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Very few of us in our saner moments believe that the particular postulates that some logicians have dreamed up create the numbers - no, most of us believe that the real numbers are simply there and that it has been an interesting, amusing, and important game to try to find a nice set of postulates to account for them.
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Even the most carefully defined philosophical or mathematical concept, which we are sure does not contain more than we have put into it, is nevertheless more than we assume. It is a psychic event and as such partly unknowable. The very numbers you use in counting are more than you take them to be. They are at the same time mythological elements (for the Pythagoreans, they were even divine); but you are certainly unaware of this when you use numbers for a practical purpose.
As for negative numbers... most mathematicians of the sixteenth and seventeenth centuries did not accept them... In the fifteenth century and, in the sixteenth, Stifel both spoke of negative numbers as absurd numbers. ...Descartes accepted them, in part. ...he had shown that, given an equation, one can obtain another whose roots are larger than the original one by any given quantity. Thus an equation with negative roots could be transformed into one with positive roots. Since we can turn false roots into real roots, Descartes was willing to accept negative numbers. Pascal regarded the subtraction of 4 from zero as utter nonsense.
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