On 11 Jun 2013, at 19:04, Jason Resch wrote:
From the video: "What we do is we use the story of math, which is
very good and very complete"
I think that summarizes the error of fictionalism. To believe math
is a human created invention requires believing that everything we
can ever know about math comes from the starting assumptions we
choose. We now know this to be untrue, our picture (or anyone's
picture) of math will always be incomplete, there is always more
math out there to discover. We make progress in math the same way
we do in all the other sciences, making observations, drawing
conclusions, seeing if our theories are consistent, etc. Over time
we develop our accepted axioms the same way we develop our
fundamental physical theories.
We observe and explore other mathematical structures/universes
through the tool of simulation (either using our brains or using
computers), and that is how information about other universes enters
our own.
I agree completely. I do take incompleteness, or the consequences of
Church thesis as illustrating very well the "objectivity" of arithmetic.
Above arithmetic, I have no problem to classify some construct as
being epistemological, but the exact frontier between ontology and
epistemology is unimportant, as the inside views will have an
objective arithmetical behavior, even when not arithmetical. And this
is well justified by the fact that although we can do easily intuitive
number theory without ever formalizing the theory (like number
theorist), this is no more the case for set theory, whose intuitive
part is just inconsistent, and when it is formalized, the communicable
part belongs to arithmetic.
So I agree with your for arithmetic, and above arithmetic it is a
question of convention.
Arithmetic is large, and I do not know of any theorem in math which is
not a theorem in arithmetic, except in mathematical logic, and
universal algebra, which are typically "meta-"mathematics.
Bruno
Jason
On Thu, Jun 6, 2013 at 5:31 PM, Stephen Paul King <[email protected]
> wrote:
For your entertainment: https://www.youtube.com/watch?feature=player_embedded&v=TbNymweHW4E
#!
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