All Quotes

"Logic and mathematics seem to be the only domains where self-evidence manages to rise above triviality; and this it does, in those domains, by a linking of self-evidence on to self-evidence in the chain reaction known as proof."

"Three conceptions are perpetually turning up at every point in every theory of logic, and in the most rounded systems they occur in connection with one another. They are conceptions so very broad and consequently indefinite that they are hard to seize and may be easily overlooked. I call them the conceptions of First, Second, Third. First is the conception of being or existing independent of anything else. Second is the conception of being relative to, the conception of reaction with, something else. Third is the conception of mediation, whereby a first and second are brought into relation."

"Logical analysis applied to mental phenomenon shows that there is but one law of mind, namely that ideas tend to spread continuously and to affect certain others which stand to them in a peculiar relation of affectibility. In this spreading they lose intensity, and especially the power of affecting others, but gain generality and become welded with other ideas."

"A certain maxim of Logic which I have called Pragmatism has recommended itself to me for diverse reasons and on sundry considerations."

"It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better."

"The utility of a science which enables men to take cognizance of the travellers on the mind's highway, and excludes those disorderly interlopers, verbal fallacies, needs but small attestation. Its searching penetration by definition alone, before which even mathematical precision fails, would especially commend it to those whom the abstruseness of the study does not terrify, and who recognise the valuable results which must attend discipline of mind. Like a medicine, though not a panacea for every ill, it has the health of the mind for its aim, but requires the determination of a powerful will to imbibe its nauseating yet wholesome influence: it is no wonder therefore that puny intellects, like weak stomachs, abhor and reject it."

"Of course I'm inconsistent! Only logicians and cretins are consistent!"

"Mathematics and logic, historically speaking, have been entirely distinct studies. Mathematics has been connected with science, logic with Greek. But both have developed in modern times: logic has become more mathematical and mathematics has become more logical. The consequence is that it has now become wholly impossible to draw a line between the two; in fact, the two are one. They differ as boy and man: logic is the youth of mathematics and mathematics is the manhood of logic. This view is resented by logicians who, having spent their time in the study of classical texts, are incapable of following a piece of symbolic reasoning, and by mathematicians who have learnt a technique without troubling to inquire into its meaning or justification. Both types are now fortunately growing rarer. 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 premises 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."

"The question of "unreality," which confronts us at this point, is a very important one. Misled by grammar, the great majority of those logicians who have dealt with this question have dealt with it on mistaken lines. They have regarded grammatical form as a surer guide in analysis than, in fact, it is. And they have not known what differences in grammatical form are important."

"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."

"I once received a letter from an eminent logician, Mrs. Christine Ladd Franklin, saying that she was a solipsist, and was surprised that there were no others. Coming from a logician, this surprise surprised me."

"The apparent world goes through developments which are the same as those the logician goes through if he starts from Pure Being and travels on to the Absolute Idea. [...] Why the world should go through this logical evolution is not clear; one is tempted to suppose that the Absolute Idea did not quite understand itself at first, and made mistakes when it tried to embody itself in events. But this, of course, was not what Hegel would have said."

"Pure logic is the ruin of the spirit."

"A crisis in doctrine occurred when they discovered that the square root of two was irrational. That is: the square root of two could not be represented as the ratio of two whole numbers, no matter how big they were. "Irrational" originally meant only that. That you can't express a number as a ratio. But for the Pythagoreans it came to mean something else, something threatening, a hint that their world view might not make sense, the other meaning of "irrational"."

"When emotion brings us ghosts from the past, only logic can root us in the present."

"[My aim is] to design logic as a calculating discipline, especially to give access to the exact handling of relative concepts, and, from then on, by emancipation from the routine claims of natural language, to withdraw any fertile soil from "cliché" in the field of philosophy as well. This should prepare the ground for a scientific universal language that, widely differing from linguistic efforts like Volapük [a universal language like Esperanto, very popular in Germany at the time], looks more like a sign language than like a sound language."

"Conceptual graphs are system of logic based on the existential graphs of Charles Sanders Peirce and the semantic networks of artificial intelligence. The purpose of the system is to express meaning in a form that is logically precise, humanly readable, and computationally tractable."

"Logic is the beginning of wisdom, not the end."

"Logic is in the eye of the logician."

"An idea starts to be interesting when you get scared of taking it to its logical conclusion."

"It takes extraordinary wisdom and self-control to accept that many things have a logic we do not understand that is smarter than our own."

"The fellahin are not descendants of the Arab conquerors, who captured Eretz Israel and Syria in the seventh century CE. The Arab conquerors did not destroy the agricultural population they found in the country. They expelled only the alien Byzantine rulers and did not touch the local population. Nor did the Arabs go in for settlement"

"Poetry — No definition of poetry is adequate unless it be poetry itself. The most accurate analysis by the rarest wisdom is yet insufficient, and the poet will instantly prove it false by setting aside its requisitions. It is indeed all that we do not know. The poet does not need to see how meadows are something else than earth, grass, and water, but how they are thus much. He does not need discover that potato blows are as beautiful as violets, as the farmer thinks, but only how good potato blows are. The poem is drawn out from under the feet of the poet, his whole weight has rested on this ground. It has a logic more severe than the logician's. You might as well think to go in pursuit of the rainbow, and embrace it on the next hill, as to embrace the whole of poetry even in thought."

"The moment we stop assuming that the ideas of any milieu form static 'propositional systems', and recognize that they constitute historically developing 'conceptual populations', we are free to abandon also the philosophers' traditional assumption that rationality is a sub-species of logicality. ...In non-intellectual contexts... we judge the rationality of a man's conduct, not by how he habitually behaves, but rather how far he modifies his behaviour in new and unfamiliar situations, and it is arguable that the rationality of intellectual performances should be judged, correspondingly, by considering, not the internal consistency of a man's habitual concepts and beliefs, but rather the manner in which he modifies this intellectual position in the face of new and unforeseen experiences."

"Logic tends to reduce everything to identities and genera, to each representation having no more than one single and self-same content in whatever place, time, or relation it may occur to us. And there is nothing that remains the same for two successive moments of its existence. My idea of God is different each time that I conceive it. Identity, which is death, is the goal of the intellect."

"As to the most prudent logicians might venture to deduce from a skein of wool the probable existence of a sheep; so you, from the raw stuff of perception, may venture to deduce a universe which transcends the reproductive powers of your loom."

"Logic is a law which must be obeyed, and man realizes himself only in so far as he is logical. He finds himself in cognition."

"Memory, then, is a necessary part of the logical faculty. ... The proposition A = A must have a psychological relation to time, otherwise it would be At1 = At2."

"Roughly speaking: to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing."

"[ Fuzzy logic is ] a logic whose distinguishing features are (i) fuzzy truth-values expressed in linguistic terms, e.g., true, very true, more or less true, or somewhat true, false, nor very true and not very false, etc2.; (2) imprecise truth tables; and (3) rules of inference whose validity is relative to a context rather than exact."

"The agricultural community that the Arabs found in Eretz Israel in the 7th century was none other than the Hebrew farmers that remained on their land despite all the persecution and oppression of the Roman and Byzantine emperors."

"The greater majority and main structures of the Muslim falahin in western Eretz Israel present to us one racial strand and a whole ethnic unit, and there is no doubt that much Jewish blood flows in their veins — the blood of those Jewish farmers, “lay persons,” who chose in the travesty of times to abandon their faith in order to remain on their land."

"Everybody sees a difficulty in the question of relations between Arabs and Jews. But not everybody sees that there is no solution to this question. No solution! There is a gulf, and nothing can bridge it... We, as a nation, want this country to be ours; the Arabs, as a nation, want this country to be theirs."

"Under no circumstances must we touch land belonging to fellahs or worked by them. Only if a fellah leaves his place of settlement, should we offer to buy his land, at an appropriate price."

"The acceptance of partition does not commit us to renounce Transjordan: one does not demand from anybody to give up his vision. We shall accept a state in the boundaries fixed today, but the boundaries of Zionist aspirations are the concern of the Jewish people and no external factor will be able to limit them."

"In our political argument abroad, we minimize Arab opposition to us. But let us not ignore the truth among ourselves. I insist on the truth, not out of respect for scientific but political realities. The acknowledgement of this truth leads to inevitable and serious conclusions regarding our work in Palestine... let us not build on the hope the terrorist gangs will get tired. If some get tired, others will replace them. A people which fights against the usurpation of its land will not tire so easily... it is easier for them to continue the war and not get tired than it is for us... The Palestinian Arabs are not alone. The Syrians are coming to help. From our point of view, they are strangers; in the point of law they are foreigners; but to the Arabs, they are not foreigners at all ... The centre of the war is in Palestine, but its dimensions are much wider. When we say that the Arabs are the aggressors and we defend ourselves — this is only half the truth. As regards our security and life we defend ourselves and our moral and physical position is not bad. We can face the gangs... and were we allowed to mobilize all our forces we would have no doubts about the outcome... But the fighting is only one aspect of the conflict which is in its essence a political one. And politically we are the aggressors and they defend themselves. Militarily, it is we who are on the defensive who have the upper hand ... but in the political sphere they are superior. The land, the villages, the mountains, the roads are in their hands. The country is theirs, because they inhabit it, whereas we want to come here and settle down, and in their view we want to take away from them their country, while we are still outside. They defend bases which are theirs, which is easier than conquering new bases... let us not think that the terror is a result of Hitler's or Mussolini's propaganda — this helps but the source of opposition is there among the Arabs."

"Terrorism benefits the Arabs, it may lay waste the Yishuv and shake Zionism. But to follow in the Arabs' footsteps and ape their deeds is to be blind to the gulf between us. Our aims and theirs run counter: methods calculated to further theirs, are ruinous to us."

"From Jewish terrorism against Arabs it is a short step to Jewish terrorism against Jews."

"If I knew that it was possible to save all the children of Germany by transporting them to England, and only half by transferring them to the Land of Israel, I would choose the latter, for before us lies not only the numbers of these children but the historical reckoning of the people of Israel."

"These Central Asian republics have a special interest for us because of our age-old contact with Middle Asia. They are even more fascinating because of the remarkable progress they have made during the past few years. Under the Tsars they were very backward and superstitious countries with hardly any education and their women mostly behind the veil. Today they are ahead of India in many respects."

"This Five Year Plan had been drawn up after the most careful thought and investigation. The whole country had been surveyed by scientists and engineers, and numerous experts had discussed the problem of fitting in one part of the programme into another. For, the real difficulty came in this fitting in... But Russia had one great advantage over the capitalist countries. Under capitalism all these activities are left to individual initiative and chance, and owing to competition there is waste of effort. There is no co-ordination between different producers or different sets of workers, except the chance co-ordination which arises in the buyers and sellers coming to the same market... The Soviet Government had the advantage of controlling all the different industries and activities in the whole Union, and so it could draw up and try to work a single co-ordinated plan in which every activity found its proper place. There would be no waste in this, except such waste as might come from errors of calculation or working, and even such errors could be rectified far sooner with a unified control than otherwise."

""For Russia, therefore, this building of heavy industries at a tremendous pace meant a very great sacrifice. All this construction, all this machinery that came from outside, had to be paid for, and paid for in gold and cash. How was this to be done? The people of the Soviet Union tightened their belts and starved and deprived themselves of even necessary articles so that payment could be made abroad. They sent their food-stuffs abroad, and with the price obtained for them paid for the machinery. They sent everything they could find a market for: wheat, rye, barley, corn, vegetables, fruits, eggs, butter, meat, fowls, honey, fish, caviare, sugar, oils, confectionery, etc. Sending these food articles outside meant that they themselves did without them. The Russian people had no butter, or very little of it, because it went abroad to pay for machinery. And so with many other goods..."

"Nations have, in the past, concentrated all their efforts on the accomplishment of one great task, but this has been so in times of war only. During the World War, Germany and England and France lived for one purpose only - to win the war. To that purpose everything else was subordinated. Soviet Russia, for the first time in history, concentrated the whole strength of the nation in a peaceful effort to build, and not to destroy, to raise a backward country industrially and within a framework of socialism."

"It was quite impossible for us to give any assistance and therefore it was not proper for us to raise any hopes in this direction... When occasion arises we can certainly put in a good word on the diplomatic plane to China. For the rest, the only policy we can adopt is to remain quiet observers."

"So far as I am concerned and the government I lead is concerned, I want to make it perfectly clear that communal forces will not be given the slightest quarter to sow seeds of dissensions among the people."

"But the privation, especially of the upper and middle-class peasantry, was very great, and often it seemed that the whole ambitious scheme would collapse, and perhaps carry the Soviet Government with it. It required immense courage to hold on. Many prominent Bolsheviks thought that the strain and suffering caused by the agricultural programme were too great and there should be a relaxation. But not so Stalin. Grin-fly and silently he held on. He was no talker, he hardly spoke in public. He seemed to be the iron image of an inevitable fate going ahead to the predestined goal. And something of his courage and determination spread among the members of the Communist Party and other workers in Russia."

"But, as I have told you, this Five Year Plan brought much suffering, and difficulties and dislocation. And people paid a terrible price willingly and accepted the sacrifices and sufferings for a few years in the hope of a better time afterwards; some paid the price unwillingly and only because of the compulsion of the Soviet Government. Among those who suffered most were the kulaks or richer peasants. With their great wealth and special influence, they did not fit into the new scheme of things. They were capitalistic elements which prevented the collective farms from developing on socialist lines. Often they opposed this collectivization, sometimes they entered the collectives to weaken them from inside or to make undue personal profit out of them. The Soviet Government came down heavily on them. The Government was also very hard on many middle-class people whom it suspected of espionage and sabotage on behalf of its enemies. Because of this, large numbers of engineers were punished and sent to gaol."

"The tremendous growth of the Soviet Union was in itself a remarkable sign of prosperity. It was not due, as in America, to immigration from outside. It showed that in spite of the privations and hardships of the people there was, as a general rule, no actual starvation. A severe system of rationing managed to supply the absolutely necessary articles of food to the population. Competent observers tell us that this rapid growth of population is largely due to a feeling of economic security among the people."

"Work remains, and must remain, though in the future it is likely to be pleasanter and lighter than in the trying early years of planning. Indeed, the maxim of the Soviet Union is: 'He that will not work, neither shall he eat.' But the Bolsheviks have added a new motive for work: the motive to work for social betterment. In the past, idealists and stray individuals have been moved to activity by this incentive, but there is no previous instance of society as a whole accepting and reacting to this motive. The very basis of capitalism was competition and individual profit, always at the expense of others. This profit motive is giving place to the social motive in the Soviet Union and, as an American writer says, workers in Russia are learning that, 'from the acceptance of mutual dependence comes independence from want or fear'. This elimination of the terrible fear of poverty and insecurity, which bears down upon the masses everywhere, is a great achievement. It is said that this relief has almost put an end to mental diseases in the Soviet Union."

"I shall tell you just a few odd facts which might interest you. The educational system in Russia is supposed by many competent judges to be the best and most up-to-date in existence."