[lojban] Re: Hintikka on Quantifier Scope

[John E Clifford <lojban-out@lojban.org>]

--- 2 = 3 <xod@thestonecutters.net> wrote:
> "Here we are beginning to see the whole horror
> of Frege's mistake.
> The notation he introduced (like the later
> notation of Russell and
> Whitehead) arbitrarily rules out certain
> perfectly possible patterns of
> dependence and independence between quantifiers
> or between connectives
> and quantifiers."
> 
>
http://www.hf.uio.no/filosofi/njpl/vol1no2/revolution/revolution.pdf

Oh, that Jaako!  What a card!  He is technically
right, of course, but he also points out most of
the reasons why little will come of it -- for a
while at least.
As for its role in Lojbanery, his notation does
suggest a partial solution for the problem of
quantifiers not getting comfortably where they
are needed (sentences about dogs biting men seem
to play quite arole here).  I suppose the
relaization here would be something like {pe}
attaching a list of binding (or of nonbinding)
variables to a variable that was out of place
linearly.  I seem to recall something like this
was proposed once a long while ago using modified
Skolem functions in place of particular
quantifiers (and eventually groups -- bunches --
for value to make the numeric cases work).  It
died for now forgotten reasons, but the {pe}-like
critter might survive.  There has been less
discussion of problems with connectives and
quantifiers, though it should be easy to get up a
few specimens.  Alas, it is less easy to see how
to apply Hintikka's notation to the connective
cases (and especially how to get workarounds for
connectives other than OR -- we can't expect
everything to be in normal form). This probably
deserves another look-at sometime along the line.
 

 
> If it rained, it did not rain hard.
> It did rain hard.
> Therefore it did not rain.

So the first premise if false, it rained and
rained hard. (strictly requires that raining hard
entails raining -- not a problematic addition,
but it reduces then to a contradiction.)