Paul E. MeehlPaul Meehl was a psychologist, philosopher, and a philosopher of science who generally followed Karl Popper's theory of falsification. He was, with Herbert Feigl and Wilfrid Sellars, a founder of the Minnesota Center for Philosophy of Science. Feigl and Meehl wrote a paper in 1974 for Paul Schilpp's festschrift volume on Karl Popper. The paper was entitled "The Determinism-Freedom and Mind-Body Problems." Popper had for many years been a Dualist and Interactionist. Following Popper usage, they called these problems Compton's problem and Descartes' problem. They argued that determinism could not be rejected simply because of the practical difficulty carrying out predictions of the future that in principle could be done by a Laplace super-intelligence. They called the accomplishments of such a prediction the "World Formula." They frame a pseudo-logical argument that the World Formula requires 1) determinism and predictability, specifically 2) measurability and 3) calculability. But because we cannot accomplish a World Formula, we do not invalidate determinism.
Now, as is agreed on all hands, the idea of the World Formula is to be understood as a logical conjunction of three propositions: (1) the doctrine of the deterministic form of all basic natural laws, (2) the precise, complete (and simultaneous) ascertainability of all initial and boundary conditions, (3) the mathematical feasibility of the hopelessly complex computations necessary for precise and complete predictions (or retrodictions). Now, as no one knows better than Popper (though this is really a matter of the most elementary propositional logic), if a conjunction of several independent propositions entails a false or absurd conclusion, not every one of the conjuncts is (necessarily) false... There are excellent reasons for regarding propositions (2) and (3) as false at any rate, thus leaving the hypothesis of determinism at least open for further consideration.In a second paper some years later, Meehl considered the problem of free will, specifically considering whether quantum indeterminacy might play a role. He assumed that quantum indeterminacy could occur at the neuronal synapses. He imagined a model of 10 "command neurons" that need to be unanimous in their firings. They are like "10 little roulette wheels in the head," By having 10, and requiring unanimity which is extremely improbable, Meehle thinks he has statistically changed chance to "non-chance."
We find further that there is pairwise independence between the local events, that is, the depolarizing inputs from the precommand cells. On those occasions when the command neurons are in the system at all the molar outcome is unpredictable and the sequence of response attributes "steal/not steal" satisfies Mises's criterion. So everything appears to be chance, until we reflect on the astounding fact that the 10 command neurons always act in concert. That is, there are no Freudian parapraxes or abortive actions, so that while we never know what will happen at a particular locus, and we cannot tell from what happens at locus A on command neuron I what will happen on locus B of command neuron X, we do know that if command neuron I spikes, so does command neuron X, and so do all eight of the others. So what we have is a radical indeterminacy (not due to ignorance - I'm talking about an ontological indeterminancy of the kind physicists believe in) at the level of the local synaptic events, as well as a complete indeterminacy at the molar level of action, provided that the actions studied are those in which the command neurons have been in the system at all. So that everything would look like a big random mess of quantum uncertain events, except for the astonishing fact that the command neurons always act configurally. That is, in concert they manifest a kind of joint intentionality with respect to their "necessary cooperation in the integrated outcome," so that the 10 part actions are either all performed (when I steal) or all inhibited (when I resist the temptation). Such a system is clearly not determined, at either the micro or molar level; but it seems equally clear that it is not "pure chance." With 10 command neurons operating, each of which has a random firing probability of 1/2 on any one occasion, when all spike or all fail to spike, we are already past the traditional statistician's .01 significance level (p < 10-3); and for such patterning to happen on 10 occasions over the course of a year has a probability that is minuscule.