Re: [lojban] ATTN: McIvor (was: Re: Re: Hintikka on Quantifier Scope

[John E Clifford <clifford-j@sbcglobal.net>]

> What is your take on IF Logic? Can it express
> ideas not expressible 
> without it? Is it simply a disguise for 2-order
> logic?
> 
Yes to the first: there is an infamous quantifier
expression that is impossible in standard logic
but easy in IF. Unfortunately, getting stuff like
that in means that all the properties that make
standard logic fruitful to study go out the
window once you get that kind of strength (more
than first order logic, less than full second
order -- no quantification over predicates,
though there are work-arounds that come close, I
gather).  On the further goings on, the fact that
IF logic is not recursively enumerable (finitely
axiomatizable) means that Goedel's theorems don't
go through and so, in principle at least,
arithmetic might be completed.  But, since it
would involve deductively unsubstantiated proof
procedures, this may not be much of a triumph. 
None of the other things that IF does in what
I've looked over this week seems to me to be
useful enough (or, indeed, obviously to involve
IF) to switch allegiance from standard logic.  On
the other (now about fourth) hand, Hintikka is a
hard man to ignore, so there is something there
worth at least looking at some more.