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Re:Banach-Tarski and the Paradox of Infinite Cloning by bobthechef on Sunday August 29, 2021 @11:38AM (#28347557)
So quantity, structure, formal necessity don't exist?

Mathematics has nothing to do with laws of physics. Even if the laws of physics[0] were different, these mathematical[1] truths would remain the same.

[0] Laws of physics don't actually exist. They're shorthand generalizations about features of particulars. The notion of some kind of abstract disembodied "laws" that somehow "govern" everything is absurd.

[1] For clarify: mathematics is a field that studies such things.

Re:Banach-Tarski and the Paradox of Infinite Cloning by throwawaygal7 on Sunday August 29, 2021 @05:44PM (#28350747)
I have never understood the opposition to the law of physics you seem to hold.

What is the alternative? That we merely observe rigid patterns that are baked into physical reality? Isn't whatever is 'baked in' more or less a 'law of physics'?

If these are just 'brute facts' are they not then 'laws'? Maybe governance is too strong an word for the correspondence but what is the alternative?

Re:Banach-Tarski and the Paradox of Infinite Cloning by snet0 on Sunday August 29, 2021 @12:10PM (#28347903)
Laws in the physics sense don't govern, though, they describe. It's akin to saying moral laws don't decide what's immoral, they simply describe it.

Given that, "laws of physics" are certainly describable. We simply write the formulae that tell us what the next state of the dynamical system is. They are ways of delimiting what is physically possible, given the current state of the art.