Le 02-oct.-06, à 18:03, markpeaty a écrit :
> I hope you will excuse my butting in here, but I was passing through on
> a different mission
> and became disturbed by reading some earlier posts of this thread.
You are welcome.
> My 2 cents worth:
> I tend to think that David Nyman has the more sceptically acceptable
> slant on this. Mathematics and logic are constructions of the human
> brain. They are extremely useful, in appropriate contexts, because they
> allow effective, efficient and economical representations of processes
> in the world.
So you assume a primitive world. From this I can already infer you have
to distrust the computationalist hypothesis in the cognitive science.
> There is no particularly good reason however to think that mathematical
> objects exist outside of human brains or phenotypic extensions such as
> computers. I think it IS fair to say though that, for example, numbers
> and formulae written on a page or blackboard are literal extenstions of
> the constructs within the active mathematical mind.
I agree. That is what makes the human mind "turing universal". When it
lacks memory space it extends itself through the use of pebble, wall,
Now, are you really saying that mathematical truth (not the
mathematical expression that humans have developed to talk about that
mathematical truth) is a human's construct. Would you say that the
number 17 was not a prime number at the time of the dinosaurs?
In which case you distrust the "Arithmetical realism" part of comp, and
you are remarkably coherent.
> That so much of what occurs in 'the world' CAN be represented by
> numbers and other mathematical/logical objects and processes, is better
> expained by assuming that the great 'IT' of noumenal nature is actually
> made up of many simple elements [taken firstly in the general sense].
> This underlying simplicity which yet combines and permutates itself
> into vast complexity, is something we infer with good reason - it
This would make sense if you can specify those simple elements.
Have you heard about Bell, Kochen and Specker and other weird facts
predicted and verified from quantum mechanics. I am afraid such simple
elements are already rule out empirically, eve, with the Many World
Now even mentioning quantum mechanics, I refer to my work (see the URL)
for an argument showing that the hypothesis that we are turing emulable
at some level (whatever that level) entails the laws of physics have to
be explained without assuming a physical primitive world.
Of course this refutes the current Aristotelian Naturalistic paradigm,
but does rehabilitate Plato and the neoplatonist conception of matter
> But you cannot DEDUCE from it that numbers and other
> mathematical objects exist 'out there', except in those particular
> regions of space time that happen now to be mathematically active
I do not believe that a number can exist "somewhere". It can be
implemented or incarnate somewhere, like a chess game, but that is
Also, this is assumed in the comp hyp, nobody pretends that we can
deduce that number exist. Actually it can be proved about the natural
number in particular that no theories at all can prove that they exist.
All theories enough rich to talk about numbers have to assume them
explicitly or implicitly.
But they does not need to exist out there or elsewhere: this is a
category error. Numbers are not located in time or space, nor are they
eternal. Poetically we could say that numbers and their relations are
beyond time and space. But I recall, this is among the comp assumption.
What we discussed is the fact that if we take comp seriously enough
then physics can be derived from number theory/ computer science.
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