Considering that Paris-Harrington is derivable from second order arithmetic, do you think any of the ideas from reverse mathematics might come into play? This paper might of interest if you aren’t very familiar with reverse mathematics, but would like to know more.
Also, it’s my intuition that a good deal of mathematics has more to say about human cognition than it does about anything else. That said, this seems like the sort of problem that should be tackled from a computational neuroscience angle first and foremost. I’m likely wrong about the ‘first and foremost’ part, but it seems like something on numerical cognition could help out.
Also, have you looked at this work? I don’t care for the whole ‘metaphor’ camp of thought (I view it as sort of a ripoff of the work on analogies), but there seem to be a few ideas that could be distilled here.
I’m familiar with reverse mathematics and it is indeed very relevant to what I want. Not so sure about Lakoff. If you see helpful ideas in his paper, could you try to distill them?
I could give it a shot. Technically I think they are Rafael Nunez’s ideas more than Lakoff’s (though they are framed in Lakoff’s metaphorical framework). The essential idea is that mathematics is built directly from certain types of embodied cognition, and that the feeling of intuitiveness for things like limits comes from the association of the concept with certain types of actions/movements. Nunez’s papers seem to have the central goal of framing as much mathematics as possible into an embodied cognition framework.
I’m really not sure how useful these ideas are, but I’ll give it another look through. I think that at most there might be the beginnings of some useful ideas, but I get the impression that Nunez’s mathematical intuition is not top notch, which makes his ideas difficult to evaluate when he tries to go further than calculus.
Fortunately, his stuff on arithmetic appears to be the most developed, so if there is something there I think I should be able to find it.
Considering that Paris-Harrington is derivable from second order arithmetic, do you think any of the ideas from reverse mathematics might come into play? This paper might of interest if you aren’t very familiar with reverse mathematics, but would like to know more.
Also, it’s my intuition that a good deal of mathematics has more to say about human cognition than it does about anything else. That said, this seems like the sort of problem that should be tackled from a computational neuroscience angle first and foremost. I’m likely wrong about the ‘first and foremost’ part, but it seems like something on numerical cognition could help out.
Also, have you looked at this work? I don’t care for the whole ‘metaphor’ camp of thought (I view it as sort of a ripoff of the work on analogies), but there seem to be a few ideas that could be distilled here.
I’m familiar with reverse mathematics and it is indeed very relevant to what I want. Not so sure about Lakoff. If you see helpful ideas in his paper, could you try to distill them?
I could give it a shot. Technically I think they are Rafael Nunez’s ideas more than Lakoff’s (though they are framed in Lakoff’s metaphorical framework). The essential idea is that mathematics is built directly from certain types of embodied cognition, and that the feeling of intuitiveness for things like limits comes from the association of the concept with certain types of actions/movements. Nunez’s papers seem to have the central goal of framing as much mathematics as possible into an embodied cognition framework.
I’m really not sure how useful these ideas are, but I’ll give it another look through. I think that at most there might be the beginnings of some useful ideas, but I get the impression that Nunez’s mathematical intuition is not top notch, which makes his ideas difficult to evaluate when he tries to go further than calculus.
Fortunately, his stuff on arithmetic appears to be the most developed, so if there is something there I think I should be able to find it.