Re: Roles, again (Pat Hayes)
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Date: Sun, 10 Sep 1995 22:44:36 -0600
To: (John F. Sowa),
From: (Pat Hayes)
Subject: Re: Roles, again
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At 12:53 PM 9/10/95 +0500, John F. Sowa wrote:
>If you want to flame, I can bring out my standard flame.....

Well, lets not flame, I agree, unless there is something worth heating up.
My 'flame' was a protest about your (I'm being serious now) completely
incomprehensible 'explanation' of N-ness for small N, and you havnt
responded to its substance here. 

>Seriously, I do believe that extensionality,
>which is a fine basis for first-order talk about concrete individuals
>in first-order language has serious limitations, which Frege and Russell
>tried to deal with in ways that have been highly influential, but which
>have led to numerous unsolved problems with contexts, situations, intentions,
>etc., etc. 

Its not at all clear that anything in modern logic has 'led to' these
problems, if that is what they are. It may have failed to resolve some of
them, but I still havnt seen any account of how you think Peirce avoided
them. All I have seen so far is an awkward notation for ordinary predicate
logic based on a misleading chemical analogy, and some vague and apparently
undefinable distinctions between 3 different kinds of something. 

>Frege, by the way, wasn't a pure extensionalist, and his
>distinction between Sinn und Bedeutung is a partial approach to what Peirce
>developed in much more detail with his semiotics.

Frege made the distinction so as to get the Sinn out of the way and just
focus on the Bedeuting, an insightful move that made modern logic possible.

>......  Peirce's semiotics
>was a theory of metalanguage and levels of metalnguage about metalanguage.
>But through it all, you can give an extensional interpretation of semiotics
>as a theory of quantification over concrete signs or signs of signs, etc.

We already have several well-worked-out accounts of these relationships.
Quine's corner-quotation for example is one elegant way to talk about
languages. The relation of language to metalanguage is certainly an
important and delicate one, as we all know since Goedel. (Peirce did not
have the advantage of acquaintance with the undecidablity theorems, and I
would be interested to know if they can be handled in his framework. How
about the idea of a 'standard model' for set theory, or the notions of
countability and recursive enumerability?) 

>I will certainly agree that Peirce's writings are not the easiest to read,
>especially when he is trying to develop his own original material.  His
>comments and criticisms of other writers are usually a model of clarity,
>but when he was trying to explore new territory "where no man had gone
>before", he struggled to find words for expressing his ideas.  And I can
>hardly blame him for that.

I do not blame Peirce for anything. I agree, he was a great man, etc. But
as I said, we have 100 years lead on him now: we have Goedel, Turing,
Carnap, Quine, Kripke, etc. etc.. not to mention work in other areas of
philosophy and psychology.

>There is a book I would recommend for its comparison of Peirce's semiotics
>to Saussure's:

Saussure!??  You keep telling us to wander in the dim outer reaches of
historical scholarship in order to discover something about C.S.Peirce.
What is it that we are likely to find there?

I'm not just trying to annoy you Peircians by these flames. This stuff is
being seriously proposed as the basis for practical ontological systems: we
are arguing here about the very top of the classification trees. But they
generate considerable confusion and puzzlement, and seem to reap no
advantage. Why don't we just toss them and get on with the work at hand? I
am sure you must think that there are some positive answers to these
questions, but I havnt seen them yet. Will I see them better after reading
150 pages on Sausurre, for Gods sake, by a literary critic?

Pat Hayes

PS. For the "irreducibility of Threeness", see my earlier message to Fritz

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