Some reductions are impossible because the functions are not computable, even in Newtonian mechanics. The set of computable functions is a miniscule (infinitesimal) subset of the set of functions. I have several papers on the dynamical basis of this (necessary and sufficient dynamical conditions, though they are not computable if the function is not computable) on my web page. Most have emergence in the title.
John From: Clark Goble [mailto:cl...@lextek.com] Sent: Wednesday, 12 April 2017 6:32 PM To: Peirce-L <PEIRCE-L@list.iupui.edu> Subject: Re: [PEIRCE-L] Laws of Nature as Signs On Apr 12, 2017, at 8:15 AM, John F Sowa <s...@bestweb.net<mailto:s...@bestweb.net>> wrote: CG I’d more put it that biological descriptions typically aren’t reducible to chemistry or physics... attempting to make the reduction... did perhaps help in getting biologists to think more carefully about the type of descriptions they make. You could say the same about "reducing" meteorology to computational physics. Weather predictions today are far more reliable than they were 50 years ago. But it's good to have an alternate date when you're planning a picnic. Yes that’s the exact way I think about it. It’s a practical issue not a metaphysical one. Further non-linear dynamics (not always at work) can make some reductions as difficult as some predictions. A little error can sometimes spiral out of control such as with a double pendulum.
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