8.To see the need for Brouwer, suppose (contra Brouwer) that relative possibility is not
symmetric. Then there could be worlds like these:
For simplicity, suppose that W1–3 are all the worlds there are, that only adjacent boxes
bear links of direct relative possibility, and that W2 is actual. Say that W1 and W3 are
possible relative to W2, but not vice versa. Then both God and Zod exist necessarily
(each exists in the only world possible relative to the world in which it exists). And they
do not possibly coexist. But both possibly exist, as W1 and W3 are both possible relative
to the actual world.
9.Kant also believed in synthetic necessities. (He discussed these under the rubric of
“synthetic a priori” truths. But he also held that whatever is knowable a priori is
necessarily true.) But these, he held, all concern how things must appear to our senses,
and God, he held, cannot appear to our senses.
10.Which probably entails that not every prima facie member of the set is actually a
member. Being omniscient seems to many a prima facie perfection/positive property. So
does being atemporal. Nobody is omniscient who does not know what time it is now. But
many think that no atemporal being can know this (e.g., Kretzmann 1966). One
conclusion from this might be that there are at least two incompatible sets of perfections,
differing at least in that one includes atemporality but not omniscience and the other
includes omniscience but not atemporality. But if we accept the Gödel/Anderson
reasoning, no genuine perfections are incompatible. So on their account, what follows is
instead that at most one of atemporality and omniscience is actually a perfection.
WORKS CITED
Adams, Robert M. 1994. Leibniz. New York: Oxford University Press.
Anderson, C. Anthony. 1990. “Some Emendations of Gödel's Ontological Proof.” Faith
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Anselm. Proslogion [1087] 1965. Trans. M. J. Charlesworth. Notre Dame, Ind.:
University of Notre Dame Press.
Charlesworth, M. J. 1965. St. Anselm's Proslogion with a Reply on Behalf of the Fool by
Gaunilo and the Author's Reply to Gaunilo. Trans. M. J. Charlesworth. Oxford:
Clarendon Press.
Descartes, René. [1641] 1993. Meditations on First Philosophy. Trans. Donald A. Cress.
Indianapolis, Ind.: Hackett.