Ben, How is maths grounded? Well I haven't actually read Lakoff on Maths (and you're right BTW about the often sprawling nature of his & the others' work) so I can't tell you what he says. But the core of numbers' groundedness seems obvious to me, when I think about it.
It lies in the composite nature of our numeral system. Our decimal number system is obviously based on the basic numbers 1 - 10 - which are countable by hand. Digital. We have numbers like 2031, 43458, 1,000,002 - which are all reducible to, and built up from, physically countable tens. We absolutely need that. We could in principle have totally arbitrary signs instead - an arbitrary figure "gx" say [sorry I'm limited here by the keyboard] which would stand for 1.000.002 and "dj" for "1,000,003". We don't. Such numbers would be impossible to make sense of. We have a compositely grounded system. And this applies too, though, in a more complex way to something like the Roman numeral system. First I, II, III - obviously grounded. Then V - a graphic, it seems to me, for a (five fingered) hand. IV - the hand minus one. VI - the hand plus one. X - seems to me like two V's on top of each other. And so on .. I won't elaborate the lot. But the Roman numeral system is also obviously a compositely grounded affair. And the need to keep developing numeral systems - and invent superior ones like the decimal one from the Roman - comes from our brain's continuous attempts to ground all numbers and symbols (and its continuous frustrations with the difficulty of so many mathematical figures and forms). P.S. You will find, I suggest, - and this is of extreme importance here - that all of people's difficulties in understanding - their confusion about - maths, lies in their brain's failure to ground/ make sense of the various forms. Their difficulties with fractions, calculus, integration, differentiation (you what, mate?)... square roots of negative numbers etc. etc. I don't think there's a serious comeback to these arguments... ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244&id_secret=52957729-f92a02
