Formerly, it was held by philosophers and mathematicians alike that the proofs in Geometry depended on the figure; nowadays, this is known to be false. In the best books there are no figures at all. The reasoning proceeds by the strict rules of formal logic from a set of axioms laid down to begin with.

An irrational fear should never be simply let alone, but should be gradually overcome by familiarity with its fainter forms.

Those who have been inspired to action by the doctrine of the class war will have acquired the habit of hatred, and will instinctively seek new enemies when the old ones have been vanquished. But in actual fact the psychology of the working man in any of the Western democracies is totally unlike that which is assumed in the Communist Manifesto. He does not by any means feel that he has nothing to lose but his chains, nor indeed is this true. The chains which bind Asia and Africa in subjection to Europe are partly riveted by him. He is himself part of a great system of tyranny and exploitation. Universal freedom would remove, not only his own chains, which are comparatively light, but the far heavier chains which he has helped to fasten upon the subject races of the world.

I think if I had met him [Lenin] without knowing who he was, I should not have guessed that he was a great man; he struck me as too opinionated and narrowly orthodox. His strength comes, I imagine, from his honesty, courage, and unwavering faith-religious faith in the Marxian gospel, which takes the place of the Christian martyr's hopes of Paradise, except that it is less egotistical... I went to Russia a Communist; but contact with those who have no doubts has intensified a thousandfold my own doubts, not as to Communism in itself, but as to the wisdom of holding a creed so firmly that for its sake men are willing to inflict widespread misery.

A life devoted to science is therefore a happy life, and its happiness is derived from the very best sources that are open to dwellers on this troubled and passionate planet.

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.

The plan we are advocating amounts essentially to this: that a certain small income, sufficient for necessaries, should be secured to all, whether they work or not, and that a larger income, as much larger as might be warranted by the total amount of commodities produced, should be given to those who are willing to engage in some work which the community recognizes as useful.

Modern physics... reduces matter to a set of events which proceed outward from a centre. If there is something further in the centre itself, we cannot know about it, and it is irrelevant to physics.

The theoretical understanding of the world, which is the aim of philosophy, is not a matter of great practical importance to animals, or to savages, or even to most civilized men.

People seem good while they are oppressed, but they only wish to become oppressors in their turn: life is nothing but a competition to be the criminal rather than the victim.

The good life is one inspired by love and guided by knowledge.

An extra-terrestrial philosopher, who had watched a single youth up to the age of twenty-one and had never come across any other human being, might conclude that it is the nature of human beings to grow continually taller and wiser in an indefinite progress towards perfection; and this generalisation would be just as well founded as the generalisation which evolutionists base upon the previous history of this planet.

Written words differ from spoken words in being material structures. A spoken word is a process in the physical world, having an essential time-order; a written word is a series of pieces of matter, having an essential space-order.

Government by majorities can be made less oppressive by devolution, by placing the decision of questions primarily affecting only a section of the community in the hands of that section, rather than of a Central Chamber. In this way, men are no longer forced to submit to decisions made in a hurry by people mostly ignorant of the matter in hand and not personally interested.

...it [is] possible to suppose that, if Russia is allowed to have peace, an amazing industrial development may take place, making Russia a rival of the United States.

The scientific attitude of mind involves a sweeping away of all other desires in the interests of the desire to know-it involves suppression of hopes and fears, loves and hates, and the whole subjective emotional life, until we become subdued to the material, able to see it frankly, without preconceptions, without bias, without any wish except to see it as it is, and without any belief that what it is must be determined by some relation, positive or negative, to what we should like it to be, or to what we can easily imagine it to be.

The supreme maxim in scientific philosophising is this: wherever possible, logical constructions are to be substituted for inferred entities.

Freedom is the greatest of political goods. I do not say freedom is the greatest of all goods: the best things come from within-they are such things as creative art, and love, and thought. Such things can be helped or hindered by political conditions, but not actually produced by them; and freedom is, both in itself and in its relation to these other goods the best thing that political and economic conditions can secure.

Physics is mathematical not because we know so much about the physical world, but because we know so little: it is only its mathematical properties that we can discover.

When the intensity of emotional conviction subsides, a man who is in the habit of reasoning will search for logical grounds in favour of the belief which he finds in himself.

In art the Chinese aim at being exquisite, and in life at being reasonable.

We are and irrefutable arbiters of value, and in the world of value Nature is only a part. Thus in this world we are greater than Nature. In the world of values, Nature in itself is neutral, neither good nor bad deserving of neither admiration nor censure. It is we who create value and our desires which confer value. In this realm we are kings, and we debase our kingship if we bow down to Nature. It is for us to determine our good life, not for Nature - not even for Nature personified as God.

Organic life, we are told, has developed gradually from the protozoon to the philosopher, and this development, we are assured, is indubitably an advance. Unfortunately it is the philosopher, not the protozoon, who gives us this assurance.

Our words tend to conceal what is private and particular in our impressions, and to make us believe that different people live in a common world to a greater extent than is in fact the case.

The method of "postulating" what we want has many advantages; they are the same as the advantages of theft over honest toil.

One who believes, as I do, that the free intellect is the chief engine of human progress, cannot but be fundamentally opposed to Bolshevism, as much as to the Church of Rome.

Every great study is not only an end in itself, but also a means of creating and sustaining a lofty habit of mind.

All traditional logic habitually assumes that precise symbols are being employed. It is therefore not applicable to this terrestial life but only to an imagined celestial existence... logic takes us nearer to heaven than other studies.

Many of the actions by which men have become rich are far more harmful to the community than the obscure crimes of poor men, yet they go unpunished because they do not interfere with the existing order.

I went to Salt Lake City and the Mormons tried to convert me, but when I found they forbade tea and tobacco I thought it was no religion for me.

All's well that ends well; which is the epitaph I should put on my tombstone if I were the last man left alive.

I hate the world and almost all the people in it. I hate the Labour Congress and the journalists who send men to be slaughtered, and the fathers who feel a smug pride when their sons are killed, and even the pacifists who keep saying human nature is essentially good, in spite of all the daily proofs to the contrary. I hate the planet and the human race - I am ashamed to belong to such a species.

I do wish I believed in the life eternal, for it makes me quite miserable to think man is merely a kind of machine endowed, unhappily for himself, with consciousness.

Mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of highest excellence, is to be found in mathematics as surely as in poetry. What is best in mathematics deserves not merely to be learnt as a task, but to be assimilated as a part of daily thought, and brought again and again before the mind with ever-renewed encouragement.

In fact the opposition of instinct and reason is mainly illusory. Instinct, intuition, or insight is what first leads to the beliefs which subsequent reason confirms or confutes; but the confirmation, where it is possible, consists, in the last analysis, of agreement with other beliefs no less instinctive. Reason is a harmonising, controlling force rather than a creative one. Even in the most purely logical realms, it is insight that first arrives at what is new.

I may as well say at once that I do not distinguish between inference and deduction. What is called induction appears to me to be either disguised deduction or a mere method of making plausible guesses.

No nation was ever so virtuous as each believes itself, and none was ever so wicked as each believes the other.

In a logically perfect language, there will be one word and no more for every simple object, and everything that is not simple will be expressed by a combination of words, by a combination derived, of course, from the words for the simple things that enter in, one word for each simple component.

Indignation is a submission of our thoughts, but not of our desires.

Is there any knowledge in the world which is so certain that no reasonable man could doubt it?

It seems to me now that mathematics is capable of an artistic excellence as great as that of any music, perhaps greater; not because the pleasure it gives (although very pure) is comparable, either in intensity or in the number of people who feel it, to that of music, but because it gives in absolute perfection that combination, characteristic of great art, of godlike freedom, with the sense of inevitable destiny; because, in fact, it constructs an ideal world where everything is perfect and yet true.

People are said to believe in God, or to disbelieve in Adam and Eve. But in such cases what is believed or disbelieved is that there is an entity answering a certain description. This, which can be believed or disbelieved is quite different from the actual entity (if any) which does answer the description. Thus the matter of belief is, in all cases, different in kind from the matter of sensation or presentation, and error is in no way analogous to hallucination. A hallucination is a fact, not an error; what is erroneous is a judgment based upon it.

Without effort and change, human life cannot remain good. It is not a finished Utopia that we ought to desire, but a world where imagination and hope are alive and active.

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.

How much good it would do if one could exterminate the human race.

The fundamental cause of the trouble is that in the modern world the stupid are cocksure while the intelligent are full of doubt.

Real life is, to most men, a long second-best, a perpetual compromise between the ideal and the possible; but the world of pure reason knows no compromise, no practical limitations, no barrier to the creative activity embodying in splendid edifices the passionate aspiration after the perfect from which all great work springs. Remote from human passions, remote even from the pitiful facts of nature, the generations have gradually created an ordered cosmos, where pure thought can dwell as in its natural home, and where one, at least, of our nobler impulses can escape from the dreary exile of the actual world.

Every philosophical problem, when it is subjected to the necessary analysis and justification, is found either to be not really philosophical at all, or else to be, in the sense in which we are using the word, logical.

What does not exist must be something, or it would be meaningless to deny its existence; and hence we need the concept of being, as that which belongs even to the non-existent.

Righteousness cannot be born until self-righteousness is dead.