Re: Recursive Peirce

sowa <>
Date: Sun, 14 Nov 93 17:03:43 EST
From: sowa <>
Message-id: <>
Subject: Re: Recursive Peirce

The mechanism of typed logic can do everything and anything
that can be done with unrestricted quantification over functions
and predicates.  If you make your sorts big enough to include
everything that would be available in unrestricted quantification,
then you have exactly the same model structures and hence semantics.

Yes, Peirce allowed his constructions to be iterated arbitrarily
far.  The same can be done with CGs and KIF.

Yes, Peirce insisted upon indivisible triads that could not be
subdivided into combinations of dyads.  And I agree with him.

I am trying to finish a new book, with first draft coming out in
May 1994 and final version in Sept. 1994.  All this will be made
clear in the book.  In the meantime, I don't have time to argue
all these details in email.  Read the references:  the HOL ref. in
particular is quite good; the book on many sorted logic by Meinke & Tucker
is also good.  

If you work with those formalisms and find specific problems, then
we can address them in detail.  quit