Abstract
On one level, there is little disagreement concerning the main features of Leibniz’s philosophy of time. No one would dispute, for instance, that Leibniz maintained the following three theses:
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(i)
Time is relational. That is, time is not itself a physical entity, but is rather a relation or ordering of such entities as are not coexistent.
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(ii)
Time is ideal. Being relational, time has no existence apart form the things it relates; it is therefore an ideal entity. What exactly Leibniz meant by this is, as we shall see, a matter of dispute: Russell’s view that it follows from an ontology which denies the reality of relational facts (such as “a is before b”) has recently been forcefully challenged by Ishiguro and others.1 But whatever its exact meaning, the ideality of time is clearly consonant with Leibniz’s belief that continuity is a concept that strictly applies only to ideal entities, and that
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(iii)
Time is a continuous quantity.
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Notes
See RuPL, Louis Couturat’s La logique de Leibniz, Paris: Alcan, 1901, RePL and Ish.
Thus in the Monadology Leibniz writes: “The passing state ticwhich enfolds and represents a multitude in unity or in the simple substance is merely what is called perception” (Monadology, #14, [1714]: G. VI. 608) Elsewhere, however, he implies that the state of a monad contains a multitude of minute perceptions at any time, as in his reply of July 1698 to Pierre Bayle’s criticisms (G.IV. 517–524) and his letter to Jean Bernoulli (21/2/1699: GM. III. 574–575). For further discussion of Leibniz’s theory of perception, see Mark Kulstad, “Some difficulties in Leibniz’s Definition of Perception”, pp 65–78 in LCIE.
See Russell’s Our Knowledge of the External World, London: Allen & Unwin, 1914, 1952, and his “On the Experience of Time”, The Monist, 25, 1915, pp 212–233, and “On Order in Time”, Proceedings of the Cambridge Philosophical Society 32, May 1936, pp 216–228. It is interesting to note that Russell retracts none of his criticisms of Leibniz’s relationalism in the preface to the second edition of RuPL in 1937, and never acknowledges indebtedness to him on this score in his papers on temporal order. Russell’s criticisms of Leibniz on dynamical grounds, on the other hand, contain the same confusion that exists in Leibniz’s writings, namely that between the relational nature of space and time and the relativity of motion to a particular frame of reference. It has been one of the great achievements of 20th century philosophy of science to demonstrate the independence of these two issues. But although Russell, Hike Leibniz, conflated ‘relational’ with ‘relative’ he almost put his finger on a fatal flaw of Leibniz’s theory: its inability to sustain a definition of sameness of place through time, or affine connection. For details of these points, see Howard Stein’s “Newtonian Space-Time”, The Texas Quarterly, Autumn 1967, pp 174–200.
Russell argues: “The definition of one state of a substance seems impossible without time. A state is not simple, on the contrary it is infinitely complex. It contains traces of all past states, and is big with all future states. It is further a reflection of all simultaneous states of other substances. Thus no way remains of defining one state, except as the state at one time.” (RuPL, p 52). Russell assumes here what he is supposed to be proving: that simultaneity cannot be defined except by presupposing an absolute time. Leibniz, on the contrary, is guilty of no such circular reasoning, since he defines simultaneity in terms of compatibility of states.
Although it is clear that Leibniz always regards the relation G as asymmetric, it is hard to see how this is justified by the appeal to the law of the series: for this law would determine not only all the states which come after any given state in the series, but equally all those which precede it too. The lack of explanation why G should be regarded as asymmetric must therefore be considered as a serious deficiency in Leibniz’s rationalistic foundation for time.
Thus Barrow (who is in a sense the first of the Newtonians): “But as Magnitudes themselves are absolute Quantums independent on all Kinds of Measure, tho’ indeed we cannot tell what their Quantity is, unless we measure them: so Time is likewise a Quantum in itself, tho’ in order to find the Quantity of it, we are oblig’d to call Motion to our Assistance….” (Geometrical Lectures, Capek, p. 204.) Newton’s conception is more complicated, in that Absolute Time is distinguished from the time whose quantity is measured by motion, its quantity being determined mathematically by the correction for the inequality of natural days, as I have argued in an unpublished paper, “The Theory of Fluxions and Newton’s Philosophy of Time” (1981). But his criticism of Leibniz, as expressed through Clarke’s pen, is still that “Space and Time are Quantities; which Situation and Order are not” (Clarke’s Third Reply to Leibniz, #4: G.VII.369).
e.g. by van Fraassen in vanF, p 71.
Cf. G.II.300: “Points are not parts of the continuum, but extremities, and there is no more a smallest part of a line than a smallest fraction of unity” (To Des Bosses). Both this and the previous quotation are taken from Russell’s excellent appendix of leading passages in his RuPL, pp. 247 and 248 respectively.
The application of Extremum Principles in Physics, based on the simplicity of the underlying monads, is an example of what Leibniz called the Middle Science, the acquisition of knowledge of the phenomenal world by means of metaphysical principles of parsimony and optimization. For a discussion of this see Loemker’s notes on pp. 27 and 61 of Loem.
Cf. also his letter to de Voider of 21/1/1704: “But all individual things are successive or subject to succession…. Nor for me is there anything permanent in them other than that very law which involves a continued succession, the law in each one corresponding to that which exists in the whole universe” (G.II.263).
See for instance Grunbaum’s Philosophical Problems of Space and time, Dordrecht/Boston: D. Reidel, 1973, for an exposition of this theory.
For Leibniz a given structure is homogeneous if the whole is similar to any of its parts; this is avowedly true of time: “a temporal whole is similar to its part” (Initia Rerum, GM.VII.22), and this is the reason why space and time cannot be real existents, as I shall explain in section 3. Cf. Primae Veritates, Cout.OF p 522: “For the diverse parts of an empty space would be perfectly similar and congruent to each other, and could not be distinguished from each other, and would therefore differ only in number, which is absurd. Time can also be proved not to be a thing, in the same way as space.”
After writing this, I discovered that much the same point has already been made, and more cogently that here, by Fred D’Agostino in an article originally published in 1976 (Philosophical Quarterly, vol. 26, pp 125–138; reprinted in revised form in Leibniz: Metaphysics and Philosophy of Science, ed. R.S. Woolhouse, Oxford: Oxford UP, 1981, pp 89-103). D’Agostino argues that if the reducibility thesis is correct, “then all individual substances are compossible, and Leibniz’s doctrine that there are many possible worlds becomes unsupportable”, and consequently that Leibniz did indeed allow relational predicates to characterize individual substances.
My claim here that duration and extension considered in the abstract are the same as abstract time and space is a contentious one. In a weighty article that has recently been translated into English (“L’espace, le point et le vide chez Leibnz” Revue philosophique de la France et de Vetranger (1946) pp. 431–452, translated as “Space, Point and Void in Leibniz’s Philosophy”, pp 284–301 in LCIE), Martial Gueroult has argued for a profound distinction between space and abstract extension in Leibniz’s conception: space, as an innate idea, “differs radically from the discursive concept of abstract extension (extensio) that is acquired by abstraction from a perceived property” (LCIE p 284). I confess that I cannot understand all Gueroult’s arguments for this claim; although it is clear that Leibniz distinguishes space and extension inasmuch as not everything which is situated in space has extension, this only distinguishes extension qua attribute from space or abstract extension. The latter two terms, on the other hand, Leibniz appears to use interchangeably. Compare, for instance, his definitions in the Initia Rerum of duration and extension as “the magnitude of time” and “the magnitude of space”, respectively, (GM.VII.18) with the claim in his critique of Malebranche quoted in the text that time and space serve to measure duration and extension (considered as attributes of things) (G.VI.584).
In his influential work, Syntagma Philosophicum, Gassendi argued: “Thus we say that the world could have been created a thousand years before its creation, not because there were years marked off by the repeated revolutions of the sun, but because Time flowed of which the appropriate measures, the revolving motions of the sun, could have existed then. And we do not say that all these times were imaginary….” (Physicae Sectio I, Liber I, transi. Milic Capek and Walter Emge, in Capek p. 201).
“De Gravitatione et Aequipondio Fluidorum”, pp. 75–156 in Unpublished Scientific Papers of Isaac Newton, ed. and transl, by A. Rupert Hall and Marie Boas Hall, Cambridge: Cambridge UP, 1962.
From the Scholium to the Definitions of Newton’s Mathematical Principles of Natural Philosophy [1687], Cajori’s 1934 transl., Capek p. 98.
There is also the question of Leibniz’s non-materialist conception of substance. From the beginning, simple substances were conceived by him as being principles of motion and continuation in existence, and thus as being more nearly mental or spiritual than material. For an excellent discussion of the interrelationship between the young Leibniz’s metaphysics and theology and his physics of matter and motion, see Daniel Garber’s “Motion and Metaphysics in the Young Leibniz”, pp 160–184 in LCIE.
I have borrowed the image of the imaginary eye from Leibniz, in the Phoranomus, Cout.OF p 590.
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Arthur, R.T.W. (1985). Leibniz’s Theory of Time. In: Okruhlik, K., Brown, J.R. (eds) The Natural Philosophy of Leibniz. The University of Western Ontario Series in Philosophy of Science, vol 29. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5490-8_10
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