[FOM] Question on Number Line (Bruckner)
Robert Tragesser
thesavvydog at mac.com
Wed Nov 16 12:54:34 EST 2005
>
> From: "Dean Buckner" <d3uckner at btinternet.com>:
>
> I have a quotation that says that Goedel also found this idea
> problematic. Is this true?
>
At a talk at SUNY-Buffalo in the early 70's, Harvey Friedman referred
to the conflict between our intuitive sense, when a line is split,
that the parts have end points (termini) with no point is lost, and
our virtually paradigmatic representation of the line continua
composed of points (so that when split, either one part has an end-
point and the other doesn't, or a point is removed and neither point
has an endpoint), as "Gödel's Paradox of Geometric Intuition". (So
maybe Harvey has some idea of how Gödel understood this?)
Dana Scott remarked that this problem arose for Tarski when he was
working on what became his paper on geometric solids (reprinted in
Logic, Semantics, Metamathematics)...and he there found a way of
resolving it.
rtragesser
nyack-on-the-hudson
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