[FOM] repairing a bridge between mainstream mathematics and f.o.m.

Timothy Y. Chow tchow at alum.mit.edu
Fri Jul 17 20:33:44 EDT 2009

Tom Dunion wrote:
> Finally, back to the dart throwing experiment.  Wherever y is, its set 
> of ordinal predecessors {z: f(z) < f(y)} has cardinality not greater 
> than aleph-one, but may well be a nonmeasurable set, not necessarily a 
> set of measure zero; the same can be said about x.  So the 
> "contradiction" to our probabilistic intuitions that arose under CH does 
> not arise here, and perhaps now we can take down the "Bridge out" sign.

I've reread your message several times, but I confess that I still don't 
understand what you think the disconnect between f.o.m. and mainstream 
mathematics is.  Do you believe that all mainstreamers accept Freiling's 
argument but that all or some f.o.m.ers don't?  This is certainly not the 
case.  There is disagreement about Freiling's argument, but it does not 
split neatly along an f.o.m./mainstream boundary.

I also don't understand what your new argument is intended to demonstrate.  
Is it supposed to bolster Freiling's argument, or undermine it, or show 
that some apparent contradiction (what apparent contradiction do you have 
in mind?) does not exist?

My point of view is that in the presence of AC, we can't trust our 
probabilistic intuitions.  (Witness the Banach-Tarski paradox.)  
Freiling's argument is just another demonstration of this fact, and does 
not really have much to do with CH per se.


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