Jon AS and Jerry LRC,
I changed the subject line to emphasize the danger of putting
anyone in a mental straitjacket by "harmonizing and synthesizing"
their writings, opinions, or way of life.
But first, I'll say that I enjoyed the following article by Jon:
"A Neglected Additament: Peirce on Logic, Cosmology, and the Reality
of God": https://tidsskrift.dk/signs/article/view/103187/152244
That's a good article with a good selection and commentary about
the quotations by Peirce. I'll just mention one from page 7:
CSP (R 843:18&20[1-2])
Indeed, meaning by "God," as throughout this paper will be meant,
the Being whose Attributes are, in the main, those usually ascribed
to Him, Omniscience, Omnipotence, Infinite Benignity, a Being not
"immanent in" the Universes of Matter, Mind, and Ideas, but the Sole
Creator of every content of them without exception...
As Peirce said, God is not immanent in any of the three universes.
That is a reasonable view that is based on Neoplatonist theology by
Plotinus, who strongly influenced Christianity and Islam. But Philo
Judeus of Alexandria had harmonized the Septuagint with an earlier
version of Platonism.
But I do not accept the claim that Peirce's semeiotic writings
rule out the possibility of God being immanent in any or all of
the three universes. In fact, John the Evangelist equated Theos
with Logos, which could be considered part of the universe of
necessity. John wrote that after Philo but before Plotinus.
JLRC
in my analysis, Sowa’s views are remote from the bedrock of CSP’s
writings. As I understand his views, first order predicate logic is
the ultimate test of CSP’s logical forms. But, first order predicate
logic is very remote from logic of chemistry and the bedrock of CSP’s
graph theory. The logic of the table of elements associates several
physical attributes (indices) and hence the propositions of chemical
logic can not be antecedents of predicate logics.
Please do not attempt to "harmonize" Peirce or me. For both of us,
our fathers inspired a lifelong interest in math & science, and we were
inspired by the diagrams of organic chemistry to prefer a graph logic
to an algebraic logic. We also agree that FOL is an important version
of logic, but that major extensions are necessary.
But the details are far more complex. I reject any attempt to force
Peirce or me into a mental straitjacket based on something that we
may have written about chemistry or anything else.
To summarize the issues, I'll cite some articles that discuss the
limitations of FOL and build on Peirce's logic and semeiotic.
1. I strongly endorse Peirce's views about vagueness and its importance
for every subject, including mathematics. See an article on fuzzy
logic, which I contributed to a Festschrift for Lotfi Zadeh's 90th
birthday: http://jfsowa.com/pubs/fuzzy.pdf
2. 20th c. work on modal logic was inspired by Peirce's writings,
and his views are still at the forefront of today's research.
See http://jfsowa.com/pubs/5qelogic.pdf
3. The view that FOL, by itself, is adequate as a foundation for
science, led Carnap and the Vienna circlers to the disaster they
called logical positivism. See the article on Signs, processes,
and language games: http://jfsowa.com/pubs/signproc.pdf
4. In 2015, I presented a 3-hour tutorial on natural logic, in
which I discussed the many complex issues in relating language
and logic. No current version of logic could qualify as a
natural logic, but Peirce's EGs, with some extensions, come
closer than the others: http://jfsowa.com/talks/natlog.pdf
JFS: I endorse Edwina's caveats. Her examples are among the "puffy
clouds" that create ambiguities in any reasoning stated in ordinary
language.
JAS: Do you likewise endorse all of Edwina's attributions of positions
to Peirce that he did not explicitly state?
I said that I endorse her caveats. Anyone is entitled to propose any
interpretation of Peirce they consider worth mentioning. But she was
proposing them as alternatives to be considered, not as claims that
they harmonize or synthesize Peirce's views.
In what sense are her own (or anyone else's) posts any less
pervaded by "puffy clouds" than you claim mine to be?
There is nothing wrong with vagueness (AKA puffy clouds of words).
It's essential for the flexibility and expressive power of language,
but other choices may be better for other purposes. FOL (in EGs or
in predicate calculus) is more precise. But that precision, which
may be an advantage in some cases, makes FOL more fragile, brittle,
harder to read, much harder to write, and much much less expressive.
From p. 6 of fuzzy.pdf
As Peirce said, “Logicians have too much neglected the study of
vagueness, not suspecting the important part it plays in mathematical
thought” (CP 5.505). In that same section, he said that the defining
characteristic of a vague sentence is a violation of the law of
contradiction: if a
