Combining Philosophers

Ideas for Melvin Fitting, Stephen Wolfram and B Russell/AN Whitehead

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2 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts

18248	A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro]
	Full Idea: For Russell the real number 2 is the class of rationals less than 2 (i.e. 2/1). ...Notice that on this definition, real numbers are classes of rational numbers.
	From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Thinking About Mathematics 5.2

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics

20660	At one level maths and nature are very similar, suggesting some deeper origin [Wolfram]
	Full Idea: At some rather abstract level one can immediately recognise one basic similarity between nature and mathematics ...this suggests that the overall similarity between mathematics and nature must have a deeper origin.
	From: Stephen Wolfram (A New Kind of Science [2002], p.772), quoted by Peter Watson - Convergence 17 'Philosophy'
	A reaction: Personally I think mathematics has been derived by abstracting from the patterns in nature, and then further extrapolating from those abstractions. So the puzzle in nature is not the correspondence with mathematics, but the patterns.