[FOM] 461: Reflections on Vienna Meeting

Timothy Y. Chow tchow at alum.mit.edu
Tue Jun 14 21:35:32 EDT 2011

Alex Simpson wrote:

>   AM: How is he confused? It *might* be inconsistent. I mean, it would
>       be a shock. That would be a genuine crisis. I think the inconsistency
>       of ZFC would not be. ... None of us know that PA is consistent.
> I don't read Angus here as saying that he believes the consistency of PA
> to be a "legitimate mathematical problem".

Does this just come down to a linguistic quibble about what the term 
"legitimate mathematical problem" means?  Compare the following 

1. The Riemann Hypothesis *might* be false.  I mean, it would be a shock. 
But none of us *knows* that the Riemann Hypothesis is true.

2. The square root of 2 *might* be rational.  I mean, it would be a shock. 
But none of us *knows* that the square root of 2 is irrational.

#1 is a completely normal assertion.  #2 sounds like someone is trying to 
pick a philosophical fight.  The main reason for the distinction is that 
it is considered a proven fact that the square root of 2 is irrational, 
while the Riemann Hypothesis is certainly not a proven fact.  Thus, 
implicit in Angus's statement is a claim that the consistency of PA is not 
a proven fact in the sense that other mathematical theorems are proven 
facts.  I think that's enough to shock Harvey, regardless of how one 
chooses to define the term "legitimate mathematical problem."


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