[FOM] Corrected response to Question on Number Line (Bruckner)
Robert Tragesser
thesavvydog at mac.com
Wed Nov 16 18:55:02 EST 2005
Corrected original (wrote 'point' when I meant 'part').
r tragesser
> From: "Dean Buckner" <d3uckner at btinternet.com>:
>
> I have a quotation that says that Goedel also found this idea
> problematic. Is this true?
>
At discussion 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 as 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 part 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.
robert tragesser
nyack-on-the-hudson
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