[Wittrs] Re: Nominalism / Neil
- From: "iro3isdx" <xznwrjnk-evca@xxxxxxxxx>
- To: wittrs@xxxxxxxxxxxxx
- Date: Mon, 07 Sep 2009 23:30:51 -0000
--- In Wittrs@xxxxxxxxxxxxxxx, "jrstern" <jrstern@...> wrote:
>> No, that was not my point.
>> It is my impression that Turing's definition involved symbols,
>> rather than physical characteristics. And it seems to me that
>> when we talk of symbols, we are implicitly talking of intentions.
> Feel free to (re-)read the paper!
> http://www.abelard.org/turpap2/tp2-ie.asp#index
<http://www.abelard.org/turpap2/tp2-ie.asp#index>
Yes, it is all about symbols. There's a lot of talk about numbers, but
those are symbols, too.
> Actually, it says very little of symbols, other than to work down
> to the fact that it needs only 0 and 1 as "symbols", and in
> retrospect, perhaps those are not even symbols at all.
I'm not sure how you are getting that idea. It is all about symbols.
Sure, there's an endnote about possible physical implementations, but
that does not try to deny the symbolic nature of the paper. It's a
mathematics paper, after all. And mathematics is very much an
intentional activity. Whether you are a formalist, a logicist, a
platonist, a fictionalist, a constructivist, an intuitionist, or even a
nominalist (Hartry Field style), mathematics is an intentional
activity.
> Remarkably enough, neither of Turing's two papers, OCN and CMAI,
> really say a darned thing about how a "symbol" has any kind of
> reference at all.
It is common for mathematicians to use symbols, where those symbols are
not required to actually symbolize anything. However, the symbols are
still ideal objects.
> /second attempted repost by email from Sunday,
> mail to wittrs@... no workee
It has not shown up on Sean's forum, which is probably a bad sign. And
I am not seeing a "Reply-To:" when I examine the message source. I'll
try that "forward" option to post a reply. If that fails, I'll revert
to email.
Regards,
Neil
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