Deisidaimoneō, “…rare in a good sense…”
δεισιδαιμονέω (deisidaimoneō), have superstitious fears, Plb. 9.19.1, D.S. 12.59, Polystr. 9, etc.: rare in good sense, to be religious, Zaleuc. ap. Stob. 4.2.19. Link to LSJ entry
At Acts 17.16, we read that when Paul first came to Athens, he was upset to see that the city was κατείδωλος (kateidōlos), “full of idols”.
If Paul came into Athens from the north—and I’m just guessing and making stuff up here—he would have had to take one of two roads to get around Mt. Parnes, which is directly north of the city. He could have come around the eastern slopes of Parnes, through Decelaia and the gap between Parnes and Mt. Pentelikon (source of Pentelic Marble). But on the assumption that Paul, Silas, and their escorting friends, came through Thebes, the quicker way to Athens would have been through the gap between Mt. Citharon (on the west) and Parnes (on the east). This road led from Thebes to Plataea, and thence to Attica, through Eleutherae and the deme of Oenoe. The Wikipedia article on Oenoe is really good at explaining why Paul might have come this way.
This road was part of the Sacred Way, the road between Athens and Delphi. As it entered the city, it was lined with shrines, altars, and statues in honor of various gods and heroes, from the biggies like Zeus, Athena, and Heracles, to imports like Thracian Bendis. I’m guessing that this display of syncretic polytheism was what incensed Paul.
But he began his speech to the Athenians (Acts 17.22) by being a little sly and witty: Ἄνδρες Ἀθηναῖοι, κατὰ πάντα ὡς δεισιδαιμονεστέρους ὑμᾶς θεωρῶ (“Athenian men, I see you all to be, in all respects, rather deeply god-fearing). The operative word is an adjective, a form of δεισιδαίμων (deisidaimōn). It is a compound built from δείδω (deidō), “I fear”, and δαίμων (daimōn), “god, divine power”. So, “god-fearing”. It is in the comparative form, so, “more god fearing” or “rather god-fearing”.
The pre-Christian (“pagan”, whatever you want to call them) Greeks loved to worship their daimones. Socrates had a close personal relationship with his own little daimōn. So for most Athenians, being told that you are “rather daimōn-fearing” was probably not an insult. But I seriously doubt that Paul considered the God of Abraham, YHWH, to be just another daimōn (the Greek word does give us English “demon”, after all). So maybe he was being sly and a little jokey, digging at their pagan beliefs without actively offending his audience. Well, it worked. Sort of.
Paul won over two converts, Dionysius the Areopagite (Διονύσιος ὁ Ἀρεοπαγίτης) and a woman named Damaris (γυνὴ ὀνόματι Δάμαρις) (Luke 17.34).
A few of observations… It is funny that a man named after the drunken-sexy god Dionysus was the first of Paul’s Athenian converts; he was an official of the court of the Areopagus, too (“Areopagite” is a title). There is a mosaic depicting him in the Hosios Loukas Monastery, in Boeotia; that the monastery is dedicated to “St. Luke” is appropriate, if Luke was indeed the author of Acts.
And, it is nice that Acts actually gives the woman Damaris a name; Acts of the Apostles is good about inclusion in that way. We know literally nothing about her otherwise, although Raphael paints her, so might as well imagine her looking like that.
Her name might come from the Greek word δάμᾰρ (damar), “wife”. Maybe she was simply the wife of Dionysius? Evidently an early translation of Acts into Georgian says so explicitly.