Just two points (or one extended point): (02)
RF> I don't know if your observation that the number would be
> countably infinite is true also. What matters to me is that,
> even for finite sets, the number of possibly "meaningful"
> relations could be very large.... (03)
If you have a finite alphabet and consider only sentences that
are finite, there are at most a countable number of sentences.
There may well be uncountably many relations that might
possibly become relevant, but only a countable subset of them
could ever be mentioned, cited, defined, specified, or designated. (04)
RF> Pat deals with this by limiting the relations he considers: (05)
PH> "...this doesn't matter because the logic isn't obliged to
> consider all of these relations, only enough to provide
> denotations for all the relation-naming terms in the language." (06)
Pat is saying something similar to what I was just saying: with
a finite alphabet and finitely long words and sentences, you can't
name or otherwise refer to an uncountable number of individuals.
(You can, of course, talk about the set of real numbers in just
12 characters -- "real numbers" -- but you can't distinguish more
than a countable number of elements of that set.) (07)
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