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Aristotle on Potential Density

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Abstract

In this paper we attempt to clear out the ground concerning the Aristotelian notion of density. Aristotle himself appears to confuse mathematical density with that of mathematical continuity. In order to enlighten the situation we discuss the Aristotelian notions of infinity and continuity. At the beginning, we deal with Aristotle’s views on the infinite with respect to addition as well as to division. In the sequel, we focus our attention to points and discuss their status with respect to the actuality–potentiality distinction. Then we focus our attention to the nature of continuity, which Aristotle tends to consider as leading to infinite divisibility and potential density of the extended.

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Notes

  1. Physics, III, 200b 17–20, Barnes, J. (Ed.) The Complete Works of Aristotle, The Revised Oxford Translation, Vol. I, Bolingen Series LXXI: 2, Princeton University Press, Princeton N. J., 1984, 342.

  2. Ibid, 203b 16–24, Barnes, op.cit. 347.

  3. Ibid, 203b 31–35, 206a 9–13, Barnes, op.cit. 347, 351.

  4. Ibid, 204a 2–7, Barnes, op. cit. 347.

  5. Ibid, 205a 8–30, Barnes, op.cit. 349–350.

  6. Charlton, W. “Aristotle’s Potential Infinites”, in Lindsay Judson (ed.) Aristotle’s Physics: a collection of essays, Clarendon Press, Oxford, 1991, 131.

  7. Physics, bk III, 206a 19–25, Barnes, op.cit. 351.

  8. Lear J., “Aristotelian Infinity”, Proceedings of the Aristotelian Society, 80, 1981, 190.

  9. Physics, III, 206b 16–18, Barnes, op. cit. 352.

  10. Addition is of the authors.

  11. Lear, op.cit. 195–196.

  12. Physics, III, 207a 7–8, Barnes, op. cit. 352.

  13. Ibid., bk I, 185b10, Barnes, op. cit. 317 & bk III 200b19, Barnes, op.cit. 342.

  14. Ibid., bk VI, 232b23, Barnes, 393.

  15. Buckley (2012, 19).

  16. Ibid., bk VI, 231a 24–28, Barnes, op.cit. 391.

  17. Ibid., bk V, 227a 26–34, Barnes, op. cit. 384.

  18. Bostock, D. “Aristotle, Zeno and the Potential Infinite”, Proceedings of the Aristotelian Society, 73 1972-73, 41–42.

  19. Charlton, W. “Aristotle’s Potential Infinites”, in Lindsay Judson (ed.) Aristotle’s Physics: a collection of essays, Oxford, Clarendon Press, 1991, 138.

  20. Physics, VIII, 262 a 21–24, 262b 30–32.

  21. Charlton, op. cit. 139.

  22. Physics, VIII, 262b 23–28, Charlton, op. cit. 139.

  23. Ibid, VIII, 263b 3–6, Barnes, op. cit. 440.

  24. Bostock, D. “Aristotle on Continuity in Physics VI”. In Lindsay Judson (ed.) Aristotle’s Physics. A Collection of Essays, Clarendon Press, Oxford, 1991, 188.

  25. Βostock, op. cit. 189.

  26. Physics, VIII, 263b 3–6, Barnes, op. cit. 440.

  27. Lear, op.cit., 199.

  28. We mean that between any two real numbers s and t with s ≠ t, there exists a rational number r′ such that s < r′ and r′ < t.

  29. Physics, bk V, 226b34–227a1, Barnes, op.cit. 383–384.

  30. Ibid., bk V, 227a 10, Barnes, op. cit. 384.

  31. Ibid., bk V 227a 10–13, Barnes op.cit. 384.

  32. Buckley, op.cit., 19.

  33. Physics, bk V, 227a 10–13, Barnes op.cit. 384.

References

  • Barnes J (ed) (1984) The complete works of Aristotle, The Revised Oxford Translation, vol I, II. Princeton University Press, Bollingen Series LXXI-2, Princeton

  • Bostock D (1972) Aristotle, Zeno and the potential infinite. Proc Aristot Soc 73:37–53

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  • Bostock D (1991) Aristotle on continuity in physics VI. In: Judson Lindsay (ed) Aristotle’s physics: a collection of essays. Clarendon Press, Οxford, pp 179–212

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  • Buckley B (2012) The continuity debate. Docent Press, Boston

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  • Charlton W (1991) Aristotle’s potential infinites. In: Judson Lindsay (ed) Aristotle’s physics: a collection of essays. Clarendon Press, Oxford, pp 129–149

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Authors and Affiliations

  1. Department of History and Philosophy of Science, National and Kapodistrian University of Athens, Athens, Greece

    D. A. Anapolitanos

  2. Department of Mathematics, National and Kapodistrian University of Athens, Athens, Greece

    D. Christopoulou

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  1. D. A. Anapolitanos
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  2. D. Christopoulou
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Correspondence to D. Christopoulou.

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Anapolitanos, D.A., Christopoulou, D. Aristotle on Potential Density. Axiomathes 31, 1–14 (2021). https://doi.org/10.1007/s10516-020-09476-w

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