Re: Modalities

From: George Levy <GLevy.domain.name.hidden>
Date: Thu, 22 Mar 2001 10:17:50 -0800

The following post was returned to me.... I'll try to send it again


Marchal wrote:

>
> But perhaps there is something more I should ask you before. You said
> in response to some post of me, in some preceeding dialog:
> <<<I smell a whiff of third person thinking.>>>
>
> Well, I know you are not stuck in third person (like Schmidhuber and
> Mallah) but I hope you are not exclusively first-person.

Actually, I think that the first person point of view is more fundamental than
third person. Yet I do not deny the third person. The objectivity of nature
(third person characteristic) is an illusion brought about because first persons
observers share the same "frame of reference." in the same way that the earth
appeared to Aristotelian physicists to be "objectively" motionless. As you know,
by frame of reference, I mean the underlying (mental) mechanization down to
atoms, electrons and quarks as well as physical mechanization also down to atoms,
electrons and quarks. We share the same "psychology."

Third person observation cannot be knowable unless we go through the first person
first. Like Descartes, we must begin by assuming the I. It is both an assumption
and an observation!

> It is useful to identify 3-person honest communication with
> belief (proof). let us write []A for: the sound machine
> can prove (believe) A.
>
> It is natural to have
>
> [](A->B) -> ([]A ->[]B)
>
> meaning that if it is provable that (A->B) then, if it is provable
> that A then it is provable that B.
>
> It is useful to identify the first person with the knower, and, if I
> write [.]A for I can know A, it is natural to have also:
>
> [.](A->B) -> ([.]A ->[.]B)
>
> Both []A -> [][]A and [.]A -> [.][.]A are quite natural once we
> treat sufficiently introspective machine or entities.
> For them: A is believable entails that it is believable
> that A is believable, and the same for knowable.
>
> It is natural to have that the knowability entails the believability:
> That is: [.]A -> []A. Do you agree ? It just mean that if A is knowable
> then A is believable.
>
> OK ?
>
> With the intuitive meaning of belief and knowledge the reverse
> is certainly wrong: the fact that A is believable does not entails
> that A is knowable. We don't have []A -> [.]A. For exemple it is
> believable that the earth is flat, but that is hardly knowable.
>
> In fact it seems that for knowledge we have [.]A -> A,
> but for belief we don't have []A -> A.
>
> Would you basicaly agree until here ...
>
> It looks like I propose you some analytical philosophy.
> Later I will propose you *arithmetical* philosophy. The meaning
> of [] and [.] and others toward observability will be defined
> in arithmetic and only then will the UDA be translated in
> that arithmetical philosophy and then the necessarily hilbertian
> structure on the consistent extensions will begin to appear.
>
> Do you know some elementary classical logics?
> The magic which will put an unexpected and rather involved
> fuzzy structure on the set of consistent extensions comes
> from godel's theorem (with [] modelize by formal provability).
> It looks like an oversimplification, but even with that
> oversimplification we will get non trivial theories of belief,
> knowledge, observation, etc.
>
> Do you know Aristote Modal Square: (read []p "necessarily p")
> "-" is not.
>
> []p []-p
>
> -[]p -[]-p
>
> or its dual (read <>p possibly p):
>
> -<>-p -<>p
>
> <>-p <>p
>
> They match. I mean []p is equivalent to -<>-p. ``It is necessary
> that p" is equivalent with ``it is not possible that -p", and
> ``it is possible that p" is equivalent with "it is not necessary
> that -p". And then []-p is equivalent with -<>p, and <>-p is
> equivalent with -[]p.
>
> Later []p will mean p is formally provable, then <>p is read as
> consistent.
> To say p is consistent is indeed equivalent with saying that -p
> is not provable.
> Consistency, that is the non provability of FALSE, is then
> equivalent with the consistency of TRUE, and Godel's theorem
> can be written:
>
> <>TRUE -> -[]<>TRUE.
>
> TRUE and FALSE are just two propositional constant. You can
> identify TRUE with the proposition (1 = 1) and FALSE with the
> proposition (1 = 0).
> We are just at the beginning. In a next post I will explain
> Leibnitz semantics. It is fun. And it will help us for
> introducing Kripke semantics, which is just a "relativisation"
> of Leibnitz semantics. That will even, perhaps, help us
> to understand the difference between the absolutist and the
> relativist in our discussions.
>
> Bruno

hmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm


George
Received on Thu Mar 22 2001 - 10:32:44 PST