Jon,
At the age of 12, Peirce acquired a knowledge of logic at the level
of a freshman at Harvard. Over the next 60 years, he developed
ideas that are at the forefront of today's research in logic,
artificial intelligence, and cognitive science. Please read
the article "Peirce's contributions to the 21st century":
http://jfsowa.com/pubs/csp21st.pdf
JFS: Since Peirce is no longer with us, somebody has to pick the nits.
JAS: No, since Peirce is no longer with us, /no one/ can presume
to speak for him; at least, that is what you have been persistently
maintaining.
I have no idea how Peirce would respond to your note. The question
I'm addressing is what Peirce's ideas mean for us: How are they
related to ongoing research in logic and cognitive science?
JAS: As helpfully diagrammed by Existential Graphs, every assertion
is the attribution of general concepts (Spots) by means of continuous
predicates (Pegs) to indefinite individuals (Lines of Identity).
JFS: Peirce would not agree with Jon's sentence above.
JAS: There you go again.
I'll rephrase my point: Anybody who had translated Peirce's EGs
to and from his algebra of 1885 would not write the above sentence.
Any feature of either notation that is lost in translation is a
syntactic item that has no semantic meaning.
JAS
Every EG asserts a proposition, claiming it to be true in the
Universe of Discourse, and thus is accurately characterized as
an assertion. That is why Peirce called the surface on which EGs
are scribed the "Sheet of Assertion," not the "Sheet of Proposition."
No. As early as 1898 (RLT, p. 151) Peirce showed how to use EGs
without asserting them. The idea is as old as Aristotle, and
Ockham developed it in detail. Peirce studied both, lectured on
both, and incorporated the distinction in his logics.
Clarence Irving Lewis and Arthur Prior are two 20th. c logicians
who learned that idea from Peirce and incorporated it in their
versions of logic. I discuss their innovations in the article
http://jfsowa.com/pubs/5qelogic.pdf
JAS
I do [use the word 'spot'] and I suspect that there are other
Peirce scholars who do.
When you're doing textual criticism, it's essential to be precise
about the exact words of the MSS. But when you're trying to reach
a 21st c audience, it's essential to use current terminology.
I've attended Peirce sessions at various APA meetings, and it's
frustrating to see Peirce's magnificent vision isolated from
the broader field. I also attended other APA sessions, where
professional philosophers are making mistakes that Peirce had
criticized and moved beyond.
JFS: He never said nor implied that a peg is a continuous predicate.
JAS: Indeed, and I have never claimed that he did; rather, it is
my own interpretation of EGs in accordance with Peirce's late 1908
analysis of propositions that throws everything possible into the
subject.
As I had pointed out, you took the word 'proper' out of context in
a single passage. There he was talking about what was proper for
just one step in a syllogism. You have never found, and I'm sure
that you never will find any example where he showed a larger EG
with all its polyadic relations eliminated.
This is another reason why it's important to look at developments
in logic during the 20th and 21st c. Logicians have discovered
a wide range of methods that go far beyond anything that was known
in Peirce's day. The method you suggested is not one of them.
JFS: The sentence "A cat is on a mat" is indefinite about the
referents of the two subjects, but neither Peirce nor any modern
logician would say that it's vague.
JAS: Lane's (and Peirce's) point is that "a cat" is indefinite/vague,
such that the principle of contradiction does not apply, because both
"a cat is black" and "a cat is not-black" might be (and, in fact, are)
true; likewise for "a mat."
Your previous example was about the existential quantifier, which
is indefinite about its referent. This point is about predicates
without attached indexes. They are indefinite about what might or
might not be. That is a way of being indefinite because of modality.
A 20th century logician would say that Peirce was talking about
two different ways of being indefinite: by the referent of a
quantifier or by the modality of a predicate. Modern logicians
don't apply the word 'vague' to either method.
In summary, I'm talking about the way a modern logician would
interpret these issues. Nobody knows what Peirce would say.
John
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