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Did Aristotle used the term contradiction or the term contradictory in his discussions of reductio ad impossibile?

Two translators who disagree:

For all those which come to a conclusion through an impossibility deduce the falsehood, but prove the original thing from an assumption when something impossible results when its contradiction is supposed (, that is, when the contradictory to the assumption is supposed.) — Aristotle, Prior analytics (translation by Robin Smith)

For all who effect an argument per impossibile infer syllogistically what is false, and prove the original conclusion hypothetically when something impossible results from the assumption of its contradictory — Aristotle, Prior analytics (translation by A.J. Jenkinson, with minor emendations by Daniel Kolak)

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    Contradiction is antiphasis. See e.g. R.L. Gallagher, Antiphasis as Homonym in Aristotle (2014) Mar 14 at 8:25
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    The typical "move" used in syllogistic derivation is reductio per impossibile: dia to adunaton. See e.g. Prior An, 37a: "Moreover it is not possible to prove the convertibility of these propositions by a reductio ad absurdum [to adunaton], i.e. by claiming that since it is false that B may belong to no A, it is true that it cannot belong to no A (for the one statement is the contradictory of the other); but if this is so, it is true that B necessarily belongs to some A; and consequently A necessarily belongs to some B—but this is impossible [adunaton]. " Mar 14 at 8:34
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    And see De Interpretatione, 17a27: "Thus it is clear that for every affirmation there is an opposite negation, and for every negation an opposite affirmation. Let us call an affirmation and a negation which are opposite a contradiction [kai esto antiphasis touto, kataphasis [κατάφαση] kai apophasis (ἀπόφασις) ai antikeimenai (ἀντικείμενος)]." Mar 14 at 13:16
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    This question seems more suitable for a group about translation. Frankly, I don't see any significant difference in the translations. Mar 14 at 16:25
  • @DavidGudeman Speakpigeon will no doubt school you here, and explain to you how real English speakers see the manifest difference, and how you should go check it since you don't understand it.
    – Frank
    Mar 14 at 16:59

1 Answer 1

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Let us set down the original text of the relevant part (I.23, 41a23-27):

πάντες γὰρ οἱ διὰ τοῦ ἀδυνάτου περαίνοντες τὸ μὲν ψεῦδος συλλογίζονται, τὸ δ᾿ ἐξ ἀρχῆς ἐξ ὑποθέσεως δεικνύουσιν, ὅταν ἀδύνατόν τι συμβαίνῃ τῆς ἀντιφάσεως τεθείσης, οἷον ὅτι ἀσύμμετρος ἡ διάμετρος διὰ τὸ γίνεσθαι τὰ περιττὰ ἴσα τοῖς ἀρτίοις συμμέτρου τεθείσης.

The term at issue (marked in bold) is a declined form of the noun ἀντίφασις. An appropriate translation of it in the context is "contradictory proposition" (not the action or process of contradicting). Since "contradiction" is more associated with the verb "contradict" of which it is a nominalisation, and "contradictory" is used as a noun (in contrast to an adjective) as a term of logic in the sense of a contradictory proposition, "contradictory" can also be taken as the literal translation of what Aristotle says.

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  • Thanks. In English we can say both its contradiction is supposed and its contradictory is supposed, with exactly the same meaning. Do you think this was also possible in ancient Greek? Mar 16 at 17:40
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    First, we have to resolve the issue about the contemporary terminology: It is not a good practice to use both phrases in the same sense. Briefly to put, contradiction involves two (ordinarily) propositions X and Y, contradictory involves one proposition Y (as the contradictory of X). Or else, "contradiction" signifies an action; for example, X contradicts Y, thus a contradiction of Y is actualised by X. By extension as a result of the action, X is a contradiction of Y. Aristotle uses ἀντίφασις in both ways —with one proposition (contradictory), and two propositions (contradiction). Mar 16 at 19:15
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    I agree. Traditionally 'contradiction' refers to a pair of propositions with the property that the truth of one entails the falsity of the other and vice versa. It is unfortunate that in modern usage it means a single proposition that is false under all interpretations. 'Logical falsehood' would be a better term for that, by contrast with 'logical truth'. As to the two translations, I would say 'contradictory' is better for that reason.
    – Bumble
    Mar 16 at 21:46
  • @TankutBeygu Thanks again, very interesting. You say "Aristotle uses ἀντίφασις in both ways", but was there a word meaning "contradictory" and not "contradiction" in Greek at the time? Mar 28 at 13:06
  • See ἀντιφατικός. You may browse the texts at Perseus Digital Library. Mar 28 at 14:19

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