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I'm studying William James. I'm mainly interested in his Radical Empiricism and Pluralism. I really like his views but I need some clarification on what is his position on conceptions that are not clearly related to perceptions.

For example consider the creation of the imaginary numbers. I cannot see how these can be abstracted from perceptions. Can someone point me to paragraphs of James on this?

In my understanding abstract constructions like the imaginary numbers are internal experiences that don't need to be related to natural phenomena. The imaginary numbers were not needed in science until quantum mechanics and, of course, were created before our experiences with subatomic phenomena.

  • Can't help you on James. But when you are standing up facing east and you make a quarter turn clockwise to face north, you are multiplying by i. If you turn again you are now facing the direct opposite of where you started: i^2 = -1. If you turn twice more you're back where you started: i^4 = 1. The number i is a perfectly sensible aspect of everyday experience. It just took people a long time to develop the proper geometric insight. – user4894 Jul 23 '18 at 18:39
  • You can say that after the abstract, theoretical work of the past created the imaginary numbers. Turning around in your feet will not show you i . I find it hard to imagine that any sense impression helped mathematicians to develop this. – Juan Manuel Jones Volonté Jul 23 '18 at 23:10
  • Which part of "It just took people a long time to develop the proper geometric insight" didn't anticipate the point you made? You are slyly swapping in "helped to develop" with "is". – user4894 Jul 24 '18 at 17:14
  • the same part that in "abstract constructions like the imaginary numbers are internal experiences that don't need to be related to natural phenomena" didn't anticipate your answer. thanks – Juan Manuel Jones Volonté Jul 24 '18 at 22:18

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