John,
Thanks very much for these historical notes... I would agree with you that in general, any and every version of logic is 'natural' for applications in which people find it to be useful.
As your note suggests, van Benthem discussed a narrower sense of 'natural logic' in his paper on the history of work on this topic from a Montagovian perspective. He described natural logic as "ubiquitous forms of reasoning that can operate directly on natural language surface form". Later in the paper he observed such systems "may require a fully fledged parse of a sentence."
Also as you predict, van Benthem did not cite Lakoff's 1970 paper on 'natural logic'. The only area of agreement with van Benthem's perspective might be on the very general points Lakoff advocated in 1970, that in a ‘natural logic’ which would account for inferences made in natural language, “the logical forms of sentences are to be represented in terms of phrase structure trees.” Thus, Lakoff in 1970 argued for an approach consistent with Hypothesis II of my thesis.
I can only vaguely recall reading Lakoff's paper in the early 70's... I was reminded of it this summer, when reading MacCartney and Manning's (2008) paper "Modeling Semantic Containment and Exclusion in Natural Language Inference". They cited Lakoff (1970), as well as van Benthem and other authors.
So, whether one takes van Benthem's mathematical perspective, or Lakoff's non-mathematical perspective on natural logic, the topic intersects with my thesis, and seemed worthy of some discussion in a brief postscript.
Full disclosure: As a child, I was fascinated by science fiction novels, which often depended on a scientific invention as the deus ex machina. So I wanted to be a scientist or engineer, and was primarily interested in physics. Since mathematics is the language of science, I found some "Tutortext" books on algebra, geometry, and trigonometry at the local library, and used them to learn the first three years of high school math, the summer before entering high school. So, I would also agree it's valuable for anybody to become a mathematician in their youth. Consistent with Goethe's observation, that it's necessary to learn other languages to get some perspective on life, I studied Latin in high school, though I'm not sure it gave me much perspective on life :)
Phil
> Date: Wed, 10 Dec 2014 11:21:28 -0500
> From: sowa@xxxxxxxxxxx
> To: ontolog-forum@xxxxxxxxxxxxxxxx
> Subject: Re: [ontolog-forum] Barbara Partee on Formal Semantics
>
> Phil,
>
> Since formal logicians are mostly mathematicians, I would quote
> Goethe to summarize my view of what they say about language:
>
> "Mathematicians are like Frenchmen. Whatever you say to them
> they translate into their own language and at once it becomes
> something entirely different."
>
> 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.
>
> 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.
>
> 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.
>
> 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).
>
> 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
>
> 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
>
> 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.
>
> John
>
> _________________________________________________________________
> Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
> Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
> Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
> Shared Files: http://ontolog.cim3.net/file/
> Community Wiki: http://ontolog.cim3.net/wiki/
> To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
>