Potentiality and Actuality of the Infinite: A Misunderstood Passage in Aristotle’s Metaphysics (Θ.6, 1048b14-17)

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In Metaphysics Θ.6, 1048b14-17, Aristotle treats the problem of what it is for the infinite to exist potentially, i.e. to be potentially actual. According to my interpretation, Aristotle argues that to exist potentially is for the infinite to have a potentiality which cannot be actualized in reality but only in thought, because it is a potentiality the process of whose actualization cannot be brought to an end.


A Journal for Ancient Philosophy



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The Greek text has been quoted from Ross 1924, vol. 2 and Jaeger 1957, who in their editions have corrected, following Christ 1886, the obviously erroneous reading τῷ δὲ χωρίζεσθαι of the manuscripts, which Bonitz (1848-1849, vol. 1) had adopted, to the reading τὸ δὲ χωρίζεσθαι, which is indirectly testified by (ps.-)Alexander (in Metaph. 581.11 Hayduck).


Answer 1(a) is endorsed by Bonitz 1890, 185 = 1994, 240; Ross 1924, ii. 250, 252; Hope 1952, 189; Apostle 1966, 152; Hintikka 1973, 131-3; the Londinenses (Burnyeat et al. 1984, 127); Reale 1993, ii. 411; Hübner 2000, 270, 274, 275 n. 20; Tricot 2000, 501; and Makin 2006, 7, 141. For answer 1(b), see Rolfes 1904, 23, 162 n. 16 = 1928, 231, 374-5 n. 17; Tredennick 1933, 447; Bassenge 1960, 212 = 1990, 222; Hussey 1983, 87; Ross 1984, 1655; Furth 1985, 68; Szlezák 2003, 158; and Beere 2009, 209-10 n. 71. Answer 1(c) seems to originate, if not in every detail, at least in outline, with Wieland (1970, 298), who has been followed by Wolf (1979, 412 n. 22). Independently of Wieland Burnyeat too (2008, 227-8), who has suggested emending γνώσει to γενέσει, seems to endorse this answer. His proposal to alter the received text, which has been accepted by Makin, will be discussed in Section v below.


Hussey 1983, 79. Hussey’s view has convincingly been defended by Hübner (cf. 2000, 273-5).


Rolfes 1904, 23 = 1928, 231.


Cf. Ross 1924, ii. 252-3.


Cf. Hintikka 1973, 132, 133-4; Wolf 1979, 71, 72, 413 n. 23. Lear, who, following Ross, interprets the text in the sense of 2(b), rightly rejects Hintikka’s interpretation (cf. 1979/1980, 192-3; see also Hübner 2000, 274).


Cf. Rolfes 1904, 23 = 1928, 231; Burnyeat et al. 1984, 128; Makin 2006, 7; Beere 2009, 209. None of the three possible answers to Question 2 is matched by the rather strange manner in which Apostle translates the second sentence of our Θ.6 passage: ‘For, to a never-ending process of division we attribute an actuality which exists potentially, but not a separate existence to the infinite’ (1966, 152; Apostle’s emphasis). Apostle seems to suppose that in this sentence τὸ ἄπειρον is to be added in thought as a second object parallel to Υ.


As Coope has convincingly argued (cf. 2012, 278-80), this view is implied also by Aristotle’s distinction between a ‘change’ (κίνησις) and an ‘activity’ (ἐνέργεια), the locus classicus of which is Metaph. Θ.6, 1048b18-35, for which see Burnyeat 2008. Makin, who has extensively discussed this distinction (cf. 2006, 141-150), describes it as a distinction between an action which is ‘incomplete’ in that it ‘leads to a distinct result, something over and above the action itself’ and an action which is ‘complete’ in that ‘there is no result distinct from the action itself’ (2006, 142).


Coope 2012, 280.


Cf. Coope 2012, 272-3.



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