Re: The word "symbol"

Paul wrote:
> VC wrote:
> > I sincerely appreciate your effort and apologize in case you've not been
> > offended by my style. ^^^
>
> Freudian slip? :)

Rather poor typing skills. The original phrase was "I hope you've not been.."

>
> <snip>
> > In short, my objections to the word (as used in our previous exchange)
> > were:
> >
> > a. The definition is ambiguos. The word was used to refer to a thing
> > name(1) and at the same time to internal value representation (2). The
> > ambiguity alone is, or should be, lethal for something that's supposed to be
> > used in a narrow and hopefully precise technical sense.
>
> Isn't that just a reflection of the fact that, like so many other
> things, whether or not something is a "symbol" depends on context?
>

Not in a technical/theoretical context where words or terms have to be defined as precisely as possible to convey the intended meaning. E.g. the word "force" can denote many things in the natural language whilst in physics it has the precise meaning of referring to the product of "mass" and "accelaration" with those being defined precisely as well.

> Consider the number "3". In one sense it is a "thing", a mark on paper,
> and not a symbol. In another sense it *is* a symbol that signifies the
> concept of "threeness" that is difficult to describe but is the
> intangible thing that 3 apples, 3 pears, 3 oranges etc. all have in
> common. It all depends on context.

You are probably right with respect to the second sense: natural numbers hypothetically appeared as an abstraction of counting, matching a collection of items with another collection: fingers, pebbles and eventually numbers.

As to the first sense, the modern mathematical definition of say "3" is quite precise and simple. In the FOL language, "3" is just a string of characters that name the abstract entity 3 (in other words, there is an assignment function that maps a set of constants to a set of integers).  The standard word for such name is a constant. Quite similar to a relation between a person name and the actual person. We do not say for exampe that 'John' is some magical symbol "representing" an actual person. We just say that a string of characters, or an audio fragment,  "John" is a name which refers to an actual person. For linguistics fans out there, the terms would be a "reference" for "John" and a "referent" for the actual person. However, there does not appear to be much point in introducing fancy terms and thus muddying waters with stuff like "referent", "symbol", etc. when simple words like name, constant, number serve quite well, thank you very much. Of course, when our domain vocabulary is insufficient, we have to use/invent new labels in order to be able to talk about new things. However, so far,  it was not demonstrated convicingly that such need exits (I am referring to the thread diascussing equality).

>
> In semiotics I think the terms used are "signifier" and "signified". See
> Roland Barthes' Mythologies for example - showing that each discipline
> uses different words for similar concepts.

That's cool. Each discipline is fully entitled to use any terminology it likes after having defined precisely what the terminlogy means. However, due to close links between computer science and math in general, and the RM and the FOL in particular, why not use the established terminology instead of trying to import pieces of vocabularies from other branches of science, or, which is even worse, from a natural language ?

>
> > b. The word itself is redundant because there are perfectly good and
> > established terms for the things we talked about, such as a constant(1) or
> > a name(1) and internal data representation(2).
>
> maybe, but sometimes it helps to use general language instead of jargon,
> for pedagogical purposes.

Right. But as soon as students mastered the terminology, it makes sense to use it instead of vague natural language words. Besides, I object to the word "jargon". Jargon is a derogatory term and it's purpose is opposite (to muddy waters) to that of terminology (make things more precise and clear). An example of the former might be "conceptual data type" whilst an example of the latter is "predicate symbol".

> Anyway, I think the choice of language is
> somewhat tangential

See above.

> ... to the main issue, which is whether relational
> engines can test values for equality purely from their "internal data
> representation", or whether they need to consult the type definition in
> order to do this.

An answer to this question depends, for example, on what type system you have in mind when you are talking about the comparison. Assuming a static type system, typing errors will be caught at the query language "compilation" stage where compiler would check for such errors. I do not see much difference, with respect to implementing comparison, from traditional programming languages.

Cheers.

>
> Paul.
Received on Fri Aug 12 2005 - 16:58:51 CEST