Conversion is one of many concepts of a philosophical origin that are used in both the psychology of religion and other social sciences as well as canonical texts. Although Plato is commonly believed to have been its creator, scholars do not agree on the term he used to refer to it. The prototype of the Christian religious conversion is taken to be the Greek verb epistrephō (“convert,” “turn,” “return,” or “go back”), whose prototype is the Old Testament Hebrew verb šȗbh (“to become converted”). The term epistrephō ascribed to Plato does not occur in those fragments of his myth of the cave in Book VII of the Republic in which he mentions conversion, first as a metaphor (the emblematic image of turning one’s head in the opposite direction) and then literally (conversion as a specific art). In both instances, Plato uses the term periagō (“turn around”) and periagōgē (“[the act of] turning around”). The latter word is used in the title of this article, which references Plato’s myth of the cave. Plato’s philosophical metaphor for conversion was then taken up by Christians, who imbued it with a religious sense. Why did they also take up the word epistrephō, which has no relation to conversion as understood by Plato? To answer this question, one must first know why the authors of the Septuagint translated the Hebrew term šȗbh as the Greek term epistrephō and not as periagō. Thus, ascribing to Plato the authorship of the term epistrephō as related to his understanding of conversion clashes with historical evidence. Instead, the author’s intentions are reflected in periagō and periagōgē.