On 18 Dec 2012, at 22:12, Stephen P. King wrote:
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
--
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. ;-)
OK for politics, but not for science. That would be worst than
solipsism, that would be nationalism, that is collective solipsism. In
science all argument per authority are invalid, and to invoke majority
would be the best way to kill the possibility of progress. history
shows that in science, very often, those who are "right" are a
minority for some period, which is normal in front of the unknown.
We have many entities that are available to agree that 2+2=4
(for all sizes of 2 and 4 that we can find),
People agree that 2+2=4 because it is a simple truth which follow from
simple definition.
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.
Measure theory has been invented to define measure on all kinds of
sets, especially infinite one. (Riemann measure, Lebesgues, etc.).
Bruno
--
Onward!
Stephen
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