Introduced as “the most clever of all of the beasts of the field that YHWH God had made,” the serpent in the Garden of Eden is portrayed as just that: a serpent. Satan does not make an appearance in Genesis 2–3, for the simple reason that when the story was written, the concept of the devil had not yet been invented. Explaining the serpent in the Garden of Eden as Satan would have been as foreign a concept to the ancient authors of the text as referring to Ezekiel’s vision as a UFO (but Google “Ezekiel’s vision” now, and you’ll see that plenty of people today have made that connection!). In fact, while the word satan appears elsewhere in the Hebrew Bible/Old Testament, it is never a proper name; since there is no devil in ancient Israel’s worldview, there can’t yet have been a proper name for such a creature.A good overview of the development of the figure of Satan.
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Past posts on Satan/the Devil are collected here plus here.