Knowledge Volume 4

Knowledge Volume 4

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1883 edition. Excerpt: ...the definitions of geometry is not strictly true; there exist no real things exactly conformable to the definitions. There exist no real points without magnitude, no lines without breadth, nor perfectly straight, no circles with all their radii exactly equal, nor squares with all their angles perfectly right. It will be said that the assumption does not extend to the actual but only to the possible existence of such things. I answer that, according to every test we have of possibility, they are not even possible. Their existence, so far as we can form any judgment, would seem to be inconsistent with the physical constitution of our planet at least, if not of the universal (sic). To get rid of this difficulty and at the same time to save the credit of the supposed system of necessary truth, it is customary to say that the points, lines, circles, and squares which are the subjects of geometry exist in our conceptions merely, and are parts of our minds, which minds, by working on their own materials, construct an d priori science the evidence of which is pnrely ment al and has nothing to do with outward experience. By howsoever high authority this doctrine haB been sanctioned, it appears to me psychologically incorrect. The points, lines, and squares which any one has in his mind are (as I apprehend) simply copies of the points, lines, and Bquares which he has known in his experience. Our idea of a point I apprehend to be simply our idea of the minimum visible--the small portion of surface I think it may be at once conceded that the truths of geometry are truths precisely because they relate to and express the properties of what Mill calls "purely imaginary objects." That these objects do not exist in Mill's sense, that they do more

Product details

  • Paperback | 442 pages
  • 189 x 246 x 23mm | 785g
  • United States
  • English
  • black & white illustrations
  • 1236801776
  • 9781236801777