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1 " Only the learned read old books, and... now... they are of all men the least likely to acquire wisdom by doing so. ...[G]reat scholars are now as little nourished by the past as the most ignorant mechanic who holds that " history is bunk..." [for] ...when a learned man is presented with any statement in an ancient author, the one question he never asks is whether it is true. He asks who influenced the ancient writer, and how far the statement is consistent with what he said in other books, and what phase in the writer's development, or in the general history of thought, it illustrates, and how it affected later writers, and how often it has been misunderstood (specially by the learned man's colleagues) and what the general course of criticism on it has been for the last ten years, and what is the " present state of the question." To regard the ancient writer as a possible source of knowledge-to anticipate that what he said could possibly modify your thoughts or your behavior-this would be rejected as unutterably simple-minded. ... [Therefore, even though] learning makes a free commerce between the ages... every generation [is cut] off from all others... [and] ...characteristic errors of one [are not] corrected by the characteristic truths of another. "
2 " At the same time, they find their mind-god has played a trick on them. For mind is a part of the very system it has closed around it, and being inside, there is no reason to think any statement made by some part concerning the whole has any validity. Mind was caused by the material universe, if mind is right. But only the greater can accurately define the lesser, never the other way round, so if mind is right, mind would never know. "
― Geoffrey Wood
3 " Life is so diversified that to any statement I could make about living organisms there are exceptions. Because of the many exceptions, I should qualify everything I say with hedging phrases such as 'generally,' 'usually,' and 'almost always' But I'm afraid the constant repetition of these hedges will slow me down and bore you. So let's make a pact now that I forego the hedging phrases and you are to understand that almost all my statements may have rare exceptions. "
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4 " Turing attended Wittgenstein's lectures on the philosophy of mathematics in Cambridge in 1939 and disagreed strongly with a line of argument that Wittgenstein was pursuing which wanted to allow contradictions to exist in mathematical systems. Wittgenstein argues that he can see why people don't like contradictions outside of mathematics but cannot see what harm they do inside mathematics. Turing is exasperated and points out that such contradictions inside mathematics will lead to disasters outside mathematics: bridges will fall down. Only if there are no applications will the consequences of contradictions be innocuous. Turing eventually gave up attending these lectures. His despair is understandable. The inclusion of just one contradiction (like 0 = 1) in an axiomatic system allows any statement about the objects in the system to be proved true (and also proved false). When Bertrand Russel pointed this out in a lecture he was once challenged by a heckler demanding that he show how the questioner could be proved to be the Pope if 2 + 2 = 5. Russel replied immediately that 'if twice 2 is 5, then 4 is 5, subtract 3; then 1 = 2. But you and the Pope are 2; therefore you and the Pope are 1'! A contradictory statement is the ultimate Trojan horse. "
― John D. Barrow , The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe
