[lojban] Re: Hintikka on Quantifier Scope

[2 = 3 <xod@thestonecutters.net>]

John E Clifford wrote:

> --- 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). 


The asymmetry in that bit's always made me somewhat queasy.

In terms of the usefulness of IF Logic:

"Broadly speaking, Hintikka has two major aims in
the book. On the one hand, he wishes to present a detailed case for the 
significance
of his Independence Friendly [IF] logic based not only on its expressive
power in service of a neo-logicist philosophy of mathematics, but also 
its ability
to solicitously model certain semantic phenomena which he claims are 
ubiquitous
in both our mathematical and everyday idioms. On the other, he wishes to
lobby against the traditional Tarskian theory of truth for rst-order 
languages on
the basis of what he takes to be its excessively liberal commitment to 
set theoretic
entities. In its stead, Hintikka proposes that we adopt a theory of 
truth based on
verication games. This approach yields a theory of truth known as game 
theoretic
semantics [GTS] which is applicable to both classical rst-order logic 
and to
IF logic." (pardon the silly ligatures provided by Acrobat)
http://www.univ-nancy2.fr/poincare/colloques/symp02/abstracts/dean.pdf


Here's a flamewar on the topic:
http://www.groupsrv.com/science/viewtopic.php?t=12412&postdays=0&postorder=asc&start=0


Here's where Hintikka defends himself against Neil Tennant ("I studied 
at the Sorbonne / Doctored in mathematics, I could have been a don")
http://www.hf.uio.no/filosofi/njpl/vol4no2/gamesem/gamesem.pdf


> 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 would be interesting to see the Skolem function proposal.

Loglan (!) gets round the issue by explicitly declaring the mapping, if 
I recall correctly.



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