On 12/18/2012 3:28 PM, meekerdb wrote:
On 12/18/2012 10:27 AM, Stephen P. King wrote:
On 12/18/2012 12:51 PM, meekerdb wrote:
On 12/17/2012 11:51 PM, Quentin Anciaux wrote:
Which implies there is some measure of 'true' other than
'provable'.
What do you mean ? that provable true is truer ?
No, just that there must be propositions we judge to be true that
aren't provable.
Brent
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Hi Brent,
How do we defend such "propositions we judge to be true that
aren't provable" from claims of subjectivity?
Of course being provable does eliminate subjectivity - it just pushes
it back to the axioms. Generally what we mean by objective is that
there is almost universal subjective agreement, e.g. given any number
x there is a successor of x not equal to x. So if there is some
proposition of arithmetic that everyone agrees must be true, then it's
as 'objective' as the axioms and as 'objective' as anything proven
from the axioms even though it is not provable from them.
Brent
Hi Brent,
You have written the magic words! "... if there is some proposition
of arithmetic that everyone agrees must be true". This is exactly what I
am talking about with my banter about "truth obtaining from agreements
between mutually communicating observers". We remove the subjectivity of
the individual by spreading it out over many individuals. When we have
many individuals in agreement, the disagreement by one of them is
inconsequential. This is the laws of large numbers at work. ;-)
We have many entities that are available to agree that 2+2=4 (for
all sizes of 2 and 4 that we can find), 2^90 entities at least! Every
particle that exist in our universe that can hold a bit of data and all
possible combinations of them that agree on some "laws of physics". If
we take this finite number to be infinite then things change; we are not
able to take about measures that are relative to agreements in
populations of entities and must be capable of comprehending that simple
fact.
Granting ourselves imaginary powers of omniscience or to some
imaginary Platonic proxy does not change anything when we are
considering the degeneracy of the very idea of a measure in the case of
infinities.
--
Onward!
Stephen
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