I wrote
> The correct (objective) a priori probability of our observations is
> defined by whatever is the true physical theory.
Nick Bostrom <nick.domain.name.hidden> replied
> Sounds like a contradiction! Objective probabilities aren't a
> priori - they depend on what physics happens to be true in the
> actual world, and that's something we only learn from experience.
I am using ``a priori probability'' here as a synonym for ``objective
probability''. I think that this is fairly common among physicists,
although I realise that this may be confusing to philosophers,
especially those raised on Kant. I would use ``propensity'' as a third
synonym.
The important point is that such probabilities are independent of
our beliefs. In my theory, they can be defined as probabilities
given the universal wavefunction and perfect knowledge of the past
history of an observer. As I have a theory in which observers are
finitely defined, such probabilities make sense and depend only on
the (objective) laws of physics (i.e. the Hamiltonian of quantum
field theory). I think Bostrom is pointing out that these laws of
physics are not ``a priori'' in the philosophical sense.
I wrote
> As a first approximation to the correct probabilities, however, it
> is not reasonable to guess that we are about as likely as most
> observers like us. This is the self-sampling assumption.
I meant ``not unreasonable'' of course. Sorry.
Bostrom wrote
> Quantum theory is irrelevant to the Adam&Eve example, because
> that is a thought experiment, so I can simply postulate that
> quantum physics is false in their world. It's important to
> distinguish between methodological or epistemological rules
> (SSA), and empirical hypotheses (quantum theory). The former can
> be applied to the latter, but mixing them up can easily result in a
> category mistake.
I don't think that the Adam and Eve example is of any interest
except in as far as it sheds light on the doomsday argument as it
applies to us in the real world. If, as I would contend, the
correctness of quantum theory changes how one should understand
the example, then I think it is highly relevant.
I wrote
> Nevertheless, Eve still must expect to be typical as an observer.
> Otherwise, she has no reason to believe her physical theories. Her
> birth rank puts her in the position of someone who has tossed a
> fair coin 1,000 times and it has always come up heads. But she is
> tossing a million other coins at the same time so it isn't really
> that surprising.
Bostrom replied
> For all she knows, she may simply be one out of two humans -
> pretty typical.
Eve should find her birth rank surprising because of her (assumed)
knowledge of human biology. The question is whether she can
deduce her own infertility from that surprise.
But my point is that if she also wants to believe that her physical
theories are correct, then she has to believe in her statistical
sampling methods and in the results provided by others.
Bostrom also wrote
> Let's assume the MWI is false.
Under any interpretation of quantum theory, it really does look as if
dice are being thrown. In my opinion, because of the way that
instabilities are magnified in the normal functioning of the
human brain, those dice affect every aspect of our behaviour on any
timescale above a millisecond.
If, as in the Bohm interpretation, probabilities are purely
epistemic, Eve will constantly acquire information which
would previously have been much more difficult to predict (given
only her past awareness) than a birth rank of 2 in a species of
trillions. In this situation, I suppose that the first part of my
argument would be that Eve has discovered lots of facts (in
particular, facts about the current state of her brain) which
were astonishingly unlikely given her prior history. She would
therefore be unwise take any particular one of those facts too
seriously.
Even in classical terms, future neural processing is quite
unpredictable from current neural processing.
The second part of my argument is that one cannot separate birth
rank from the other facts about Eve's mental life. Birth rank is not
the sort of fact that one could imagine Eve ever being asked to
guess, as if she had no idea of the answer. As long as she has been
aware, she has had lots of clues that her birth rank was
expectional, just as we have always had lots of implicit clues of
our birth rank (e.g. the taste of powdered baby milk).
Matthew Donald (matthew.donald.domain.name.hidden)
web site:
http://www.poco.phy.cam.ac.uk/~mjd1014
``a many-minds interpretation of quantum theory''
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Received on Sat Sep 23 2000 - 02:56:38 PDT