The aim of this paper is to argue that the (alleged) indeterminism of quantum mechanics, claimed by adherents of the Copenhagen interpretation since Born (1926), can be proved from Chaitin's follow-up to Goedel's (first) incompleteness theorem. In comparison, Bell's (1964) theorem as well as the so-called free will theorem-originally due to Heywood and Redhead (1983)-left two loopholes for deterministic hidden variable theories, namely giving up either locality (more precisely: local contextuality, as in Bohmian mechanics) or free choice (i.e. uncorrelated measurement (...) settings, as in 't Hooft's cellular automaton interpretation of quantum mechanics). The main point is that Bell and others did not exploit the full empirical content of quantum mechanics, which consists of long series of outcomes of repeated measurements (idealized as infinite binary sequences): their arguments only used the long-run relative frequencies derived from such series, and hence merely asked hidden variable theories to reproduce single-case Born probabilities defined by certain entangled bipartite states. If we idealize binary outcome strings of a fair quantum coin flip as infinite sequences, quantum mechanics predicts that these typically (i.e. almost surely) have a property called 1-randomness in logic, which is much stronger than uncomputability. This is the key to my claim, which is admittedly based on a stronger (yet compelling) notion of determinism than what is common in the literature on hidden variable theories. (shrink)

This is a joint review of Jenann Ismael's 'How physics makes us free' (OUP).

My review summarizes the book's constituent papers, with occasional brief comments. All of the contributions are competent and interesting.

Recent work in the philosophy of religion has resurrected Leibniz’s idea that there is a best possible world, perhaps ours. In particular, Klaas Kraay’s [2010] construction of a theistic multiverse and Nevin Climenhaga’s [2018] argument from infinite value theory are novel defenses of a best possible world. I do not think that there is a best world, and show how both Kraay and Climenhaga may be resisted. First, I argue that Kraay’s construction of a theistic multiverse can be resisted (...) from plausible assumptions about set theory. Next, I argue against the value-theoretic assumptions that underlie Climenhaga’s argument and show how to give an infinite value theory where there is no best world. (shrink)

I provide the account of divine creation found in multiverse theorists Donald Turner, Klaas Kraay, and Tim O’Connor. I show that the accounts Kraay and Turner offer are incoherent. God does not survey all possible worlds and necessarily actualize those universes in the (on balance) good worlds or the worthy worlds. If God necessarily actualizes the multiverse, we have no idea which universes are parts of that multiverse. I show next that Tim O’Connor’s multiverse account of creation is also (...) incoherent. I argue that a preferable multiverse would include a much greater variety of universes than are included in Turner, Kraay or O’Connor. In the last section I offer some concluding remarks. (shrink)

In replying to certain objections to the existence of God, Robert Adams, Bruce Langtry, and Peter van Inwagen assume that God can appropriately choose a suboptimal world, a world less good than some other world God could have chosen. A number of philosophers, such as Michael Slote and Klaas Kraay, claim that these theistic replies are therefore committed to the claim that satisficing can be appropriate. Kraay argues that this commitment is a significant liability. I argue, however, that the (...) relevant defenses of theism are committed to the appropriateness of, not satisficing, but motivated submaximization. When one submaximizes with motivation, one aims at the optimum but accepts the good enough because of a countervailing consideration. When one satisfices, one aims at the good enough and chooses the good enough because it realizes her aim at the good enough. While commitment to the appropriateness of satisficing may be a significant liability, commitment to the appropriateness of motivated submaximization is not. (shrink)