Re: The word "symbol"

David Cressey wrote:
> "Paul" <paul_at_test.com> wrote in message
> news:42fc7a2d$0$17487$ed2e19e4_at_ptn-nntp-reader04.plus.net...
>
> VC, if I read him right, views everything at two levels of abstraction:
> the logical level and the physical level.

Well, no. The two things I see are a formal structure and its model. E.g. Peano axioms as a formal stucture and integers as the standard model of the PA. A formal structure has a language which is used to talk about the model. The language vocabulary( a set) contains names(constants, function names, connectives, etc) for various things in the model. Sometimes, those names are called symbols. I have no objection to such use of the word "symbol" although this use does not occur in the modern math practice very frequently. In other words, if you said: " by a symbol I undestand an element from the first-order language vocabulary", there would have been no objection on my part.

>
> I think that there are multiple levels of abstraction. I'm not even going
> to guess how many. And in order to know what a piece of data expresses,
> you have to know not only the context, as VC said, but also the level of
> abstraction.

See above. Of course there are multiple levels of abstraction depending on what and how you want to model. At any level of abstraction you operate with some objects using their names in the context of your formal model. There is no need, or at least you've not convinced me yet that there is such need, to introduce the new word "symbol" in the sense other than the one I've described above.

>
> The word "symbol" has a consistent meaning, I think, across multiple
> levels of abstraction. VC claims my use is inconsistent. It remains to be
> seen where the discussion goes from here.

OK, please define "a/the? consistent meaning" (not multiple meanings) of the word symbol.

Cheers. Received on Fri Aug 12 2005 - 17:58:08 CEST