On 12/20/2012 4:29 AM, Bruno Marchal wrote:


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.

Dear Bruno,

Could you stop with your anthropocentric bias for once in your life? "Everyone", as I used the word, about is not just human beings. Yes, it is collective solipsism. It has a name: Multisolipsism.

It is we we consider all entities that are capable of being defined as having a 1p and that are capable of communication with each other. This includes, for instance, every electron, every quark, every proton, every atom, every molecule, every animal, every planet, every solar system, every galaxy, ... any entity capable of having a 1p and that their individual 1p includes aspects that are bisimilar to aspects of the 1p of others. What you need to understand is that the mereology of the systems that can have a 1p cannot be confined to a unique partition of some irreducible set of primitives in a regular or well founded way. You need to understand the statistical implication of non-well foundedness!

The "nationalist allegiance" here, to use your strange metaphor, would be to the Reality that all of them - the entities with 1p - participate in. Did you notice the huge number of entities that have to be considered, in my discussion with LizR? As it stands, we need to consider at least 10^23 entities just to take into account smallish phenomena at our human level, because that is the average number of entities that are at our level of substitution as an ensemble of equivalence. This is well known in chemistry and engineering...

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.


Rubbish, you are being a hypocrite, invoking that "truth from authority" crap. I am a minority of one here. So my minority status beats your minority status every day all day. Do we really need to "go there" and act like children? You really should take a class on statistic taught by an engineer and not a cloistered academic mathematician. I am merely trying to make the principles of COMP useful to an engineer, because, as I have been explaining to LizR, I see a use for comp.


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.

Sure, and those people don't notice that the universe is not "everything that I can see with my eyes, touch with my hands, hear with my ears, smell with my nose, etc." The universe is far far more than we can distinguish at our level of substitution which is a function of our very coarse measurements. I am considering way more than "people". I am considering any and every entity with a 1p. If you believe that only people have a 1p, then well....


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.).

I understand that and in the process of the invention (or discovery) many things are completely neglected. Things like the laws of thermodynamics.


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Onward!

Stephen

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