On 20 Oct 2013, at 00:48, Russell Standish wrote:

On Sat, Oct 19, 2013 at 03:16:52PM -0700, meekerdb wrote:

Bruno seems to equate "know" with "provable and true".  So we know
that 17 is prime.  In fact we *know* infinitely many theorems that
are provable, but which no one will ever prove - which seems like a
strange meaning of "know".


I agree that it is strange, but acknowledge that the definition does
have some history. ATM, I'm trying to just understand why he says
certain things, given the definitions he uses.

Assuming 17 is prime, then yes - we know that 17 is prime. But do we
know that we know 17 is prime?

[o][o] (17 is prime) is true, because

[o] ([] 17 is prime & 17 is prime)

That is

[] ([] 17 is prime & 17 is prime) &   [] (17 is prime) & 17 is prime




On the other hand, if p is prime, then p is divisible only by 1 and
p. This statement is indisputably true, as it is the definition of
"prime". So we can know this, and we know we know this.

We have always that [o]p -> [o][o]p (like we have also always that []p -> [][]p)



Which is an example of an x satisfying [o]([o]x), that is not of
subjective character. Hmmm....

?
Sometimes we know objective things.
The knowledge is subjective, but the known thing can be objective.

Bruno


http://iridia.ulb.ac.be/~marchal/



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