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A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.

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There are no fools so troublesome as those of the mind

Fine minds are seldom fine souls.

I have always been impressed by the fact that there are a surprising number of individuals who never use their minds if they can avoid it, and an equal number who do use their minds, but in an amazingly stupid way.

There are men of a certain type of mind who are never wearied with gibing at mathematics, at mathematicians, and at mathematical methods of inquiry. It goes almost without saying that these men have themselves little mathematical bent. I believe this to be a general fact; but, as a fact, it does not explain very well their attitude towards mathematicians. The reason seems to lie deeper. How does it come about, for instance, that whilst they are themselves so transparently ignorant of the real nature, meaning, and effects of mathematical investigation, they yet lay down the law in the most confident and self-satisfied manner, telling the mathematician what the nature of his work is (or rather is not), and of its erroneousness and inutility, and so forth? It is quite as if they knew all about it. It reminds one of the professional paradoxers... They, too, write as if they knew all about it. Plainly, then, the anti-mathematician must belong to the same class as the paradoxer, whose characteristic is to be wise in his ignorance, whereas the really wise man is ignorant in his wisdom. ...What is of greater importance is that the anti-mathematicians sometimes do a deal of mischief. For there are many of a neutral frame of mind, little acquainted themselves with mathematical methods, who are sufficiently impressible to be easily taken in by the gibers and to be prejudiced thereby; and, should they possess some mathematical bent, they may be hindered by their prejudice from giving it fair development. We cannot all be Newtons or Laplace's, but that there is an immense amount of moderate mathematical talent lying latent in the average man I regard as a fact; and even the moderate development implied in a working knowledge of simple algebraical equations can, with common-sense to assist, be not only the means of valuable mental discipline, but even be of commercial importance (which goes a long way with some people), should one's occupation be a branch of engineering for example.

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It may be true that only those minds which are habituated to think logically can safely trust their intuitive conclusions, on the theory that the subconscious level will do its kind of work as faithfully as the conscious does its kind.

The sane understand that human beings are incapable of sustaining conspiracies on a grand scale, because some of our most defining qualities as a species are inattention to detail, a tendency to panic, and an inability to keep our mouths shut.

Do not be so open-minded that your brains fall out.

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