ignorance, conceit of knowledge
In Plato, ἄγνοια is not merely a lack of information but a definite state of the soul (ψυχή), turned not toward what is but toward what is not. In the fifth book of the Republic, Socrates arranges three "powers" of the soul according to their objects: knowledge (ἐπιστήμη) is set over being (τὸ ὄν), opinion (δόξα) over what lies between being and non-being (μεταξὺ τοῦ ὄντος καὶ μὴ ὄντος), and ἄγνοια over non-being (τὸ μὴ ὄν) (Resp. V 477a). ἄγνοια is therefore not an empty deficit but a perverted relation of the soul to reality: one supposes one sees what is not there, or fails to see what is.
Plato gives particular weight to "double ἄγνοια" — ignorance of one's own ignorance, when one δοκεῖ εἰδέναι ἃ μὴ οἶδεν, supposes one knows what one does not know (Soph. 229c). This very ἄγνοια is the root of sophistry and of every evil, since it blocks the very search for truth (ἀλήθεια) and substitutes for true speech (ἀληθὴς λόγος) a merely plausible opinion (δόξα). Within the circle of notions bound up with λόγος, it stands as the direct opposite of knowledge (ἐπιστήμη): the one who dwells in ἄγνοια is unable to "give an account" of what he believes (λόγον διδόναι) — and so all genuine philosophizing, according to Socrates, begins with the acknowledgement of one's own ignorance (Apol. 21d).