[FOM] Re: Could PA be inconsistent?

Vladimir Sazonov V.Sazonov at csc.liv.ac.uk
Mon May 17 19:27:15 EDT 2004

Timothy Y. Chow wrote:

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?

I wrote on *non-critical* beliefs, those which are/were forbidden
or dangerous or shameful to criticize.

You yourself are sufficiently selfcritical about your beliefs
mentioned above in your next posting (although that your
posting requires separate  comments).

All of us have some beliefs, intuitions, etc. There is no
problem with this. Otherwise, it would be even impossible
to do anything interesting and meaningful in mathematics or
in Science in general. The problem appears when some beliefs
become dogmatic or meaningless. I consider that such are
platonistic beliefs. My old question to platonists here in
FOM: WHAT DOES IT MEAN the ABSOLUTE concept of standard model
of PA (not relativised to ZFC or the like) has no rational
answer.  Of course, this does not mean that we should not have
some intuitive, may be vague image of natural numbers when
working in PA (even if it will happen that PA is inconsistent).

The recent threaten that PA might be inconsistent (even if no
real inconsistency will be found this time or in the future)
is a good occasion for reconsidering some beliefs, especially
platonistic ones.

Kind regards,


> Tim

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