Neither acquiescence in skepticism nor acquiescence in dogma is what education should produce. What it should produce is a belief that knowledge is attainable in a measure, though with difficulty; that much of what passes for knowledge at any given time is likely to be more or less mistaken, but that the mistakes can be rectified by care and industry. In acting upon our beliefs, we should be very cautious where a small error would mean disaster; nevertheless it is upon our beliefs that we must act. This state of mind is rather difficult: it requires a high degree of intellectual culture without emotional atrophy. But though difficult, it is not impossible; it is in fact the scientific temper. Knowledge, like other good things, is difficult, but not impossible; the dogmatist forgets the difficulty, the skeptic denies the possibility. Both are mistaken, and their errors, when widespread, produce social disaster.
British philosopher and logician (1872–1970)
Bertrand Arthur William Russell, 3rd Earl Russell (May 18, 1872 – February 2, 1970) was a British philosopher, logician, mathematician, historian, and social critic. In 1950, he was awarded a Nobel Prize in Literature.
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It seems to me that science has a much greater likelihood of being true in the main than any philosophy hitherto advanced (I do not, of course, except my own). In science there are many matters about which people are agreed; in philosophy there are none. Therefore, although each proposition in a science may be false, and it is practically certain that there are some that are false, yet we shall be wise to build our philosophy upon science, because the risk of error in philosophy is pretty sure to be greater than in science. If we could hope for certainty in philosophy, the matter would be otherwise, but so far as I can see such a hope would be chimerical.
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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 Chinese are a great nation, incapable of permanent suppression by foreigners. They will not consent to adopt our vices in order to acquire military strength; but they are willing to adopt our virtues in order to advance in wisdom. I think they are the only people in the world who quite genuinely believe that wisdom is more precious than rubies. That is why the West regards them as uncivilized.
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I must confess that I am unable to appreciate the merits of Confucius. His writings are largely occupied with trivial points of etiquette, and his main concern is to teach people how to behave correctly on various occasions. When one compares him, however, with the traditional religious teachers of some other ages and races, one must admit that he has great merits, even if they are mainly negative. His system, as developed by his followers, is one of pure ethics, without religious dogma; it has not given rise to a powerful priesthood, and it has not led to persecution. It certainly has succeeded in producing a whole nation possessed of exquisite manners and perfect courtesy. Nor is Chinese courtesy merely conventional; it is quite as reliable in situations for which no precedent has been provided. And it is not confined to one class; it exists even in the humblest coolie. It is humiliating to watch the brutal insolence of white men received by the Chinese with a quiet dignity which cannot demean itself to answer rudeness with rudeness. Europeans often regard this as weakness, but it is really strength, the strength by which the Chinese have hitherto conquered all their conquerors.
So much of modern mathematical work is obviously on the border-line of logic, so much of modern logic is symbolic and formal, that the very close relationship of logic and mathematics has become obvious to every instructed student. The proof of their identity is, of course, a matter of detail: starting with premisses which would be universally admitted to belong to logic, and arriving by deduction at results which as obviously belong to mathematics, we find that there is no point at which a sharp line can be drawn, with logic to the left and mathematics to the right. If there are still those who do not admit the identity of logic and mathematics, we may challenge them to indicate at what point, in the successive definitions and deductions of Principia Mathematica, they consider that logic ends and mathematics begins. It will then be obvious that any answer must be quite arbitrary.
In obedience to the feeling of reality, we shall insist that, in the analysis of propositions, nothing "unreal" is to be admitted. But, after all, if there is nothing unreal, how, it may be asked, could we admit anything unreal? The reply is that, in dealing with propositions, we are dealing in the first instance with symbols, and if we attribute significance to groups of symbols which have no significance, we shall fall into the error of admitting unrealities, in the only sense in which this is possible, namely, as objects described.