>Martin Brown writes: > > Re geometry. I think Goedel's paradox tends to refute your [Justin's??] >statement. ...< > >which statement? and how does Goedel do so? > >I'm not great mathematician, but I think that Goedel says that geometry and >many other sub-fields of mathematics, are, in some sense, circular, because >they are not reducible to a set of primitive fundamentals that are in some >sense self evidently true. That's not what logicians means by circularity. G's theorem is as I have explained here before) that for any formal system that is powerful enough to state simple arithemaetic, there is at least one true proposition in that system that is not provable within it. E.g., for arithemetric, you need set theory, etc. There is no implication of circularity, which is a matter of defining term A in terms of term B and vice versa. I met G and spoke to him when he was at the Institute and I was a Tigertown undergrad . . . . jks _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com
