SUO: Re: General Design
Tom,
The attached diagram illustrates a point, which has been strongly
influenced by Peirce and which makes much of the old terminology
obsolete. (Note, by the way, I consider Peirce's terminology "new"
because it has had very little influence on 20th century analytic
philosophy, despite the fact that he coined most of the terms in
the 19th century.)
At the left of mthworld.gif is an icon of the world, which is
much messier and more complex than any of us or our theories can
comprehend. At the right is a simple elegant theory, which is
supposed to say something about the world. What it says can only
be interpreted in terms of some model (in Tarski's sense, a set
of individuals and a set of relations over those individuals).
The axioms of the theory have denotation T or F in terms of the
model, but the model is only an approximation to some aspect
of the world for some purpose.
I use this diagram to illustrate many different points:
1. The signs in the theory and the signs in the model are
all semiotic entities, which are not the world, but which
bear some relationship to something in the world for
somebody for some purpose.
2. Truth and falsity (a la Tarski) are relationships between
a theory and a model. Approximation or fuzziness (a la Zadeh)
is a relationship between a model and the world. My major
complaint about fuzzy logic is that is suffers from the
"fallacy of misplaced fuzziness" -- it attributes fuzziness
to the truth values, when it should attribute fuzziness to
the measure of how well the model approximates the world.
3. One of my favorite quotations about models is by the
statistician and professor of engineering, George Box,
who said "All models are wrong, but some are useful."
(And I consider engineering models and Tarski-style
models to be two alternate ways of getting to the same
kind of representation -- a semiotic system with some
symbols that represent things called individuals and
other symbols that represent relations among individuals.)
4. Box's slogan is a succinct statement of Peirce's pragmatism:
Peirce believed that there does exist a real world, which
is fundamental for determining truth, and any formulation
we may put together is likely to be wrong in the details,
but perhaps adequate for some purpose in gross structure.
One of Peirce's sayings: "It's easy to be certain; one
has only to be sufficiently vague."
5. I regard all the obsolete terminology, such as "family
resemblance", "analytic/synthetic", etc., to be useful
ways of talking about semiotic systems and their
relationship to the world. But I also believe that
those distinctions can be refined and extended in much
greater detail by using Peirce's work on classifying
signs and their relationships to one another, to logic,
and to the world.
6. I don't know of anybody who has fully come to grips
with the entire scope of what Peirce was trying to
express -- and Peirce himself admitted that there was
much more that he still had not had a chance to finish
writing. There is a great deal of gold in the unpublished
manuscripts that nobody has yet mined. (Yet there is
also a lot of good, easily accessible material that
has already been published.)
John Sowa
Tom Johnston wrote:
> One way to contextualize my earlier email today, and my still earlier
> comments re Rorty, Quine, Wittgenstein 2, etc, is to say that I agree with
> all four of your points. My notion that family resemblances can be combined
> with Aristotelian definition is perhaps my less formally rigorous way of
> making some of those same points. I still have to spell out what I mean, but
> I wouldn't be surprised to find, after doing so, that you and others had
> already reached that conclusion, and had already expressed it more
> rigorously than I ever could.
>
> On the other hand, that position of mine is consistent with the thesis that
> analytic/synthetic is a matter of degree; and I'm not sure you agree. It is
> consistent with synonymy in natural language being a matter of fuzzy
> boundaries; and I'm not sure you agree. It is consistent with Rorty's
> anti-representationalism and rejection of a correspondence theory of truth;
> and I'm not sure you agree. So I'll continue on, and see what happens.
>
> I am grateful that you're better versed in the language I am comfortable
> with than I am in yours. Otherwise we wouldn't be having these
> conversations!
