On Tue, Sep 18, 2012 at 10:19 PM, Rex Allen <rexallen31...@gmail.com> wrote:
> On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam <terren.suy...@gmail.com>
>> Do you have a non-platonist explanation for the "discovery" of the
>> Mandelbrot set and the infinite complexity therein?
> I find fictionalism to be the most plausible view of mathematics, with all
> that implies for the Mandelbrot set.
I'm curious about what a plausible "fictionalist" account of the
Mandelbrot set could be. Is fictionalism the same as constructivism,
or the idea that knowledge doesn't exist outside of a mind?
> But ;et me turn the question around on you, if I can:
> Do you have an explanation for how we "discover" mathematical objects and
> otherwise interact with the Platonic realm?
> How is it that we are able to reliably know things about Platonia?
I think just doing logic and math - starting from axioms and proving
things from them - is interacting with the Platonic realm. It is
reliable because such proofs are necessarily valid no matter what sort
of computational agent is computing them. Bruno really takes it to the
next level though when he talks of "interviewing ideally correct
machines" and treating them as entities (strictly platonic, of course)
that can talk about what they can prove (believe).
> I would have thought that quarks and electrons from which we appear to be
> constituted would be indifferent to truth.
> Which would fit with the fact that I seem to make a lot of mistakes.
> But you think otherwise?
I didn't understand the above... what do quarks and electrons have to
do with arithmetical platonism?
>> How can you make
>> sense of that in terms of the constructivist point of view that you
>> are (I think) compelled to take if you argue against arithmetical
>> platonism? It seems obvious that all possible intelligences would
>> discover the same forms of the Mandelbrot so long as they iterated on
>> z' = z^2 + c, but maybe I am missing the point of your argument.
> I will agree with you that all intelligences that start from the same
> premises as you, and follow the same rules as inference as you, will also
> draw the same conclusions about the Mandelbrot set as you do.
> However - I do not agree with you that this amenable group exhausts the set
> of all *possible* intelligences.
I only meant that all possible intelligences that start from a
mathematics that includes addition, multiplication, and complex
numbers will find that if they iterate the function z' = z^2 + c, they
will find that some orbits become periodic or settle on a point, and
some escape to infinity. If they draw a graph of which orbits don't
escape, they will draw the Mandelbrot Set. All possible intelligences
that undertake that procedure will draw the same shape... and this
seems like discovery, not creation.
> Could there be intelligences who start from vastly difference premises, and
> use vastly different rules of inference, and draw vastly different
Of course, but then what they are doing doesn't relate to the Mandelbrot Set.
> If not - what makes them impossible intelligences?
> What are the limits of belief, do you think? Is there any belief that is so
> preposterous that even the maddest of the mad could not believe such a
I don't think so... based on my understanding of how mad "maddest of
the mad" can get.
> And if there is no such belief - then is it conceivable that quarks and
> electrons could configure themselves in such a way as to *cause* a being who
> holds such beliefs to come into existence?
I'm guessing you meant to say "and if there is such a belief...". I'm
having a tough time understanding where you're going with this... it
seems like an interesting line of questions, but I have no idea how it
relates to what we were discussing.
> And if this is beyond the capacity of quarks and electrons, does it seem
> possible that there might be some other form of matter with more exotic
> properties that might be up to the task?
> And if not - why not?
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