Dear Pat, Matthew, and Azamat, (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. (02)
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. (03)
I'll acknowledge that if you define your sets so broadly that they
include (04)
1. The full extent of everything at all times in the past and
future for the entire duration of our universe, (05)
2. All possibilities in all possible worlds under any and every
conceivable notion of modality, (06)
3. All universes, in the case that the hypotheses about multiple
universes turn out to be confirmed (or even if they remain
imaginary), (07)
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, (08)
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. (09)
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. (010)
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. (011)
But note that even for finite sets, an intensional definition is
necessary. 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. (012)
AA> First Meaning, then Word; to shortly remind some critical
> semantic things for those who still in doubt. (013)
I agree, but I would add Peirce's remark "Meanings grow."
A century ago, the word 'car' was synonymous with 'horseless
carriage', they looked like carriages, and they even had hooks
to attach a horse in the frequent cases when they broke down.
But today, we apply the word 'car' to things that would have
been unimaginable to the people who invented and used the
early cars. (014)
AA> Real semantics is concerned with material signs... (015)
Every instance of a sign, when used, is material (sound, light,
marks on paper, electricity on a wire, a magnetized spot, etc.).
Every definition of a sign type is an abstract proposition that
is independent of any particular medium on which it is written. (016)
AA> Semantics precedes Syntax, any syntactic constructions,
> as well as Meaning precedes Truth. (017)
It's not clear whether you mean 'precedes' in a logical sense,
a historical sense, or a psychological sense. But in any case,
every use of a sign (spoken, gesture, or whatever) has a form
(syntax), a meaning (semantics), and a purpose (pragmatics). (018)
So I'd say that all three aspects are always present in every
sign, and I rather not get bogged down in discussions about
precedence. (019)
John (020)
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