Abstract
The Newtonian theory, as expressed by Clarke, of absolute time and space, and the opposing Leibnizian theory of relational time and space, are both advocated in the context of the question of divine freewill. For Clarke and Newton the Freedom of God entails the choice of creating the world here or there, at an earlier time or a later — so that space and time are conceived of as constituting a pre-existing matrix, independent of the world, into which, at this or that temporal or spatial position, the world is placed. The choice of such temporal or spatial positions is entirely free, there being nothing to recommend one position over another. For Leibniz, on the other hand, such a choice, if it were possible, would be arbitrary, inexplicable, and contrary to the rational structure which the scientist expects the universe to exhibit. For Leibniz then there is no such arbitrary divine choice, and consequently, time and space are not a pre-existing matrix offering such a choice. They are not a framework into which the world is placed but a framework which arises only as a result of the creation of the world; they are relations between created things. Clarke objects that it is not clear how time and space as relations between things afford the mathematical magnitudes which the scientific view requires. Leibniz’s reply seems weak, as it does not show exactly how relations between things can exhibit quantity. The subsequent history of physics however has seemed to bear out the Leibnizian rather than the Newtonian view. Hence we must ask whether in fact it is the Leibnizian view, that time and space are relations between things, which has triumphed, or something much more like the Newtonian view: that time and space inherently, and not merely derivatively, exhibit a quantitative nature.
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Notes
In so far as this paper deals with Leibniz on time it can be taken as complementary to the paper of Waldemar Voisé’s, “On Historical Time in the Works of Leibniz,” in The Study of Time II.
In this paper all references to the correspondence will be made in terms of The Leibniz-Clarke Correspondence, ed. H. G. Alexander (Manchester: The Manchester University Press, 1956) by identification of the letter number, the paragraph number, and the page of the book. Thus ‘L, V, 16, p. 59’ will refer to Leibniz’s fifth letter, paragraph 16, page 59. Such references will be bracketed and incorporated into the text of the paper.
Nichomachean Ethics, vii. 2–3. 1145b21–1147b20.
See, for example, Summa Contra Gentiles, II, 48.
Max Jammer, Concepts of Space, 2d ed. (Cambridge, Massachusetts: Harvard University Press, 1969), p. 127.
Jammer, p. 139.
Jammer, p. 140.
Jammer, pp. 140–141.
Jammer, pp. 141–144.
Some modern philosophers have attempted to do somthing of the kind, notably Alfred North Whitehead. He attempts to define such concepts as ‘instant’ and ‘point’ in terms of extensive temporal or spatial “regions.” A point is an “abstractive set” of such extensions, extending over one another (that is, getting smaller and smaller) to infinity. This “method of extensive abstraction” has been variously attacked, largely on the ground that in order to construct the abstractive set it already depends upon the point-like in some way, and so turns out to be circular. Adolf Grunbaum has argued also that the method will not identify the point-like uniquely — that is, will not distinguish between two arbitrarily close point-like positions. For a brief account of the various criticisms see Paul F. Schmidt, Perception and Cosmology in Whitehead’s Philosophy (New Brunswick, New Jersey: Rutgers University Press, 1967), pp. 71–73. In addition the following may be said. The method of extensive abstraction seems to depend upon the concept of the mathematical limit; indeed the point can be considered as a “limit approached by a geometrical representation of the extensive features of an abstractive set” (Nathaniel Lawrence, “Whitehead’s Method of Extensive Abstraction,” Philosophy of Science 19 1950, p. 148). This being so, the method depends upon the point-like “elements” of the mathematical theory of the continuum, in which case again circularity may arise — or at least a Newtonian rather than Leibnizian account of time and space ultimately prevail, as I go on to argue.
For an account of the basic theory of the continuum see Edward V. Huntington, The Continuum and Other Types of Serial Order, 2d ed. (Cambridge, Massachusetts: Harvard University Press, 1917).
Leibniz, Basic Writings, tr. Montgomery (La Salle, Illinois: The Open Court Publishing Company, 1962), “The Monadology,” 3, p. 251.
Herbert Wildon Carr, Leibniz (London: Constable and Company, Ltd., 1929), p. 153.
This criticism again applies to some interpretations of Whitehead’s method of extensive abstraction. Victor Lowe has said: “Approximation is the only way in which we can handle space and time [The point] is the idea of an undefined superlative not exemplified in experience.... The definition and realization of the ideal, the superlative, can be achieved only by an unending series of comparatives. This is the lesson of extensive abstraction.” (Victor Lowe, Understanding Whitehead Baltimore: The Johns Hopkins Press, 1962, pp. 68–69). The trouble is that, mathematically speaking, approximation is always to some definite value, which is thus presupposed rather than established by the method of approximations. There is simply no well-defined sense to the notion that the physical approximates to the mathematical, thus enabling us to find and identify the mathematical through the physical.
We must take ‘Platonist’ here in a rather wide sense of the term, suitable to the seventeenth century. There is a dispute (See Guthrie, History of Greek Philosophy, vol. IV) about whether “the mathematicals” are for Plato forms themselves or intermediates between forms and sensibles.
For the outline of one such attempt see my “The Continuum,” The Review of Metaphysics, 1969.
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Corish, D. (1978). Time, Space and Freewill: The Leibniz-Clarke Correspondence. In: Fraser, J.T., Lawrence, N., Park, D.A. (eds) The Study of Time III. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6287-9_27
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