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In this Wikipedia article on modal realism, section "Main tenets of modal realism", there's a list of six tenets. Here are the fifth and the sixth of them:

5.Possible worlds are unified by the spatiotemporal interrelations of their parts; every world is spatiotemporally isolated from every other world.

6.Possible worlds are causally isolated from each other.

My question is: are these two equivalent? What's the difference between being spatiotemporally isolated and causally isolated? Googling doesn't help.

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Well, what I can tell you is that asking this at a party will make you socially isolated. –  Christian Mar 9 at 21:41
    
@Christian: apparently, you were going to wrong parties. :) –  Michael Mar 10 at 1:27
    
@Michael Iiiii'm not too sure about that ;) Maybe I even have more experience with that kind of party than I care to admit. –  Christian Mar 10 at 1:55
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2 Answers 2

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As you know, the two terms mean something different, as spatio-temporal relations aren't in themselves causal relations. Being spatio-temporally isolated simply means not standing in spatio-temporal relations like “before,” “10 minutes after,” “beside,” “10 meters below.” Being causally-isolated just means not having any causal relations, such that nothing that happens in A affects B, and nothing that happens in B affects A.

So the question is, can things — and let's not talk about possible worlds for a moment since possible worlds are defined in terms of these relations — be spatio-temporally isolated without being causally isolated and vice-versa?

In the first case, some people imagine God as living in a spatio-temporally isolated realm, but as knowing things that happen in our space-time (i.e. having beliefs caused by events in another space-time). That offers an example of causal but not spatio-temporal relations. The events are spatio-temporally isolated, but not causally isolated. Remember I'm not trying to offer a physically-possible example, only illustrating the difference between the concepts.

Meanwhile, in the second case, imagine two things popping in and out of existence for only a second in the same space-time, and so standing in spatio-temporal relations. But imagine that they do not have common origins, and that they are further than a light-second from one another, so that no information traveling at the speed of light from one to the other could reach the other. I would say the two things are causally isolated, but not spatio-temporally isolated.

Remember that nothing turns on these being terribly plausible scenarios. (It may well be, for instance, that causation in our actual universe always involves spatio-temporal connection.) Indeed, the possible worlds that the concepts are used to define may themselves be a little strange! What matters is just that the concepts — these two kinds of relations — are distinct.

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Absolutely brilliant insights. It's a shame I can't upvote. –  user132181 Mar 9 at 16:10
    
Great, I'm glad that's helpful. –  ChristopherE Mar 9 at 16:32
    
It's interesting that these distinctions can describe worlds that make no physical sense while at the same time they are not powerful enough to describe our actual universe with a spacetime that is not absolute. For example, are we spatiotemporally isolated from something outside of the observable universe? Both "yes" and "no" are unsatisfactory answers. And while we seem definitely causally isolated, there might be events in the past that affect us both. –  Christian Mar 9 at 21:52
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They are neither distinct nor useful! For Whitehead, only the concrete can explain the abstract in the same way the abstract derives from the concrete. Abstractions convey the determinateness of things, but their definiteness stems from the concrete. He is a radical empiricist and knowledge comes by way of contrasts as a process of working backwards from our experience to abstractions.

Time and space are not necessary conditions of the “extensive continuum,” but as Whitehead explains, they are peculiar to our immediate experience. We cannot superimpose this cognitive feltness on to other possible universes, which tenet 5 assumes. Whitehead has a universal algebra or algebraic geometry which offers a theory of physical space as conditioned by cosmic epochs. He devoted himself to the problems of space for over forty years! He found that our notions of causation and possibility, commonly subscribed to, are not without qualifications. Tenet 6 fails because there “is no intelligible definition of rest and motion [or causation] that is possible for historic routes including them, because they correspond to no inherent spatialization† of the actual world” (PR, 177). A Nexus or causal link is what Whitehead calls “a public matter of fact” and results from any “particular fact of togetherness among actual entities . . . The ultimate facts of immediate actual experience are actual entities, prehensions, and nexūs. All else is, for our experience, derivative abstraction.” (Process and Reality, 20, 28).

We do not deal with pure possibility as in the “primordial nature of God,” as the divine envisagement. We experience possibilities as “ingressions of actuality,” already negotiated through the positive and negative or inclusive and exclusive “prehensions” (relations) of selection or “objectivifications.” Our experience happens to be governed by temporal and spatial atomizations, this includes our abstractions and not the other way around. So, these tenets are not distinct they are governed by the parameters of concrete experience that abstract semantics falsely disregards! Whitehead eventually had to be persuaded why is it in our interest to ignore the interrelated concreteness of experience in order to play modal logic games--he thought it wasn't.

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