ONT Re: Identity & Teridentity
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BU = Ben Udell
BU: Generally I'm not saying that there is no problem
in computer programming like what you & Jon have
been talking about. I wish you or Jon could state
the problem in a way that would make it easier for
non computer-programmers like me to understand what
it is, even if it means providing some oversimplified
examples, or writing at the level where the reader of
a popular science magazine like 'Scientific American'
can understand.
Ben,
I believe that the basic issues were written up in 'Popular Science' some time ago.
If I knew the emoticon for "not entirely tongue in cheek" (NETIC), I would insert
it at this point. I have already recommended to you the second half of Smullyan's
book 'To Mock a Mockingbird' as a light-hearted but very non-shabby introduction to
combinator calc and combinator logic and many related issues. The main reason that
some bitty.gritty.practical.engineering.untouchable.and.darn.near.unmentionable.caste
like computer programming comes into this garden of philosophical e-lightenment is
a bit like this: It was only with the 20th Century re-discovery of the reality of
the information dimension and the critical importance of "effective description" in
the theory of computability (recursive function theory) that many people started to
appreciate many of the things that Peirce had been talking about a half-century before.
Most of the people who went through these intellectual revolutions, with a handful of
notable exceptions, had never even heard of Peirce, in spite of using conceptual frames
and systems of notation that he had played the lion's share in shaping, and so they had
to learn all this stuff all over again the hard way.
The key notion in computability theory is that of "effective description".
Like the notion of "operational definition", this is easily recognized as
yet another variation on the theme of the "pragmatic maxim". When we are
talking about the effective description of the objects that we imagine we
denote by means of our informal concepts, say, like the square root of 2,
and the effective description of the actions that it would take to begin
producing a less obscure approximation to it, it is almost an incidental
motiv that we have built machines which have the capacity to act in ways
that "model" these effective specifications.
Formal intellectual procedures like computations and proofs -- and it is one of
the leitmotivs of recursive function theory that computations, rightly conceived,
have very much the same structures as proofs by mathematical induction -- are
examples of semiosis, that proceed from obscure signs of objects, say, "2+2",
to clear or canonical signs of the same objects, in this case, "4" for 4.
This is what Frege was talking about with all that Hesperus/Phosphorus business.
He was a mathematicion, and his audience would have understood his illustration
as referring to their common problems about diverse descriptions denoting the
same formal objects -- they all knew that he did not care a Fig. 1 about this
example taken literally. It is like Bernard's comment that we should not let
the illustration of the theory reduce us to the theory of the illustration.
My best bet at present for making any of this clear is to continue with
the "Critique" and the "New List" threads. I hope eventually to give
the careful reader a sense of how Peirce would have read the logical
formulas that he wrote, and to put that in a comparative context
with the way that many of us apparently learned was the only
possible way to read them
Until then,
Jon Awbrey
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