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Re: Alternative area postulate for geometry
Posted:
Jul 11, 2012 1:08 AM
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On Tue, Jul 10, 2012 at 9:20 PM, Joe Niederberger
<niederberger@comcast.net> wrote:
> Kirby says:
>>Yes, and new formal systems often arise as a result of such explorations. Such explorations should be encouraged
>
> I agree that encouragement is good, but I thought you were unclear on what "formal system" meant.
>
No, I was unclear what *you* meant by formal system. I am happy to
talk about formal systems independently of that.
Note "formal language" as a related topic in Wikipedia under "formal
system" -- mentions computer science is vested in that.
Is chess a "formal language"? It has symbols, a notation, and rules.
A semantics. But we're quite fuzzy about the "axioms", so not a
"system" then?
A lot of rigorous / formal stuff masquerades as "axiomatic" without
really being clear what its "axioms" might be. Do we always care?
I think there's a lot of pseudo precision in this neighborhood.
> See --
> Kirby says:
>>"Formal system" has not been defined. Something rigorous no doubt.
>
> &
>
>>"Formal system?"
>
> Something fishy here.
> Joe N
What's fishy is the English language. You can pretend all this stuff
is nailed down, but it's not, it's a seething hodgepodge of shifting
meanings.
I'm happy to get clearer between us what we mean, but I don't see that
as nailing down global meanings necessarily.
When it comes to "formal systems", I'm willing to talk about local
namespaces in which that has a specific meaning.
http://www.earlham.edu/~peters/courses/logsys/machines.htm (agree with this?)
Kirby
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