Dear John, (01)
> PC>> A 4-D advocate like Matthew West will note that the 4-D view
> >> eliminates the time element from the context set, but that
> >> still does not eliminate all the other ways that a context can be
> >> defined, and the problem of multiple sets for the same type
> MW> No. There is the set of all X in any context (any possible world,
> > any time etc. Etc.) which is analogous to the intentional type X.
> I'll acknowledge that if you define your sets so broadly that they
> 1. The full extent of everything at all times in the past and
> future for the entire duration of our universe,
> 2. All possibilities in all possible worlds under any and every
> conceivable notion of modality,
> 3. All universes, in the case that the hypotheses about multiple
> universes turn out to be confirmed (or even if they remain
> 4. All other circumstances that may be imaginary, hypothetical,
> science-fiction, supernatural, and truly weird, outlandish,
> and humanly inconceivable but perhaps conceivable to some
> alien intelligence,
> then I would agree that there would indeed be a one-to-one
> correspondence between the intension of a term and that very
> extended (I would even say "hyperextended") extension.
> If you like that definition, I won't attempt to dissuade you.
> On the other hand, I would claim that for the practical purposes
> of reasoning and computation, it is desirable to have something
> more compact to work with.
> Therefore, I claim that the notion of _intension_ as a finite
> statement or rule that defines a term is useful. Given an
> intensional definition of a term, say 'cow', one can examine
> a thing, ask "Is this a cow?", and get a simple yes/no answer. (02)
[MW] I equally will not try to persuade you to give up your types. I do not
claim they will not work. But I get just as simple an answer to your
question with my set, and it is a set.
> But note that even for finite sets, an intensional definition is
> necessary. (03)
[MW] I would challenge necessary, but I agree they are useful. There is
nothing to prevent sets having intensional definitions, just as long as that
definition does not lead to varying memberships. (04)
> Just consider the set of all cows in the current time
> slice of planet earth: there is no database that lists all cows.
> Therefore, it would be impossible (or at least impractical) to use
> an extensional definition to check whether something standing in
> front of us is a cow. (05)
[MW] Let's be clear about what I mean by an extensional definition. I don't
mean that you know all the members, only that the membership (whatever it
is) does not change. This is after all ontology not epistemology. (06)
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