Robert and Auke, I agree with the points you made. But I believe that a good way to put an end to the "false debate" is to broaden the dichotomy to an open-ended diversity. Every branch of the sciences (i.e., every branch in Peirce's 1903 classification) has methods that are specialized for the subject matter. For that reason, I changed the subject line to "Methodology" -- Methodeutic would be an acceptable term, but Peirce's discussion of that term has too few examples to support all the issues that need to be considered. For example, the methods for studying linguistics, archaeology, chemisty, astronomy, and medicine are radically different. But they do have a common foundation: observation, induction, abduction, deduction, testing, and repeat. Although the theorems of mathematics are determined by deduction, mathematical discovery is just as empirical as any other science. For example, Euler: "The properties of the numbers known today have been mostly discovered by observations... long before their truth has been confirmed by rigid demonstrations." Laplace: "Even in the mathematical sciences, our principal instruments to discover the truth are induction and analogy." Paul Halmos: "Mathematics this may surprise or shock some is never deductive in its creation. The mathematician at work makes vague guesses, visualizes broad generalizations, and jumps to unwarranted conclusions. He arranges and rearranges his ideas, and becomes convinced of their truth long before he can write down a logical proof... the deductive stage, writing the results down, and writing its rigorous proof are relatively trivial once the real insight arrives; it is more the draftsmans work not the architects. * * Halmos, Paul R. (1968) Mathematics as a creative art, _American Scientist_, vol 56, pp. 375-389. There is, of course, much more to be said. John
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