On 10/19/2013 3:08 PM, Russell Standish wrote:
On Tue, Oct 08, 2013 at 08:17:17PM +0200, Bruno Marchal wrote:
On 08 Oct 2013, at 11:51, Russell Standish wrote:

I understand Bp can be read as "I can prove p", and "Bp&p" as
"I know
p". But in the case, the difference between Bp and Bp&p is
entirely in
the verb, the pronoun "I" stays the same, AFAICT.
Correct. Only the perspective change. "Bp" is "Toto proves p", said
by Toto.
"Bp & p" is "Toto proves p" and p is true, as said by Toto (or not),
and the math shows that this behaves like a knowledge opertaor (but
not arithmetical predicate).
It's the same Toto in both cases... What's the point?
The difference is crucial. Bp obeys to the logic G, which does not
define a knower as we don't have Bp -> p.
At best, it defines a rational believer, or science. Not knowledge.
But differentiating W from M, is knowledge, even non communicable
knowledge. You can't explain to another, that you are the one in
Washington, as for the other, you are also in Moscow. Knowledge
logic invite us to define the first person by the knower. He is the
only one who can know that his pain is not fake, for example.

You've hinted at fixed points being relevant here for the concept of

So to have an 'I', you need the statement []p->p to be a theorem?

and Bp&p as "he knows p", so the person order of
the pronoun is also not relevant.
Yes, you can read that in that way, but you get only the 3-view of
the 1-view.

Let us define [o]p by Bp & p

I am just pointing on the difference between B([o]p) and [o]([o]p).


B([o]p) is the statement made by the ideal rationalist believer (B)
on a first person point of view ([o]). Here [o]p can be seen as an
abbreviation for Bp & p.
In English, the first statement is that I believe I know something,
and the second is that I know I know somthing.

[o]([o]p is the first person statement ([o]) on a first person point
of view ([o]).

So, according to you, knowledge is a first person point of view. What
I still get stuck on is that we may know many things, but the only
things we can know we know are essentially private things things, such
as the fact that we are conscious, or what the colour red seems like
to us.

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".


Are these all things you would say satisfy the proposition [o]([o]p)

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