There are two basic components of Quantum Theory. The first is the Schrödinger wave function, the Ψ—function. Each physical process has corresponding to it, a wave function—a simple Ψ—function for a simple subatomic event such as the motion of a free photon; a very complicated Ψ—function indeed for any larger-scale physical event. The Ψ—function evolves with time in a completely deterministic way. The second component is the theory of measurement, which allows us to calculate from the Ψ—function, when we make a measurement, what will be the probability of its having this result rather than that result. The Heisenberg indeterminacy principle shows how probabilities of getting a certain result of one measurement are affected by how precisely we have made another measurement.

There result different kinds of interpretation of Quantum Theory according to which of its terms we interpret realistically (i.e. as designating substances and properties) and which we interpret as terms whose sole meaning arises from their role as part of a successful theory. At one extreme positivist end of the spectrum, there is the interpretation which regards Quantum Theory simply as a theory about ‘observable’ physical phenomena, the results of measurements. The two parts of the theory fit together—but none of its terms—not just ‘Ψ—function’ but ‘position’, ‘momentum’, ‘energy’, etc. taken separately designate substances or properties. They just form part of a theory which predicts different measurements such as readings of pointers on dials or marks on photographic plates, and including what we may call ‘measurements of position’ of particles but which must not be thought of as measuring something which exists independently of being measured. Only the macroscopic is regarded realistically. This, or something like it, is often called the Copenhagen interpretation of Quantum Theory, associated with the name of Niels Bohr. Quantum Theory correlates observables; the indeterminacy lies in the indeterminism governing these correlations.

Then there is the kind of interpretation, which was in effect adopted in the text. Like the first kind of interpretation, it regards the two parts of Quantum Theory as fitting together and concerned solely with the physical world. But it understands the physical world as including not just the observable but also what lies behind and is postulated to explain the observable—electrons, photons, protons, etc., and their states. But these entities are rather strange substances—somewhat wavelike and somewhat particle-like; and their states are very strange—states of distant particles are ‘entangled’ with each other. Measurement then measures these states—the position, momentum, energy, or whatever of particles. The indeterminism in the outcome of the measurement results from the indeterminism of the physical world. Measurement is no more indeterministic a process than any other physical interaction; in general it simply reveals the actual state that the indeterministic evolution of nature has reached. There are, I believe, good reasons to think of the physical world as consisting of the things that physicists tell us about—photons and protons, electrons and neutrons, etc.; and so for preferring the second kind of interpretation to the first. But on either of these two kinds of interpretation, the result argued in the text follows—that there is some reason to suppose that the brain is a multiplying device, so constructed that Quantum Theory has the consequence that its macroscopic behaviour is not fully determined. Quantum Theory leaves room for the non-deterministic causation of the physical by the mental, for the actual operation of which I produced further arguments.

There is then a third kind of interpretation which interprets the development of the Ψ—function realistically, claiming that this part of Quantum Theory alone is concerned with the physical world. The Ψ—function develops purely deterministically, and—since the physical world can be represented by one big Ψ—function—the physical world is fully deterministic, unless it is interfered with. Indeterminism enters with the process of measurement. This process ‘collapses the wave packet’ in a non-deterministic way, although we can calculate from the Ψ—function the probabilities of the various possible measurements being made. A measurement now creates a different Ψ—function whose subsequent development is again deterministic—until measured. ‘Measurement’ plays a crucial role in this kind of interpretation; and you get different versions of the kind, according to how you understand the notion of measurement. On one extreme version any interaction at all which alters the state of a substance (e.g. the velocity of an electron) is a measurement. On another version any interaction which produces a fairly long enduring change of state in a medium-sized object such as a photographic plate or a tape-recorder is a measurement. At the other extreme, only an interaction with a conscious agent which affects his belief states, is a measurement—e.g. you only have a measurement when some human observes the reading on a dial or listens to the reading on a tape.² But Quantum Theory claims to be all-embracing—to be able on this kind of interpretation to describe in terms of a deterministic Ψ—function all physical interactions, small scale or large scale. So if the ‘interaction of two electrons’ is really, until measured, a perfectly deterministic process; we cannot regard one of these electrons as measuring the position or velocity of the other in a non-deterministic way. And since larger-scale physical objects such as photographic plates are made of small-scale objects, they too correspond to a Ψ—function and their interactions also cannot be regarded as infected with indeterminism. If indeterminism arises with measurement, only measurement which involves some non-physical event can count—only the final version of the third kind of interpretation is coherent. We have to regard the physical/mental boundary as the locus of the indeterminism of Quantum Theory. But in that case, not merely as on the first two kinds of interpretation, does Quantum Theory allow the possibility of non-determined purposing to affect brain states; but now, on this third interpretation, all physical/mental interactions are necessarily infected with indeterminism—and, among those interactions, the interaction between their prior brain states and the purposings which humans form. The Ψ—function of the brain can be collapsed in various alternative ways leading to different bodily movements, and there are various probabilities of the different collapses—but non-determined consciousness brings about the collapse.³ What brain science can show is the extent of the different purposings open to humans—i.e. how probable are the different alternative collapses which make a difference to which purposings and so which different intentional actions humans perform. But on this version of the third kind of interpretation of Quantum Theory, it is not just that Quantum Theory makes room for human purposings to affect brain states, it is a consequence of the interpretation that they do.

There are of course many problems about this interpretation to be ironed out. In the case of an ordinary observation of the physical world, as with a normal measurement, the observation which collapses the Ψ—function of a subject's brain thereby makes a difference to the Ψ—function corresponding to the observed physical state outside the subject's body, and so to the observations which other humans will make—by a route which is not a causal route of the normal kind. But Quantum Theory is saddled with this problem anyway in consequence to the EPR-phenomenon. Here is an example of this. Consider an atom emitting a pair of photons travelling in opposite directions, each of which after travelling a given direction encounters a polarizer which allows only photons with a certain polarization to pass—both polarizers being set in the same way. Quantum Theory predicts and experiments show that whenever one polarizer lets a photon through, the other one will do so also. And yet there are also strong reasons for denying that the direction of polarization of the photons is fixed in advance before the photons meet the polarizers. From that it follows that the result of one encounter (whether the polarizer lets the photon through) is correlated (either causally or through the ‘entanglement’ of the photons with each other) with the result of the other virtually simultaneously. If that is correct, there is no further problem in supposing the result of my observation of the physical world to be correlated with yours by a process of the same kind—whatever that is.

A fourth kind of interpretation of Quantum Theory—known as a Many Worlds interpretation—purports to take it as a perfectly deterministic theory; it claims that the Ψ—function develops—both before and after a measurement—perfectly deterministically. The effect of a ‘measurement’ is to ensure that the different ways the Ψ—function could develop after a ‘measurement’ are all realized—the ‘more probable’ developments simply being those which are realized in more worlds. If there are two ‘equally probable’ results of a measurement—that a particle has ‘spin up’ or ‘spin down’, then the measurement splits the present world into just two worlds—one where the particle has ‘spin up’, and another where the particle has ‘spin down’. If one result of a measurement is ‘twice as probable’ as another, then what this really amounts to is that the measurement creates three worlds, two in which the former result is realized and one in which the latter is realized. Just how often this proliferation of worlds takes place will of course depend on how widely or narrowly the notion of ‘measurement’ is construed. But it will be seen, even on the narrowest construal (where all measurements involve conscious agents), that measurement soon creates endless infinities of worlds. To postulate such an endless realm when there are available various other less farfetched interpretations of Quantum Theory seems crazy. It violates in a massive way the principle that we should postulate no more entities than are needed to explain the phenomena, and must be dismissed. And in my view its alleged advantage in being a deterministic theory is spurious. For it leaves unanswered the question why a particular observer of some phenomenon—e.g. myself—remains after the observation in this world rather than another one. The indeterminism affects in which world an observer finds himself.⁴

But given one of the three more plausible kinds of interpretation of Quantum Theory, the case argued in the text stands.