Doxa is usually translated as opinion, but this only goes half-way to capturing the meaning of the word for the Greeks. As such it does not allow us to understand why Theatetus, after the refutation of his first answer, now appeals to doxa, in the same way he had first appealed to aisthesis, as that which immediately and unreflectively appears to constitute the essence of knowledge.
Heidegger points out that doxa has a double meaning, which reflects the previously seen dual determinations of knowledge as the “self-showing of the beings themselves” and the soul’s relationship to being. Doxa is both the look, the idea that something offers, and the image or picture that one makes of what shows itself. A thing’s doxa is what it appears as, what it shows itself as; towards which we take-up a stance, we are of the view, we have an opinion, this is our doxa. Both aspects are present in one word.
To illustrate how we experience doxa, Heidegger, in Introduction to Metaphysics (YUP, 2000), calls on the idea of a city and the variety of views it offers us; which we take up and use in the construction of our views, our opinions of it:
A city offers a grand vista. The view that a being has in itself, and so can offer from itself, lets itself then be apprehended at this or that time, from this or that viewpoint. The vista that offers itself alters with each new viewpoint. Thus this view is also one that we take and make for ourselves. In experiencing and busying ourselves with beings, we constantly construct views for ourselves from their look…We construct an opinion for ourselves about it. (109)
This construction of an opinion by ourselves often happens without our looking closely at that which shows itself. “Thus it can happen that the view we adopt has no support in the thing itself.” (ibid) Therefore “with doxa we are immediately in a region that is indifferent in respect of truth and falsity.” (ET, 184) This means the duality of doxa, as appearance and opinion, is further doubled. Socrates says “doxa has two faces” by this he means that doxa as appearance can present what the being itself is, but can also make it out to be what it is not, likewise doxa as our view, our opinion of what is seen can be correct or incorrect. Thus both aspects of doxa, look and view, have the capacity to be be pseudos, false, distorted.
This opens up the realm of untruth for the first time, the stated aim of Heidegger’s engagement with the Theatetus dialogue, and which only now, half way through the lecture course, makes an appearance.