¹ In the case of laws captured by linear equations, these details would be available by solving the appropriate equations. With non-linear equations, arriving at the details could be more time-consuming: one might have to work through innumerable iterations of the formulae. With either type, some cases could be actually non-computable. On the compatibility of determinism with non-computability see Penrose, Roger, The Emperor's New Mind (Oxford: Oxford University Press, 1989).Google Scholar

² I am assuming here a hierarchy of levels such as: sub-atomic particles, atoms, molecules, cells, organs, organisms, social structures – though this is only rough and ready, since, for instance, some cells are also organisms. More importantly, some laws, such as gravity, apply throughout, so it should be obvious that I do not mean by ‘higher-level law’ just any law that applies to objects at a higher level, only such as apply specifically at that higher level and not any lower. For example, the laws of biological replication apply at the molecular level, but of sexual reproduction at the organismic level.

³ See Campbell, Donald T., ‘“Downward Causation” in Hierarchically Organized Biological Systems’, Studies in the Philosophy of Biology, ed. Ayala, F. J. and Dobzhansky, T. (Berkeley: University of California Press, 1974), pp. 179–86.CrossRefGoogle Scholar In my article, ‘Van Rooijen and Mayr versus Popper: is the Universe Causally Closed?’ (British Journal for the Philosophy of Science, XL (1989), 389–403)Google Scholar, I explain the sense in which my usage differs from Campbell's. Campbell is not to be blamed for any of my views on downward causation, especially the view that spontaneity is causally effective.

⁴ Sometimes, of course, spontaneity will seem lawlike and predictable – for example, when someone acts in character – but its distinctive feature is more the creation of character than its expression.

⁵ There is another way in which determinism and compatibilism might not stand or fall together: a person could accept that the freedom we actually have is incompatible with determinism – and determinism therefore false – but nonetheless maintain that determinism is compatible with a kind of freedom worth wanting. I am grateful to my colleague John Leslie for pressing upon me the need to distinguish at least these two kinds of compatibilism, though this is not quite how he put the distinction he thought I needed to make. (He made other helpful comments on this paper, for which, also, thanks.) In the terms of this distinction, the argument of my paper is to the effect that determinism coupled with quantum theory implies that there would be no kind of freedom worth wanting – no freedom of any kind, actually – and, thus, no kind of compatibilism worth endorsing.

⁶ Everett, Hugh III, ‘“Relative State” Formulation of Quantum Mechanics’, Reviews of Modern Physics, XX (1957), 454–62CrossRefGoogle Scholar, is the earliest statement of his position. This is reprinted in The Many-Worlds Interpretation of Quantum Mechanics, ed. Bryce DeWitt and Neill Graham (Princeton: University Press, 1973), which contains also a much longer exposition by Everett, plus various commentaries and discussions.

⁷ In my view, the best we can legitimately say is that quantum theory is approximately true. The failure of physicists so far to combine quantum theory with cosmology can as easily raise doubts regarding quantum theory's truth as regarding cosmology's, as Roger Penrose remarks in his, ‘Newton, Quantum Theory and Reality’, in Three Hundred Years of Gravitation, ed. S. W. Hawking and W. Israel (Cambridge: University Press, 1987), pp. 17–49Google Scholar. (See p. 35). But any revision needs to yield the statistics of quantum theory as an approximation, since it is so well confirmed in practice.

The deterministic nature of the wave function is not in doubt under any interpretation. The wave function of any system unfolds deterministically so long as the system remains isolated. When it becomes correlated with some other system, say by a measurement or some other collision, this deterministic unfolding is interrupted, and a definite (unpredictable) result, which obeys the statistics, is obtained. The theoretical problem is to combine the deterministic aspect with the statistical aspect. There are, no doubt, many people who hold to determinism without endorsing Everett's interpretation of quantum theory. They are waiting, perhaps, for quantum theory to be improved upon by some new theory that will resolve the problems Everett drew attention to without yielding ground to a stochastic intrepretation. And they may be right to wait – though I think not. But waiting with this hope does not supply me with a deterministic alternative to Everett's gloss on quantum theory. I go with what is at hand.

⁸ Lewis, David, On the Plurality of Worlds (Oxford: Basil Blackwell, 1986), p. vii.Google Scholar

⁹ ‘In divergence…Two worlds have duplicate initial segments, not one that they share in common. …I reject genuine branching in favour of divergence.’ Lewis, p. 206.

¹⁰ Lewis relativizes actuality within his all-encompassing realism. Everything that is possible is ‘real’ (if that is the right word), within one world or another, but what is in one world is actual only to the inhabitants of that world (Lewis, pp. 97–101). For Everett, by contrast, ‘From the viewpoint of the theory all elements of a superposition (all “branches”) are “actual”, none any more “real” than the rest’ (Everett, 1957, p. 459/1973, p. 146). Everett is viewing the whole space-time universe of relativity theory as a single system represented by a single wave function. The other Everett-trees I have postulated for the sake of argument do not show up in his theory, but if they did they would be independent systems represented by independent wave functions. These would then be non-actual possibilities.

¹¹ Leibniz, Gottfried, Essaies de Théodicée sur la bonté de Dieu, la liberté de l'homme et l'origine du mal (Amsterdam: 1710)Google Scholar. I used Diogenes Allen's abridgement of Huggard's, E. M. 1952 translation: Theodicy (Indianapolis: Bobbs-Merrill Co., 1964).Google Scholar

¹² Incidentally, for Leibniz, ‘world’ includes heaven and hell, it is not just the spatio-temporal cosmos. This is an extremely important distinction for understanding Leibniz's theodicy, but it makes no difference to whether the argument in this paper is successful, since the argument restricts itself to whether choice exists in our space-time cosmos.

¹³ See, for instance, Griffin, David Ray, Evil Revisited (New York: SUNY Press, 1991)Google Scholar, especially pp. 26–9.

¹⁴ Mackie, John L., ‘Evil and Omnipotence’, Mind, LXIV (1955), 200–12CrossRefGoogle Scholar. See also his ‘Theism and Utopia’, Philosophy, XXXVII (1962), no. 140, pp. 153–8Google Scholar, and his The Miracle of Theism (Oxford: University Press, 1982).Google Scholar

¹⁵ ‘Divine Omnipotence and Human Freedom’, in New Essays in Philosophical Theology, ed. A. Flew and Alasdair Macintyre (London: SCM Press, 1955), pp. 144–69.Google Scholar