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.
...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.
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
>
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