A System of Synthetic Philosophy (Volume 5) - Bookswagon UAE
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A System of Synthetic Philosophy (Volume 5)

A System of Synthetic Philosophy (Volume 5)


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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 IV. IMPERFECT AND SIMPLE QUANTITATIVE REASONING. 284. Ability to perceive equality implies a correlative ability to perceive inequality: neither can exist without the other. But though inseparable in origin, the cognitions of equality and inequality, whether between things or relations, differ in this; that while the one is definite the other is indefinite. There is but one equality; but there are numberless degrees of inequality. To assert an inequality involves the affirmation of no fact, but merely the denial of a fact; and therefore, as positing nothing specific, the cognition of inequality can never be a premiss to any specific conclusion. Hence, reasoning which is perfectly quantitative in its results, proceeds wholly by the establishment of equality between relations, the members of which are either equal or one a known multiple of the other. Conversely, if any of the magnitudes standing in immediate relation are neither directly equal nor the one equal to so many times the other; or if any of the successive relations which the reasoning establishes are unequal; the results are imperfectly quantitative. The truth is illustrated in that class of geometrical theorems in which it is asserted of some thing that it is greater or less than some other; that it falls within or without some other; and the like. Let us take as an example the proposition? Any two sides of a triangle are together greater than the third side. Let A B C be a triangle; any two sides of it are, together, greater than the third side; namely, B A, A C, greater than B C; and A B, B C, greater than A C; and B C, C A, greater than A B. Produce B A to D, and make A D equal to A C; and join D C. Because D A is equal to A C, the angle A D C is equal to the angle A C D; but the...


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Product Details
  • ISBN-13: 9780217906876
  • Publisher: General Books
  • Publisher Imprint: General Books
  • Height: 246 mm
  • No of Pages: 198
  • Spine Width: 11 mm
  • Width: 189 mm
  • ISBN-10: 0217906877
  • Publisher Date: 03 Jan 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 363 gr


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