At 12:00 AM 10/26/2005, you wrote:
>Leo, Barry, et al.,
>I certainly agree that we must make all these distinctions
>very clear in any ontology. But the term "real thing" should
>also be clarified, since mathematicians usually think of
>numbers and such as "real", but not physical.
>All the issues of distinguishing types, instances, and symbols
>arise when we're talking about mathematical entities. For
>example, 23 is an instance of an integer, but "23" is a
>numeral, which is a symbol that represents the integer.
>This distinction (instance - 23; name - "23"; type - integer)
>arises with both physical and mathematical entities.
>The words "physical" and "mathematical" are probably safer
>than the word "real", which raises so many philosophical
>issues that it would be better to avoid it.
>And when we start talking about numbers and other mathematical
>entities, we have to consider their use in measuring and
>characterizing physical entities. For example, cubes and
>spheres are mathematical entities, but we might talk about
>them as characteristic "shapes" of certain kinds of physical
>objects. The earth, for example, might be called a sphere or
>an oblate spheroid, but it is not a mathematical entity. It
>is a physical object that happens to be characterized by a
>mathematical entity (at least to a reasonable approximation,
>whose degree of "reasonableness" can vary with different
>Ignoring these distinctions can cause a lot of confusion.
>For example, somebody might say "Bob and Tom earn the same
>salary." But that does not mean that Bob and Tom receive the
>same paycheck. Instead, some number such as 40,000 is used to
>_measure_ a quantity of money relative to the unit _dollar_.
>Bob and Tom each receive distinct quantities of money, both of
>which happen to have the same measure.
> >Ps. The "triangle of signification" is sometimes used to help elucidate
> >these relations [Ogden, C. K., and I.A. Richards. 1923. The Meaning of
> >Meaning. London: Kagen Paul; and adapted by various folks, including
> >me; and having antecedence back to Peirce, and perhaps further].
>Yes. Ogden & Richards included a number of excerpts from
>Peirce's writings in the appendix to their book. Those were
>letters from Peirce to Lady Victoria Welby, who was one of
>Ogden's early mentors (and the author of an entry on "significs"
>in the 1911 edition of the _Encyclopedia Britannica_).
>But Peirce emphasized that there's a lot more to semiotics
>than just that one triangle. In talking about salaries,
>for example, we have to distinguish the number 30,000 from
>the numeral "30,000", the measure of the salary using the
>combination of the number and the unit "dollar", and the
>instance of each individual employee's quantity received.
>Then, of course, the dollar had been backed by 1/35 oz. of
>gold until 1933, after which it was still exchangeable for
>silver, but now it is just an IOU from the Federal Reserve
>Bank -- and it is not at all clear what the bank owes you,
>if you demand payment. And when you use electronic fund
>transfers, what happens is that a lot of electrons move around
>in ways that represent many signs of signs of signs....
>Classifying all those signs and keeping track of them in all
>the steps of representation and reasoning is a major challenge
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