Phil, (01)
Since formal logicians are mostly mathematicians, I would quote
Goethe to summarize my view of what they say about language: (02)
"Mathematicians are like Frenchmen. Whatever you say to them
they translate into their own language and at once it becomes
something entirely different." (03)
Barbara Partee is too good a linguist to be completely seduced by
the mathematicians, but she fell under the spell of Montague and his
colleagues in her youth (associate prof. at UCLA). But she tends to
change point of view with husbands. In her Montagovian stage, she
was married to Emmon Bach. But when she became more sympathetic to
lexical semantics, she married a Russian lexical semanticist. (04)
Full disclosure: I began life as a chemist (my father had studied
chemical engineering), but with 10th grade geometry, I fell in love
theorem proving methods. So I became a mathematician. I believe
that it's valuable for anybody to become a mathematician in their
youth. But as Goethe observed, it's necessary to learn other
languages to get some perspective on life. (05)
My current view of natural logic: Any and every version of logic
is *natural* for whatever application any human finds it useful.
For example, chess notations are natural versions of logic for
chess players. Some write N-KB3 and others write g1-f3. Either
notation is equally natural for those who like it. (06)
But *every* version of logic is derived from abbreviations for
NL words and phrases. Note that chess logics are abbreviations
for "Move the knight to the third rank on the king bishop file"
or "Move the piece on g1 to f3" (where g1 and f3 are names
assigned to the squares on the chessboard). (07)
Re inference methods: Every human method of reasoning is intimately
connected with the mental models that people use when thinking about
the subject matter. For an excellent study, see Adriaan de Groot's
book, _Thought and Choice in Chess_, which led Herb Simon to invite
de Groot to spend some time at CMU. The rules of inference in formal
logics are based on the way mathematicians *write*, not on the way
they *think*. See my slides http://www.jfsowa.com/talks/micai.pdf (08)
I noticed that you cite van Benthem's history of natural logics:
http://www.illc.uva.nl/Research/Publications/Reports/PP-2008-05.text.pdf (09)
That's a good, but very narrow summary. Van Benthem is the kind of
mathematician Goethe was thinking of, and he would never cite Lakoff's
writings on natural logic. But I put Lakoff and van Benthem at two
ends of a spectrum, with reality somewhere in the middle. (010)
John (011)
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