Re: Mentalism and Calculus
Posted by
Tom Carter on
URL: http://friam.383.s1.nabble.com/Mentalism-and-Calculus-tp526405p528472.html
Nick -
So, ummm . . . in a carefully done axiomatization of Euclidean geometry, the terms "point", "line", "plane" (among others . . .) are left explicitly *undefined* . . . See, for example, Hilbert's axiomatization as described here:
There are very good reasons for leaving terms such as these explicitly undefined -- this allows a multiplicity of models for a given axiomatic system . . .
A book I like on a variety of these issues is "Introduction to Model Theory and Metamathematics" by Abraham Robinson (North Holland Press, 1965) (warning: this is a real mathematics book, probably not for the faint of heart . . . :-)
tom
On Jul 14, 2008, at 8:28 PM, Nicholas Thompson wrote:
No! You have gone a bridge to far, unless you are willing to rewrite the role of definitions in axiom systems.
In a system in which a definition is, "a point is a position in space lacking dimension"
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