Lakoff ...
"Where Mathematics Comes From" ... George Lakoff / Rafael E. Nunez
I've talked about this text in several places. I have to admit, however, that my only real draw to the text is that we (myself and the authors) have a common starting point, which happens to lie outside the mainstream, and a common task.
Starting point (in my words, not their's): The truths of mathematics apply to the physical world for the reason that the most elementary mathematical concepts are "learned" about the world. They ARE science.
(When i say "learned" here, i caveat, so as not to avoid directly in conflict with everything i just posted on Natalie's site, i am including the evolutionary refinements of a species. Creatures "learned" genetically to subtize about the world. I mean that very metaphorically.)
Common task (again in my words): To extend these most basic scientific facts (that we call simple arithmetic) to cover all (non- deviant/alternative) math and logic up to Kurt Goedel, and therefore to cover the science that uses said math.
That said, reading the text "Where Mathematics Comes From" immediately throws me back in memory to my days of studying Hegelian Dialectical Structure (of the world) charts. It takes very little reading of such things by a minimalist like myself to say, "this can't possibly be even close to correct".
Note - that is merely an intuition, not an argument.
I don't mean to imply that Lakoff/Nunez are merely engaged in Hegelian type metaphysics ... what i hope to get across is the feeling i had while reading the text ... the closest i had to it previously was very directly in Hegel.
Its not just the complication of the structure. In my computational theory classes digging through Goedel, Peano, Kleene, etc i often felt lost in the structures, had trouble comprehending the reasons for their philosophical moves, and the like, but it never felt derived ... that is the word, derived ... those structures.
These Lokoff structures, taken at face value, seem derived.
Even so, i still found them interesting. They point out, intentionally so, exactly what the human brain would need to know in order to accomplish X, Y or Z. The lists of what is necessary to know to accomplish certain thoughts, and the lists of what would need to be accepted metaphors in the brain ... they are staggering. It is good to point them out.
In my heart, though, i think it will turn out to be far more simple than it looks. Most tasks the brain does, i believe, are like that. They look complex, but often they are just the meshing of many simpler mechanisms butressed by a newer part of the brain that can create, form, hold and use symbols (what Lakoff and Nunez prefer to call metaphors).
Metaphors ... yes ... we must remember that Lakoff has a grander theory into which this effort is tying and his concept of the conceptual metaphor as a framing device is very important.
And the moral of that is ...
"Kleeneliness is next to Goedeliness"
... okay, no it isn't.
But i just recalled that phrase from somewhere and i felt the need to include it.
Its funny.
So laugh.
Laugh, damn you!
I've talked about this text in several places. I have to admit, however, that my only real draw to the text is that we (myself and the authors) have a common starting point, which happens to lie outside the mainstream, and a common task.
Starting point (in my words, not their's): The truths of mathematics apply to the physical world for the reason that the most elementary mathematical concepts are "learned" about the world. They ARE science.
(When i say "learned" here, i caveat, so as not to avoid directly in conflict with everything i just posted on Natalie's site, i am including the evolutionary refinements of a species. Creatures "learned" genetically to subtize about the world. I mean that very metaphorically.)
Common task (again in my words): To extend these most basic scientific facts (that we call simple arithmetic) to cover all (non- deviant/alternative) math and logic up to Kurt Goedel, and therefore to cover the science that uses said math.
That said, reading the text "Where Mathematics Comes From" immediately throws me back in memory to my days of studying Hegelian Dialectical Structure (of the world) charts. It takes very little reading of such things by a minimalist like myself to say, "this can't possibly be even close to correct".
Note - that is merely an intuition, not an argument.
I don't mean to imply that Lakoff/Nunez are merely engaged in Hegelian type metaphysics ... what i hope to get across is the feeling i had while reading the text ... the closest i had to it previously was very directly in Hegel.
Its not just the complication of the structure. In my computational theory classes digging through Goedel, Peano, Kleene, etc i often felt lost in the structures, had trouble comprehending the reasons for their philosophical moves, and the like, but it never felt derived ... that is the word, derived ... those structures.
These Lokoff structures, taken at face value, seem derived.
Even so, i still found them interesting. They point out, intentionally so, exactly what the human brain would need to know in order to accomplish X, Y or Z. The lists of what is necessary to know to accomplish certain thoughts, and the lists of what would need to be accepted metaphors in the brain ... they are staggering. It is good to point them out.
In my heart, though, i think it will turn out to be far more simple than it looks. Most tasks the brain does, i believe, are like that. They look complex, but often they are just the meshing of many simpler mechanisms butressed by a newer part of the brain that can create, form, hold and use symbols (what Lakoff and Nunez prefer to call metaphors).
Metaphors ... yes ... we must remember that Lakoff has a grander theory into which this effort is tying and his concept of the conceptual metaphor as a framing device is very important.
And the moral of that is ...
"Kleeneliness is next to Goedeliness"
... okay, no it isn't.
But i just recalled that phrase from somewhere and i felt the need to include it.
Its funny.
So laugh.
Laugh, damn you!
posted by Thomas F. Schminke at 6:58 PM
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