Why Does the World Exist: An Existentia - By Jim Holt Page 0,111

S prevailed in determining reality, or there isn’t. If there isn’t, then it is a brute fact that S is the Selector. But this violates Sufficient Reason. Dead end.

So suppose there is an explanation for S being the Selector. In other words, suppose there is a meta-Selector (at level 2) that selected S (at level 1). Call this meta-Selector M.

Now ask, What could M be?

We know that M could not be the same as S. That would violate the Principle of Foundation. For instance, if S were Goodness (in which case reality would have taken the ethically best possible form), the explanation for that could not be that it is ethically best that Goodness should be the Selector. The same goes for the other Selectors that pick out cosmic possibilities intermediate between the Null possibility and the All Worlds possibility—like the Causal Orderliness Selector, or the Mathematical Elegance Selector, or the Evil Selector. These Selectors all select themselves at the meta-level, and that is circular.

In fact, only two meta-Selectors at level 2 could serve as M. These are Simplicity and Fullness. Neither of these selects itself, and hence neither violates the Principle of Foundation. If Simplicity were the meta-Selector that prevailed at level 2, it would not select itself at level 1. Rather, it would select the No Selector possibility, since that is the simplest of the explanatory possibilities—that there is no explanation. And if Fullness were the meta-Selector that prevailed at level 2, it would not select itself at level 1. Rather, it would select all the Selectors at level 1.

Thus, assuming the Principle of Foundation, it is a logical truth that there are only two possible meta-Selectors at level 2: Simplicity and Fullness. One or the other of them has to constitute the ultimate explanation.

So there are two cases left to consider.

Case 1: Simplicity is the meta-Selector. Then it would pick out the No Selector possibility at level 1 (just as Simplicity at level 1 would pick out the Null possibility at level 0). But if there is no Selector at level 1, then A, the cosmic possibility that reality takes, would be randomly picked, a matter of pure chance. Yet this would not be a brute fact; rather, it would be explained by Simplicity at the meta-explanatory level.

Case 2: Fullness is the meta-Selector. Then it would pick out all the Selectors at level 1 (just as Fullness at level 1 would pick out the All Worlds possibility at level 0). But it is logically impossible for all Selectors at level 1 to dictate the form reality takes. That is because they contradict one another. Reality cannot be perfectly full and perfectly empty at the same time. Nor can it be ethically the best and causally the most orderly at the same time (since the occasional miracle could make reality better). And it certainly can’t be the ethically best and the most evil at the same time. At most, the Selectors at level 1 could all operate together only as partial Selectors. Then A, the cosmic possibility selected at level 0 to be reality, would be thoroughly mediocre. It would be as full and as empty as possible, as good and as evil as possible, as orderly and as chaotic as possible, as elegant and as ugly as possible, and so on.

In case 1, A would be chosen at random from among the cosmic possibilities. In case 2, A would be the most mediocre of the cosmic possibilities. These are the only level 0 reality outcomes that are consistent with the principles of Sufficient Reason and Foundation. And they are overwhelmingly likely to amount to the same thing! A cosmic possibility chosen at random is overwhelmingly likely to be thoroughly mediocre.

This is a matter of sheer numbers. Of all the possible forms reality might take, only a vanishingly small proportion of them possess special features—like being perfectly simple, or perfectly good, or perfectly full. The vast majority have no special feature at all. They are generic realities.

And what would such a generic reality look like? First of all, it would be infinite. Realities consisting of infinitely many worlds are vastly more numerous than those consisting of finitely many worlds. (This, of course, follows from an elementary result in set theory. The number of finite subsets of the natural numbers, though infinite itself, is of a smaller order of infinity than the number of infinite subsets of the natural numbers.)

But even in its infinity, a generic reality would fall