Le 16-août-06, à 18:04, David Nyman a écrit :
>
> Bruno Marchal wrote:
>
>> The self-reference logics are born from the goal of escaping circular
>> difficulties.
>
> I think here I may have experienced a 'blinding flash' in terms of your
> project. If, as I've said, I begin from self-reference - 'indexical
> David', then I have asserted my 'necessary' point of origin.
Yes but this "necessity" will appear to be a first person necessity,
and as such is not communicable, and even not capturable by the
self-reference logic. Note that the fact that that necessity is first
person explains probably why you want to take the first person as
primitive at the start. Unfortunately, as Godel as seen as early as
1933, the self-reference logic does not capture, neither the knower
(the first person) nor the its necessity.
So, curiously enough (without doubt) formal provability capture only
"opinion" or "belief" (we lack Bp -> p, with B = formal proof). But
that is what makes the Theaetetical definition of knowledge (true
belief, or true proof, or true justified opinion) working in this aera,
and leading then to a notion of (unameable) first person. We will come
back.
Of course, the more you will be precise, the more I can criticize you
by comparing what you say with what G and G* says. That's normal.
> From this
> point of origin, I can interview myself (and entity-analogs simulated
> or modeled within myself) and consequently discover the statements that
> express my beliefs, the truth of which I can then evaluate in terms of
> my theology. This theology will derive its consistency from provable
> theorems, its relevance from generative and explanatory power (e.g.
> with respect to both 'physical' and 'appearance' povs) and its ultimate
> validity from faith in the number realm and the operations derived from
> it. So, in performing such a process I undertake a personal voyage
> through indexical reality, and never leave it, but there is no
> tautological circularity since it's a genuinely empirical exploration
> of the prior unknown, and what I discover could be totally surprising.
>
> Is grandma anywhere in the right area?
Very very close indeed.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Thu Aug 17 2006 - 05:38:36 PDT