On 24 Feb 2014, at 23:04, LizR wrote:
On 24 February 2014 07:57, Bruno Marchal <[email protected]> wrote:
About [](A -> B) -> ([]A -> []B), let me ask you a more precise
exercise.
Convince yourself that this formula is true in all worlds, of all
Kripke multiverses, with any illumination.
Hint: you might try a reductio ad absurdum. try to build a
multiverse in which that law would be violated.
[](A -> B) -> ([]A -> []B)
OK. For a disconnected universe this is t -> (t -> t) or t -> t
which is true.
And for a Leibniz universe, I'm fairly sure this is also true.
So that leaves {alpha R alpha} and {alpha R beta} and .... so on,
for any number of universes + relations.
Maybe I can come back on this one.
Sure. Me too. (I will myself be plausibly slowed down, as I have two
weeks of teaching, take your time, just try to not forget what you
learn, by having good summary, that you can read from time to time).
Well, does an illuminated Kripke universe effectively act as a
Leibniz universe?
In both you need the notion of "all illuminations" to have the notion
of law for a multiverse.
In the realm of the Kripke multiverse, the Leibnizian one are the much
more particular one characterized by having their relation being
"equivalence relation" (they are reflexive, symmetric, and transitive).
Indeed, in Leibniz, []p is true if true in all universes, no matter
how accessible their are or not. It is like their are all equivalent
with respect to accessibility.
Brent, Liz, here is my gift from the 24th February: an exercise!
Below.
If so this is definitely true (OK I try to jump in quickly here...)
You do good work, but I am not sure if you have good notes. That is
not grave, but not helpful to you.
Yes, I know - about the notes, I mean. (Maybe I just need to search
the list for []p to find some...)
You will get too many, and it is only in writing the information, that
you will maximize the ability to integrate them, and develop some
familiarity.
Never hesitate to ask for any definition or recall.
Thank you, don't worry I will :)
And Liz-Washington said "I don't know if I am the one from Washington
I drunk to much whisky and I lost the diary!"
And Liz-Moscow said "I don't know if I am the one from Moscow, I drunk
too much vodka and I lost the diary".
The modal logic part is not the real thing. The "real thing" will be
the interview of universal and Löbian machines, and some modal
logics will just sum up infinite conversations we can have with
them, notably on predictions and physics.
Yes, that is where it all happens! But I feel like I am quite a way
from that.
I told you we have to empty the ocean with a tea spoon.
Don't worry, modal logic, here, will be a powerful tool.
Take it easy, I know that studying this is time consuming.
I hope you will see the main line. Keep in mind that the reversal
physics/number-theology is justified in UDA, AUDA just translates it
more constructively in arithmetic, and give the "comp" arithmetical
quantizations. It is an open problem if they emulate or not a quantum
computer.
Bruno
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http://iridia.ulb.ac.be/~marchal/
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