Re: Decision theory

From: Jacques Bailhache <>
Date: Mon, 4 Jan 1999 16:25:46 -0000

Jacques M Mallah wrote:
>In fact, the whole concept
>of free will never made any sense. The only possibilities are determinism
>and randomness, neither of which allows any 'decisions'.

I wonder if there couldn't be another possibility, neither determinism, nor
randomness, but free will, which I agree to be something rather mysterious.

>At one level of description I can describe a process as a physical system
>evolving in time according to the laws of mechanics; at another level, I
>can describe it as a computer, following a certain algorithm, without
>getting into physical details; at another level, I can describe it as a
>person making a decision, without getting into algorithmic details.

This idea of description levels seems very important to me. This is perhaps
the key idea for understanding the spirit and its properties, consciousness,
free will and creative intelligence.
My idea is that the universe, and the living beings in particular, could be
made of an infinity of material organization levels : body, cell, molecule,
atom, particle, quark, ..., with different physical laws at each level. In
this case a human being cannot be considered as a finite machine, since he's
infinite in the infinitely small. Any physical theory is only approximation
of the physical reality. In fact, the physical reality could be just an
infinite mathematical theory, defined by an infinite converging sequence of
finite theories. In this model, the spirit would be relative to the
considered level : if X1 is not explained by some theory T1, then X1 belongs
to the domain of spirit relatively to this theory T1. But there exist a more
precise theory T2 which explains X1. Then X1 belongs to the domain of matter
according to T2. But there exist another X2 which T2 does not explain, and
which belongs to spirit relatively to T2. But there exist a more precise
theory T3 which explains X2, and so on... Spirit would be something tending
to nothing without reaching it.
See also

I see also an analogy with Feferman's transfinite iteration of the
reflection principle on formal systems : for a theory T0, there exist a
Godel proposition G0 which is true but not provable in T0. But by adding
reflection to T0 we can obtain a more complete theory T1 in which G0 is
probable. But T1 is itself a finite theory, and we can construct another G1
which is true but not provable in T1, and so on...
Adding reflection is a mechanical construct, but this leads to an infinite
sequence T0, T1, T2... which we can integrate in one theory Tw (w = omega),
and we can go on with Tw+1... giving a transfinite sequence of theories.
Generating the sequence of transfinite ordinals is a creative, not
mechanizable process, which requires creative intelligence to perceive
regularities when we fall in a loop, to skip out of the loop.
See also

>On Thu, 31 Dec 1998, Jacques Bailhache wrote:
>> If MWI is true and if every possible decision is made in one universe, it
>> clear that the concept of decision has no sense. This leads to the
>> of ethics.
> The above paragraph makes no sense to me.

I meant that a decision is significant if it consists in chosing to act in a
certain way which makes real a certain state of the world, excluding other
states led by other possible (but not actualized) acts.
If every possible decision is made in one world, there is no real decision
in this sense. It does not make sense to ask ourself which decision we
should take to obtain a state of the world which we consider as good if
anyway every possible decision is taken in some world and then every
possible state of the world is real is one world.

> This is the part that got me riled up. Pascal's bet is the height
>of stupidity. I'd rather live as an atheist and go to hell than spend an
>eternity kissing up to a god so evil and self centered that he'd send me
>to hell just for not believing in him when I had no evidence.

The subject of Pascal's Bet is not whether an eternity in Paradise is a good
thing or not, it's that supposing it has an infinite value, then for any
probability p that we will spend an infinite time in Paradise if we behave
well, the corresponding value (infinite times a finite probability) is
infinite. But you're right in the sense that Pascal forgot that there is
also a (rather strange) possibility that we suffer for an infinite time if
we behave well. Suppose this has probability p'. Then the value of behaving
well would be (p - p') * infinite. In fact we should behave well only if we
believe that p > p'.

Concerning decision theory, it's not exactly the same situation :
Let P be the proposition : "Decisions has no sense" (for example if MWI is
true or if everything is predeterminated), and suppose P has probability p
to be true, according to our knowledge of the world.
Let A be the choice of acting as if decisions make sense, and B as it does
This leads to 4 possibilities :
~P, A : Decisions make sense and know it, I take them knowing it make sense,
trying to take the correct decision. This situation has a positive value v.
P, A : Decisions does not make sense, but I think they do. I do not really
have the choice of thinking decisions make sense or not. At the global
level, everythink is determinated. No good, no bad, all that can happen
happens. I would attribute a value 0 to this situation.
~P, B : Decision make sense, but I am convinced thai in fact they don't.
This is the catastrophic situation. I don't make any effort to take the
correct decision, thinking it does not make sense.This situation has a
negative value -v'.
P, B : Decisions does not make sense and I know it, and I don't have the
possibility of thinking anything else. This situation has also the value 0.
In summary, taking in account the probabilities, choice A has value (1-p) *
v + p * 0 = (1-p) * v, and choice B has value (1-p) * (-v') + p * 0 = -
(1-p) * v'.
For any p, the value of A is greater than the value of B, then we should
chose A.

Wei Dai wrote:
>I think you're suggesting that we think of decisions as selecting which of
>the you-like beings is really you, instead of as changing the universe
>somehow. This seems like a promising approach, and I've tried it too, but
>I haven't figured out how it can be formalized. It may require a
>different formal framework from "classical" decison theory.

I agree. See

Jacques M Mallah wrote:
> I'll say it again: my mental processes *are* the laws of physics
>in action, and *do* have consequences. My choice *does determine* the
>actual utility, which is to say, the laws of physics determine it.
Interesting idea. But these laws of physics should be infinite if we are not
Jacques Bailhache
Y2K Centre of Expertise (BRO)
DTN: 856 ext. 7662
Tel: +32-2 729.7662, Fax: +32-2 729.7985
Visit my home page :
Received on Mon Jan 04 1999 - 08:35:19 PST

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