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Physical Laws Are Not Axioms

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Posted by Clerk on June 22, 2004 12:13:00 UTC

To quote you:
"the physical system of axioms-the physical laws"

The problem with your thinking is that you consider phycal laws to be axioms. They are not.

As you say they are mathematical relationships, but they are not axioms. They actually are equations, like Maxwell's equations, from which you can derive the behaviour of electromagnetic waves given boundary and initial conditions. These are solutions to Maxwell's equations.

Goedel's incompleteness theorem applies to the mathematics used to derive solutions to the equations. The implication, and I do not know if this is really true, is that for systems of mathematics,like equations having a host of solutions for a variety of boundary conditions, there are still some solutions possibilities that cannot be derived from the equations. These possibilities are known as emergent and have been detected physical. So the math is closely related to physical reality.

I will not go any further unless you can understand what I have already written


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