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.
Brunschwig, J. (ed., tr.) 2007. Aristote: Topiques. Tome II: Livres V-VIII. Paris.
Burnet, J. (ed.) 1900–1906. Platonis Opera, 5 vol., Oxford.
Heiberg, J.L. (ed., tr.) 1876–1988. Euclidis opera omnia: Euclidis Elementa, 4 vol., Leipzig.
Reeve, C.D.C. (tr.) 2024. Aristotle’s Dialectic: Topics, Sophistical Refutations, and Related Texts. Indianapolis / Cambridge.
Ross, W.D. (ed.) 1958. Aristotelis Topica et Sophistici Elenchi. Oxford.
Triantafyllidis, M. 1998. Λεξικό της κοινής Νεοελληνικής (Dictionary of Standard Modern Greek). Thessaloniki.
Comment
In Topica VI.4 (142b11–19), Aristotle reports an etymology according to which δίχα (‘in half’) is derived from δύο (‘two’). The etymology rests on a semantic reduction rather than on strict morphological derivation: δίχα διαιρούμενον is glossed as ‘divided in half,’ and since δύο is an even number (ἄρτιον), the term δίχα is taken to carry an implicit reference to evenness. Aristotle treats this derivation as involving dependence on a ‘lower’ (derivative) term (δύο). 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 ὁ δίχα διαιρούμενον, that δίχα is derived from δύο, and that a definition may not employ derivative terms. Aristotle attributes these assumptions to his interlocutors—most plausibly 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 δίχα διαιρούμενον (‘divisible in half’) and διαιρούμενος εἰς ἴσα δύο μέρη (‘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: ἄρτιος ἀριθμός ἐστιν ὁ δίχα διαιρούμενος (Elementa VII, Def. 6; Euclidis opera omnia II, 184.11 Heiberg).