Re: SUO: Set/Class Distinction
Pat and Ian,
This is another issue where the abstract mathematical notions
bump into the per- and en- issues, which are usually associated
with physical entities.
Patrick Cassidy wrote:
> I thought that one of the distinctions was that
> sets are necessarily defined extensionally, whereas
> a Class may have a membership criterion such that
> the same class may have different members at
> different times. Is this a misunderstanding of what
> the present definitions mean?
Whatever set of conventions are adopted for physical entities
should be compatible with the conventions adopted for mathematical
entities. Every time I take a breath, I lose or gain molecules.
Does that mean that I am a different physical entity at each
moment?
Following is a brief summary of Whitehead's position about
physical entities:
1. He reserves the term "actual entity" for something that
exists for only a very short duration of time (for the
length of whatever the shortest measurable interval is in
the granularity that is being used for some application).
2. Each actual entity perishes at the end of each moment,
to be replaced by a new actual entity at the next moment.
So at each moment, there is a new actual entity that has
the same name and most, but not all of the same molecules.
3. The time-extended collection of all the actual entities
named John Sowa form a "nexus", which consists of all the
embodiments of that person at different moments throughout
his life.
4. A similar solution could be adopted for any other kind of
structure. You could talk about a time-ordered sequence
of sets, which all had the same name S. But S would actually
be a function from times to sets; i.e., S(t) would be the set
of entities at time t.
John Sowa