Chris, (01)
CP> However, it seems to me that in the late 20th century this
> tradition was abandoned. That logicians (like mathematicians)
> wanted to develop systems with little or no ontological commitment. (02)
First of all, logic is a prerequisite for ontology, as Aristotle
said. So any attempt to avoid ontological commitment in the logic
is a very traditional Aristotelian approach. (03)
The application of logic to mathematics is also very traditional.
Euclid was inspired by Aristotle to systematize the mathematics
of his day, and much of his terminology was adopted from Aristotle.
Since the syllogisms didn't support full FOL, Euclid couldn't use
them to formalize the reasoning. But there is a direct line of
influence from Aristotle to Euclid to Hilbert, Tarski, and Gödel.
(Tarski, by the way, quoted Aristotle in the famous paper that
introduced his model theory.) (04)
But as I have written in many email notes and publications,
the most serious blunder was by Frege, Russell, and Carnap:
the deprecation of natural language as a degenerate version
of logic. That is the source of the "grave errors" (schwere
Irrtümer) that Wittgenstein addressed in his later philosophy. (05)
The most brilliant work in ontology during the 20th century
was written by Peirce, Whitehead, and the later Wittgenstein.
As logicians, they were just as brilliant as Frege, Russell,
and Carnap, but they rejected their blunders. (06)
CP> So, if I look through the philosophy -- ontology textbooks on
> my bookcase, for example, Lowe's 'The Possibility of Metaphysics:
> Substance, Identity and Time', I find only a brief mention of
> logic, typically where it is distinguished from metaphysics. (07)
The 20th century is an aberration caused by the split between the
analytic philosophers and the so-called continental philosophers.
(And I blame that split on the schwere Irrtümer of Frege, Russell,
and Carnap.) But note the work on ontology in Husserl's
_Logical Investigations_, Carnap's _Logische Aufbau_, and
Nelson Goodman's _Structure of Appearance._ (08)
CP> So it seems to me that as a historical comment my original
> point stands -- where 'tradition' is understood as current
> mainstream, rather than historical mainstream. (09)
There is a direct continuity between what people are currently
doing and the historical developments from Aristotle to Peirce,
Husserl, Whitehead, Wittgenstein, and modern AI. See, for example,
the following paper: (010)
http://www.jfsowa.com/pubs/csp21st.pdf
Peirce's Contributions to the 21st Century (011)
If you don't believe me, please look at the very extensive
analysis by the Danish philosopher Frederick Stjernfelt
in his very large book, _Diagrammatology_. In that book,
Stjernfelt notes the very strong affinities between Peirce
and Husserl. Both of them were much closer to one another
than either was to Frege or Russell. (012)
CP> It does seem to me that if there is relationship, then it is
> something to do with Husserl and Russell's notion that logic
> can be a tool to describe ontologies. (013)
Excuse me. That was Aristotle's position: logic is the
_organon_ (tool) for doing philosophy, including ontology,
the first philosophy. (014)
John (015)
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