"The gods are there. To side with the Greeks in recognizing and acknowledging this as an accepted fact is the first requirement for an understanding of their beliefs and culture. Our knowledge that they are there rests on a perception, be it internal or external, and be the respective gods perceived directly are only via the recognizable effects" (Wilamovitz-Moellendorff, quoted in Feyerabend, Philosophy of Nature, p. 71).
Quite so: if you tried telling a Greek in 600 BC that Dionysus does not exist, he would simply think you must have never gotten drunk or even been around people getting drunk. One could perceive the god entering into oneself, or the others drinking, and feel one's own (or their) enthusiasm (the entering in of a god). Similarly with Aphrodite: the Greek would ask how you could possibly avoid feeling her presence when you fall for some pretty young thing?
It is interesting to note in this regard that scripture certainly does not deny the existence of the multitude of gods. No, it instructs us not to worship them; i.e., the enthusiasm they bring about in us is to be rejected when it conflicts with our worship of the One God.