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View Diary: Math mania: Why teach math? Why sing? (92 comments)

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  •  Some "traditional" questions have become (1+ / 0-)
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    irrelevant as scientific discovery replaces philosophical inquiry.  Over time, the Empiricists win.

    •  I don't know if I agree with that. (4+ / 0-)
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      haileysnana, MajorFlaw, plf515, cynndara

      Philosophers remain divided, of course, as ever.  It's said that mathematicians are platonists throughout the work week and formalists on Sundays.  Similarly, I'd bet that most scientists are realists throughout the week and empiricists on Sundays.

      •  Not sure I follow. (2+ / 0-)
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        haileysnana, plf515

        Scientists are by definition empiricists.  It's the difference between scientific method and philosophical speculation.  Why speculate when there is evidence.  When Plato, Aristotle etc. tried to understand  the cosmos they could only turn inward.  Now we have Astronomy.  

        •  IF (3+ / 0-)
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          MajorFlaw, play jurist, plf515

          you can get far enough away from the city to actually see the stars at night. Which is not a bad metaphor for clearing out the musty smog of social illusions/delusions before getting down to clear perception and thought.

          There are a HELL of a lot of social illusions centered around Science, too.

        •  We have different ideas of "empiricism". (4+ / 0-)
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          haileysnana, MajorFlaw, plf515, cynndara

          Of course, science by definition involves subjecting theories to observational scrutiny.  If that's what you mean by "empiricist" then you are correct.  That seems to be the common meaning of the term for a lot of people.  In philosophy specialized meanings have arisen.  The distinction between a realist and empiricist (very, very roughly) is that a realist thinks observation provides evidence that things like atoms, electrons, quarks, etc. actually exist while the empiricist holds that we never have reason to believe anyhting more than that our theory is empirically adequate.  The empiricist thinks of things we cannot directly observe (things like electrons) as theoretical constructs not real entities.

          Theoretical phycists, btw, still do plenty of inward turning.  You are correct that they also turn outward and aim to check their theories by observation (hopefully, eventually, etc--see string theory).  But I think that the contrast between Plato/Aristotle, etc. is not as strong as you might think.  In Physics Aristotle opposede Parmenides on motion and change because the fact of change was evident to the senses, for example.  Plato and the Pythagoreans founded a research program of using mathematics to study the world.  It's true that they were less advanced than we are, but it is not clear that our advances are due to fundamental methodological differences so much as time and technology.

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