Those are some very interesting results, I must say.
Why the letter choice of B? Does it "secretly" stand for "believes" or
something else? If x is true then ~Bx seems to imply that if a
hypothesis is true then science will never prove it no matter how much
time you give them (barring any sort of infinite time). Is that right?
I've had some exposure to Alan Watts and all I have seen is both
profound and simple.
DDDDDt is a bit hard for me to understand. Would you elaborate for me?
Bruno Marchal wrote:
On 05 Jan 2011, at 21:45, Brian Tenneson wrote:
"The Tao that can be described is not the
ultimate Tao"
I <3 Lao tseu, and all the taoists. There is a full chapter on
Lao-tseu in the long version of my PhD(*). They were aware of the dream
argument. In fact, I call the modal formula:
x -> ~B x (or its contrapositive Bx -> ~x) with B intended for
the scientific communication or proof: the Lao-Tseu Watts Valadier
principle, there.
Alan Watts describes indeed something similar in his book "the wisdom
of insecurity", and Valadier, a french jesuit, wrote a remarkable book
where it shows that making moral is immoral.
Gödel's theorem (and Löb, Solovay) provides many solutions, having an
arithmetical content, for such an equation. Indeed all x belonging to
G* \ G obeys to that equation.
With x = Dt (= ~Bf = consistency), you get Gödel's second
incompleteness theorem: Dt -> ~BDt. But DDDDDt is also a solution.
Most formula beginning by D (= ~B ~) are solutions. Correct machines
cannot prove that they cannot prove something.
Tarski's theorem provides even more insightful solutions, which are
analytical, and on which the correct machine can only be mute.
It led me also to a very simple theory of intelligence. A machine is
intelligent if she is not stupid, and a machine is stupid if either she
believes that she is intelligent, or she believes she is stupid. Aagain
incompleteness provides solution. From that I showed that intelligence
has a positive feedback on competence, but that competence has a
negative feedback on intelligence.
Interesting. I wonder if it's so. Whether or not the ultimate Tao can
be described has been the object of all my research-related thinking
for a while now. I finally made a breakthrough this year on the
problem. I still have to manipulate what I think on it and massage the
document about it. At least I can say that I'm not trying to describe
the Tao. I'm trying to describe a description of the Tao. The reduced
product of all structures is my candidate for my description for a
description of the Tao.
Perhaps Lao Tzu already put in his two cents regarding this kind of
TOE.
In "conscience and mechanism" I argue in detail that most of the
writing of Lao-Tseu, Tchouang-Tseu, and especially (my favorite)
Lie-Tseu can be interpreted by the discourse of the self-referentially
correct machine. But Plotinus is closer to us. I have studied classical
chinese and modern chinese, for years, to discuss on Lao-Tseu with
scholars. It is difficult.
Mechanism makes a bridge between Smullyan's "Tao is silent" and
Smullyan's "Forever undecided". I still don't know if Smullyan would
agree on this. Some remark by him makes me think he is not aware of
that connection, or that mechanism favors that connection.
If you like Lao-Tseu, you might appreciate Smullyan's book "tao is
silent".
Bruno
(*) http://iridia.ulb.ac.be/~marchal/bxlthesis/consciencemecanisme.html
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