[FOM] Psychological basis of Intuitionism
rweyhrauch at yahoo.com
Tue Jun 4 20:30:11 EDT 2013
I just read your paper (not yet finished with the context one) and am interested in this subjct.
1) As a matter of setting the record strait about the origins of the concept of 'context' in AI ... please read the 'historical remarkks' in 'http://disi.unitn.it/~context/', which appears in the bibliography of your paper 'Logic in Context' , which credits me with the first (and extensive) use of contexts in the FOL project at the AI lab. The discussion at the time at the AI lab was extensive and McCarthy was simply a popularizer.
2) the FOL project had running code that implemented this notion in a much richer way than described by JMC. Even Martin Davis used this system when he visited there. The "prolegomena' paper (in eg Fausto's bibliography) is the second most reprinted AI article (after McCarthy and Hayse). 11 times. The original is the one in the AI journal which was a version of an AI report I wrote in 1977 and was 'forced to publish' by Danny Bobrow ... (note its in a strangs palce (ie the special issue on non-monotonicity). You should be aware that the examples in that paper are actual printout (as the AI lab had keyboards and printers with the logical symbols ... ) I only realized that people thought these were just my writing, NOT actual output, many years later. There are at least 200 actual papers about the FOL system and its use and there are many references to its ideas (which eg included the ability to use sound reflection principles (see Kowalski's use of
reflection (and credit to me))) and a lot of writing and ideas about formalized metstheory ...
3) Although I left the university (in 1982), work on the use of contexts for formal reasoning has continued (although unpublished). Fausto carried the ball at Trento for a time but as these things go he developed some of the ideas with his multi-context reasoning systems. John piled on later. My motivations and goals were similiar to those you describe in the paper mentioned below, but they were somewhat different and resulted in a somewhat different direction. I have only lately been thinking about this and intuitionism. I am interested in discussion if you want. Send me an email.
--- On Tue, 6/4/13, Arnold Neumaier <Arnold.Neumaier at univie.ac.at> wrote:
> From: Arnold Neumaier <Arnold.Neumaier at univie.ac.at>
> Subject: Re: [FOM] Psychological basis of Intuitionism
> To: "Foundations of Mathematics" <fom at cs.nyu.edu>
> Date: Tuesday, June 4, 2013, 2:20 AM
> On 05/28/2013 02:38 PM, Steve
> Stevenson wrote:
> > “Intuitionism is based on the idea that mathematics
> is a creation of
> > the mind. The truth of a mathematical statement can
> only be conceived
> > via a mental construction that proves it to be true,
> and the
> > communication between mathematicians only serves as a
> means to create
> > the same mental process in different minds.”
> > (http://plato.stanford.edu/entries/intuitionism/)
> > Now that I'm retired, I would like to research how
> exactly this plays
> > out, especially metacognitive processes. The question,
> simply put, is
> > “Just how do we do it?”
> I give a (nonintuitionistic) answer in Chapters 1 and 3 of
> my (so far
> unpublished) manuscript
> I didn't finish this as project funding was unsuccessful.
> Your comments (but not through FOM) are appreciated.
> Best wishes,
> FOM mailing list
> FOM at cs.nyu.edu
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