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Pure mathematics consists entirely of such asseverations as that, if
such and such a proposition is true of anything, then such and such
another proposition is true of that thing... It's essential not to discuss
whether the proposition is really true, and not to mention what the
anything is of which it is supposed to be true... If our hypothesis is
about anything and not about some one or more particular things,
then our deductions constitute mathematics. Thus mathematics may
be defined as the subject in which we never know what we are talking
about, nor whether what we are saying is true.
-- Bertrand Russell
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