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Possible Worlds on a Linear Time Line

 
 
Reply Wed 2 Feb, 2011 07:25 am
Let the letter W denote the set of all possible worlds (including our world, which we will call the actual world 'a'), and let each possible world be set to a time T* (where * is an integer greater than or equal to zero). Now let 'a' be set at time T0 on a linear time line which can be shown as...
_____a_______>

Now let 'a' be placed on the time line at some arbitrary point and have it labeled T0:
____T0______>

Since by definition every other possible world is set to a time T*, we can add more to the line like so:

__T0__T1__T2__T3....Tn__>

Given that every possible world is set to a time T*, we can say (I think) that whatever statements are true in any possible world (which we will call 'w') are true only at the time at which they can be located. However, this may not entirely be the case. Let 'R' stand for the accessibility relation to two possible worlds at two different times T* and T*+1. Now let T1RT2. We can say (also another 'I think') that T1 and T2 are related by an element x, which is a statement (or proposition) of a first-order predicate calculus. Now given that there is an x in both T1 and T2, x is necessary in T1 and T2. However, this does not mean that x is necessary from T2-T3. So what we can say is as follows:

1. Given a possible world w at time T* and given another possible world w which follows after T* and is called T*+1, if there is an element x that is in both, we can say that x is a necessary truth in both T* and T*+1.

If I messed up somewhere, let me know. Thank you.
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Fil Albuquerque
 
  1  
Reply Wed 2 Feb, 2011 08:35 am
@Ding an Sich,
1 - Is there any causal relation between these two or more worlds ? If not, time line is of no interest...if there is I don´t see a particular reason to call them separate worlds as they all interact along the time and space line and can be represented in function of one another...which in turn makes their description relative to its correlative partners, as they all form a System.
So I guess I am at odds on what you mean with "worlds" here...

...meaning: Is T1, T1 in function of T0 or what ?
What would T1 be in function of any other World in W ?

2 -
Quote:
that whatever statements are true in any possible world (which we will call 'w') are true only at the time at which they can be located


How so ? or do you mean actual ?

3 -
Quote:
accessibility relation to two possible worlds at two different times T* and T*+1.


For whom an observer or between themselves ? Again if between them where is the element of distinction ? You make an assumption which is not clear regarding their separate natures...

4 -
Quote:
Given a possible world w at time T* and given another possible world w which follows after T* and is called T*+1, if there is an element x that is in both, we can say that x is a necessary truth in both T* and T*+1.

4.1 - I suppose you meant not w but in w...
4.2 - If x resides in w, then x is true in w period...
(even if just as an abstraction and not an actuality)
Ding an Sich
 
  1  
Reply Thu 3 Feb, 2011 12:36 pm
@Fil Albuquerque,
Fil Albuquerque wrote:

1 - Is there any causal relation between these two or more worlds ? If not, time line is of no interest...if there is I don´t see a particular reason to call them separate worlds as they all interact along the time and space line and can be represented in function of one another...which in turn makes their description relative to its correlative partners, as they all form a System.
So I guess I am at odds on what you mean with "worlds" here...


I would imagine there are, but I did not explicitly point this out. We could have an object A at w1 on T1 cause B at w2 at T2. But I am not addressing causal relations. I am simply addressing statements in a first order predicate calculus.

Fil Albuquerque wrote:

...meaning: Is T1, T1 in function of T0 or what ?
What would T1 be in function of any other World in W ?


T1 could be a function of T0 and vice-versa, but indirectly through an accesibility relation 'R'. Keep in mind, I defined each possible world as a time on the line, marking them T0, T1, T2, etc. But we could say that T0RT1, which means "T0 is accessible from T1".

Fil Albuquerque wrote:

2 -
Quote:
that whatever statements are true in any possible world (which we will call 'w') are true only at the time at which they can be located


How so ? or do you mean actual ?


No. I mean all possible worlds including the one we are in, which just so happens to be the actual world; keep in mind though, our world, even though it is actual, is also possible.

Fil Albuquerque wrote:

3 -
Quote:
accessibility relation to two possible worlds at two different times T* and T*+1.


For whom an observer or between themselves ? Again if between them where is the element of distinction ? You make an assumption which is not clear regarding their separate natures...


I did not make an explicit distinction between these worlds, but I did make an implicit one. Each world may be different from the last except that in relation to two worlds at two successive instants, there has to be a generic element x. So there are differences between each world, but that is negligible to some extent.

Fil Albuquerque wrote:

4 -
Quote:
Given a possible world w at time T* and given another possible world w which follows after T* and is called T*+1, if there is an element x that is in both, we can say that x is a necessary truth in both T* and T*+1.

4.1 - I suppose you meant not w but in w...
4.2 - If x resides in w, then x is true in w period...
(even if just as an abstraction and not an actuality)


If you mean by "x is true in w period" that it is necessarily true then no it does not have to be true necessarily. Remember, x is represents a generic statement in a first-order predicate calculus, so the truth or falsity of it could change at another time (which just so happens to be, if we are going off of my interpretation of modalities as time based) given another possible world in which it is false.

Hope this clears some things up.
Fil Albuquerque
 
  1  
Reply Thu 3 Feb, 2011 02:10 pm
@Ding an Sich,
Ding an Sich
Quote:
that whatever statements are true in any possible world (which we will call 'w') are true only at the time at which they can be located


Filipe
Quote:
How so ? or do you mean actual ?



Ding an Sich
Quote:
No. I mean all possible worlds including the one we are in, which just so happens to be the actual world; keep in mind though, our world, even though it is actual, is also possible.


1 - My question was why they are true only at the time at which they can be located, given if true always true ?...

Ding an Sich
Quote:
Given a possible world w at time T* and given another possible world w which follows after T* and is called T*+1, if there is an element x that is in both, we can say that x is a necessary truth in both T* and T*+1.


and then:

Ding an Sich
If you mean by "x is true in w period" that it is necessarily true then no it does not have to be true necessarily. Remember, x is represents a generic statement in a first-order predicate calculus, so the truth or falsity of it could change at another time (which just so happens to be, if we are going off of my interpretation of modalities as time based) given another possible world in which it is false.

2 - So could you clarify which one is it ?

Regards>FILIPE DE ALBUQUERQUE
Ding an Sich
 
  1  
Reply Fri 4 Feb, 2011 01:13 pm
@Fil Albuquerque,
Fil Albuquerque wrote:

Ding an Sich
Quote:
that whatever statements are true in any possible world (which we will call 'w') are true only at the time at which they can be located


Filipe
Quote:
How so ? or do you mean actual ?



Ding an Sich
Quote:
No. I mean all possible worlds including the one we are in, which just so happens to be the actual world; keep in mind though, our world, even though it is actual, is also possible.


1 - My question was why they are true only at the time at which they can be located, given if true always true ?...


A statement at time T0 does not have to be true at time T1 or T2,etc. Ill give you an example; say that at time T0 I am wearing a blue shirt. The statement, "Ellis is wearing a blue shirt.", at time T0 is a true statement. Now let us say that at time T4 I am not wearing a blue shirt and someone still mentions, "Ellis is wearing a blue shirt.". We would say that this is false at time the present time it is uttered. So I am not making the claim that, if something is true it will always be true. Instead I am making the claim that, given two possible worlds at two successive times T* and T*+1, if x is true in both, then x is a necessary truth only in those possible worlds. But it does not have to be that way two other possible worlds. In fact, it may be the case that x is false in between two other successive possible worlds.
Fil Albuquerque
 
  1  
Reply Fri 4 Feb, 2011 02:40 pm
@Ding an Sich,
Quote:
A statement at time T0 does not have to be true at time T1 or T2,etc. Ill give you an example; say that at time T0 I am wearing a blue shirt. The statement, "Ellis is wearing a blue shirt.", at time T0 is a true statement. Now let us say that at time T4 I am not wearing a blue shirt and someone still mentions, "Ellis is wearing a blue shirt.". We would say that this is false at time the present time it is uttered. So I am not making the claim that, if something is true it will always be true. Instead I am making the claim that, given two possible worlds at two successive times T* and T*+1, if x is true in both, then x is a necessary truth only in those possible worlds. But it does not have to be that way two other possible worlds. In fact, it may be the case that x is false in between two other successive possible worlds.


It certainly it is true at T4 that at T1 you were wearing a blue shirt, know it or not...and so will be for eternity...now I get what you meant...given different worlds, different conditions, different facts...
A OK ! So what ?
contrex
 
  1  
Reply Fri 4 Feb, 2011 02:44 pm
Let G be a guy who gets stoned and posts on Able2know and let W be the weed in his bong, and let N be the nonsense he posted. How much W does it take to produce this much N?
Fil Albuquerque
 
  1  
Reply Fri 4 Feb, 2011 03:26 pm
@contrex,
How much nonsense is needed until something comes out right eh ? Just ask a scientist...or do you get it always at your first or second try ?
Sometimes it takes allot of wrongs and much will to endure enough to get it right...now in turn is allot easier to point the finger and look good in the picture...I personally don´t give a F*** on how it looks, if who´s trying is truthful in is intent...

Work takes true commitment, given that, true knowledge eventually follows at its own pace...while pointing the finger produces nothing.
0 Replies
 
Ding an Sich
 
  1  
Reply Sun 6 Feb, 2011 07:17 pm
@contrex,
None, precisely because this G is not stoned and was not stoned at the time of the posting. Read up on your modal logic and you might understand.
0 Replies
 
Ding an Sich
 
  1  
Reply Mon 7 Feb, 2011 03:11 pm
@Fil Albuquerque,
Fil Albuquerque wrote:

It certainly it is true at T4 that at T1 you were wearing a blue shirt, know it or not...and so will be for eternity...now I get what you meant...given different worlds, different conditions, different facts...
A OK ! So what ?


Well I would like to prove that all truths are contingent, and can only be necessary given a specified domain of possible worlds; to whit, that there are no necessary truths for all possible worlds. This is merely a start (a small start mind you).

This would get rid of silly notions such as God being necessary for all possible worlds.
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