It now becomes clear that consistency is not a property of a formal system per se, but depends on the interpretation which is proposed for it. By the same token, inconsistency is not an intrinsic property of any formal system.
I should attempt to treat human vice and folly geometrically... the passions of hatred, anger, envy, and so on, considered in themselves, follow from the necessity and efficacy of nature... I shall, therefore, treat the nature and strength of the emotion in exactly the same...
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Baruch Spinoza
If you can't test it, it's not theorics -- it's metatheorics. A branch of philosophy. So, if you want to think of it this way, our test equipment is what defines the boundary separating theorics from philosophy.
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Neal Stephenson
Physicists have come to realize that mathematics, when used with sufficient care, is a proven pathway to truth.
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Brian Greene
The difference between the poet and the mathematician is that the poet tries to get his head into the heavens while the mathematician tries to get the heavens into his head.
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G.k. Chesterton
This is the team. We're trying to go to the moon. If you can't put someone up, please don't put them down.
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NASA
More Quotes By Douglas R. Hofstadter
People enjoy inventing slogans which violate basic arithmetic but which illustrate “deeper” truths, such as “1 and 1 make 1” (for lovers), or “1 plus 1 plus 1 equals 1” (the Trinity). You can easily pick holes in those slogans, showing why, for instance, using...
It turns out that an eerie type of chaos can lurk just behind a facade of order - and yet, deep inside the chaos lurks an even eerier type of order.
Sometimes it seems as though each new step towards AI, rather than producing something which everyone agrees is real intelligence, merely reveals what real intelligence is not.
And one of my firmest conclusions is that we always think by seeking and drawing parallels to things we know from our past, and that we therefore communicate best when we exploit examples, analogies, and metaphors galore, when we avoid abstract generalities, when we use...
I am a lifelong lover of form—content interplay, and this book is no exception. As with several of my previous books, I have had the chance to typeset it down to the finest level of detail, and my quest for visual elegance on each page...
