Doug and Jack, (01)
Before commenting on your comments, I'd like to repeat the
point that these are two "short and general" definitions of
the way the words 'class', 'type', and 'set' are used in most
discussions the relate all three. (02)
But there are many different schools of thought that use and
develop those notions much further. In most cases, their
definitions are consistent extensions or specializations of
the two short definitions below. (03)
JFS
>> My recommendation is to use the following definitions:
>>
>> 1. A class is a set of all x of a given type.
>>
>> 2. Every type can be specified by a monadic predicate that is
>> true of every instance of that type.
>>
>> These two definitions are sufficiently short and general that they can
>> be specialized to all the major notations and schools of thought. (04)
DF
> This raises the question of what to do about Xes that are sometimes
> of one type and sometimes of another. At any given time (and context)
> there is a set of all X of a given type. However, at another time (or
> context) there may be a different set of all Y of that same type. (05)
As I said, those definitions are sufficiently general that they are
consistent with any such extension. For example, if x=2.7, then
the predicates real(x) and rational(x) are both true of x. Therefore,
x an instance of the class of real numbers and the class of rational
numbers. (06)
The question about times and sets raises other issues. Since the
identity conditions for sets are determined by their instances,
you can't change the instances of a set without causing it to become
a different set. (07)
In programming languages, you can talk about the value of a variable
at different times. The variable x can denote different sets at
different times, but the sets themselves don't change. The only
thing that changes is the denotation of the variable x. (08)
In any case, none of these issues require any change to the above
definitions. (09)
JR
> To me this says that 'ontologists' do not discern content and
> structure (endogenous attributes) from behavior (exogenous
> attributes). Am I understanding your intent? (010)
Again, my only intent was to state definitions of the common ways
that three words are used: 'class', 'type', and 'set'. (011)
But the distinction you're making about endogenous and exogenous
attributes have been made by ontologists since Plato and Aristotle. (012)
In Aristotelian terms, the essence of something is determined by
its *substantial form* which doesn't change as long as it exists.
For a cat or horse, the substantial form corresponds to its DNA,
which controls its growth from fertilized egg to death. You could
call everything determined by the DNA its endogenous attributes,
but that is not a term that Aristotle used. (Actually, he didn't
use the term DNA, but if he had known about DNA, he would probably
have said that the DNA is part of the essence of a living thing.) (013)
For what you're calling exogenous attributes, Aristotle used
the term 'accident'. In his ontology, he assumed 9 kinds of
accidents: Relation, Quantity, Quality, Active, Passive,
Condition, Position, Time, and Place. (014)
A cat or horse can't change its DNA, but any or all of the
accidents can change at any time. (015)
In any case, all of these issues are compatible with the
definitions I suggested for the terms 'class' and 'type'.
And these are not definitions I invented. They or something
equivalent are commonly used. (016)
John (017)
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