On Sep 21, 2012, at 8:13 AM, Rex Allen <rexallen31...@gmail.com> wrote:
On Wed, Sep 19, 2012 at 12:27 AM, Jason Resch <jasonre...@gmail.com>
wrote:
On Sep 18, 2012, at 9:19 PM, Rex Allen <rexallen31...@gmail.com>
wrote:
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?
We study and create theories about objects in the mathematical realm
just as we study and create theories about objects in the physical
realm.
So in the physical realm, we start from our senses - what we see,
hear, feel, etc.
From this, we infer the existence of electrons and wavefunctions and
strings and whatnot. Or some of us do. Others take a more
instrumental view of scientific theories.
Right, and we have similarly inferred the existence of primes,
fractals, non-computable functions, etc.
So you're saying that "thought" is another kind of sense?
Thought is needed for inference and building theories, equally in the
physical sciences and math.
And that what occurs to us in thought can also be used as a basis to
infer the existence of objects which help "explain" those thoughts?
Right, like you might think up genesis and dualism, or big bang and
materialism, or platonic truth and computationalism. These are
ontological theories for what exists, and why we are here experiencing
it.
If you say math is fiction and only exists only as a story in our
brains, then obviously you can't use platonic truth and
computationalism as one if your theories of existence.
I think the fact that mathematics can serve as a theory for our
existence shows absolutely that mathematical theories and physical
theories are on equal footing. We can gather evidence for them and
build cases for them, find out we were wrong about them, and so on.
Why do we believe in quarks, electrons, strings, etc.? Because they
can explain our observations. Why do I believe in the platonic
realm? For the same reasons.
But we believe that electrons interact causally with us because we
are made from similar stuff - and by doing so make themselves known
to us...right?
How do Platonic objects interact causally with us? Via a Platonic
Field? PFT - Platonic Field Theory?
How did the warping of space and time cause Einsteins brain to figure
out relativity?
I think you are looking at it in the wrong way. Our brains seek good
explanations. They sometimes find one. That's all that is going on.
Now you say our explainations when it comes to mathematics are
fiction, but if that is so, why not say the same of the physical
theories? Why not say the big bang is fiction, or matter is fiction?
I think this leads to declaring everything but one's current thought
is fiction, which does not seem very useful.
It's not much different from how we develop theories about other
things we cannot interact with: the early universe, the cores of
stars, the insides of black holes, etc.
We test these theories by following their implications and seeing if
they lead to contridictions with other, more established, facts.
Just as with physical theories, we ocasionally find that we need to
throw out the old set of theories (or axioms) for a new set which
has greater explanatory power.
So you think our current mathematical theories are not "true" in any
metaphysical sense - but rather are approximations of what exists in
Platonia?
They may or may not be true, but they are certainly incomplete. Just
like our physical theories may or not be true descriptions of the
universe, and are certainly incomplete.
Is there an equivalent of the idea of "domains of validity" that
holds in some circles in physics?
I don't know what this concept means well enough to say.
I'm not sure any of this counts as being evidence in favor of
Platonism...
How is it that we are able to reliably know things about Platonia?
The very idea of knowing implies a differentiation between true and
false.
Nearly any intelligent civilization that notices a partition between
true and false will eventyally get here.
True in what sense? A coherentist conception of truth? A
correspondence conception of truth?
In the sense of the notion that a proposition is either true or false.
How do we know truth? Do we have an innate "truth sense"?
How do we know anything? Do we know anything?
Does the ability to know truth require free will?
Comparabalist or incompatibalist?
For instance:
If we say a statement is true because it is true,
What we say or think has no effect on platonic truth.
that is different than saying it is true because our neurons fired
in a way that determined our response. If all our decisions were
predetermined from the moment of the big bang then rational
discussion is meaningless.
Are you saying there is no reason to correspond on this list if the
future is determined? I don't agree with that at all.
Whether or not anyone agrees with you has nothing to do with the
truth of your claim. Their beliefs were "hardwired" from the
beginning of time.
It follows then that your own beliefs are not based on their truth
value.
To believe this is to believe that rationality and the scientific
method never bring us closer to the truth.
You believe what you believe because your neurons have determined
that you will believe in this rather than that.
I think you may be focused on the wrong level again. Think of things
on the level of the thoughts those neurons support and the picture
becomes clearer.
You can't easily answer "Why Euclid concluded the sum of the angles of
a triangle is 180 degrees" in terms of atomic interactions or neuron
firings.
SO - what is this "truth" stuff, really?
I think it is the infinite, self existent, ground of all being. The
best theory we have for the reality we see.
I would have thought that quarks and electrons from which we appear
to be constituted would be indifferent to truth.
The unreasonable effectiveness of math in the physical sciences is
yet further support if Platonism. If this, and seemingly infinite
physical universes exist, and they are mathematical structures, why
can't others exist?
Which would fit with the fact that I seem to make a lot of mistakes.
But you think otherwise?
We are imperfect beings.
What is the source of imperfection? Where does it come from? What
explains it?
Natural selection.
Objectively, intrinsically, absolutely imperfect?
Have you heard the term "Works as coded", with respect to software
development?
I have heard "it's not a big it's a feature".
So I can write a program that has a bug in it - and the computer
will run it perfectly. The computer will do exactly what I told it
to do.
The program works as coded. When running my program, the computer
is perfectly imperfect.
I am the source of its imperfection.
However, in a functionalist theory of mind - I am actually just
executing my own "program" right? Given the initial conditions of
the universe and the causal laws that govern it - I could not do
other than I did when I wrote that buggy code.
I also "work as coded". I also am "perfectly imperfect". And since
in this view I am not the source of my own imperfection - the
universe's initial conditions and causal laws must be that source.
But what explains that imperfection?
You were the one who said you make a lot of mistakes. Without knowing
the particulars I have no idea what the explanation might be.
But - maybe there really is no such thing as imperfection? It's all
just made up...like mathematical truth.
Maybe?
Maybe, but Platonism is the theory I use to explain the appearence of
the world.
What theory do you use and why is it immune to the label of "fiction"?
Jason
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