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Ideas for 'Review of Tait 'Provenance of Pure Reason'', 'Physics and Philosophy' and 'Timaeus'

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2 ideas

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
If it can't be expressed mathematically, it can't occur in nature? [Heisenberg]
     Full Idea: The solution was to turn around the question How can one in the known mathematical scheme express a given experimental situation? and ask Is it true that only such situations can arise in nature as can be expressed in the mathematical formalism?
     From: Werner Heisenberg (Physics and Philosophy [1958], 02)
     A reaction: This has the authority of the great Heisenberg, and is the ultimate expression of 'mathematical physics', beyond anything Galileo or Newton ever conceived. I suppose Pythagoras would have thought that Heisenberg was obviously right.
6. Mathematics / C. Sources of Mathematics / 8. Finitism
If functions are transfinite objects, finitists can have no conception of them [Parsons,C]
     Full Idea: The finitist may have no conception of function, because functions are transfinite objects.
     From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §4)
     A reaction: He is offering a view of Tait's. Above my pay scale, but it sounds like a powerful objection to the finitist view. Maybe there is a finitist account of functions that could be given?