page 155 note 1 Russell, B., The Analysis of Mind (London, 1921) p. 78.
page 156 note 1 Laplace, of course, made this larger claim in the famous remark: ‘Une intelligence qui, pour un instant donné, connaitraît toutes les forces dont la nature est animée, et la situation respective des êtres qui la composent, si d'ailleurs elle élait assez vaste pour soumettre ces données à l'analyse, embrasserait dans la même formule les mouvements des plus grands corps de l'univers et ceux du plus léger atome: rien ne serait incertain pour elle, et l'avenir comme le passé serait présent à ses yeux. L'esprit humain offre dans la perfection qu'il a su donner à l'astronomie une faible esquisse de cette intelligence.’ de Laplace, P. S., Theorie Analytique des Probabilités, Introduction. Œuvres Complètes (Paris, 1847) vii, p. vi.
page 156 note 2 See, for example, Pap, A., An Introduction to the Philosophy of Science (New York, 1962) p. 311, where he is in doubt whether to treat the sentence as making a claim or giving a piece of advice.
page 157 note 1 Warnock has argued in favour of the view that the sentence makes a statement, but claims that the statement is vacuous, because nothing could count against it. There could never, he writes, ‘occur any event which it would be necessary or even natural to describe as an uncaused event’. (Warnock, G. J., ‘Every event has a cause’, in Logic and Language, Second Series, ed. Flew, A. G. N. (Oxford, 1953) p. 106.) Men have been mistaken, Warnock claims, in considering the scientific evidence which they have adduced to be relevant to the cited claim. I hope to show this view to be mistaken by analysing in detail what would count for or against the claim.
page 157 note 2 Kant, I., Critique of Pure Reason, Second Analogy. For detailed criticism of Kant's arguments, see Bennett, J. F., Kant's Analytic (Cambridge, 1966) ch. 15, and Strawson, P. F., The Bounds of Sense (London, 1966) Part ii, Section 3.
page 162 note 1 Popper, K. R., ‘Indeterminism in Quantum Physics and Classical Physics’, in British Journal of the Philosophy of Science, i (1950), 117–33 and 173–95.
page 166 note 1 A well-known theorem of von Neumann has sometimes been interpreted as a proof that no more fundamental theory T8 yielding perfect predictions of all physical states, yet making all the predictions of the statistical theory T1, can even be constructed, let alone confirmed, for quantum theory as T1. The most that von Neumann proved, however, is that the basic laws of quantum theory cannot be supplemented by laws containing ‘hidden parameters’, that is, laws about further properties of physical systems, in such a way as to yield perfect predictions of all physical states, where present quantum theory yields only statistical predictions. (See J. von Neumann, Mathematical Foundations of Quantum Mechanics, English edition (Princeton, N.J., 1955) Gh. 4.) But all that this means is that the axiom set of T3 cannot consist of T1 and certain other laws as well; it must drop at any rate some of the laws of T1 and bring in laws about properties of different kinds. T3 could nevertheless yield all the predictions of T1 and further predictions as well. (This was shown by Bohm: see Bohm, David, ‘A suggested interpretation of the Quantum Theory in terms of Hidden Variables’, in Physical Review, LXXXV (1952) 166–93, esp. pp. 187 f.) Some T3 must always be constructible, at any rate in the trivial way described on p. 165, from the statistical laws about physical states and their properties deducible from T1 and put in the form ‘n% A's are B’. The fundamental laws of quantum theory are of course normally expressed in a far more complicated notation than this.