God and possible worlds (What's Wrong with the World)

God and possible worlds

by Edward Feser

Some reflections over at my own blog, which will be of interest to more philosophically inclined readers. Possibly.

Posted by Edward Feser on June 10, 2010 6:20 PM | Del.icio.us | Permalink

Comments (10)

http://en.wikipedia.org/wiki/Boltzmann_brain

Posted by Step2 | June 10, 2010 8:33 PM

Speaking as a complete non-AT, let me join Ed in saying that the very notion of "possible worlds" presupposes the concept of possibility and hence cannot ground it. I tend to think that "possible worlds" talk is _at best_ a mere metaphor or heuristic device for understanding (and it hardly ever helps me understand anything anyway), but never more than that.

At the very end of the post, Ed, you get into the notion of God as the ground of necessary truths. Is part of the idea here that a mathematical Platonist should instead take numbers to exist in the mind of God? What about propositions?

Posted by Lydia | June 10, 2010 9:29 PM

Ed,

I think your post is pretty much spot-on. There is a simpler way to express it (at least for me). Back in the late 90s to early 2000s, I was doing research on so-called transworld projection, i.e, how objects get projected across possible worlds to form counterparts. In order for God to be God, because of his divine simplicity, his transworld set must be identical in every possible world - the transfer function (to borrow language from engineering) must be equal to the identity matrix. If this is so, then, by using a form of set theory called situated set theory and God's simplicity, one can show that the different possible worlds can be considered to exist like spokes on a wheel with God as the hub. No one talks about there being the possibility of possible world overlap, but with this wheel/hub concept and Barwise's situated set theory governing the possible worldsets, it is possible to imagine a possible world made from the overlap of many possible worlds into a superset, a super-possible world. In other words, it seems, because of God's simplicity, he is free to pick and choose from all possible worlds to form the best possible world.

This last part is conjecture, but Barwise's set theory (based on the work of Peter Aczel, who formulated a set theory which relaxes the foundation axiom of the ZFC form of set theory) allows for possible worlds to contain other possible worlds, so it is at least plausible. In any case, divine simplicity is something that is very tricky to deal with in possible world theory. Divine simplicity becomes a sort of fixed point across possible worlds. I don't know of anyone who has studied fixed points across worlds, but I haven't kept up on the literature for a few years.

When I have free time, I will eventually get this work published (the transworld projection process I was working on was not developed for theology - I have adapted it, here) along with the mountain of other papers on various topics I have presented at conferences for the last so many years. A colleague of mine was considering using a variant of possible world logic for the same problem I was working on, but decided that there were too many limitations and so developed a whole new type of ontological semantics to deal with the problem. Whether his approach and mine can be shown to be identical remains to be seen.

In other words, it is not that God exists across possible worlds, but that possible worlds derive their existence from a singular God, as you point out. Otherwise, the concept of God would be meaningless across possible worlds, since the concept of God would be subject to the constraints of the possible worlds and hence not singular and simple, but contaminated by each possible world.

I doubt I've been clear. What I mean is much easier to show with diagrams and symbols. Hard to do in comboxes.

As for the Boltzmann brain - not really possible. Classical fluctuations, even of a chaotic nature, are smeared out by the Heisenberg Uncertainty principle at the quantum level. This has been known since the early 1990's (I wrote a paper on it in graduate school). That is why the concept of quantum chaos is somewhat nebulous and depends on special definitions adapted for mesoscopic states. The Wikipedia article, by the way, has a misstatement at the beginning. It should read:

The concept arises from the need to explain why we observe such a large increase of organization in the universe. The second law of thermodynamics states that the entropy in the universe will always increase. We may think of the most likely state of the universe as one of high entropy, closer to uniform and without order. So why is the observed entropy so low?

The Chicken

P. S. In the event that the above sounds like gibberish - it isn't. It is merely poorly explained. That seems to be my theme for the day.

Posted by The Masked Chicken | June 10, 2010 9:33 PM

I tend to think that "possible worlds" talk is _at best_ a mere metaphor or heuristic device for understanding (and it hardly ever helps me understand anything anyway), but never more than that.

That is exactly the point at which the colleague I mentioned above and I disagreed, so I guess the nature of possible worlds is unsettled. Eventually, we both decided that possible worlds are the worlds where counterfactuals live. He described them by developing something called ontological semantics, I kept doing mathematical modeling. I think we will eventually be able to show the two approaches are identical. They seem to give rise to the same lattice structure.

The Chicken

Posted by The Masked Chicken | June 10, 2010 9:41 PM

Which of you, MC, you or your colleague, agreed with me? :-)

On this,

In other words, it seems, because of God's simplicity, he is free to pick and choose from all possible worlds to form the best possible world.

you might be interested in an old post of mine called "The Fallacy of the Clickable Universe" from before your time, MC. (Unless you were lurking _very_ quietly or commenting under another handle.)

http://whatswrongwiththeworld.net/2008/09/the_fallacy_of_the_clickable_u.html

Posted by Lydia | June 10, 2010 9:54 PM

Actually, the wheel/hub model is not exactly like a clickable universe you posit, because such a situations assumes a one-time choice for God. Here is how the wheel hub model works:

In each possible world in any given situation, you make a choice. Let us call the total number of possible worlds N (where N may be uncountably infinite). In X such worlds, you make choice 1. Let us call this subset X1. Likewise, there is a subset of worlds where you make choice 2. Call this X2. Now, your possible range of free will choices partitions (called an ultrafilter in topology) the set of possible worlds into a new set Y = {X1, X2, ... Xm}, where m =

Now, let us say that there are A people in existence at time T. Each persons choice, moment by moment, exists or could exist in a unique filter of N, forming unique sets Y1, Y2, ...YA corresponding to the choices of each person. Since there is a unique set of possible worlds for each person which correspond to the actual choice they did make, we get (using Aczel/Barwise set theory) an overlap of the Xp of each set, Ym, to form a possible world set that can encompass the actual choices of each individual.

This overlap set Z = {Xp1, Xp2...XpA} is brought together by God's simplicity and united into a single consistent world, moment by moment, which forms the world as we know it based on the choice we make, moment by moment. Thus, it is because of God's simplicity that free will can exist. One can have a clickable universe and free will if the clicking happens moment by moment and is dependent on people's free will.

God is the context of every possible world. It is he who creates the world, moment by moment. It is he who holds the world and the wills of people together, moment by moment. It is because God is connected to each person that we can have free will.

The Chicken

Posted by The Masked Chicken | June 11, 2010 9:12 AM

Greetings. First time I have visited this and pleased. 'It is because God is connected to each person that we can have free will.' Lovely because in an anxiety now I feel the comfort. All arround me try to bashing, dashing with their Godless concepts.
I like to think all religiously. Is it Einstine's theory based on religion like E=MC2

E=EHUDIA
M=MUSLIM
C=CHRISTIANS
CATHOLICS
ORTHODOX

Regards
PPR

Posted by Pronoy Polycarp Rozario | June 15, 2010 4:54 AM

Speaking as a complete non-AT, let me join Ed in saying that the very notion of "possible worlds" presupposes the concept of possibility and hence cannot ground it.

But that's not true. Lewis does not assume that there are possible worlds. There are for him worlds, not possible worlds. Neither does Sider, for whom there is a pluriverse (many universes) which makes no appeal to 'possible' worlds nor to many concrete universes. Now these might finally fail as reductions, but not because they overlook some simple circularity.

Posted by Mike | June 25, 2010 8:25 PM

I just said that "possible worlds" presupposes the concept of possibility. That is to say, if one talks about a possible world, one presumably already has a concept of possibility, for otherwise one would not be able to talk about a world as possible. But in that case, "possible worlds" are not being used to explicate the notion of possibility, which appears to be more primitive.

Posted by Lydia | June 25, 2010 9:39 PM

A baby learns the idea of possibilty with its second breath.

Posted by The Masked Chicken | June 26, 2010 6:45 AM

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