[Wittrs] Re: Nominalism / Neil
- From: "jrstern" <jrstern@xxxxxxxxx>
- To: wittrs@xxxxxxxxxxxxx
- Date: Tue, 08 Sep 2009 16:42:57 -0000
I had a short response to this, I held it out,
and it becamse a too long response to this.
So I'll just make a few brief notes here,
and see what I can do with the rest of my stuff later.
--- In Wittrs@xxxxxxxxxxxxxxx, "iro3isdx" <xznwrjnk-evca@...> wrote:
>
> Yes, it is all about symbols. There's a lot of talk about
> numbers, but those are symbols, too.
1. Computing machines.
2. Definitions.
Automatic machines.
Computing machines.
Circle and circle-free numbers.
Computable sequences and numbers.
3. Examples of computing machines.
4. Abbreviated tables
Further examples.
5. Enumeration of computable sequences.
6. The universal computing machine.
7. Detailed description of the universal machine.
8. Application of the diagonal process.
9. The extent of the computable numbers.
10. Examples of large classes of numbers which are computable.
11. Application to the Entscheidungsproblem.
There is some talk of numbers, and even some talk of symbols,
but the historical value of the paper is clearly in the process
and machine points. It was never about numbers as such, nor
about symbols with external meaning. It uses these things much
as it uses the 26 alphabetic letters, to make such points as
it makes, but it is not about the Roman alphabet as such.
> 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.
Writing any paper on any subject is an intentional activity,
but if I write a paper about rocks, that does not mean rocks
are intentional agents.
It would seem to me that, depending on which style of mathematics
is being done, this would imply a different form of intentionality
anyway.
So, (at the risk of drifting away from nominalism in the
direction of intentionality - before we are ready to do so)
what do you even mean, in this context, by intentionality?
Josh
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