Alhtough Basque maite 'love, affection; dear, beloved' has been since long suspected to be a Celtic loanword, the suggested etymon (Old Irish maith 'good' < Proto-Celtic *mati-1) is in my opinion semantically inadequate2.
On the other hand, we've got Galician neitegada 'expressive demonstration of affection or tenderness', presumably a Gallaecian substrate loanword from Proto-Celtic *neito-3 > Welsh nwyd 'passion, emotion', Old Irish nia 'warrior, champion', archaic gen. sing. Neth (Ogam NETTA-, -NETTAS)4. We've also got Iberian neitin 'dear', often found in the epistolary formula neitin iunstir 'Dear Sir'5.
This way, the Basque word would be derived from an apophonic Celtic variant *noite- with secondary labialization of the initial nasal as in Roncalese moite 'love, tenderness'.
On the other hand, we've got Galician neitegada 'expressive demonstration of affection or tenderness', presumably a Gallaecian substrate loanword from Proto-Celtic *neito-3 > Welsh nwyd 'passion, emotion', Old Irish nia 'warrior, champion', archaic gen. sing. Neth (Ogam NETTA-, -NETTAS)4. We've also got Iberian neitin 'dear', often found in the epistolary formula neitin iunstir 'Dear Sir'5.
This way, the Basque word would be derived from an apophonic Celtic variant *noite- with secondary labialization of the initial nasal as in Roncalese moite 'love, tenderness'.
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1 R. Matasović (2009): Etymological Dictionary of Proto-Celtic, pp. 259-260.
2 Koldo Mitxelena (1977): Fonética histórica vasca, p. 526, adduces the formal parallelism between Old Irish an-as maith la cách 'what each one deems good' and modern Basque bat-bederak maite duena 'what each one loves' (formerly bat bederak onhesten duena, with onhesten 'to be loved', lit. 'to esteem good') as an example where maite was equivalent to on 'good'.
3 This is an IE lexeme *neiH- 'to shine' also found in Proto-Celtic *neibo- > Middle Welsh nwyf 'strong feeling, passion, desire', Old Irish níab 'vigour'. There's also an apophonic variant *noibo- reflected in Old Irish noíb- 'holy', Gaulish Noibio. See R. Matasović (2009): op. cit., p, 286.
3 This is an IE lexeme *neiH- 'to shine' also found in Proto-Celtic *neibo- > Middle Welsh nwyf 'strong feeling, passion, desire', Old Irish níab 'vigour'. There's also an apophonic variant *noibo- reflected in Old Irish noíb- 'holy', Gaulish Noibio. See R. Matasović (2009): op. cit., p, 286.
4 N. Zair (2012): The Reflexes of the Proto-Indo-European Laryngeals in Celtic, pp. 232-233. See also R. Matasović (2009), op. cit., p. 291.