Re: The word "symbol"

"vc" <boston103_at_hotmail.com> wrote in message news:1123862288.790137.272990_at_f14g2000cwb.googlegroups.com...
>
> 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 can accept the above, from the point of view of a math centered person. I'm not a math centered person,
although I took some math in college, some 40 years ago. I'm a data modeler (retired). And I've found the word "symbol" useful enough to keep it part of my active vocabulary.

The above definition of symbol makes sense to me, in the context of this discussion. But I never would have arrived at it in a million years, left to my own devices. "An element of the first-order language vocabulary" is not a phrase from my active vocabulary.

The difference that arose between you and me appears to be about the way each of us uses language, rather than a substantive one. And I'm content to let the matter rest there.

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

Let's just go with "an element of the first-order language vocabulary", for now.
But first, maybe you can give me a definition of "first-order language". Received on Sat Aug 13 2005 - 13:16:36 CEST