"An axiomatic system comprises axioms and theorems and……" — David Berlinski
"An axiomatic system comprises axioms and theorems and requires a certain amount of hand-eye coordination before it works. A formal system comprises an explicit list of symbols, an explicit set of rules governing their cohabitation, an explicit list of axioms, and, above all, an explicit list of rules explicitly governing the steps that the mathematician may take in going from assumptions to conclusions. No appeal to meaning nor to intuition. Symbols lose their referential powers; inferences become mechanical."
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David Berlinski
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29 Quotes by David Berlinski
David Berlinski has 29 quotes on this site.
A few more worth reading:
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Darwin's theory of evolution is the last of the great nineteenth-century mystery religions. And as we speak it is now…
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There are gaps in the fossil graveyard, places where there should be intermediate forms, but where there is nothing whatsoever…
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Ultimately, Leibniz argued, there are only two absolutely simple concepts, God and Nothingness. From these, all other concepts may be…
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If moral statements are about something, then the universe is not quite as science suggests it is, since physical theories,…
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Commentators who today talk of 'The Dark Ages' when faith instead of reason was said to ruthlessly rule, have for…
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Just who has imposed on the suffering human race poison gas, barbed wire, high explosives, experiments in eugenics, the formula…
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Darwinism is not a sufficient condition for a phenomenon like Nazism but I think it's certainly a necessary one,
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I do not know whether any of this is true. I am certain that the scientific community does not know…
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Although every novel is derived directly from another novel, there is really only one novel, the Quixote.
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While science has nothing of value to say on the great and aching questions of life, death, love and meaning,…
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Validity is the touchstone of inference, and truth of judgment: the fact that vichyssoise is cold ratifies the judgment that…
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The definition of a limit is essentially his [Cauchy's] creation and is as much of a miracle as those fantastic…
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More All Quotes
This quote is filed under All Quotes,
one of 128,558 quotes in that category. Here are a few more:
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Total loyalty is possible only when fidelity is emptied of all concrete content, from which changes of mind might naturally…
— Hannah Arendt
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No cause is left but the most ancient of all, the one, in fact, that from the beginning of our…
— Hannah Arendt
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The ultimate end of human acts is eudaimonia, happiness in the sense of living well, which all men desire; all…
— Hannah Arendt
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The new always happens against the overwhelming odds of statistical laws and their probability, which for all practical, everyday purposes…
— Hannah Arendt
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Where all are guilty, no one is; confessions of collective guilt are the best possible safeguard against the discovery of…
— Hannah Arendt
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We have almost succeeded in leveling all human activities to the common denominator of securing the necessities of life and…
— Hannah Arendt
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I keep my friends as misers do their treasure, because, of all the things granted us by wisdom, none is…
— Pietro Aretino
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We must all make peace so that we can all live in peace.
— Jean-Bertrand Aristide
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The spirit of Ubuntu, that once led Haiti to emerge as the first independent black nation in 1804, helped Venezuela,…
— Jean-Bertrand Aristide
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As we all know, many people remain buried under tons of rubble and debris, waiting to be rescued. When we…
— Jean-Bertrand Aristide
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Wise people, even though all laws were abolished, would still lead the same life.
— Aristophanes
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A friend to all is a friend to none.
— Aristotle
See all 128,558 All Quotes »