On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam <terren.suy...@gmail.com>wrote:

> Rex,
>
> 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.

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 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?



> 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.

Could there be intelligences who start from vastly difference premises, and
use vastly different rules of inference, and draw vastly different
conclusions?

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
thing?

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?

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?

Rex

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