He identified what has come to be known as Russell's Paradox to show that Frege 's naive set theory led to a contradiction. The paradox can be stated as the set of things, x , that are such that x is not a member of x , and is sometimes explained by the simplistic but more easily understood example, "If a barber shaves all and only those men in the village who do not shave themselves, does he shave himself?
When he found out about this breakthrough, Frege completely abandoned his Logicism. Russell however, 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 three-volume "Principia Mathematica" the first volume, published in , is largely ascribed to Russell.
During the ten years or so that Russell and Whitehead spent on the "Principia", draft after draft was begun and abandoned as Russell constantly re-thought his basic premises. Eventually, Whitehead insisted on publication of the work, even if it was not and might never be complete, although they were forced to publish it at their own expense as no commercial publishers would touch it.
Perhaps more than any other single work, it established the specialty of mathematical or symbolic logic , and it established Russell's name in the international mathematical and philosophical community.
So, it was only with the effective abandonment of the Principia project, by which time Russell was nearly 40, that he turned away from Logic and towards other aspects of philosophy , where he was to prove himself almost as influential.
Perhaps more than anyone before him, Russell made language or, more specifically, how we use language , a central part of philosophy. Philosophers such as Ludwig Wittgenstein and the practitioners of Ordinary Language Philosophy were to a large extent amplifying or responding to Russell's earlier ideas often using many of the techniques that Russell himself originally developed.
His most significant contribution to Philosophy of Language is his theory of descriptions , which he presented in his seminal essay, "On Denoting" The theory is often illustrated using the phrase "the present King of France" when France has no king , and Russell's solution was basically to analyze not the term alone but the entire proposition that contained a definite description , and then allow the definite descriptions to be broken apart and treated separately from the predication that is the obvious content of the entire proposition.
Russell's most systematic treatment of philosophical analysis was what he called Logical Atomism , developed in a set of lectures in He set forth his concept of an ideal, isomorphic language that would mirror the world, whereby our knowledge could be reduced to terms of atomic propositions and their truth-functional compounds.
He believed that the world consists of a plurality of logically independent facts , and that our knowledge depends on the data of our direct experience of them. Thus, every meaningful proposition must consist of terms referring directly to objects with which we are acquainted or they must be defined by other terms referring to objects with which we are acquainted , a kind of radical Empiricism. In time, he came to doubt the value of this theory, and was particularly troubled by the required assumption of isomorphism a one-to-one relation between two sets, which preserves the relations existing between elements in its domain.
In Epistemology , he distinguished between two ways in which we can be familiar with objects, "knowledge by acquaintance" our own sense data, momentary perceptions of colours, sounds, etc and "knowledge by description" everything else, including the physical objects themselves, which can only be inferred or reasoned to and not known directly. In his later philosophy, however, Russell subscribed to a kind of neutral monism similar to that held by William James and first formulated by Baruch Spinoza which maintained that the distinctions between the material and mental worlds were really arbitrary , and that both could be reduced to neutral properties.
Russell remained throughout his life, though, an out-and-out empiricist , in the tradition of Locke and Hume , and he always maintained that the scientific method - knowledge derived from empirical research verified through repeated testing - was the appropriate method of analysis Scientism , although he believed that science and philosophy, for that matter could only reach tentative and piecemeal answers, and that attempts to find organic unities were largely futile.
However, the very fact that he made science a central part of his method was instrumental in making the Philosophy of Science a full-blooded separate branch of philosophy, and he greatly influenced both the verificationists in the Logical Positivism movement as well as the falsificationists. Moore 's "Principia Ethica" , he did not believe that Ethics was really a bona fide part of philosophy. In time, however, he abandoned any belief in objective moral values and came to prefer a view closer to the Ethical Subjectivism of David Hume.
For most of his life Russell maintained religion as well as other systematic ideologies such as Communism to be little more than superstition , and remained a high profile Atheist although he did accept the ontological argument for the existence of God for a time during his undergraduate years.
He was careful, however, to distinguish between his Atheism as regards certain types of god concepts , and his Agnosticism regarding some other types of superhuman intelligence. He believed that, despite any positive effects it might have, religion was largely harmful to people, serving to impede knowledge , foster fear and dependency , and cause much of the war , oppression and misery that have beset the world. Russell had a good ear for a well-turned aphorism and among his many quotable quotes are: I would never die for my beliefs because I might be wrong.
Government can easily exist without laws, but law cannot exist without government. I shouldn't wish people dogmatically to believe any philosophy, not even mine. Bertrand Russell made his first pioneering contributions within the branch of philosophy that deals with logic and mathematics. His authorship came to encompass considerably larger areas, however. His writing is characterized by levity and humor and extended knowledge about science and philosophy to a wide circle of readers.
As Russell puts it, even in logic and mathematics We tend to believe the premises because we can see that their consequences are true, instead of believing the consequences because we know the premises to be true.
But the inferring of premises from consequences is the essence of induction; thus the method in investigating the principles of mathematics is really an inductive method, and is substantially the same as the method of discovering general laws in any other science. Moore led the way, but I followed closely in his footsteps. Although we were in agreement, I think that we differed as to what most interested us in our new philosophy.
I think that Moore was most concerned with the rejection of idealism, while I was most interested in the rejection of monism. In contrast to this doctrine, Russell proposed his own new doctrine of external relations: The doctrine of internal relations held that every relation between two terms expresses, primarily, intrinsic properties of the two terms and, in ultimate analysis, a property of the whole which the two compose. With some relations this view is plausible. Take, for example, love or hate.
If A loves B, this relation exemplifies itself and may be said to consist in certain states of mind of A. Even an atheist must admit that a man can love God. It follows that love of God is a state of the man who feels it, and not properly a relational fact. But the relations that interested me were of a more abstract sort. Suppose that A and B are events, and A is earlier than B.
I do not think that this implies anything in A in virtue of which, independently of B, it must have a character which we inaccurately express by mentioning B. Leibniz gives an extreme example. He says that, if a man living in Europe has a wife in India and the wife dies without his knowing it, the man undergoes an intrinsic change at the moment of her death.
For example, consider two numbers, one of which is found earlier than the other in a given series: If A is earlier than B, then B is not earlier than A. If you try to express the relation of A to B by means of adjectives of A and B, you will have to make the attempt by means of dates. You may say that the date of A is a property of A and the date of B is a property of B, but that will not help you because you will have to go on to say that the date of A is earlier than the date of B, so that you will have found no escape from the relation.
This distinction between logical forms allows Russell to explain three important puzzles. Sentence 3 , for example, is a necessary truth, while sentence 4 is not. The affinities of a given thing are quite different in the two orders, and its causes and effects obey different laws.
Two objects may be connected in the mental world by the association of ideas, and in the physical world by the law of gravitation. But if I were to go on to say that, since my assertion cannot be disproved, it is intolerable presumption on the part of human reason to doubt it, I should rightly be thought to be talking nonsense.
If, however, the existence of such a teapot were affirmed in ancient books, taught as the sacred truth every Sunday, and instilled into the minds of children at school, hesitation to believe in its existence would become a mark of eccentricity and entitle the doubter to the attentions of the psychiatrist in an enlightened age or of the Inquisitor in an earlier time.
It is customary to suppose that, if a belief is widespread, there must be something reasonable about it. I do not think this view can be held by anyone who has studied history. Before He created the world He foresaw all the pain and misery that it would contain; He is therefore responsible for all of it. It is useless to argue that the pain in the world is due to sin. In the first place, this is not true; it is not sin that causes rivers to overflow their banks or volcanoes to erupt.
But even if it were true, it would make no difference. If I were going to beget a child knowing that the child was going to be a homicidal maniac, I should be responsible for his crimes. If God knew in advance the sins of which man would be guilty, He was clearly responsible for all the consequences of those sins when He decided to create man. Today, no one believes that the world was created in BC; but not so very long ago skepticism on this point was thought an abominable crime … It is no credit to the orthodox that they do not now believe all the absurdities that were believed years ago.
The gradual emasculation of the Christian doctrine has been effected in spite of the most vigorous resistance, and solely as the result of the onslaughts of Freethinkers A, It is intellectual blindness not to recognize the revolutionary import of early Christianity, whatever the contemporary feeling concerning the sacrament of marriage may be, when it set itself like a wall against the tides of boundless sensuality and impressed upon the Roman world the sanctity of human life.
Kayden , 88 Contrary to what was often said about his personal life, it is also worth noting that Russell did not practice or defend a libertine ethic. As Wood also notes, Perhaps the finest tribute to his success is that few people now even realize the nature of the old ideas. Russell, it must be repeated, was fighting a cruel and indefensible state of affairs where sexual ignorance was deliberately fostered, so a boy might think the changes of puberty were signs of some dreadful disease, and a girl might marry without knowing anything of what lay ahead of her on her bridal night; were women were taught to look on sex, not as a source of joy, but of painful matrimonial duty; where prudery went to the extent of covering the legs of pianos in draperies; where artificial mystery evoked morbid curiosity, and where humbug went hand in hand with unhappiness ….
Russell says much the same thing when he notes that Religion has three main aspects. In the second place there is theology.
In the third place there is institutionalized religion, i. Schilpp , —6. As Russell explains, Suppose, for instance, your child is ill. Love makes you wish to cure it, and science tells you how to do so. There is not an intermediate stage of ethical theory, where it is demonstrated that your child had better be cured. Your act springs directly from desire for an end, together with knowledge of means. This is equally true of all acts, whether good or bad. Instead, they are positively frustrated: If theology is thought necessary to virtue and if candid inquirers see no reason to think the theology true, the authorities will set to work to discourage candid inquiry.
In former centuries, they did so by burning the inquirers at the stake. In Russia they still have methods which are little better; but in Western countries the authorities have perfected somewhat milder forms of persuasion.
Of these, schools are perhaps the most important: the young must be preserved from hearing the arguments in favour of the opinions which the authorities dislike, and those who nevertheless persist in showing an inquiring disposition will incur social displeasure and, if possible, be made to feel morally reprehensible.
A, Societies as well as individuals, says Russell, need to choose whether the good life is one that is guided by honest inquiry and the weighing of evidence, or by the familiarity of superstition and the comforts of religion.
Partly this is due to our need to understand nature, but equally important is our need to understand each other: The thing, above all, that a teacher should endeavor to produce in his pupils, if democracy is to survive, is the kind of tolerance that springs from an endeavor to understand those who are different from ourselves. One of the best summaries is given by Alan Wood: Russell sometimes maintained, partly I think out of perverseness, that there was no connection between his philosophical and political opinions.
This was perfectly legitimate, and even praiseworthy, in a world which never stays the same, and where changing circumstances continually change the balance of arguments on different sides. If they are successful, they carry out the behest of Power, becoming themselves as powerful, in terms of Mr. Even though they spread the good life to millions, the more successful they are, the more usurpatious and dangerous.
As a young man, he says, he spent part of each day for many weeks reading Georg Cantor, and copying out the gist of him into a notebook. At that time I falsely supposed all his arguments to be fallacious, but I nevertheless went through them all in the minutest detail.
This stood me in good stead when later on I discovered that all the fallacies were mine. Girard, Kansas: Haldeman-Julius Publications, Muirhead ed. Norton, Slater ed. Pears ed. Schapiro, C. Darlington, Francis Watson, W.
Aa, Russell on Ethics , London: Routledge. Ab, Russell on Religion , London: Routledge. A, Russell on Metaphysics , London: Routledge. Rempel and John G. Slater eds. Lewis eds. Moore ed. Rempel, Andrew Brink and Margaret Moran eds. Rempel ed. Lewis and Mark Lippincott eds.
Rempel and Beryl Haslam eds. Bone and Michael D. Stevenson eds. Bone ed. Planned Vol. Ayer, A. Irvine ed. Banks, Erik C. Jackson ed. Broad, C. Klemke ed. Together with his second wife, he opened and ran an experimental school during the late s and early s. He became the third Earl Russell upon the death of his brother in The appointment was revoked following a large number of public protests and a judicial decision, in , which stated that he was morally unfit to teach at the College.
Nine years later he was awarded the Order of Merit. He received the Nobel Prize for Literature in During the s and s, Russell became something of an inspiration to large numbers of idealistic youth as a result of his continued anti-war and anti-nuclear protests.
Together with Albert Einstein , he released the Russell- Einstein Manifesto in , calling for the curtailment of nuclear weapons. In , he was a prime organizer of the first Pugwash Conference, which brought together scientists concerned about the proliferation of nuclear weapons. He became the founding president of the Campaign for Nuclear Disarmament in and was once again imprisoned, this time in connection with anti-nuclear protests, in Upon appeal, his two-month prison sentence was reduced to one week in the prison hospital.
He remained a prominent public figure until his death nine years later at the age of References show. Biography in Encyclopaedia Britannica. A J Ayer, Bertrand Russell Cape, R Clark, Bertrand Russell : and his world London, C W Kilmister, Russell E D Klemke ed. P G Kuntz, Bertrand Russell
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