Re: incompleteness and inconsistency


lugita15@xxxxxxxxx wrote:

the original
poster wanted to know whether it is possible to know the consistency of
PA with *absolute certainty*.

Peter_Smith wrote:
A very interesting bit of mind-reading :) The original poster didn't
mention "certainty" at all, let alone "absolute certainty" (whatever
exactly that might be). He asked whether we can *know* that PA is
consistent.

I don't know which (if either) of these people is alleging the
existence of a DIFFERENCE between "knowing something" and
"knowing something with absolute certainty", but just in case
either of them is, I loudly disagree.

Which we can.

For sufficiently small values of epsilon^H^H^H^H^H^H^H know, yes.

There are familiar philosophical riffs that try to get us from fanciful
or neurotic worries about "absolute certainty" that P to doubting
whether we know that P. For example, we can make play with the old
familiar fantasies of evil demons and brains-in-vats, and end up with
student-confusing arguments that seem to show that, e.g., you can't
know that you are reading words right now. But those arguments can and
should be resisted: of course, we *do* know such things in the everyday
sense of "know" (and why should we care about other senses?).

Because (obviously) "the everyday sense" of MOST things in this
realm is fundamentally incoherent, that's why. Otherwise the students
wouldn't be confusable. They, after all, start OUT with the everyday
sense of everything.

.

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