Numbers, Variables and Mr. Russell's Philosophy

Numbers, Variables and Mr. Russell's Philosophy

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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. 1915 edition. Excerpt: ...of the variable have commonly an arrangement in order--an arrangement which with some variables is immutable but with others is not. An arrangement under which the quantities are consecutive may, as we have said, occur, but other arrangements are common, and some variables are not even capable of having their quantities arranged in a sequence. So it is certainly not a happy thought to bring succession into the definition of a variable. use of the name or symbol of a variable, it is not surprising that he should confound the names of variables with ordinary class names. There is really an analogy between such a proposition as "Every y having an x corresponding to it is equal to or identical with the square of the corresponding x," and a proposition in which occurs the class name of a class of quantities formed solely for the study of properties which the quantities of that class possess as individuals. Be it noted however that the closest analogy is not found with those general propositions of mathematics which Mr. Russell takes as typical propositions involving the symbols of variables. Thus consider a--b = b + a which, when put forward as enunciating the commutative law of addition, is a fair example of these general propositions. This should be read: "Every a when any b of the same sort53 is added to it gives a sum equal to or identical with the sum of the same b as before plus the same a as before." Here we have what might be called an equation of sameness; in reading it we are obliged to specify that the second a taken is the same as the first a, and that the second b is also the same as the first b. Otherwise the proposition would not be true; for a and b are both general class symbols each of which takes more

Product details

  • Paperback | 28 pages
  • 189 x 246 x 2mm | 68g
  • United States
  • English
  • black & white illustrations
  • 1236911512
  • 9781236911513