Abstract
In this chapter we’ll speak of “indivisibilism” rather than of “atomism”, even though no clear distinction exists between these two concepts: originally “atomism” was characteristic of the Democritean system in which no continuum exists except atoms themselves. In this system the question of knowing if a continuum can be composed out of indivisibles or not, has no sense at all. For Aristotle water and flesh are continua, and the problem of “indivisibilism” was originated from this. Now mathematical objects are, for him, physical ones seen from the point of view of quantity, so a mathematical model gives us an adequate description of the last ones, and this model is that of continuous magnitude which is the object of geometry. We summarize here what Aristotle is writing in the beginning of book 6th of Physics: no continuum can be composed out of indivisibles. And Aristotle’s proof is first about a line which can neither be composed of points in continuity, nor of points in contiguity, nor of points immediately next to one another; then this proof is extended to a time and proves that it is not composed out of indivisible instants; finally the property is extended to a motion. From this, Aristotle proves the indefinite divisibility of a continuum. Let us stress the point: for Aristotle indivisibles must exist; but, for him, continua are not composed out of them.
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Notes
- 1.
For a clear presentation of the Democritean physics see Salem (1996, pp. 31–95).
- 2.
Phys. VI, 231 a21–232 a22.
- 3.
Indivisibles are necessary for a general definition of continuity and contiguity; so they specially happen when time or motion are studied. Point, instant are indivisibles but they are not only ones. Aristotle doesn’t question what are these indivisibles, but Commentators will do.
- 4.
- 5.
In the major work of every medieval theologian, his Commentary of Sentences, the problem of structure of a continuum is usually treated in book II in connection with angel’s motion. It is the case for the Walter Chatton’s question quoted in the following.
- 6.
Phys. III, 5 204a8–206a8, especially 204a 25–26 et 204b 4–9.
- 7.
The first question on the subject by Harclay, “utrum mundus potuit fuisse ab eterno” has been edited by R.C. Dales in Archives d’Histoire doctrinale et littéraire du Moyen Âge, 1983, pp. 223–255. In the second one, “utrum mundus poterit durare in eternum a parte post”, Harclay exposes his indivisibility theory. Large excerpts of this question have been published in Murdoch (1981, pp. 219–261). All the Harclay’s ordinary questions are now edited, Harclay (1300). The two questions aforementioned are in vol. XVIII. The first one is pp. 732–773, the second one is pp. 1008–1097.
- 8.
For the most part Chatton’s doctrina is exposed in the question utrum motus componatur ex indivisibilibus, Chatton (1330 dist. 2, quest. 3, pp. 114–146).
- 9.
Wodeham (1340). The Ockhamist position is described by R. Wood, pp. 10–12.
- 10.
This treatise is still unedited. A detailed presentation is given in Murdoch (1987, pp. 103–137).
- 11.
His questio de continuo is being edited by Sander de Boer from the manuscript Ms. Madrid, Biblioteca Nacional 4229, ff. 179rb–186vb.
- 12.
An analysis of Nicholas of Autrecourt’s atomism and of his argumentation is given in Celeyrette (2006).
- 13.
Phys. V, 227a 27 sq.
References
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Celeyrette, J. (2015). From Aristotle to the Classical Age, the Debates Around Indivisibilism. In: Jullien, V. (eds) Seventeenth-Century Indivisibles Revisited. Science Networks. Historical Studies, vol 49. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-00131-9_2
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