Leo, Barry, et al., (01)
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. (02)
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. (03)
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. (04)
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
applications). (05)
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. (06)
>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]. (07)
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_). (08)
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. (09)
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.... (010)
Classifying all those signs and keeping track of them in all
the steps of representation and reasoning is a major challenge
for ontology. (011)
John Sowa (012)
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