the 'argument from equals' in the Phaedo — Wayfarer
I've been mulling over your post and I don't have a simple response to it. I might spend some time actually looking at the Phaedo and then start a thread on it. In the meantime, I have some remarks.
1. I think it may not be possible to resolve our differences, because I am not sure they can be expressed cleanly, that there's some proposition or set of propositions you hold true and I false, for instance. Maybe, but I have my doubts.
2. There is a broad sense in which you seem to believe there is a world of concrete particularity, accessible to the senses, and a world of abstract generality, accessible to reason. It looks like there's little room for disagreement; I can't taste or see or touch the relation of equality, only things that are or are not equal.
3. That's not so far from Hume's observation about causality, but he didn't conclude that we can learn through rational insight what we cannot learn by looking; he concluded that the belief in causality is in some sense a fiction, a useful simplification.
4.
If Plato's argument is right -- not clear to me yet -- if the concept of equality is unlearnable, then we might also conclude that we have no such concept, rather than concluding it must be innate.
5. "But of course we have the concept of equality!" --- We are adept at doing the things that having a concept of equality was supposed to explain, certainly. But if we cannot have such a concept, then the explanation must change.
6. It seems to us we see the entire environment before us, like a high-definition movie on a screen, our visual field. This is false. There is no such rendering of our environment present anywhere in our brains, and could not be. The truth is that we move our eyes frequently, much more than we are aware of, and we see a section of about a degree or two of our visual field clearly each time; the complete visual field is patched together without our awareness, giving the impression of a seamless whole.
That's an example of how an explanation can change to make something impossible possible.
7. The assumption that we must have the abstract concept of equality to judge whether two sticks are the same length suggests a computational model of the mind, with abstract rules being applied to concrete cases as they come up. I have my doubts.
8. Presumably the argument against materialism will continue before birth: if it's not a concept that could have been learned, it will also turn out to be a concept evolution could not have provided us with.
9. As you see it, Plato provides a dispositive argument that equality cannot be learned, but we have the concept, therefore ... If that argument is watertight, there's no need to consider empirical evidence, which could only mislead us.
10. On the contrary, I'm inclined to look at the research. Mathematical concepts have always been a central focus of developmental psychologists from Piaget on down to today. Parents and teachers spend time teaching children how to count, how to recognize shapes, similarity and difference, and so on, or at least providing them the appropriate setting for learning those concepts.
11. At what age do children actually acquire the concept of equality? What does the proto-concept look like, and how do they use it? Are there differences between cultures?
12. Mostly I think making claims about what can be learned and what cannot without looking at the development of children is worse than a waste of time.
As I said, I may post something about Plato, just because it might be interesting, though, not because it would lead to anything.