¹ Shoemaker, Sydney, ‘Time without Change’, Identity, Cause, and Mind, expanded edition (Oxford: Oxford University Press, 2003), 49–56Google Scholar. Originally published in Journal of Philosophy 66 (1969).

² Scott, Michael, ‘Time and Change’, The Philosophical Quarterly 45 (1995), 216CrossRefGoogle Scholar. In this paper Scott also opposes the contention of Teichmann, Roger in ‘Time and Change’, The Philosophical Quarterly 41 (1991), 158–77Google Scholar, that ‘statements about changeless duration can be shown to be intelligible given a Wittgensteinian account of meaning’ – Scott, 213.

³ Shoemaker, op. cit., 54. In the same place he allows himself ‘to consider “possible worlds” in which the physical laws differ drastically from those which obtain in the actual world’.

⁴ Shoemaker, op. cit., 58.

⁵ Shoemaker, op. cit., 59.

⁶ Shoemaker, op. cit., 52.

⁷ Even Leibniz, who, in The Leibniz-Clarke Correspondence, championed relative time (and space) as opposed to Newton's absolutes, seems to falter, when in effect challenged by Newton's proxy, Samuel Clarke, to show how relative time could produce the ideal mathematics of time. Leibniz falls back on the notion that time ‘can only be an ideal thing’ – which, if it means is an abstraction, is surely correct – but he provides an odd argument to show that ideality. Time cannot exist since it ‘perishes eternally’ (so that only the instant exists, which is itself, as durationless, not a part of time), and ‘how can a thing exist, whereof no part does ever exist?’ … Whoever considers these observations, will easily apprehend that time can only be an ideal thing' – Alexander, H. G. (ed), The Leibniz-Clarke Correspondence (Manchester: The Manchester University Press, 1956), 72Google Scholar. But it is surely a very equivocal argument to say that time cannot exist, therefore ‘can only be an ideal thing’, and therefore possesses the ideal mathematical properties. Leibniz has here an impossible ens rationis, the ‘cannot exist’ of which is not merely physical but logical.

⁸ Coope, Ursula, Time for Aristotle (Oxford: Clarendon Press, 2005), 32CrossRefGoogle Scholar.

⁹ Ibid.

¹⁰ These two postulates are the foundation of the special theory, as expressed in Einstein's famous June 1905 paper ‘Zur Elektrodynamik bewegter Kőrper’ in Annalen der Physik, and may be found (37-38) in A. Einstein, H.A. Lorentz, H. Weyl and H. Minkowski, The Principle of Relativity: A Collection of Original Papers on the Special and General Theory of Relativity, with notes by A. Sommerfeld, translated by W. Perrett and G. B. Jeffery (New York: Dover Publications – an unaltered republication of the 1923 translation first published by Methuen), 37-38.

¹¹ ‘In the early 1970s scientists at the U. S. Naval Observatory in Washington carried out a simple experiment in which a physicist flew with a scheduled airline once around the globe. He traveled with several atomic clocks… After his return to Washington, his clocks were compared with similar clocks that had remained in Washington. And true enough, the traveling clocks lagged slightly behind the stationary clocks. The result was in perfect agreement with Einstein's theory’, Fritzsch, Harald, An Equation that Changed the World, translated by Karin Heusch (Chicago and London: University of Chicago Press, 1994), 135Google Scholar.

¹² The term for ‘change’ here is metabolē. For the definition of time as the number of motion, later, Aristotle uses kinēsis for ‘motion’. The terms metabolē and kinēsis seem often synonymous for Aristotle. So, for example, at Physics IV.14.223a29-223b1, he gives as examples of kinēsis, as numbered by time: generation and perishing, growing, altering, as well as moving locally.

¹³ In English, Andrew Marvell says to his coy mistress: ‘But at my back I always hear/ Time's wingèd chariot hurrying near, / And yonder all before us lie/ Deserts of vast eternity’, similarly using a spatial metaphor for time.

¹⁴ There is one situation, in English and Greek, in which ‘after’, say, may indicate both behind in space and afterwards in time, as in ‘You came after us to Washington’. What is indicated there is not so much the going from one point to the other as the maintaining the same distance, both spatial and temporal, from someone so going.

¹⁵ It has been argued, by G. E. L. Owen and others, that Aristotle, in trying to derive the temporal from the spatial before-after order begs the question by considering motion temporal in the first place, before trying to derive the before-after order of time from it. See, for example, Annas, Julia, ‘Aristotle, Number, and Time’, The Philosophical Quarterly 25 (April, 1975), 97–113CrossRefGoogle Scholar; Owen, G. E. L., ‘Aristotle on Time’ in Machamer, P. and Turnbull, R (eds.), Motion and Time, Space and Matter (Columbus, Ohio: Ohio State University Press, 1976), 3–27Google Scholar; Corish, Denis, ‘Aristotle's Attempted Derivation of Temporal Order from that of Movement and Space’, Phronesis 21 (1976), 241–251CrossRefGoogle Scholar.

¹⁶ For an account of such series see, for example, Huntington, Edward V., The Continuum and Other Types of Serial Order (Cambridge, MA: Harvard University Press, 1917)Google Scholar. An example of such a simply ordered class is, according to Huntington, ‘The class of all instants of time, arranged in order of priority’ (16).

¹⁷ This is a summary of the rather elaborate discussion in Physics I.7-9, quoted from Ursula Coope, op. cit., 6.

¹⁸ Immanuel Kant's Critique of Pure Reason, translated by Norman Kemp Smith (New York: St. Martin's Press, 1965), 76.

¹⁹ I have tried to give some ontological account of all this in Corish, Denis, ‘Time Reconsidered’, Philosophy 81 (2006)CrossRefGoogle Scholar.

²⁰ Leibniz, despite his odd grounding for the ideal in time, gave, in The Leibniz-Clarke Correspondence, at least a hint of what should be required. Suggesting that ‘time [is not] any thing distinct from things existing in time’, he goes on: ‘instants, consider'd without the things, are nothing at all; and … they consist only in the successive order of things’, 27. The challenge, of course, would be to show just how – rather than merely assume that – time, as such a relation between things, can produce the mathematically necessary notion of the durationless instant.