What insight can babies in scientific experiments provide philosophy? If we
I don't have a clear fix on the question, but insofar as I do, I don't see how philosophy alone could answer it. You seem to be saying that there's a real-world, repeatable phenomenon: babies in certain situations behave this way rather than that. That may be true—is true, far as I know. But if it's true, there's nothing a priori about it; the opposite behavior is perfectly conceivable and might have been true for all we could have said in advance. I don't see how philosophical analysis could tell us why things turned out one way rather than another. At least as I and many of my colleagues understand philosophy, it doesn't have any special access to contingent facts. A philosopher might come up with a hypothesis, but insofar as the hypothesis is about an empirical matter, it will call for the usual sort of empirical investigation that empirical claims call for.
As for blank slates, philosophy can't tell us by itself whether we're born with blank slates as minds, but as a matter of fact, there seems to be reason to think we aren't. The mind seems to come pre-wired in certain ways. Understanding what that amounts to calls for doing some science, whether it be cognitive science or neuroscience or whatever. Philosophers may have contributions to make to clarifying relevant notions and questions, sorting out methodological issues and the like, but what they can't do is sit in their studies and settle the answers by themselves.