Paulian Idea, Bayesianism and Quantum Solipsism. Note Quote.

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The best way to begin a more thoroughly QBist delineation of quantum mechanics is to start with two choice quotes on personalist Bayesianism itself. The first is from Hampton, Moore, and Thomas,

Bruno de Finetti believes there is no need to assume that the probability of some event has a uniquely determinable value. His philosophical view of probability is that it expresses the feeling of an individual and cannot have meaning except in relation to him.

and the second from Dennis Lindley,

The Bayesian, subjectivist, or coherent, paradigm is egocentric. It is a tale of one person contemplating the world and not wishing to be stupid (technically, incoherent). He realizes that to do this his statements of uncertainty must be probabilistic.

These two quotes make it absolutely clear that personalist Bayesianism is a “single-user theory.” Thus, QBism must inherit at least this much egocentrism in its view of quantum states ρ.

For, the “Paulian Idea”—which is also essential to the QBist view—goes further still. It says that the outcomes to quantum measurements are single-user as well! That is to say, when an agent writes down her degrees of belief for the outcomes of a quantum measurement, what she is writing down are her degrees of belief about her potential personal experiences arising in consequence of her actions upon the external world

With regard to the Paulian Idea there are two points that are decisive for dismissing the charge of solipsism. One is the conceptual split of the world into two parts—one an agent and the other an external quantum system—that gets the discussion of quantum measurement off the ground in the first place. If such a split were not needed for making sense of the question of actions (actions upon what? in what? with respect to what?), it simply would not have been made. Imagining a quantum measurement without an autonomous quantum system participating in the process would be as paradoxical as the Zen koan of the sound of a single hand clapping. The second point is that once the agent chooses an action {Ei}, the particular consequence Ek of it is beyond his control. That is to say, the particular outcome of a quantum measurement is not a product of his desires, whims, or fancies—this is the very reason he uses the calculus of probabilities in the first place: they quantify his uncertainty, an uncertainty that, try as he might, he cannot get around. So, implicit in this whole picture—this whole Paulian Idea—is an “external world . . . made of something,” just as Martin Gardner(1) calls for. It is only that quantum theory is a rather small theory: Its boundaries are set by being a handbook for agents immersed within that “world made of something.”

(1) “Well then, it is incomplete after all. Go seek hidden variables!” But that is to misunderstand the problematic here. Theories of decision that really are theories of decision just don’t “port” to theories or visions of the world in that way. From the point of view of being a theory for taking actions and gambles, quantum theory is already all that it can be.

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