Peter Duren's A Century in Mathematics in America PDF

By Peter Duren

ISBN-10: 0821801384

ISBN-13: 9780821801383

ISBN-10: 082180152X

ISBN-13: 9780821801529

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Extra info for A Century in Mathematics in America

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Kant would argue that this case cannot happen be­ cause the principles are necessary conditions of experi­ ence, or, in other words, because, in the case considered, experience as an ordered system of observations would not be possible. But how does he know that experience 47 SPECULATIVE PHILOSOPHY will always be possible? Kant had no proof that we would never arrive at a totality of observations which could not be ordered in the frame of his a-priori principles and which would make experience impossible, at least expe­ rience in the Kantian sense.

Now, Plato’s use of the word “ existence” is not of the scientific type. If it were, the statement that ideal objects exist would have been defined in terms of other statements that do not contain such a questionable term, and would not have been used independently as having a meaning com­ parable to that of physical existence. W e may define the existence of an ideal triangle as meaning that we can speak about triangles in terms of implications. Or, using algebra for an illustration, we may say that for every al­ gebraic equation concerning an unknown quantity, pro­ vided it satisfies certain conditions, there exists a solu­ tion; in this usage, the word “ exists” means that we know how to find the solution.

W e do not see our own selves in the way we see houses and people around us. W e may perhaps speak of an observation of our acts of thought, or of doubt; they are not perceived, however, as the prod­ ucts of an ego, but as separate objects, as images accom­ panied by feelings. T o say “ I think” goes beyond the immediate experience in that the sentence employs the word “ I” . T h e statement ”1 think” represents not an observational datum, but the end of long chains of thought which uncover the existence of an ego as distinct from the ego of other persons.

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A Century in Mathematics in America by Peter Duren


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