logical matters

["John E. Clifford" <pcliffje@CRL.COM>]

I didn't mean to push an expensive book.  If you know a reasonably
adequate but cheaper text, use it and let us know.  McCawley is
pretty thorough and very well-written (I was about to say "for a
linguist," but most of them can write circles around the best
logician -- who once wrote an article that demonstrated that a
certain technique was the right way to do logic, but that he has
claimed ever since showed that that technique was the wrong way
to do logic.)  McCawley is a gifted non-professional who likes
logic and wants to make it clear to people who know langauges.
And he does.

JCB uses "set" for "mass" (which is not a very good word for that
particular semantic object either, though better for some of teh
other things that _loi_ point out).  He is presently trying yet again
to explain his concept (_lo_ in Loglan) to his minions.  Nothing
much seems to have improved there on that front either.

McCawley does not say much about intesions of predicates or
sentences or ..., but he gives the basics from which we can work
out the details, if we ever have a need to.  They don't work too well
in Lojban because of the reductions back to first order objects all
the time.

And:
[I]t turns out that pc thinks A does entail E,
while everyone else (this includes a lot of people) thinks it doesn't.
pc:
Open challenge.  Find me a logician (or even a mathematician who
knows a bit of logic) who thinks that AxFx does not entail ExFx in
the ordinary system (that is, one not doing free logic at the time he
says it.  Indeed, the fact that there is a non-standard system of free
logic, which differs only by the fact that that inference -- or rather
the intermediate steps in the proof of that inference -- does not
hold, shows that it does hold in the standard system.)  And, since
the restricted quantifiers are just the quantifiers restricted, the
inference holds for them as well, (AxFx)Gx implies (ExFx)Gx.

Now, it is true that in the jargon of mathematics and logic, "All Fs
are Gs" need not imply "Some Fs are Gs" (uniformly in
mathematics, mixedly in logic, which does try to say"every" with
the inference and "any" without it).  But that is because "everybody
knows" (since 1858 at least) that "All Fs are Gs" is -- in the jargon -
- short for "for every x, if Fx then Gx" and the conditional is
material, true if the antecedent is false, as it will be universally
when ther are no Fs.  Rather like Spanish, the trick is not in the
quantifier at all, but, in this case, in the connective in the scope
(BTW, anyone know a good Spanish logic book?).

McCawley's test on this issue is not -- at least in the first edition --
so inconclusive as xorxes suggests.  He wants there only to show
that the existential import cannot come from conversational
implicature and for that the test is decisive, since the "right"
responses on that view are all clearly wrong and the best answer on
that view is the wrongest of the lot.  Of course, he would have had
more positive results if he had used "every" rather than "all,"  but
old habits die hard.  Still, since implicature is the only alternative
regularly presented to explain the admitted usual existential import
of even "all," its demise tends to leave the field in the hands of its
holder these two and a half millennia.

But, as noted, that speaks, in Lojban, only to _ro da poi broda_ (and
plain _ro da_ of course -- has anyone ever really challenged it?).  All
the others, that somehow got identified in with these, _ro broda_ and _ro
lo broda_ at least, are too far out of the ken of logicians (who don't do
plurals well, remember) to be bound by that.  So they can be cheerfully
employed referring to empty sets if there is any need for it.  (That seems
a better use that trying to solve second order or branching problems --
though the critters may be second order when push comes to shove).
pc>|83