On Mar 30, 2008, at 4:36 PM, [EMAIL PROTECTED] wrote:
Admittedly, though Godel's imagination was "technical", it did produce a startling new insight. But it stopped there. The insights of such folk are into mathematics -- not how we think.
I disagree with (what appears to be) your assumption that insights into mathematics are not--do not include, do not address, exclude (some notion like that)--insights into how one thinks.
Isn't all of mathematics--or for that matter, all of any discipline, and all of all disciplines and metiers--insights into how we think. Perhaps you are misled by the fact that the mode of discussing your own areas of interest (writing and talking about thinking) use the tools of the trade, namely, language. But for others, for mathematicians and painters and cabinetmakers and shipwrights and dancers and cooks, the mode of discussing their work is different from how they do their work, which is the empirical way they think about it. And how a mathematician thinks about his his work, or a dancer thinks about dancing, or a baseball player baseball is embodied more in the doing than in the talking about it.
How often has this happened: "This is what I mean: this is how you draw the elbow." "I want you two to cross and spin, here, and then spread your arms like this." Etc. And so, Godel's or Russell's mathematical insights are insights into thinking that is expressed in mathematics. How else can anyone know mathematics but by means of mathematics? Words don't help, but they do provide a way to gloss the experience in retrospective.
| | | | | | | | | | | | | | | | | | | Michael Brady [EMAIL PROTECTED]
