Apology 27e, negations

I understand everything about this except the bolded οὐ – it seems like one negation too much.

ὅπως δὲ σύ τινα πείθοις ἂν καὶ σμικρὸν νοῦν ἔχοντα ἀνθρώπων, ὡς οὐ τοῦ αὐτοῦ ἔστιν καὶ δαιμόνια καὶ θεῖα ἡγεῖσθαι, καὶ αὖ τοῦ αὐτοῦ μήτε δαίμονας μήτε θεοὺς μήτε ἥρωας, οὐδεμία μηχανή ἐστιν.

Literally, I take it as:

how you would convince even the least intelligent of people, that it is not (characteristic) of the same person to believe in both spiritual and divine things, and also (characteristic) of the same person not to believe in either spirits, gods or heroes, there is no way

I know Greek negations don’t always work like you expect. But how do you explain this one? To me, it looks like it makes perfect sense if you just cut the bolded word out.

Here is Fowler’s translation from Perseus. Does it make the logic stand out better?

there is no way for you to persuade any man who has even a little sense that it is possible for the same person to believe in spiritual and divine existences and again for the same person not to believe in spirits or gods
https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0170%3Atext%3DApol.%3Asection%3D27e

Not quite. I want “there is no way for you to persuade any man who has even a little sense that it is not possible for the same person …” from reading the Greek.

The new Oxford text drops the puzzling οὐ. So feel free to ignore it. The mss. on which the editors primarily base their text, however, all retain οὐ. A later ms. drops οὐ, but this may just be a happy conjecture, rather than preserving an alternative reading from a different tradition.

I don’t have access to the new Loeb.

You got me consistebat! I thought I understood the negation, but when I read your reply, and thought about it, my confidence slipped away. ;-(

Oh thank you for looking it up, what a turn of events! Then I can rest confident that I’m among the best in being confused.

Could it be a case of Greek Sprachgefühl just being illogical here, sort of like how English “I could care less” is used to mean its opposite?

American English. We say ‘couldn’t care less’.