Jeff and Jerry,
Everything in Peirce's philosophy is related to everything else.
This thread could fan out in all directions, and I have work to do.
So I'll just end my contribution with a couple of short comments
and a copy of the summary from the end of my previous note:
JFS
Summary: What I'm trying to emphasize is the fundamental importance
of diagrammatic reasoning for logic, mathematics, language, science,
and everyday life. The model-theoretic semantics used to define
truth in formal logics is a special case of diagrammatic reasoning.
Jeff
Peirce points out that someone such as an ancient Egyptian property
tax collector, a Chinese astronomer, or an Indian engineer asks a
practical question that couldn't be answered by the normal means,
so the mathematicians were called in for assistance...
most people who play games such as chess and go are not engaged in
mathematical inquiry--at least not in a scientific spirit. They just
want to win the game.
I certainly agree. And I would add that the same point is true
for nearly everybody who uses mathematics. Bankers, tax collectors,
engineers, astronomers... are not engaged in mathematical inquiry.
They just want to do their job.
Jerry
Rosenthal states: … the literature on Peirce contains “no fewer
than thirteen distinct interpretations of Peirce’s views on the
nature of truth”
I haven't counted, but I'm not surprised. As I imply in the summary
above, I'm not adding any new interpretations. I mentioned model-
theoretic semantics, of which Peirce's endoporeutic is an example.
And I'll just make three comments about it.
1. It meets Peirce's criteria for diagrammatic reasoning.
2. For any model M in Tarski's sense and any sentence s for which
M is used to determine a truth value, endoporeutic can be used
to determine exactly the same truth value.
3. The really thorny and controversial issues concern the way the
diagrams are related to perception, reasoning, language, and
purposeful action in, about, and on the world.
For more detail about endoporeutic and points #1 and #2, see
pp. 17 to 20 of http://www.jfsowa.com/pubs/egtut.pdf
For a discussion of #3, see http://www.jfsowa.com/pubs/signproc.pdf
John
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