Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?
tchow_at_lsa.umich.edu
Date: 01/29/05
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Date: 29 Jan 2005 18:23:21 GMT
In article <ctg43l01cjo@drn.newsguy.com>,
Daryl McCullough <stevendaryl3016@yahoo.com> wrote:
>I don't understand why not. What is there to mathematical
>platonism other than commitment to the existence of sets?
First of all, I'll say that personally I lean towards platonism. I didn't
always used to be this way; many years ago I was much more influenced by
formalism, but have gradually changed my point of view. So *my* commitment
to the existence of sets is tinged with platonism.
That aside, I would answer your question by quoting something you said later
in the same article:
>I think it's a little hazy in what sense sets exist or don't
>exist. We can certainly talk about them meaningfully *as* if
>they exist, but that doesn't require anything any more than
>some kind of coherence of our story about them.
As you say, committing to the existence of sets is something of a hazy
commitment until the nature of this "existence" is fleshed out a bit.
I can commit to the existence of sets, yet flesh out the details in
different ways. I might adopt a fictionalist posture, somewhat like
what you describe here. That is, I regard my statements as meaningful
*according to a certain story*. Oliver Twist exists according to a
certain story; this is a meaningful statement and not just a syntactic
entity to be manipulated according to syntactic rules, yet Oliver Twist
is of course a fictional character.
A platonist doesn't regard sets as "useful fictions" but as real, and
hence is likely to say that meaningful statements about sets are either
true or false, whereas a fictionalist is usually happy to say that some
statements are intelligible ("Oliver Twist's left thumbprint was a whorl")
but have indeterminate truth value.
-- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences
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