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John Sowa - very nice outline of 'thinking', which is, as you say,
diagrammatic. And as you say, independent of any language or
notation. The ability of the human species to 'symbolize', i.e., to
transform that diagrammatic reasoning into symbols was certainly a
massive evolutionary capacity. BUT, we must acknowledge that this
transformation is just that, a transformation, and can mislead,
mistransform from the one to the other. Then, we become rigid and
'stick to our words' and our 'symbolic meanings' and ignore the
vitality of the diagram. I think that the triadic semiosis, with that
mediative process, is a key factor in helping to prevent such
rigidity.
Edwina Taborsky
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On Tue 07/03/17 9:56 AM , John F Sowa s...@bestweb.net sent:
Jerry,
We already have a universal foundation for logic. It's called
"Peirce's semiotic".
JLRC
> the mathematics of the continuous can not be the same as the
> mathematics of the discrete. Nor can the mathematics of the
> discrete become the mathematics of the continuous.
They are all subsets of what mathematicians say in natural
languages.
In Wittgenstein's terms, they are "language games" that
mathematicians
play with a subset of NL semantics. It's irrelevant whether they
use
special symbols or words like 'set', 'integral', 'derivative' ...
For that matter, chess, go, and bridge are just as mathematical as
any other branch of mathematics. They have different language
games,
but nobody worries about unifying them with algebra or topology.
I believe that Richard Montague was half right:
RM, Universal Grammar (1970).
> There is in my opinion no important theoretical difference between
> natural languages and the artificial languages of logicians;
indeed,
> I consider it possible to comprehend the syntax and semantics of
> both kinds of languages within a single natural and mathematically
> precise theory.
But Peirce would say that NL semantics is a more general version
of semiotic. Every version of formal logic is a disciplined subset
of NL (ie, one of Wittgenstein's language games).
JLRC
> I am simply saying that the thought processes of the scientific
> community (and my thought processes) did not stop on April 19,
1914.
Peirce would certainly agree. He said that building on the
foundations he laid "would be a labor for generations of analysts,
not for one" (MS 478). The 20th c logicians who ignored Peirce were
on the wrong track. Many of them haven't yet reached the 14th c.
Peirce was far ahead of the 20th c because he did his homework.
JLRC
> For a review of recent advances in logic, see
> http://www.jyb-logic.org/Universallogic13-bsl-sept.pdf [1],
> 13 QUESTIONS ABOUT UNIVERSAL LOGIC.
Thanks for the reference. On page 134, Béziau makes the following
point, and Peirce would agree:
> Universal logic is not a logic but a general theory of different
> logics. This general theory is no more a logic itself than is
> meteorology a cloud.
JYB, p. 137
> we argue against any reduction of logic to algebra, since logical
> structures are differing from algebraic ones and cannot be reduced
> to them. Universal logic is not universal algebra.
Peirce would agree.
JYB, 138
> Universal logic takes the notion of structure as a starting
> point; but what is a structure?
Peirce's answer: a diagram. Mathematics is necessary reasoning,
and all necessary reasoning involves (1) constructing a diagram
(the creative part) and (2) examining the diagram (observation
supplemented with some routine computation).
What is a diagram? Answer: an icon that has some structural
similarity (homomorphism) to the subject matter.
JYB, 138
> structuralism as we understand it is something still larger that
> includes linguistics, mathematics, psychology, and so on...
> what concerns us are not so much historical and sociological
> considerations about the development of structuralism, but rather
> the issue of the ultimate view of structuralism as underlying
> mathematical structuralism and universal logic.
If you replace 'structuralism' with 'diagrammatic reasoning',
Peirce would agree.
JYB, 145
> Some wanted to go further and out of the formal framework, namely
> those working in informal logic or the theory of argumentation.
> The trouble is that one runs the risk of being tied up again in
> natural language.
See my comment above about Montague, Wittgenstein, and Peirce.
Universal logic (diagrammatic reasoning) is *independent of* any
language or notation. The differences between the many variants
are the result of drawing different kinds of diagrams for sets,
continua, quantum mechanics, etc. (Note Feynman diagrams.)
Whatever the reasoning stuff may be, it would support NL-like
reasoning as a more general version of the 20th c kinds of logic.
I develop these points further in the following lecture on Peirce's
natural logic: http://www.jfsowa.com/talks/natlogP.pdf [2]
See also "Five questions on epistemic logic" and the references
cited there: http://www.jfsowa.com/pubs/5qelogic.pdf [3]
John
Links:
------
[1]
http://webmail.primus.ca/parse.php?redirect=http%3A%2F%2Fwww.jyb-logic.org%2FUniversallogic13-bsl-sept.pdf
[2]
http://webmail.primus.ca/parse.php?redirect=http%3A%2F%2Fwww.jfsowa.com%2Ftalks%2FnatlogP.pdf
[3]
http://webmail.primus.ca/parse.php?redirect=http%3A%2F%2Fwww.jfsowa.com%2Fpubs%2F5qelogic.pdf
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