On some argumentatively central occasions, Plato refers to an intellectual “aha!” experience of seeing some point (say, something philosophical or mathematical). This is supposed to be evidence for the theory of recollection, because the experience is similar to remembering a nearly forgotten thing.
After insightful comments from students in my philosophy of mathematics seminar today, I think “aha!” experiencess come in two varieties. We might express paradigm instances of the two varieties like this:
Aha! I’ve always thought this, but never quite put it into words!
Aha! Now that I think about this, I see it’s got to be true!
An example of the first variety might be someone who hears about the Golden Rule, and realizes that whenever they were at their best, they were acting in accordance with it. I had a case of the second variety when I was introduced to the distributive law in arithmetic in grade three: I had never thought about whether a ⋅ (b+c) = a ⋅ b + a ⋅ c, but as soon as the question came up, with some sort of an illustrating mental picture, it was clear that it was true.
The two experiences are phenomenologically quite distinct. Type (i) experiences fit better with the Platonic picture of innate knowledge, since type (ii) experiences feel like a new acquisition rather than the recovery of something one already had. Another difference between type (i) and type (ii) experiences is that in type (ii) experiences, we not only take ourselves to have evidence for the thing being true, but the thing becomes quite unmysterious: we see how it has to be true. But type (i) experiences need not have this explanatory feature. When I have the vision of the truth of the distributive law of arithmetic, I see why it’s got to be true though I may not be able to put it into words. Not so with the Golden Rule. I can continue to be mystified by the incumbent obligations, but cannot deny them.
Literal remembering of a forgotten thing seems less like (ii) than like (i). When I remember a forgotten phone number by some prompt, I don’t have an experience of seeing why it’s got to be that.
Plato’s theory of recollection does not account for the phenomenology of type (ii) experiences. And perhaps Plato would admit that. In the Republic, he talks of “the eye of the soul”. The context there is the abilities of this life, rather than recollection. Perhaps type (ii) experiences fit more with the activity of the eye of the soul than with recollection.
At the same time, while (i) is a bit more like remembering, it’s not exactly like it, either. Remembering need not have any “I’ve thought this all along” aspect to it, which type (i) experiences tend to have. So I think neither of our “Aha!” experiences is quite like the theory of recollection leads us to. Is there a third “Aha!” experience that does? I doubt it, but maybe.
