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
> remains.
>
> 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
> include
>
> 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
> imaginary),
>
> 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)
Regards (07)
Matthew West
Information Junction
Tel: +44 560 302 3685
Mobile: +44 750 3385279
matthew.west@xxxxxxxxxxxxxxxxxxxxxxxxx
http://www.matthew-west.org.uk/ (08)
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