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Re: [ontolog-forum] A Question About Mathematical Logic

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Fri, 16 Oct 2015 16:31:20 -0400
Message-id: <56215E98.4@xxxxxxxxxxx>
On 10/16/2015 1:44 PM, Obrst, Leo J. wrote:
> Example: Student. Employee. Buyer. Seller. And so on.
> These are roles, and can be characterized in a role hierarchy,
> if one wishes.    (01)

I agree that it's important to distinguish roles.  In my CS book
(1984), I distinguished them as role type (e.g., Student) vs.
natural type (e.g., Human).  Nouns that represent role types have
more typical or expected relationships than those that represent
natural types.  But natural types also have expected relationships
(e.g., Human vs Elephant vs Rose vs Cabbage).    (02)

> But e.g., Student is not a subclass of Person (or, more clearly Human).    (03)

That is a prime example of a typical confusion.  The phrase
'more clearly' is a clue that it's not clear.    (04)

A class is normally defined as a set that is characterized by some
criterion that may be stated by a monadic predicate.  The students in
a school form a set that may be represented by a monadic predicate.    (05)

Q: Why would anyone claim that 'Student' is not worthy of being a class?    (06)

A: Some philosopher said so.    (07)

Q: Does that distinction make a difference in how the term is
    represented in ordinary language?    (08)

A: Role types and natural types are both represented as nouns.
    But a noun that represents a role may occur in some phrases
    that are not expected for a natural type:  e.g., "a student
    of physics", "a teacher of physics", but it's unusual to say
    "a man of physics".  In any case, 'unusual' means "unexpected,
    but not impossible".    (09)

Q: Does it make a difference in how the term is represented in logic?    (010)

A: Not in predicate calculus.  But some people choose different
    ways of making that distinction in some versions of logic.    (011)

Q: Does it make a difference in a theorem prover?    (012)

A: No.  If you represent all the required, expected, and unusual
    relationships, you get the same implications.    (013)

Q: So why does anyone make that distinction?    (014)

A: Because some philosopher said so.    (015)

Q: Do all philosophers agree on that point?    (016)

A: No.  Some say it's a pseudo-problem.  Others say there's
    a continuum with many borderline cases.    (017)

Summary:  I have a high regard for good philosophy.  But I have
little patience with those who make a fetish of distinctions that
don't make a difference in computing the implications.  I have even
less patience when those distinctions create incompatibilities
between systems that happen to make different choices.    (018)

John    (019)

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