Trevor Salyzyn
Was John Locke correct in that there are no innate ideas or principles? (e.g., that not everyone is born knowing even something so obvious as A=A) Are humans blank slates at birth, learning everything from our collision with the empirical world?

Richard A. Nichols III
Obviously, nobody is born knowing A=A, that kind of logic and symbolic thinking is something learned. Why would a baby want to take the same thing, duplicate it by thinking about it twice at the same time, and then reunite the the two thoughts by inferring some symbol of equivalence between them? It would have no use for that.
I don't think humans are entirely blank slates at birth. If we were, children wouldn't so quickly and effortlessly develop such honed and unique personalities, I'd think that should take a lot longer if it would happen at all, so to me it suggests reincarnation. And if it doesn't suggest reincarnation, it may suggests some inherent aspects of the personality embedded in the DNA, but that seems unlikely because it's so unique, and it's unique in a way as simple as essence, rather than being a complex collection of traits whose uniqueness is guaranteed merely by their combinatorial power, and it usually doesn't reflect the personality of either the mother or the father very much.
And there are other, known aspects in which children's minds aren't blank slates. For example, we have a specific region of the brain responsible for the development of language, which is why we can develop it while other animals can't. Though you could argue that that doesn't make the child not a blank slate before the process of learning language begins and that aspect of the mind is "activated" or utilized.
Another example is that there's a section of the brain specifically geared toward seeing faces, which is the reason we have periedolioa of faces, and that would make the child particularly able/likely to recognize faces.
And there are a few things babies do instinctively, like suck on a tit, eat, breathe, yawn, smile, laugh, avoid falling from a high place, hold their breath under water, cry, sleep, etc., but I wouldn't necessarily say those mean it's not a blank slate in spirit because those are very specific behaviors.
Kant argued that time and space are a priori concepts, so I guess he would say that a baby necessarily has the paradigm of time and space embedded in its mind to enable it to more quickly learn to interact with the world, but I don't know if that's true. It's not hard to imagine that such an inherent framework in the mind would develop through evolution, though. It would be an obvious advantage, so it probably depends only on whether it's even possible for a basic understanding of space and time to be programmed into a human's DNA.
There are also numerous other specific regions of the brain that perform specific cognitive, emotional, perceptual, expressive and motor functions, but I'm not considering those relevant to the question of whether we're born a blank slate, because they somehow all work together in a way that seems completely neutral, natural, and singular, so that they're invisible to us and our intelligence seems to be some kind of general/universal, free, simple consciousness.
Our emotions also seem totally natural and obvious, but if they are, why does everybody possess the same set of very specific qualia we call emotions? I mean, yes, it's possible to have any kind of emotion, known or unknown, or some arbitrary combination of emotions, but there are also things like sadness, anger, fear, love, etc. that are practically universal, so I think we have to say that we're not really a blank slate when we're born regarding emotions. Though the answer to the first question the OP asked could still be yes, as emotions aren't ideas or principles. And neither are personalities.