[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.


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