On 1/19/2015 10:01 AM, Bruno Marchal wrote:
If it is true that 8 is a composite, doesn't that require the existence of a number
between 1 and 8 which divides 8?
Only in the mathematicians sense of "exist" which means "satisfies an expression", Dr
Watson satisfies the expression "X is a sidekick of Holmes."
Only in a model (reality) where Holmes and Watson exist.
That model might be different from our intended model of the physical reality, making
this into fiction, but in the context of that fiction, Watson does exist.
Obviously, the theory does not applied to our plausible physical reality, but is used
just because it is recreatively pleasant, and we read for the fun.
That is not so for the numbers, you get problem if you attribute false property to some
number, or if you are wrong in converting units of measurement, etc. Numbers relation
kicks back, even when not physically implemented. You can't divide a non null number by
zero in N or in R, you get catastrophic results if you try.
You get problems if you attribute false properties to Sherlock Holmes and you try to join
"The Bailey Street Irregulars". But your theory depends on the numbers being infinite and
I don't think anything in physics requires that - at least not yet. It's just a
convenience, albeit a great one.
Incidentally, what do you think of super-Turing computation?
http://binds.cs.umass.edu/papers/2013_Siegelmann.pdf
Brent
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