[CL] "Lambdas changed my life," Barbara Partee

[Jay Halcomb]

It's older now, but a very nice discussion of comprehension axioms 
(extensional and intensional) and related issues (in the context of Montague 
semantics) appears in

Gallin, Daniel: Intensional and Higher-Order Modal Logic (with Applications 
to Montague Semantics), North-Holland, 1976.

This work discusses relations of Intensional Logic and Modal Logic to type 
theories,  and to Henkin generalized semantics, and to algebraic semantics, 
and proves various completeness and (relative) interpretatibility results.

I agree, though, that simplifying CL (or keeping it simple) is more 
desirable than otherwise.

-Jay'
----- Original Message ----- 
From: "Chris Menzel" <cmenzel at tamu.edu>
To: "Fabian Neuhaus" <fneuhaus at web.de>
Cc: <cl at philebus.tamu.edu>
Sent: Friday, August 26, 2005 1:48 PM
Subject: Re: [CL] "Lambdas changed my life," Barbara Partee


> On Fri, Aug 26, 2005 at 04:30:57PM -0400, Fabian Neuhaus wrote:
>> > Hmmm.  Maybe proving functions exist is going to take some
>> > comprehension axioms.  But they would be nice, unproblematic
>> > statements such as
>> >
>> >    (forall (f1 f2)
>> >       (exists (f)
>> >          (forall (x) (iff (f x) (and (f1 x) (f2 x))))))
>> >
>> >    (forall (g)
>> >       (exists (f)
>> > (forall (x) (iff (f x) (not (g x))))))
>> >
>> >    (forall (g)
>> >       (exists (f)
>> > (forall (x) (iff (f x) (exists (y) (g x y))))))
>>
>> In order to proof these formulas you need a form of a comprehension
>> principle.
>
> I think Drew's idea was that these (perhaps among others) *are*
> comprehension principles.
>
> -chris
>
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