A bridge from Smullyan to Smullyan

From: Bruno Marchal <marchal.domain.name.hidden>
Date: Tue, 21 Mar 2006 12:27:23 +0100

Sometimes I really don't understand how some people, in the literature,
did not see what I have seen, and I begin to harbor doubt on my work.
The most famous case was the case of Einstein and Godel, who met at
Princeton, but seems not having try to really understand each other on
some of the most fundamental question. Eventually I discovered that
Einstein was a quasi-"conventionalist" in math, and this could explain
his lack of interest in logic and in Godel's work.

A more vexing case was the case of Smullyan. Indeed all his technical,
recreative or not, books on logic turn around Godel's theorems. But
Smullyan wrote also books on religious/theological (in a wide sense).
Still he never tried to connect them. I am thinking about his books
"The Tao is Silent", "5000 BC", and "Who knows".

I have recently discovered that Smullyan never talk on Church's thesis.
He does not seem aware of the "simple" proof of Godel's incompleteness
which follows almost directly from Church's thesis, nor does he use it
to motivate some link between computer science and mathematical logic.
In particular his book "Forever Undecided", although mentioning two
times the "artificial intelligence" motivation is rather striking in
that respect: indeed his chapter "the heart of the matter" is almost
presented without motivation. He presents his "Godelized Universe" like
if it was just a new kind of game or puzzle, not really more motivated
than the *fairy* Knight-Knave Island.

So, there is a sort of missing paragraph or section before the "heart
of the matter", and I am working on it, so that "Forever Undecided"
could be use more easily by those interested in the comp reversal.

But then, what I got makes a bridge between his work on Godel's
incompleteness and his philo/theo-logical writings, and I feel now
sufficiently confident in that link to recommend those books. They does
not present a metaphysical system, unlike Plotinus, but present rather
many interesting short reasonings in the religious field, arguably
converging toward Plotinus, notably through his comment on "cosmic
consciousness" in the second part of "Who knows".

I will, soon or later, expand a little bit on all this, especially on
the importance, not just for comp, but for theoretical computer
science, of Church's thesis. Meanwhile you could still study the 24
first sections of the FU book, i.e. until page 206. Particularly
interesting for the "consciousness thread" is the succession of more
and more self-aware sort of reasoners (type 1, type 1*, type 2, type 3,
type 4) in his chapter "logicians who reason about themselves" (page
89) all that driven toward the "well known" type G). My approach to
consciousness adds "inductive inference ability", with the automated
(unconscious) bets on personal self-consistency, or of any proposition
belonging to the corona G* \minus G. We can come back on this later.

To be sure, all this is not necessary for the understanding of the UDA
reversal argument, but it is necessary for the translation of that
argument in the language of an introspective universal machine, and
this is necessary for the actual derivation of the comp "propositional
physics" (and then for its comparison with quantum logic).

Bruno


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


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Received on Tue Mar 21 2006 - 06:28:27 PST

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