in Paris, where he became familiar with the work of the Italian mathematician, Giuseppe Peano. He mastered Peano's new symbolism and his set of axioms for arithmetic. Peano defined logically all of the terms of these axioms with the exception of 0, number, successor, and the singular term, the, which were the primitives of his system. Russell took it upon himself to find logical definitions for each of these. Between 1897 and 1903 he published several articles applying Peano's notation to the classical Boole-Schröder algebra of relations, among them On the Notion of Order, Sur la logique des relations avec les applications à la théorie des séries, and On Cardinal Numbers.

Russell eventually discovered that Gottlob Frege had independently arrived at equivalent definitions for 0, successor, and number, and the definition of number is now usually referred to as the Frege-Russell definition. It was largely Russell who brought Frege to the attention of the English-speaking world. He did this in 1903, when he published The Principles of Mathematics, in which the concept of class is inextricably tied to the definition of number.^[8] The appendix to this work detailed a paradox arising in Frege's application of second- and higher-order functions which took first-order functions as their arguments, and he offered his first effort to resolve what would henceforth come to be known as the Russell Paradox. Before writing Principles, Russell became aware of Cantor's proof that there was no greatest cardinal number, which Russell believed was mistaken. The Cantor Paradox in turn was shown (for example by Crossley) to be a special case of the Russell Paradox. This caused Russell to analyze classes, for it was known that given any number of elements, the number of classes they result in is greater than their number. This in turn led to the discovery of a very interesting class, namely, the class of all classes. It contains two kinds of classes: those classes that contain themselves, and those that do not. Consideration of this class led him to find a fatal flaw in the so-called principle of comprehension, which had been taken for granted by logicians of the time. He showed that it resulted in a contradiction, whereby Y is a member of Y, if and only if, Y is not a member of Y. This has become known as Russell's paradox, the solution to which he outlined in an appendix to Principles, and which he later developed into a complete theory, the Theory of types. Aside from exposing a major inconsistency in naive set theory, Russell's work led directly to the creation of modern axiomatic set theory. It also crippled Frege's project of reducing arithmetic to logic. The Theory of Types and much of Russell's subsequent work have also found practical applications with computer science and information technology.^[8]

Russell continued to defend logicism, the view that mathematics is in some important sense reducible to logic, and along with his former teacher, Alfred North Whitehead, wrote the monumental Principia Mathematica, an axiomatic system on which all of mathematics can be built. The first volume of the Principia was published in 1910, and is largely ascribed to Russell. More than any other single work, it established the specialty of mathematical or symbolic logic. Two more volumes were published, but their original plan to incorporate geometry in a fourth volume was never realized, and Russell never felt up to improving the original works, though he referenced new developments and problems in his preface to the second edition. Upon completing the Principia, three volumes of extraordinarily abstract and complex reasoning, Russell was exhausted, and he felt his intellectual faculties never fully recovered from the effort.^[9] Although the Principia did not fall prey to the paradoxes in Frege's approach, it was later proven by Kurt Gödel that neither Principia Mathematica, nor any other consistent system of primitive recursive arithmetic, could, within that system, determine that every proposition that could be formulated within that system was decidable, i.e. could decide whether that proposition or its negation was provable within the system (Gödel's incompleteness theorem).

Russell's last significant work in mathematics and logic, Introduction to Mathematical Philosophy, was written by hand while he was in jail for his anti-war activities during World War I. This was largely an explication of his previous work and its philosophical significance.

[edit] Philosophy of language

Russell was not the first philosopher to suggest that language had an important bearing on how we understand the world; however, more than anyone before him, Russell made language, or more specifically, how we use language, a central part of philosophy. Had there been no Russell, it seems unlikely that philosophers such as Ludwig Wittgenstein, Gilbert Ryle, J. L. Austin, and P. F. Strawson, among others, would have embarked upon the same course, for so much of what they did was to amplify or respond, sometimes critically, to what Russell had said before them, using many of the techniques that he originally developed. Russell, along with Moore, shared the idea that clarity of expression is a virtue, a notion that has been a touchstone for philosophers ever since, particularly among those who deal with the philosophy of language.

Perhaps Russell's most significant contribution to philosophy of language is his theory of descriptions, as presented in his seminal essay, On Denoting, first published in 1905 in the Mind philosophical journal, which the mathematician and philosopher Frank P. Ramsey described as "a paradigm of philosophy." The theory is normally illustrated using the phrase "the present King of France," as in "The present king of France is bald." What object is this proposition about, given that there is not, at present, a king of France? (Roughly the same problem would arise if there were two kings of France at present: which of them does "the king of France" denote?) Alexius Meinong had suggested that we must posit a realm of "nonexistent entities" that we can suppose we are referring to when we use expressions such as this; but this would be a strange theory, to say the least. Frege, employing his distinction between sense and reference, suggested that such sentences, although meaningful, were neither true nor false. But some such propositions, such as "If the present king of France is bald, then the present king of France has no hair on his head," seem not only truth-valuable but indeed obviously true.^[2]

The problem is general to what are called "definite descriptions." Normally this includes all terms beginning with "the," and sometimes includes names, like "Walter Scott." (This point is quite contentious: Russell sometimes thought that the latter terms shouldn't be called names at all, but only "disguised definite descriptions," but much subsequent work has treated them as altogether different things.) What is the "logical form" of definite descriptions: how, in Frege's terms, could we paraphrase them in order to show how the truth of the whole depends on the truths of the parts? Definite descriptions appear to be like names that by their very nature denote exactly one thing, neither more or less. What, then, are we to say about the proposition as a whole if one of its parts apparently isn't functioning correctly?^[2]

Russell's solution was, first of all, to analyze not the term alone but the entire proposition that contained a definite description. "The present king of France is bald," he then suggested, can be reworded to "There is an x such that x is a present king of France, nothing other than x is a present king of France, and x is bald." Russell claimed that each definite description in fact contains a claim of existence and a claim of uniqueness which give this appearance, but these can be broken apart and treated separately from the predication that is the obvious content of the proposition. The proposition as a whole then says three things about some object: the definite description contains two of them, and the rest of the sentence contains the other. If the object does not exist, or if it is not unique, then the whole sentence turns out to be false, not meaningless.^[2]

One of the major complaints against Russell's theory, due originally to Strawson, is that definite descriptions do not claim that their object exists, they merely presuppose that it does.

Wittgenstein, Russell's student, achieved considerable prominence in the philosophy of language after the posthumous publication of the Philosophical Investigations. In Russell's opinion, Wittgenstein's later work was misguided, and he decried its influence and that of its followers (especially members of the so-called "Oxford school" of ordinary language philosophy, whom he believed were promoting a kind of mysticism). However, Russell still held Wittgenstein and his early work in high regard, he thought of him as, "perhaps the most perfect example I have ever known of genius as traditionally conceived, passionate, profound, intense, and dominating."^[10] Russell's belief that philosophy's task is not limited to examining ordinary language is once again widely accepted in philosophy.

[edit] Logical Atomism

Perhaps Russell's most systematic, metaphysical treatment of philosophical analysis and his empiricist-centric logicism is evident in what he called Logical Atomism, which is explicated in a set of lectures, "The Philosophy of Logical Atomism," which he gave in 1918.^[11] In these lectures, Russell sets forth his concept of an ideal, isomorphic language, one that would mirror the world, whereby our knowledge can be reduced to terms of atomic propositions and their truth-functional compounds. Logical Atomism is a form of radical empiricism, for Russell believed the most important requirement for such an ideal language is that every meaningful proposition must consist of terms referring directly to the objects with which we are acquainted, or that they are defined by other terms referring to objects with which we are acquainted. Russell excluded certain formal, logical terms such as all, the, is, and so forth, from his isomorphic requirement, but he was never entirely satisfied with our understanding of such terms. One of the central themes of Russell's atomism is that the world consists of logically independent facts, a plurality of facts, and that our knowledge depends on the data of our direct experience of them.^[11] In his later life, Russell came to doubt aspects of Logical Atomism, especially his principle of isomorphism, though he continued to believe that the process of philosophy ought to consist of breaking things down into their simplest components, even though we might not ever fully arrive at an ultimate atomic fact.

[edit] Epistemology

Russell's epistemology went through many phases. Once he shed neo-Hegelianism in his early years, Russell remained a philosophical realist for the remainder of his life, believing that our direct experiences have primacy in the acquisition of knowledge.^[2] While some of his views have lost favour, his influence remains strong in the distinction between two ways in which we can be familiar with objects: "knowledge by acquaintance" and "knowledge by description". For a time, Russell thought that we could only be acquainted with our own sense data—momentary perceptions of colors, sounds, and the like—and that everything else, including the physical objects that these were sense data of, could only be inferred, or reasoned to—i.e. known by description—and not known directly. This distinction has gained much wider application, though Russell eventually rejected the idea of an intermediate sense datum.^[12]

In his later philosophy, Russell subscribed to a kind of neutral monism, maintaining that the distinctions between the material and mental worlds, in the final analysis, were arbitrary, and that both can be reduced to a neutral property—a view similar to one held by the American philosopher/psychologist, William James, and one that was first formulated by Baruch Spinoza, whom Russell greatly admired.^[13] Instead of James' "pure experience," however, Russell characterised the stuff of our initial states of perception as "events," a stance which is curiously akin to his old teacher Whitehead's process philosophy.

[edit] Philosophy of science

Russell frequently claimed that he was more convinced of his method of doing philosophy, the method of analysis, than of his philosophical conclusions. Science, of course, was one of the principal components of analysis, along with logic and mathematics. While Russell was a believer in the scientific method, knowledge derived from empirical research that is verified through repeated testing, he believed that science reaches only tentative answers, and that scientific progress is piecemeal, and attempts to find organic unities were largely futile.^[14] Indeed, he believed the same was true of philosophy. Another founder of modern philosophy of science, Ernst Mach, placed less reliance on method, per se, for he believed that any method that produced predictable results was satisfactory and that the principal role of the scientist was to make successful predictions.^[15] While Russell would doubtless agree with this as a practical matter, he believed that the ultimate objective of both science and philosophy was to understand reality, not simply to make predictions.

The fact that Russell made science a central part of his method and of philosophy was instrumental in making the philosophy of science a full-blooded, separate branch of philosophy and an area in which subsequent philosophers specialised. Much of Russell's thinking about science is expressed in his 1914 book, Our Knowledge of the External World as a Field for Scientific Method in Philosophy.^[14] Among the several schools that were influenced by Russell were the logical positivists, particularly Rudolph Carnap, who maintained that the distinguishing feature of scientific propositions was their verifiability. This contrasted with the theory of Karl Popper, also greatly influenced by Russell, who believed that their importance rested in the fact that they were potentially falsifiable.

It is worth noting that outside of his strictly philosophical pursuits, Russell was always fascinated by science, particularly physics, and he even wrote several popular science books, The ABC of Atoms (1923) and The ABC of Relativity (1925).

[edit] Ethics

While Russell wrote a great deal on ethical subject matters, he did not believe that the subject belonged to philosophy or that when he wrote on ethics that he did so in his capacity as a philosopher. In his earlier years, Russell was greatly influenced by G.E. Moore's Principia Ethica. Along with Moore, he then believed that moral facts were objective, but known only through intuition; that they were simple properties of objects, not equivalent (e.g., pleasure is good) to the natural objects to which they are often ascribed (see Naturalistic fallacy); and that these simple, undefinable moral properties cannot be analyzed using the non-moral properties with which they are associated. In time, however, he came to agree with his philosophical hero, David Hume, who believed that ethical terms dealt with subjective values that cannot be verified in the same way as matters of fact.

Coupled with Russell's other doctrines, this influenced the logical positivists, who formulated the theory of emotivism or cognitivism, which states that ethical propositions (along with those of metaphysics) were essentially meaningless and nonsensical or, at best, little more than expressions of attitudes and preferences. Notwithstanding his influence on them, Russell himself did not construe ethical propositions as narrowly as the positivists, for he believed that ethical considerations are not only meaningful, but that they are a vital subject matter for civil discourse. Indeed, though Russell was often characterised as the patron saint of rationality, he agreed with Hume, who said that reason ought to be subordinate to ethical considerations.

[edit] Religion and theology

For most of his adult life Russell maintained that religion is little more than superstition and, despite any positive effects that religion might have, it is largely harmful to people. He believed religion and the religious outlook (he considered communism and other systematic ideologies to be forms of religion) serve to impede knowledge, foster fear and dependency, and are responsible for much of the war, oppression, and misery that have beset the world.

In his 1949 speech, "Am I an Atheist or an Agnostic?", Russell expressed his difficulty over whether to call himself an atheist or an agnostic:

“

As a philosopher, if I were speaking to a purely philosophic audience I should say that I ought to describe myself as an Agnostic, because I do not think that there is a conclusive argument by which one can prove that there is not a God. On the other hand, if I am to convey the right impression to the ordinary man in the street I think that I ought to say that I am an Atheist, because, when I say that I cannot prove that there is not a God, I ought to add equally that I cannot prove that there are not the Homeric gods.

”

Though he would later question God's existence, he fully accepted the ontological argument during his undergraduate years:

“

For two or three years…I was a Hegelian. I remember the exact moment during my fourth year [in 1894] when I became one. I had gone out to buy a tin of tobacco, and was going back with it along Trinity Lane, when I suddenly threw it up in the air and exclaimed: "Great God in Boots! -- the ontological argument is sound!"

”

This quote has been used by many theologians over the years, such as by Louis Pojman in his Philosophy of Religion, who wish for readers to believe that even a well-known atheist-philosopher supported this particular argument for God's existence. However, elsewhere in his autobiography, Russell also mentions:

“

About two years later, I became convinced that there is no life after death, but I still believed in God, because the "First Cause" argument appeared to be irrefutable. At the age of eighteen, however, shortly before I went to Cambridge, I read Mill's Autobiography, where I found a sentence to the effect that his father taught him the question "Who made me?" cannot be answered, since it immediately suggests the further question "Who made God?" This led me to abandon the "First Cause" argument, and to become an atheist.

”

Russell made an influential analysis of the omphalos hypothesis enunciated by Philip Henry Gosse—that any argument suggesting that the world was created as if it were already in motion could just as easily make it a few minutes old as a few thousand years:

“

There is no logical impossibility in the hypothesis that the world sprang into being five minutes ago, exactly as it then was, with a population that "remembered" a wholly unreal past. There is no logically necessary connection between events at different times; therefore nothing that is happening now or will happen in the future can disprove the hypothesis that the world began five minutes ago.

”

As a young man, Russell had a decidedly religious bent, himself, as is evident in his early Platonism. He longed for eternal truths, as he makes clear in his famous essay, "A Free Man's Worship", widely regarded as a masterpiece of prose, but a work that Russell came to dislike. While he rejected the supernatural, he freely admitted that he yearned for a deeper meaning to life.

Russell's views on religion can be found in his popular book, Why I Am Not a Christian and Other Essays on Religion and Related Subjects (ISBN 0-671-20323-1). Its title essay was a talk given on March 6, 1927 at Battersea Town Hall, under the auspices of the South London Branch of the National Secular Society, UK, and published later that year as a pamphlet. The book also contains other essays in which Russell considers a number of logical arguments for the existence of God, including the first cause argument, the natural-law argument, the argument from design, and moral arguments. He also discusses specifics about Christian theology.

His conclusion:

“

Religion is based, I think, primarily and mainly upon fear. It is partly the terror of the unknown and partly, as I have said, the wish to feel that you have a kind of elder brother who will stand by you in all your troubles and disputes. […] A good world needs knowledge, kindliness, and courage; it does not need a regretful hankering after the past or a fettering of the free intelligence by the words uttered long ago by ignorant men.

”

[edit] References