From: Lee Corbin (lcorbin@tsoft.com)
Date: Mon Jun 17 2002 - 08:27:24 MDT
Wei Dai writes
> Suppose nothing exists physically. Would mathematical structures still
> have a platonic existence? For example would the fact that 1+1=2 or the
> fact that the decimal expansion of PI begins with 3.1415 still exist? It's
> hard for me to conceive that they wouldn't.
Yes, it also seems possible to me that the Platonic world of
mathematics would get along very nicely without the physical
universe. But, yes, critics would have a point if they say
that it being "hard to conceive" is not a good argument.
> We believe that there is a mathematical structure that corresponds with
> our physical universe, which implies that mathematical structures can
> contain sentient beings.
Only in a passive sense; yes, there are extremely large
integers, and even more real numbers, which definitely
are me. Quite a few even start with the sequence
.080512121599122599140113059909199912050599031518020914...
which is easily discerned to mean
. h e l l o m y n a m e i s L e e C o r b i n ...
and it goes on in rather excruciating detail giving my life
history, my beliefs, a large number of funny anecdotes, and
all too many mundane and tremendously boring philosophical
digressions. It even has an enormous question and answer
session where you look up your question, and then are directed
to a large number of one billion or so digits, which is the
place where further down in the sequence you find the answer.
Moreover, that real number vigorously defends the notion that
it itself is conscious! (It's one of the few places where
it clearly shows some emotion, and gets a bit defensive, going
on and on about the hubris and arrogance of non-integer life
and how especially biological organisms so insufferably look
down upon integers and real numbers such as itself.)
But it is WRONG. It is *not* sentient, no more than I would
be if cryonically suspended. It is a frozen state. It is
*not* executing. Despite its well spoken claims to the
contrary, it is not conscious.
> Taking this idea one step further, there is no need to assume
> that anything exists physically. We ourselves could be living
> inside a platonic mathematical structure.
I don't agree.
> So that solves the problem, at least if you're a mathematical
> realist.
I *am* a complete mathematical realist, and my
favorite mathematical philosophy book is Penelope
Maddy's marvelous "Realism in Mathematics".
Her book is so great!
Lee
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