Is there a relationship between καθαιρέω ("destroy") and καθαίρω ("purify")?

Question

καθαιρέω and καθαίρω look remarkably similar and seem to have similar meanings: "destroy" and "purify/purge," respectively.

It came as some surprise to me, though, that I couldn't find an obvious relationship between the two.

• καθαιρέω obviously comes from κατα- +‎ αἱρέω ("seize," "take away"). Wiktionary lists a pretty straightforward etymology from PIE:

  From Proto-Hellenic *həřřéyō, from Proto-Indo-European *ser- (“to take, grasp”).

• καθαίρω, on the other hand, seems to come from the adjective καθαρός ("pure"), about whose etymology Wiktionary is much less certain:

  No Indo-European cognates can be drawn. This implies a borrowing from Pre-Greek.

Is it just a strange accident that these two words are so similar in spelling (and, to a certain extent, meaning)? Is there really no relationship (even if only in the prefix καθ-) between them?

Answer 1

You and Wiktionary are correct: they're unrelated. The big tell is that καθ- is not a prefix, and the Doric and Aeolic forms have an omicron there instead of an alpha, which isn't something you would have seen with κατα-.

Here is what Beekes says:

ETYM No etymology, see Frisk and DELG for unsuccessful older attempts. The variation α/ο points to Pre-Greek origin (Fur.: 391 even connects it with ἀθαρής, but this is doubtful). Alternatively, Peters 1993b: 95ff. takes up the old connection with Skt. śithirá- 'loose', reconstructing *kr̥th₂-ro-, but this etymology needs too many ad hoc assumptions: independent dissimilatory loss of the first r in both branches, doubtful laryngeal aspiration *tH > θ (πλατύς is a strong counterexample, and cannot be explained away by πλαταμών), and too complicated semantics.

Either Pre-Greek or connected to Sanskrit, what's clear is that κατα- is not the prefix for καθαίρω/καθαρός, and thus the words look a lot less similar when you're comparing καθαίρω/καθαρός with αἰρέω alone.