[FOM] Re: Could PA be inconsistent?

[Timothy Y. Chow]

Vladimir Sazonov wrote:
>Say, what is the eternal reason to believe that even PRA (without any
>epsilon_0-induction) or even Elementary (Exponential) Arithmetic is
>consistent?
[...]
>Alas, it is also well-known that nobody wants to listen lessons
>of the History (which shows that non-critical beliefs were often
>against scientific progress).

Since you've been on FOM longer than I have, you may already have 
addressed the following question (or something like it) in the past;
sorry if that's the case.  However, I'd like to understand your
position better.

Suppose I define two processes.  Process A starts with the string
"1" and it proceeds according to the rule, "append 11 to the end of
the previously generated string."  So, Process A will generate 1,
then 111, then 11111, then 1111111, etc.

Process B is exactly the same, but it starts with "11" instead, so
it generates 11, 1111, 111111, etc.

I happen to believe that there is no string that is generated both by
Process A and by Process B.  Is it your view that the lesson of history is
that this belief of mine is against scientific progress, and that nobody
really knows if there is a string that both Process A and Process B will
generate?

Tim