Le 11-mars-06, à 10:59, Georges Quénot wrote (to John):

<snip>


>
> Yes also and indeed, the way of thinking I presented
> fits within a reductionist framework. Nobody is required
> to adhere to such a framework (and therefore to the way
> of thinking I presented). If one rejects the reductionist
> approach, all I can say isn't even worth reading it for
> him. And, again, all of this is pure speculation.


Personally I disagree with any reductionist approach. But, given that I 
agree with many of your statement, perhaps we have a "vocabulary" 
problem.
I do even believe that a thoroughly "scientific attitude" is 
automatically anti-reductionnist, whatever theories are used. Science, 
being modest, just cannot be reductionist(*).
Even the numbers are nowadays no more completely reductible to any 
"unifying theory".
Only pseudo-scientist (or some scientist during the week-end) can be 
reductionist.

(*) ... and this is reflected into the fact that no loebian machine can 
ever believe (assert, prove) any proposition of the form ~Bp.

>
>> A physicist once retorted: "I can live with paradoxes"
>> well, I cannot. I rather rely on MY common sense, even
>> if it is "not on the level".
>
> You are free to rely on whatever you want. However, it
> seems that we have no choice about the world we live in.


OK. You are a realist like I am.


> I would say that we discovered them. The argument (a
> weak one I concede) is that we did not have so much
> freedom while doing so. We find and proved that the
> Fermat's conjecture was true and we *could not* find
> that is was false. This constraint is intemporal and
> it exists whether there are men or not and even
> whether there is something or not (but there cannot
> be nothing because there is least this constraint).
> The set of such constraints is likely to include or
> define that natural numbers themselves.


I agree.


>
>
>>> Let's also consider the possibility that the
>>> universe in which we live strictly follows some
>>> "mathematical rules" and that it is completely
>>> determined by them (this is another speculation).
>>
>> I don't think this is attributable to English: in all
>> languages people speak in reverse: The universe (or
>> whatever Bruno may call it) does not FOLLOW any rules
>> that humans derive from their ways of thinking -
>> explaining the (easily misunderstood) observations. We
>> observe, evaluate (right or wrong) and deduct "rules"
>> (again right or wrong). As long as they do not bounce
>> into contradiction, we pride ourselves by "nature is
>> following our rules". When the tachyons showed higher
>> speed than 'c' the verdict was "wrong observation",
>> not a speed exceeding Einstein's assumed limit for
>> nature.
>
> This is a speculation. It might be that the universe
> in which we live is completely ruled by mathematical
> laws. Indeed one can doubt of that or believe it but I
> can't see how this can be either proved or refuted.


Proving or refuting is always relative. (Unlike the notion of 
computability which can be absolute (Church thesis)).
Actually, in the "theory" comp (or weaker), the physical (the machine 
observable) can be shown to be necessarily mathematical.



>
>>> This is equivalent to say that this universe is
>>> isomorphic to one of the above mentionned "higher
>> level objects".
>>
>> Nice words. Do they mean something?
>
> This means something to me. I would say that meaning
> is relative to individuals or group of individuals.
> I understand that this might not mean anything to
> other people just as what other people sometimes
> refer to has no precsie meaning to me.


Some mathematical realist seems to believe that the physical universe 
could be a mathematical object among others mathematical objects. With 
comp the relation is more that the physical is a mode of the 
mathematical. It is the mathematical as anticipable from first person 
plural point of view of locally finite entities.  As a mode it has a 
(modal) mathematical structure itself. This made the physical 
distributed in some way in the mathematical.  Not just a simple 
ownership relation.



> That was the idea. That particles might not exist
> as such does not prevent the universe to have a
> mathematical structure and I mentionned that this
> was a (possibly very) simplified view.


OK with me, then; except that the word "universe" is ambiguous. If you 
defined it as the structure making coherent our sharable observations, 
then it has indeed a mathematical structure once you have a good 
definition of "observer" and "observation".

Bruno


http://iridia.ulb.ac.be/~marchal/


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