PHIL 2100 Lecture Notes - Lecture 3: Formation Rule, Bertrand Russell, Logical Positivism
9 May 2016
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Proof and demonstration: proofs or demonstrations in mathematics. The sum of any two even integers is even. Then, x = 2a and y = 2b, for some integers a and b (by evenness). So x + y = 2a + 2b. By distributivity, 2a + 2b = 2(a + b), and so x + y = 2a + 2b = 2(a + b). Therefore x + y = 2(a + b) and by evenness it follows that x + y is even. (cid:3) Evenness: an integer x is even if and only if x = 2k, for some integer k. Distributivity: z(x + y) = zx + zy. Symbolic notation: given any two numbers, the result of adding them together in one order is the same as the result of adding them together in the reverse order, x + y = y + x. And have a rigorous method of expressing and computing any truth.
