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
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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. ;-)

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




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Onward!

Stephen

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