On 19 Jan 2015, at 08:27, meekerdb wrote:
On 1/18/2015 10:05 PM, Jason Resch wrote:
On Sun, Jan 18, 2015 at 3:48 PM, meekerdb <[email protected]>
wrote:
On 1/18/2015 9:16 AM, Jason Resch wrote:
If you assume it is true (independent of our ability or anything
in the universe's ability to conceive it), then it is true
independently of the universe, and hence you get arithmetical
realism.
No, you just keep assuming that true=real. The truths of arithmetic
are about the relation of numbers. And they are true whether or
not the numbers exist, just as Dr. Watson is Holmes sidekick.
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.
Bruno
Brent
In any case, while I agree there is always room to doubt the
existence of the numbers and their relations, it is the most
plausible explanation for existence that I have encountered.
Jason
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