¹ For this, see Gillispie, C. C., The Edge of Objectivity, 1960, Ch. 3, especially p. 93.Google Scholar

² For details on this, see my ‘Descartes's Anticipation of a Logic of Scientific Discovery’, in Crombie, A. C. (ed.), Scientific Change, London, 1963.Google Scholar

³ For this distinction, see also my ‘The Philosophical Basis of Physics’, in Contemporary Physics, 3, 1962, 282–394, section 1.Google Scholar

⁴ For a case-study of the relations between technical exemplification as against the justification-use of fundamental philosophical terms, see my Aristotle, Induction and Necessity, Pamphlet of the Aquinas Society, 1963.

⁵ For a discussion by Descartes of the nature of sensory knowledge, see Meditations, 6, A.T., ix, 57ff.Google Scholar, noting especially his doctrine of the ‘teaching of nature’, his calling ‘sensings … confused modes of thinking’; and his contention that ‘sensuous apprehensions have been given me by nature only as testifying to my mind what things are beneficial or harmful’—a doctrine reminiscent of Hume's subsequent doctrine. It is only when it is pointed out (rightly or wrongly) that sense is not confused thought (cp. Kant, Crit. of Pure Reason, B57; Prolegomena, §13, Note III), that we realize that there is a distinction in kind; a distinction which has of course become a commonplace since the 18th century, though questioned once again in more recent times, by such writers as Quine, Waismann, and Wittgenstein.

⁶ Compare: We ‘know’ that the sun will rise tomorrow because our inference from past occasions of this sort is dependable in the light of the ‘uniformity of nature’. And compare also Berkeley, Principles of Human Knowledge, sect. 107: ‘By diligent observation of the phenomena within our view, we may discover the general laws of nature, and from them deduce the other phenomena, I do not say demonstrate; for all deductions of that kind depend on a supposition that the Author of nature always operates uniformly, and in a constant observance of those rules we take for principle: which we cannot evidently know.’ Berkeley is usually called a ‘British Empiricist’! (On this, see also my ‘Inductive Process and Inductive Inference’, Aust. J. Phil., 34, 1956, 164–181, especially sect. i).

⁷ But note what is said below, p. 236 about Descartes's versions of the causal principle.

⁸ See also Smith, Kemp, New Studies in the Philosophy of Descartes, 1952, p. 301Google Scholar: ‘The centre of gravity of Descartes' philosophy thus shifts away from the self to that which in thought is disclosed to the self, as other than the self, and as preconditioning the self’, etc. This is a comment on the passage in the Meditations, iii, but it has also quite general significance.

⁹ For all this, cp. A. Koyré, Etudes Galiléenes, iii, Galilée et la loi d'inertie, ch. 3 and App. B.

¹⁰ This is a fairly close version of the original Latin text, of 1644. It was translated into French by Picot, a friend of Descartes's, and published 3 years later, after having been examined and corrected by Descartes, who seems to have made frequent alterations and clarifications to the original. For interest, we therefore add the French version of the law: ‘Chaque chose en particulier continue d'être en mème état autant qu'il se peut, et que jamais elle ne le change que par la rencontre des autres.’ This brings out more clearly than the Latin that Descartes wants to say that ‘every free particle continues in the same state unless…’; and also that any changes must be due to impact.

¹¹ French version: ‘Chaque partie de la matière, en son particulier, ne tend jamais a continuer de se mouvoir suivant des lignes courbes, mais suivant des lignes droites.’

¹² To say that God conserves speed and direction of free particles is to say (I think), negatively, that such conservative tendencies do not follow from the concepts of speed and direction, so that the resulting statement is not ‘analytic’ but ‘synthetic’. Again, to say that God is immutable, in this context is Descartes's way of saying that there are conservation laws governing the material universe, a statement which he would believe to be true though not founded on conclusive empirical evidence, if evidence at all; we might say it had for him the status of an a priori truth. Finally, even if there are conservation principles, it does not follow that speed and direction or momentum (if you add ‘mass’, a non-Cartesian concept, giving us, via the product of mass and velocity, the concept of momentum) are the appropriate candidates. This was Leibniz's famous complaint against the Cartesians; cp. his commentary on the Principles: ‘Although the constancy of God may be supreme, and he may change nothing except in accordance with the laws of the series already laid down, we must still ask what it is, after all, that he has decreed should be conserved in the series—whether the quantity of motion [=m v] or something different, such as the quantity of force.’ (Loemker, ed., Leibniz's Philosophical Papers and Letters, ii, 42., pp. 648–649Google Scholar, on Article 36 of the Principles.) Leibniz's reference to ‘force’ is to what we call vis viva, mv², the conservation of which was discovered by Leibniz, partly as an attempt to show that purely geometrical characteristics were insufficient to exhaust a description of the nature of the universe, contrary to the opinion of the Cartesians.

¹³ In Dreams of a Spiritualist, ii, 2, in Works, Hartenstein, ed., 1868, ii, p. 366–367.Google Scholar

¹⁴ For Poincaré's views on the law of inertia, see his Science and Hypothesis, iii, 6, the section on The Principle of Inertia; also Whitrow, G. J., ‘On the Foundations of Dynamics’, in Brit. J. Phil. Sci., 1, 1950, 92–107CrossRefGoogle Scholar, on Newton's First Law; and my article on the Second Law, in Brit. J. Phil. Sci., 2, 1951, 217–235Google Scholar, concerning the relations between testing and conceptual formulation of such fundamental laws.

¹⁵ ‘These principles [sc. laws of motion] are deduced from the phenomena and made general by induction, which is the highest evidence that a proposition can have in this philosophy.’ (From a letter to Cotes, in Thayer, H. S. (ed.), Newton's Philosophy of Nature, 1953, p. 6.)Google Scholar

¹⁶ For this term, see, for instance, Braithwaite, , Scientific Explanation, Cambridge, 1952, pp. 77f., 100f.Google Scholar

¹⁷ For some evaluations of Descartes' biological approach, see for instance Rostand, Jean, ‘Descartes et la Biologie’ in his L'Atomisme en Biologie, 1956, pp. 152–161Google Scholar, especially 156–157, emphasizing Descartes's preoccupation with mechanistic models. Also, Passmore, J. A., ‘William Harvey and the Philosophy of Science’, Aust. J. Phil., 36, 1958, 85–94CrossRefGoogle Scholar, which contrasts Harvey with Descartes.

¹⁸ The passage to which Descartes is here referring is quoted below (p. 245), where I discuss it in connection with Descartes's notions of analysis and models.

¹⁹ My translation of this important passage slightly varies from that of most of Descartes's commentators. Cp. also Gilson, E.'s commentary on the Discourse, pp. 470–474Google Scholar, which cites correspondence throwing further light on the questions involved, particularly the letter to Vatier, 22.2.1638, in which Descartes explains that he thought it sufficient in the Dioptrique to supply ‘a posteriori demonstrations’; that to try to give a priori demonstration of everything would have involved an exposition of the whole of his physics; but finally, that since he believes himself capable in principle to deduce these suppositions from the first principles of his metaphysics (as he will also say in the Discourse presently!), there doesn't seem to be any need to go in for any detailed a priori physical proofs (literally: ‘… for any other sorts of proofs…’). Moreover, he goes on, it just is not true that you always need to have a priori reasons in order to satisfy truth (persuader une verité), witness Thales's theory that the moon receives its light from the sun, which he can surely have proved only through the consequence of this hypothesis, i.e. its power to explain, e.g. the various phases of its light.

²⁰ Concerning ‘analysis’ I have written at greater length in the chapter in Crombie (ed.), Scientific Change, already referred to. See also Dijksterhuis, E. J., ‘La Methode et les Essais de Descartes’, in Descartes et le Cartesianisme Hollandai, 1950, by various writers, pp. 21–44Google Scholar; Gilson, E., Commentaire, pp. 181–182, 187, 195, 222, 223.Google Scholar

See also Leibniz, , On the Elements of Natural Science, Loemker ed., vol. i, sect. 32, pp. 426–447, especially p. 439.Google Scholar

²¹ Cp. Reply to Objections II (A.T., IX, 121–122), where Descartes speaks of ‘the method of proof’ as being ‘two-fold, one being analytic, the other synthetic’, the former—as we see from this passage—not reserved just for scientific but also philosophical exposition, e.g. the Meditations.

²² Hanson, N. R., Patterns of Discovery, 1958, ch. iv.Google Scholar

²³ We omit reference here to the fact of the rays lying in the same plane. Also Descartes's expression for the ratio of the velocities is the inverse of the ‘correct’ value. The deeper reason for this is that his is a particle-theory, and not a wave-theory, agreeing thus with the same expressions reached by Newton and Maupertuis, against those of Huygens and Fermat.

²⁴ The following is a geometrical property of the ellipse: If we call i the angle made by a line parallel to the major axis meeting the ellipse at a point B with the normal to the tangent to the ellipse at B; and r the angle made by the line BI, where I is a focus of the ellipse, with the same normal, then sin i: sin r is constant. (Cp. Milhaud, G., Descartes Savant, 1921, Ch. 5, especially pp. 108–117Google Scholar, and see p. 113 for the diagram illustrating the property of the sines referred to.)