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Re: [ontolog-forum] Prospects made into Customers and Vice Versa

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Mon, 26 Oct 2015 15:48:20 -0400
Message-id: <562E8384.7030507@xxxxxxxxxxx>
Tom,    (01)

I hit SEND too soon.    (02)

> What I think would be useful is a pair of terms to distinguish
> "static sets" from "dynamic sets", and to relate the two concepts
> in something like...    (03)

No.  That would be contrary to every version of set theory.
For infinite sets, there must be some predicate that specifies
membership in the set.  For finite sets, you can always convert
an enumeration to a monadic predicate:    (04)

   P(x) = x=x1 or x=x2 or x=x3 or ... or x-xN.    (05)

Therefore, you can always say that for any set S, there exists
a predicate P such that x is in S iff P(x).    (06)

> (ii) A dynamic set is a temporal sequence of static sets    (07)

It's much better to take a widely used term, such as 'type',
which is common in computer science and other fields.    (08)

In any programming language that specifies types, the definition
of a type is a monadic predicate.  During a computation, any type
you specify would have a temporal sequence of sets at each step
of the computation.    (09)

This terminology would be easy to explain to any programmer,
and most people who do any work in applied ontology also
have some knowledge of programming.    (010)

For the distinction between intension and extension, I recommend
a short comment by Alonzo Church.  He used it to talk about the
intension/extension of functions, but you can also adapt it to
talk about relations:    (011)

    http://www.jfsowa.com/logic/alonzo.htm    (012)

John    (013)

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