On 06 Jul 2015, at 19:39, John Clark wrote:
On Mon, Jul 6, 2015 at 1:16 PM, Bruno Marchal <[email protected]>
wrote:
>>> You (or anyone) are in Helsinki, you will be duplicated,
and both copies will get a cup of coffee in W and in M. The
question is asked to you (or to anyone doing that experiment) in
Helsinki, before pushing the button: "what is your personal first
person expectation of drinking a cup of coffee after having push on
the button.
>> If both get the coffee then "I" would expect to
get the coffee regardless of the precise meaning of the personal
pronoun "I" ;
> So you agree that P("experience of getting a cup of coffee
soon") = 1.
OK?
OK I guess,
You guess?
but that's a pretty dull thought experiment. if everything in the
universe will get a cup of coffee then it doesn't matter what the
referent to "you" is because whatever it is he she or it will get
some coffee. What's your point?
If you agree that P(experience of getting a cup of coffee soon") = 1,
then you have to agree that
P(experience of opening the door and writing W or opening the door and
writing M in a personal diary) = 1, and that
P(experience of writing "W and M" in a personal diary) = 0.
Which would make the point.
In modal logic []p is reasonable for a probability one, evaluated in a
world alpha in case:
1) all the worlds beta accessible from alpha satisfy p
2) the set of accessible worlds from alpha is non-empty, i.e. alpha is
not a cul-de-sac world.
That is the case with alpha = helsinki, and the accessibility relation
is the set of computational (at the right level, etc.) continuations,
here beta1 = M, and beta2 = W. (M abbreviates Moscow, W abbreviates
Washington).
P(coffee) = 1, because the experience of drinking coffee is done at
both places.
The experience "that city is W or M" is done at both places too (as "p
or q" is true if one of them is true). So if you agree that P(coffee)
= 1, you should agree with P("W or M") = 1.
As you have also agree that the experience are exclusive, and that
there are two independent consciousness, and that each experiencers
(which remembers being the Helsinki guy) see one and only city, from
its own first person experiencer pov, so P("W and M") = 0. None will
write I have the personal experience of seeing two cities.
If you are sure to get that coffee, you are sure to arrive in *one*
city. Because *that* experience happens in all the "accessible worlds".
Then you can predict in advance that after pushing the button, you are
in front of *one* door, and that behind that door there is *one*
precise city, and that you have no clue which one it could be. Indeed
that was predictable already in Helsinki. And again, that happens with
probability one.
Once you (both of you, the copies) open the door, both of view look at
the (unique) city, and write the result in the diary: it is W, for one
of them, and M, for the other. It confirms the old P("W or M") = 1,
and P("W and M") = 0.
> later, I can explain that the Theaetetus definition of the
knower
Congratulations, you've taught me to really hate the ancient
Greeks.
>What Jason was 'babbling' about, is that the thesis is mainly
the UDA
I'm just not hungry for more of your homemade alphabet soup.
> Smullyan's "Forever Undecided" is a good introduction to the
main modal logic of self-reference, the modal logic G.
I love that book and first read it decades ago. Anything by
Smullyan is good if not great.
Then, honestly, you should have no problem with any hypostases, as
Smullyan book is a book on G, and they are all represented in G. Note
that the Theatetus' idea is so natural that Smullyan use it in some
place without noticing. There is a chapter on the Kripke semantics of
G, and, well, the relation with computability and logic is treated too
much concisely. It is quite extended in his "diagonalization and self-
reference" book, or in other books. I don't think Smullyan is much
aware of Church's thesis, (never cite it) and he lacks rigor when
making some point in philosophy.
So, you should read the AUDA part, which is the part two of my SANE04
paper without too much problems. That's the thesis in computer
science. In the original thesis, UDA and MGA are UDP and MGP
(Universal Dovetailer Paradox, and Movie Graph Paradox). I explained
to the directors that it was an argument, but that is was more
diplomatic to call it a paradox, and to use it only for the motivation
for the intensional variant of G ([]p & p, []p & <>t, ...).
Bruno
John K Clark
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