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Home > Law > Jurisprudence and general issues > Lectures on the Philosophy of Mathematics: (English)
Lectures on the Philosophy of Mathematics: (English)

Lectures on the Philosophy of Mathematics: (English)

          
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About the Book

Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: CHAPTER III SPACE AND THE GEOMETRIZATION OF MATHEMATICS In the consideration of the problems of geometry we meet at the very outset the question of the reality of the visible and tangible universe. At first to question the existence of this startles us in the same way as the assertion of the motions of the earth with its rock-ribbed hills and fertile valleys. Nothing seems more stationary as we look out over the stretch of plain or ocean than the earth. In a similar manner we are prone to believe that things are as we see them, or as we think they would be if we could come in contact with them. But the study of perspective drawing soon convinces us that objects surely do not have the shapes we see them in, for these alter with changes of position, and they even do not appear as they should in correct perspective. We learn that a hundred feet vertically does not look like a hundred horizontal feet, and that the sky reaches the ground many times farther away than it is above us at the zenith. Yet we find as the result of our endeavor to organize our daily experiences into a consistent and coherent whole that we have a notion of a real and permanent extension of three dimensions which we call empty space, and we assume that every real body must occupy more or less of this real space. In geometry we think we are studying the properties of this real space, which are not due to our physiological nor our psychological character, but are impersonal and have objective validity. The success which our deductions meet in innumerable predictions and calculations thatare afterward verified in the construction of engineering feats which are marvels of the ages leads us to believe that we have found eternal truths in the world of nature as imperishable as those of number. Geometry appeared t...


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Product Details
  • ISBN-13: 9780217011969
  • Publisher: General Books
  • Publisher Imprint: General Books
  • Height: 246 mm
  • No of Pages: 58
  • Series Title: English
  • Weight: 122 gr
  • ISBN-10: 0217011969
  • Publisher Date: 02 Feb 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Spine Width: 3 mm
  • Width: 189 mm


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