Much of the time, we talk as though there is only knowledge and its absence with no in- between. But none of us has much experience with either pure ignorance (which would imply an absence of experience too at any rate) or pure knowledge. We spend most (if not all) of time in the hazy mental space between ignorance and knowledge, a space Plato calls doxa, which is usually translated as “opinion.” Doxa is an intermediate between ignorance and knowledge. From the side of greater knowledge it looks like ignorance and from the side of lesser ignorance it looks like knowledge. But to understand Plato’s notion of doxa, it is important to understand that it participates in both sides of the ignorance/knowledge distinction. To hold an opinion is to intend the truth, but to remain still in ignorance. Even “true belief” conceals ignorance; even false belief harbors truth.
Knowledge is only approached by way of doxa. At its most developed, doxa is dynamic, a movement (kinesis) from ignorance toward knowledge. At its least developed, doxa is static, “the residue that remains when thinking has stopped” (Joe Sachs). Plato calls the more developed, dynamic form dianoia, which I translate as “thinking.” He calls the less developed, static form pistis, which I translate as “belief.” Belief is opinion that holds itself against the questions that would undermine it. Thinking by contrast is opinion that focuses on its own defects as an avenue toward greater knowledge.
The type of opinion that is aware of itself as still participating in ignorance is thinking (dianoia). Thinking is thus necessarily bound up with self-knowledge. Every opinion should invite questions (or at least mild qualms) about itself. But these qualms are not focal components of the opinion itself, but are subsidiary components of the holder of the opinion. To bring a qualm out of the murky depths of preconscious irritation into the full radiance of a well-formed question requires an attentive self-consciousness.
Belief represses this awareness of ignorance, abstracts from it, reacts against it as threatening. Belief is an escape from the anxiety of ignorance; it is satisfying in contrast with the dissatisfactions of doubt. This is both a strength and a weakness. It’s strength is that it allows practical perseverance, since doubt and anxiety are in themselves paralyzing to action. Its weakness is that it tends to be allergic to any opinion or question that threatens to reintroduce the doubt from which it has escaped. Belief is deaf to the qualms and doubts that would unsettle it, that would goad it to self-transcend.
All of this makes it sound like we must dispense with belief and pursue dianoia. But we cannot live without belief. All perseverant action requires the steadiness of belief to push through the discouraging headwinds of doubt that oppose it. (In Plato, pistis is related analogically to the virtue of courage.) Even thinking (dianoia) contains a germ of belief at its core, since thinking intends knowledge that it does not yet know. Dianoia has at its heart an active abiding belief in knowledge. Without this pistis, this faith, dianoia devolves into a mere skepticism, self-contradictory and impotent in itself. In the Republic, Thrasymachus is the examplar of dianoia without pistis, whereas Glaucon is one who healthily combines the two, simultaneously critical of his own opinions but trusting of the guidance of Socrates.
Opinion is thus the intermediate between ignorance and knowledge, but dianoia is the intermediate between belief and knowledge and pistis is intermediate between ignorance and dianoia. (See the Divided Line at the end of Book VI of the Republic.)