δύο
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Etymon-lemma
Transliteration (Word)
English translation (word)
Transliteration (Etymon)
English translation (etymon)
Century
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Quotation
Ὁμοίως δὲ καὶ εἰ διὰ τῶν ὑποκάτω τὸ ἐπάνω ὥρισται, οἷον ἄρτιον ἀριθμὸν τὸν δίχα διαιρούμενον ἢ τὸ ἀγαθὸν ἕξιν ἀρετῆς· τό τε γὰρ δίχα ἀπὸ τῶν δύο εἴληπται, ἀρτίων ὄντων, καὶ ἡ ἀρετὴ ἀγαθόν τί ἐστιν, ὥσθ᾽ ὑποκάτω ταῦτα ἐκείνων ἐστίν. ἔτι δ᾽ ἀνάγκη τὸν τῷ ὑποκάτω χρώμενον καὶ αὐτῷ χρῆσθαι. ὅ τε γὰρ τῇ ἀρετῇ χρώμενος χρῆται τῷ ἀγαθῷ, ἐπειδὴ ἀγαθόν τι ἡ ἀρετή, ὁμοίως δὲ καὶ ὁ τῷ δίχα χρώμενος τῷ ἀρτίῳ χρῆται, ἐπειδὴ εἰς δύο διῃρῆσθαι σημαίνει τὸ δίχα διῃρῆσθαι, τὰ δὲ δύο ἄρτιά ἐστιν.
Translation (En)
Similarly, look to see whether he has defined a higher one through a lower one—for example, even number as ‘what is bipartitely divisible’; or good as ‘a state of virtue’; for bipartitely is derived from two, which is an even number, and virtue is a sort of good, so that the former are lower than the latter. Further, in making use of what is lower than a thing, one will necessarily make use of the thing itself as well. For a person who makes use of virtue, makes use of good, since virtue is a sort of good, and, similarly, a person who makes use of bipartitely makes use of even, since ‘bipartitely divisible’ signifies divisible by two, and two is an even number.
(transl. Reeve 2024, 98)
Other translation(s)
De même encore, si l’on a défini ce qui est supérieur à l’aide de choses qui lui sont inférieures, par exemple le nombre pair comme celui qui est divisible de façon bipartite, ou le bien comme la possession de l’excellence ; car bipartite se comprend a partir de deux, qui est pair, et l’excellence est une forme du bien, de sorte que ces choses-là sont subordonnées à celles-ci. En outre, celui qui se sert de ce qui est subordonné à une chose donnée se sert nécessairement aussi de cette chose elle-même. De fait, celui qui se sert de l’excellence se sert du bien, puisque l’excellence est un bien ; de même, celui qui se sert de «bipartite» se sert du pair, puisqu’être divisible de façon bipartite signifie être divisible par deux, et que deux est pair.
(transl. Brunschwig 2007, 53–4)
Parallels
There are no parallels.
Bibliography
- Beekes, R. 2010. Etymological Dictionary of Greek, 2 vol. Leiden / Boston: Brill.
- Brunschwig, J. (ed., tr.) 2007. Aristote: Topiques. Tome II: Livres V-VIII. Paris: Les Belles Lettres.
- Burnet, J. (ed.) 1900–1907. Platonis opera, 5 vol., Oxford: Clarendon.
- Heiberg, J.L. (ed., tr.) 1876–1988. Euclidis opera omnia: Euclidis Elementa, 4 vol., Leipzig: Teubner.
- Reeve, C.D.C. (tr.) 2024. Aristotle’s Dialectic: Topics, Sophistical Refutations, and Related Texts. Indianapolis / Cambridge: Hackett.
- Ross, W.D. (ed.) 1958. Aristotelis Topica et Sophistici Elenchi. Oxford: Clarendon.
- Triantafyllidis, M. (Τριανταφυλλίδης, Μ.) 1998. Dictionary of Standard Modern Greek (Λεξικό της κοινής Νεοελληνικής). Thessaloniki: Ινστιτούτο Νεοελληνικών Σπουδών (Ίδρυμα Μανόλη Τριανταφυλλίδη).
Comment
In Topica VI.4 (142b11–19), Aristotle reports an etymology according to which dikha (‘in half’) is derived from duo (‘two’). The etymology rests on a semantic reduction rather than on strict morphological derivation: dikha dihairoumenos is glossed as ‘divided in half,’ and since duo is an even number (artion), the term dikha is taken to carry an implicit reference to evenness. Aristotle treats this derivation as involving dependence on a ‘lower’ (i.e. derivative) term (duo). The passage reflects an Academic background, in which phonological proximity and semantic containment suffice for etymological explanation.
Contextualization of the passage:
(1) Aristotle’s argument at Topica VI.4, 142b11–19 is dialectical rather than doctrinal: it proceeds from the interlocutor’s accepted commitments, not from Aristotle’s own views. These include the claims that an even number is defined as ho dikha dihairoumenos, that dikha is derived from duo, and that a definition must not employ derivative terms. Aristotle attributes these assumptions to his interlocutors—namely, Academic philosophers such as Plato or Xenocrates—and derives a contradiction from them.
(2) The definition of even number targeted by Aristotle belongs to a Platonic-Academic context. Although it is not preserved verbatim in Plato, Plato treats dikha dihairoumenos (‘divisible in half’) and dihairoumenos eis isa duo merē (‘divisible into two equal parts’) as equivalent and defines the even number accordingly (Leges 895e1–3 Burnet). Euclid later adopts precisely the definition attacked in Aristotle: artios arithmos estin ho dikha dihairoumenos (Elementa VII, Def. 6; Euclidis opera omnia II, 184.11 Heiberg).