On 12/16/2018 2:04 PM, Jason Resch wrote:
On Sun, Dec 16, 2018 at 4:01 PM Bruce Kellett <[email protected] <mailto:[email protected]>> wrote:On Mon, Dec 17, 2018 at 8:56 AM Jason Resch <[email protected] <mailto:[email protected]>> wrote: On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker <[email protected] <mailto:[email protected]>> wrote: But a system that is consistent can also prove a statement that is false: axiom 1: Trump is a genius. axiom 2: Trump is stable. theorem: Trump is a stable genius. So how is this different from flawed physical theories? Physical theories do not claim to prove theorems - they are not systems of axioms and theorems. Attempts to recast physics in this form have always failed.Physical theories claim to describe models of reality. You can have a fully consistent physical theory that nevertheless fails to accurately describe the physical world, or is an incomplete description of the physical world. Likewise, you can have an axiomatic system that is consistent, but fails to accurately describe the integers, or is less complete than we would like.
But it still has theorems. And no matter what the theory is, even if it describes the integers (another mathematical abstraction), it will fail to describe other things.
ISTM that the usefulness of mathematics is that it's identical with its theories...it's not intended to describe something else.
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