Le 17-août-06, à 00:14, complexitystudies a écrit :
>
>> Again we are discussing the arithmetical realism (which I just
>> assume).
>
> A bold assumption, if I may say so.
Frankly I don't think so. Set platonism can be considered as a bold
assumption, but number platonism, as I said you need a sophisticated
form of finitism to doubt it. I recall it is just the belief that the
propositions of elementary arithmetic are independent of you. Do you
sincerley belief that 37 could be a non prime number? Or that the
square root of 2 can equal to a ratio of two integers?
Or that if you run a program fortran it could neither stop nor not
stop? (When all the default assumption are on, to evacuate contingent
stopping of a machine implemented in some deep story)?
> But my exploration into cognitive neuroscience has exposed to me
> how mathematical thinking comes about, and that it is indeed not
> separable from our human brains.
I have not yet seen a book on human brain which does not presuppose the
understanding of the natural numbers. Note just for using the index,
but in the neuronal explanation themselves, implicitly or explicitly.
Eventually with comp the brain itself appears as a construct of the
mind. The mathematical mind of the "Lobian" machines. Those are the
self-referentially correct universal (sufficiently chatty) machines.
> Numbers are symbols we create in our minds to communicate with
> fellow individuals about things of importance to us.
Numbers are not symbol. Symbols can be used to talk about numbers, but
they should not be confused with numbers.
> To paraphrase Descartes very liberally:
> We group, therefore we can count.
>
> Our act of arbitrary grouping (made a bit less arbitrary by
> evolution, which makes us group things which are good to
> our survival, like gazelles and spears or berries) let's us
> count and communicate the number.
The notion of "same number" seems to have occur much before we
discovered counting. Farmers have most probably learn to compare the
size of the herds of sheep without counting, just by associating each
sheep from one herd to the another. But this as nothing to do with the
fact that sheeps were "countable" before humans learn to count it.
Humans and brains learn to count countable things because they are
countable.
I think you are confusing the subject or object of math, and the human
mathematical theories, which are just lantern putting a tiny light on
the subject.
If numbers and their math was really invented, why should
mathematicians hide some results, like Pythagoras with the
irrationality of the square root of two, ... As David Deutsch says:
math kicks back.
> For the universe "one apple" may not exist, because in effect
> there are only quarks interacting. And at this level indeterminacy
> strikes mercilessly, making it all but meaningless to count quarks.
You will not find a book explaining that "meaninglessness" without
taking for granted the idea of counting at the start.
>
> Also, concepts like infinity are most definitely not universal
> concepts "out there", but products of our mind.
I doubt any mind could ever produce infinity.
> Of course, symbolisms are arbitrary, but physical instantiation makes
> all the difference.
(note that my goal consists in explaining "physical instantiation"
without using "physical things" at all. My point is that if we
postulate comp, then we have to do this).
>
>> Note that if you understand the whole UDA,
>
> Unfortunately, not yet, but I'm reading!
Ah, ok. UDA mainly shows that the mind-body problem is two times more
difficult than most materialist are thinking. Indeed, with comp, matter
can no more be explained by postulating a physical world. I let you
discover that, and feel free to ask questions if you have a problem
with UDA.
>
>> you should realize that the
>> price of assuming a physical universe (and wanting it to be related
>> with our experiences *and* our experiments) is to postulate that you
>> (and us, if you are not solipsistic) are not turing emulable. No
>> problem.
>
> Why is that so? Could you clarify this issue?
It is really the point of the UDA. It shows that computationalism (the
idea that I am a digitalizable machine) is incompatible with "weak
materialism" (the idea that there is a primary stuff or matter or
aristotelian substances).
> Absolutely. But I think we have to start with our assumptions and
> try to scrutinize them very carefully. After all, we want to devote
> our minds to problems arising out of them during our lives, and
> thus the initial choice should not be made rashly, but only after
> careful review of our current body of knowledge.
OK, but don't forget that here the idea is also to get some
contradiction from hypotheses, so as to abandon them.
But until now, comp leads only to weirdness, not contradiction. And
then that weirdness seems to explain the quantum weirdness ...
Intuitively and qualitatively (already by UDA), and then technically
through the interview of some universal turing machine.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Thu Aug 17 2006 - 10:05:50 PDT