Logical Analysis and Betrand Russell


Logical Analysis emerged as an important philosophy in the early 20th century and is still the dominant school of philosophy in most universities of the English speaking world. Logical analysis attempts to resolve philosophical disputes by clarifying language and analysing the expressed in ordinary assertions. Restating a philosophical problem in precise logical terminology, instead of everyday language, is likely to reveal its possible solution. Hence, it aims to resolve problems which emerge as a result of linguistic confusion. This philosophical movement has emerged along two lines of development. One is the advancement in mathematical logic, particularly with the development of symbolic logic by Russell and Frege in contrast to Aristotelian logic. The second line is an increasing concern towards the philosophy of linguistics, the ways in which misuse of language leads to philosophical problems.

English philosophers G. E. Moore (1873 – 1958) and Bertrand Russell (1872-1970) are generally seen as the founders of contemporary analytic philosophy, while the founders of modern symbolic logic are the mathematician Gottlob Frege (1848-1925) and Bertrand Russell. Russell, along with A. N. Whitehead (1861-1947), wrote the monumental work Principia Mathematica, in which he showed that all of arithmatic could be deduced from a restricted set of logical axioms. Russell’s work was soon eclipsed by that of Austrian philosopher Ludwig Wittgenstein (1889-1951) who became the central figure of analytical philosophy with his Tractatus Logico-Philosophicus. Logical analysis gave rise to the movement known as Logical Positivism, whose proponents believed that the task of philosophy was to analyze problems to determine whether they belonged to the domain of logic or science, or whether they were ‘meaningless’.

We can consider Russell’s theory of descriptions as an illustration of this analytic technique. Description is a phrase in which an object or a person is specified by any of the properties or qualities associated with it or him, and not by a name. For example, ‘George W. Bush’ is a name, while ‘the present President of America’ is a description. Descriptions had caused a lot of confusion among philosophers. For instance, Meinong was of the opinion that as we can truly say “The golden mountain does not exist” there must be such an object as the ‘golden mountain’ although it must be a non-existent object. Similarly, when we say “The round square does not exist” it appears as if we are attributing some kind of existence to the ‘round square’, that there is a thing, the round square, which does not exist.

The theory of descriptions overcame these difficulties with an analysis of the propositions and maintained that the grammatical structure of a proposition is different from its logical structure. For example, when it is said “Scott is the author of Waverly” it logically means
“One and only one person wrote Waverly and that man was Scott.”
Or in a more logical manner,
“There is an entity c such that the statement ‘x wrote Waverly’ is true if x is c and false otherwise; morover c is Scott.”
And in symbolic notation,
($x){[Wx · (y)(Wy É y=x)] · Sx}

When this theory is applied to statements like “The golden mountain does not exist” it is seen on analysis that the ‘golden mountain’ is not being mentioned when this statement is said. Its logical structure is:

“There is no entity c such that ‘x is golden and mountainous’ is true when x is c, but not otherwise.”
[In simple words, it means something like ‘There is no object in the world which corresponds to the description of being golden and mountainous’.]

In this manner, analysis removes the confusions associated with the descriptions. (We have seen an application of this theory on the Ontological argument.)

There is a famous mathematical problem known as Russell’s paradox which was discovered by Russell in the course of writing Principia Mathematica. There are some sets which are members of themselves, and there are some sets which are not members of themselves [such as a null set]. Russell asks to consider the set of all sets which are not members of themselves. The questions arises, is this set a member of itself?
First consider a possibility that it is a member of itself. But how can it be a member of this set, because the set contains only those sets which are not members of themselves.
So, let us consider the second possibility that it is not a member of itself, but if it is not a member of itself, it is a set which is not a member of itself, and therefore should be included in the set of all sets which are not members of themselves! As obvious, this is indeed a very puzzling paradox. A number of philosophers proposed answers to this paradox, including Russell himself, but which solution is correct is still a matter of debate.

On the metaphysical side, Russell had presented a form of Logical Atomism. But since Logical Atomism found its most complete statement in Wittgenstein’s Tractatus, we’ll deal with it in the chapter on Wittgenstein.

For the general public, Bertrand Russell is not famous for his mathematical philosophy but rather for his social and literary writings. Russell was a very prolific writer and wrote a large number of books and essays in his life. He is well known as a social critic, an educational innovator, a champion of intellectual, social and sexual freedom, and an active campaigner for peace and human rights.

Russell was a pacifist in the First World War and due to his constant opposition to the war, which he saw as sheer madness on part of both sides, he was not only dismissed from Trinity College but was also imprisoned for six months. Later, Russell was greatly concerned about the development of atomic weapons after the Second World War and believed that an atomic war would result in the extermination of the human race.

Russell’s religious views provoked a diversity of responses from the people. While they were extremely influential in helping reduce the dogmatism of religion, they also faced extreme opposition from the conservative, religious classes of the society. These religious ideas, expressed in Why I am not a Christian, were generally concerned with outlining the harmful social aspects of organized religion. He showed that there were not sufficient proofs for the existence of God and analyzed how the Christian beliefs affected the social life. His early essay on religion A Free Man’s Worship is now regarded as a masterpiece of prose.

His work on sexual ethics and his bold criticism of the traditional sexual morality in Marriage and Morals put Russell in social and legal trouble, when he was prevented from taking up the teaching post at City College New York in 1940. He was an excellent writer and his eloquent writings such as What I Have Lived For and A Liberal Decalogue brought him extreme popularity and fame. Russell was awarded the Order of Merit in 1949 followed by the Nobel Prize for Literature in 1950 "in recognition of his varied and significant writings in which he champions humanitarian ideals and freedom of thought".

Russell’s colleague and friend, G. E. Moore was also a very influential philosopher of analytical tradition. During the youth of Russell and Moore, Idealism was the dominant school of philosophy in the British and American circles, and Moore was instrumental in breaking this hold of Idealism. In The Refutation of Idealism Moore showed that the essential principle upon which Idealism stands is Berkeley’s "to be is to be perceived." And this principle in itself is not necessarily true, because it is not an analytical statement. Hence, Idealists assume with any sufficient evidence the necessary truth of their basic principle.

Later Moore wrote A Defence of Common Sense in which he expressed the view that the ordinary, common sense beliefs humans have about the world are to be accepted at face value, such as the view that an objective world exists and that other humans also exist in this world apart from one’s own self. The purpose of analytical philosophy is to explain the precise implications of the truth of such beliefs. This has given rise to the popular image of Moore as a philosopher of plain common sense, which is a bit of injustice to Moore’s brilliance.

Moore’s work on ethics, Principia Ethica, is one of the most influential works on ethics. In it, Moore expounded a version of Ethical Intuitionism, defining ‘good’ to be “a simple, non-natural, indefinable quality that good things have”. That is to say, we recognize good through intuition but we cannot define it. Moore considered it an error to associate ‘good’ with some other natural property, such as pleasure, and called it the "naturalistic fallacy". All such attempts are still unsafe from the Open Question, which states, “Is this really good?” For example, when a hedonist says that “Good is Pleasure”, the Open Question immediately arises in a person’s mind, “Is Pleasure always Good?” The Open Question is the indication that all attempts to associate good with some natural property are erroneous.