On Tuesday, August 7, 2012 7:34:28 PM UTC+4, clifford wrote:
Well, now I am more confused than before. What is the role of the second level here, where the universe of worlds is also selected from a universe of universes? Is there another sense of possibility involved here that is not obtainable in the ordinary one-tier system? Partly, this all seems backward to me. We generally start from the given world (obviously) and then work outward to possibilities in various ways: changing circumstances, changing history, changing laws, and so on. These are covered
by different
interworld connections, typically, or
(what probably amounts to the same thing) by different structures placed on the universe. So, I suppose the different bags correspond to these different structures, but, unlike the case in the usual theories, there does not seem to be a systematic
way of distinguishing them. To say that an event is necessary in a universe in which it occurs in every world is not very illuminating -- unlike saying it is necessary in every universe in which all the present laws of physics hold, say. But then, rather than one notion of possibility applied in different universes, I would explain matters in terms of different notions of possibility applied to one universe -- not that it probably makes any difference in results.
Let me try to explain. There is a set of alternative worlds. Let's take the middle set where we have both white and black balls.
So we have a set of balls (or bags of balls? I'm sticking with balls for the moment) and we take a subset (how specified? random? saying it is the middle makes no sense in a set,
which is unordered).
This set has both black and white balls (how do we know this? If we picked it by this, then it is hard to see what it is going to have to do with possibility, since that is exactly about not picking).
It means that it's us who chose exactly this set of balls and put them into the bag, i.e. into consideration.
See above. I am not clear to what in the calculation of possibility this correlates with,
We don't know which of the balls represents Our World. Our World doesn't exist yet. Still we believe that there is a possibility for a black ball to be extracted. This is what we call {ka'e} i.e. possibility or probability of being extracted.
OK. Now this looks like
standard possibility,
given that we know that neither black nor white is impossible (by whatever means). By the way, I would leave probability out of this, since that is a metrical notion that requires a much more complex world structure.
In case when we extract a black ball all Alternative Worlds immediately disappear and we have only one world, Our World, This World. This state is called {pu'i} i.e. demonstrated potential.
Well, strictly, this looks like ca'a, since pu'i seems to me to have past reference, but since we seem to have is an English perfect aspect, the difference is minor. But, in what sense do the other worlds disappear? They must still be there to support the notion of potential, which can't be present (in any usual system) in a single world, and to block off the notion of necessity.
In case when we extract a white ball this potential hasn't been realized and this situation is called {nu'o}.
Again, presumably the other worlds disappear and so we just have a non-occurrence but not a potential occurrence to go unrealized.
In other bags where we have
white balls only there is no choice. As .xorxes. said the result at M-level is " just a consequence of all of them being white in that bag. "
The same in case of black balls, i.e. {bi'ai}.
That is, if we pick a universe with only white balls, then whatever ball we pick is white. I guess that is bi'ai, although xorxes points to an obvious more clear reading. But what, in the end, does this have to do with possibility, since here we have fixed the case so that the desired result is impossible given the initial conditions -- but the initial conditions are just that the desired case be impossible, which makes for an uninteresting situation.
In other words, when we move down
to M-level the previous A-level disappears. It is actually similar to quantum physics theories where alternative realities collapse to one reality only in the moment of observation by the observer. So Lojban looks like an up-to-date instrument :)
But here, of course, the "observer" has been mucking about from the get-go, choosing which bag to make the pick from. And the others don't disappear, if we are really doing modals here.
As for F-level it's just another philosophy. At
first glance {pu'i} is like {ca'a} but {ca'a} doesn't make any assumptions about the probability of such event.
Nor does pu'i; it only talks about possibilities (or potentials, which might be somewhat different, but that is not the present problem). What philosophies? I don't even see two interpretations of possibility, let alone probability, here.
Both philosophies are important.
John, sorry for your confusion. I knew only popular descriptionsof quantum physics when started drawing this scheme.
Probably we speak different languages. I just invented my own in this scheme as I knew no other. .a'o this is the only reason for misunderstanding.
I think this is largely true, but I don't see how quantum physics got into this brew in the first place. In one way of working out Prior (temporal modalities) the multiple worlds interpretation of the probabilities involved in quantum physics is taken as a model for the structure of time (without all the details, of course, or much of the understanding of what is happening in quantum physics) and that projects a certain range of modal theories. But the association is merely handy and nowise essential to modal logic.
I started with revising mu'ei. Yes, mu'ei due to PA can be much more precise. I just don't feel I wanna be so precise in my speech. Probably it's my feeling. May be others would still like to use mu'ei.
mu'ei seems a fairly pointless notion for modalities, since the count of possible worlds is rarely (if ever) a factor. It won't help a lot for probability, either, since it is relative sizes, not absolute one that play there (and the apparatus of logic, per se, is not up to messing with that.
No problem. We can fill A-level with complex cmavo that include mu'ei and announce {ka'e, bia'i} as obsolete cmavo.
But it won't affect M-level and F-level. mu'ei isn't enough. It describes A-level only. This is what I came
to.
OK. I just don't see the need for A level at all. M and F seem to do all that is needed. What have I missed?
On Tuesday, August 7, 2012 2:34:44 AM UTC+4, xorxes wrote:
On Mon, Aug 6, 2012 at 9:44 AM, Gleki Arxokuna
<gleki.is.my.name@gmail.com> wrote:
>
> OK. If no other criticism I'll correct it and post it to lojban.org wiki.
Strictly speaking, "ka'e" only says that the bag contains black balls.
It doesn't say whether it also contains white balls or not, although
pragmatically one expects that it will, just as when someone says
"some" one pragmatically expects "but not all" to be true as well.
Similarly "ka'e na" would say that the bag contains white ball, saying
nothing about whether it contains black ones as well.
I believe that here we must postulate the meaning of {ka'e}.
Yes, we don't mean that the must be at least one white ball. We don't know it.
And in this scheme we probably even don't want to determine the number
of white balls.
However, {bi'ai} and {naka'e} speak about the probability =1 of balls of one color present in the bag.
In order to say that it contains both black and white balls you may
need something like "su'opame'iro mu'ei", "in some but not all
worlds". "May or may not", as opposed to just "may".
I'd put "bi'ai" at the same level as "ka'e",
OK. done.
it's not really about
materialization. That the ball picked is black is just a consequence
of all of them being black in that bag, so of course the one that
materializes will be as well, but "bi'ai" has nothing to do with the
materialization itself. Similarly it's not all that relevant to "na
ka'e" that the ball picked is white, it's just a consequence of all of
them being white in that bag.
mi tugni
> Are there still other voices for mu'ei?
"mu'ei" allows a more fine grained description of the contents of the
bags, "so'u mu'ei", "so'o mu'ei", "so'i mu'ei", "so'e mu'ei", "so'a
mu'ei", "du'e mu'ei", "rau mu'ei", "mo'a mu'ei".
.ie
mu'o mi'e xorxes
The new version of the scheme attached in two formats. Now it includes F-level where {ca'a} is placed.
Is everyone able to open this file?
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