What does “Kata ton daimona eaytoy” mean and why does it have more than one meaning?

Thank you to Achilleas Vortselas for doing most of the work. The proximate source is possibly the album of Rotting Christ, as he explains.

But as the Wikipedia page about the album, Κατά τον δαίμονα εαυτού, says, the phrase occurs on Jim Morrison’s tombstone: Jim Morrison . (The OP knew this too, if I can judge from the topics included in the question.)

So while Rotting Christ might have been thinking of Thelema, the first appearance of the phrase likely doesn’t—and I wouldn’t be surprised if someone did think of Jimbo’s “inner d(a)emons” when using it for him.

But it’s always safe to check the ancients for any Ancient Greek that turns up in modern times; and I see that something quite close to the phrase occurs in Dio Chrysostom , Orations 23.7: ΛακουσΚούρτιος • Δίων Χρυσόστομος / LacusCurtius • Dio Chrysostom . Close enough in fact, that this has to be the source.

Οὐκοῦν καὶ δαίμονα, εἴπερ τινὰ ἀγαθὸν ἡγῇ, δῆλον ὡς δίκαιον ἡγῇ καὶ χρήσιμον καὶ φρόνιμον; — Πῶς γὰρ οὔ; —Δ. Ἦ γὰρ ὃν κακόν τινα νομίζεις, πονηρὸν οἴει τὸν αὐτὸν εἶναι καὶ ἄδικον καὶ ἀνόητον; — Ἀνάγκη πάντως. —Δ. Τί δαί; οὐ τῶν ἀνθρώπων ἕκαστον κατὰ τὸν αὑτοῦ δαίμονα βιοῦν, ὁποῖος ἂν ᾖ ποτε, ἀλλὰ καθ’ ἕτερον; — Οὐδαμῶς καθ’ ἕτερον. —Δ. Οὐκοῦν τὸν τυχόντα ἀγαθοῦ δαίμονος ἡγῇ δικαίως ζῆν καὶ φρονίμως καὶ σωφρόνως; τοιοῦτον γὰρ ὁμολογεῖς εἶναι τὸν δαίμονα αὐτοῦ. — Πάνυ γε. —Δ. Τὸν δὲ μοχθηροῦ δαίμονος πονηρῶς καὶ ἀφρόνως καὶ ἀνοήτως καὶ ἀκολάστως; —Φαίνεται ταῦτα συμβαίνειν ἐκ τῶν εἰρημένων νῦν. —Δ. Ἆρα ὅστις ἄνθρωπος νοῦν ἔχων ἐστὶ καὶ δίκαιος καὶ σώφρων, οὗτος εὐδαίμων ἐστὶν ἀγαθῷ δαίμονι συνών· ὅστις δὲ ἀσελγὴς καὶ ἄφρων καὶ πανοῦργος, ἀνάγκη κακοδαίμονα φάσκειν ἐκεῖνον κακῷ δαίμονι συνεζευγμένον καὶ λατρεύοντα; — Ἀληθές. —

Dio. Then in the case of a guardian spirit also, if you really consider any to be good, is it not clear that you consider it just and useful and sensible?

Int. Why, of course.

Dio. Pray, when you think that any person is bad, do you believe that he is at the same time evil and unjust and senseless?

Int. Most assuredly so.

Dio. Well, then, do you not think that each man lives under the direction of his own guiding spirit, of whatever character it may be, and is not directed by a different one?

Int. Certainly not directed by that of a different one.

Dio. Then do you believe that the man to whom Fortune has given a good guardian spirit lives justly and prudently and temperately? For this is the character that you agree his spirit has.

Int. Certainly.

Dio. And that the man to whom Fortune has given the bad guardian spirit lives wickedly and senselessly and foolishly and intemperately?

Int. That appears to follow from what we have just said.

Dio. Then when a man is in possession of intelligence and is just and temper, is this man fortunate because he is attended by a good spirit; but when a man is dissolute and foolish and wicked, must we maintain that he is unfortunate because he is yoked to a bad spirit and serves it?

Int. True.

κατὰ τὸν αὑτοῦ δαίμονα is just a variant of κατὰ τὸν δαίμονα ἑαυτοῦ. (Modern Greek speakers, note the daseia on αὑτοῦ: this is not modern αυτός.)

So Achilleas’ intuition was correct: daemon does indeed refer not to your own inner will, but to an external guiding spirit—whether it’s a guardian angel or a guardian devil. And while I don’t know much about Thelema, I assume that Tolis’ Crowley-inspired interpretation of Jimbo’s tombstone is inaccurate.

Thanks, Achilleas, that was fun!