David Mermin deserves respect. He is a clear writer who has published outstandingly good expositions of the GHZ and Hardy scenarios, which tighten and shed light on Bell’s theorem; of the remarkable Kochen-Specker result in quantum mechanics; and of quantum computing, at book length. But I don’t believe that this present paper is one of his useful contributions. It seems to have been inspired by the view that probability is the degree of belief which it is justified for someone to have in a proposition, in the light of other propositions held to be true. The word “belief” of course means that someone is doing the believing. I prefer the definition that p(A|B) is how strongly the (assumed) truth of proposition B implies the truth of proposition A. In all problems in which uncertainty is involved, this quantity is what we actually want; and from the (Boolean) calculus of propositions it can be shown that the p’s, which have propositions as their arguments, obey the well-known sum and product rules.
This is of course moving back towards impersonalism – the wrong direction according to Mermin. But his paper raises other questions. If someone is doing the believing and cannot be eliminated from the analysis, then the laws of physics – which are quantum – can also be applied to that someone. We get the familiar problem: when is an interaction a measurement, and how can we reconcile the description of “system + observer” with “interaction described quantum-mechanically”? The usual infinite regression problem looms. It seems to me that Mermin is terminating it by insisting on the role of consciousness, but without saying so explicitly. Yet what is consciousness? s a dog conscious? A fish? An amoeba? A virus?

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