First consider that at any given moment a person is not consciously aware of most of the things they know; the knowledge is stored in long-term memory until it is needed. You may know that a green light at an intersection means "go," but were you consciously aware of it until just now?
Consider second that we often may say a book contains knowledge, though it is not a mind.
The language in the article is a little ambiguous. Earlier in the same article they say, "When we inquire into the truth of a theorem, we both do and do not already know it." So they're already talking about a kind of "partial" knowledge.
We can interpret it as saying that there are two kinds of knowledge according to Plato, and two kinds of beliefs:
- knowledge possessed by the soul, beliefs possessed by the soul, which we have prior to any experience, and the conscious mind may be unaware of
- knowledge possessed by the living mind, beliefs possessed by the living mind
If you say, "an experience causes us to remember the innate knowledge P," in this context it would mean that the experience causes the living mind to believe P, whereas the soul already believed and knew it. The experience triggers a transfer of information from the soul to the living mind.
From a more materialist perspective, they describe Chomsky and Carruthers' views about the innate nature of language or of folk psychology. In this case the soul would be replaced by the genome, and again we'd have two kinds of knowledge and two kinds of beliefs:
- knowledge and beliefs directly encoded in the genome, which we have prior to any experience, and the conscious mind may be unaware of because the genes have not yet had full effect
- knowledge and beliefs possessed by the mind
If you say, "an experience causes us to remember the innate knowledge P," in this context it would mean that initially there are latent structures that are ready to make your mind believe P. The structures might be unconscious patterns of neural connections in your brain, that developed independently of experience, as a result of blueprints encoded in your genes. It would be similar to how your hand or other organs developed from genetic blueprints, largely independent of experience. The experience then activates these latent structures so that you can consciously believe and act on P.
You might argue that to say your genes or unconscious soul have "knowledge" or "beliefs" can only be metaphorical. That just depends on your definition (and much of language is metaphorical). You could interpret "knowledge" and "beliefs" in a more flexible way that allows you to say your genes or unconscious soul literally have them, or that a book can literally contain knowledge. Or you could rigidly say that knowledge and beliefs can only be had by a conscious mind or that conscious mind's long-term memory, and say it is a metaphor.