# Re: Numbers, Machine and Father Ted

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Le 09-nov.-06, à 13:53, 1Z a écrit :```
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> If you can show that subjective experience exists in Platonia,
> you can use that to show that some things will "seem" dynamical.
>
> If you can show that there a dynamic processes in Platonia,
> you can use that to show there are running computations
> and therefore minds, and therefore experiences.
>
> But can you do both without circularity?

Yes. That "circularity" is worked out through a mathematical theory of
self-reference. Of course that is not something I can explain in just
one post.

I suggest you search in the archive, or you consult my papers, or you
could wait some explanation I have promised to David (but he seems busy
right now).

What can be explained in a few lines is that *discourses* about
"subjective experience" and "time" appears naturally in the modal
variant of self-reference.

I study what a "ideally correct" machine can prove about herself. Then
I borrow one of Theaetetus' definition of the knower/first person: so
that
"to know p" is defined by to "((I can justify p) & p)". This makes
sense thanks to the fact that no machine can prove that" proving p
entails necessarily p" (and this is a consequence of incompleteness).
Then math shows that the "arithmetical knower" so defined has a
discourse similar to the "Berson/Brouwer ..." theory of the creative
and temporal subject, + a lot of mathematical property making it closer
to some intuitionistic view of math. This gives a subjective time
theory, but also an arithmetical topos, etc.
In the same way we get a "physics" (according to the UDA) when we
define "I observe p", by "I am measuring p with a
probability/credibility of one". This means we can define "observing p"
by "I  can justify p and p is consistent". By Godel *completeness*
theorem this is equivalent with p is true in all accessible world and p
is true in at least one accessible world). Note that here I am using
implicitly a lot of theorems in the math of self-reference---I just
summarize, look into my papers for more). Here we should get some
geometry, and we already get a quantum like probability logic,
including a purely arithmetical interpretation of it.

Of course nobody can prove the existence of subjective experience in
Platonia or anywhere. We know that "exists" because somehow we live
them, but they cannot be communicated.
But once we grant that similarity of some possible "discourses" on
subjective experience can be taken as evidence of the presence of
subjective experience (what I have sometimes refer to as the
"politeness principle"), then what I say above can help to figure out
how subjective experiences and subjective times can appear as internal
modality of any arithmetical realm. Put in another way, if this would
not be true, it would entails the existence of many zombies in
platonia. But of course this is a short way to present this and I ask
you to not taking too much literally what I try to explain shortly.

To sum up: circularity is handled by the mathematical theory of
self-reference (encapsulated by the modal logic G and G* at the
propositional level). Psychological and physical things are either
modelised or recovered by "intensional variants" of the self-reference
logic G (for the provable) and G* (for the true but not necessarily
provable).

Note that here I was talking on "subjective time". The running UD in
platonia defined implicitly another notion of time, which is just the
number of steps the UD needs to access states. This can be well defined
up to some constant thanks to machine independence theorem in computer
science. But this as nothing to do with subjective time, or with the
feeling or seeming of time flows.

Bruno

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

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