On 20 Oct 2013, at 00:08, 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?

Yes. ([o]p -> p). It is the main axiom of knowledge. We can know, by definition, only truth. If we realize we were wrong, we realize that it was not knowledge but belief. We can never be sure if we know or belief, except for "consciousness here and now".

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.

Yes. Knowledge is given by the beliefs that we share with God (Truth).

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.

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

Yes. for the correct machines. Of course we don't know that we are correct, so in practice, it is less easy, far less easy. But we don't need that to get the physics.



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