knowable a priori -
plenty of them.
But they are all analytic statements or tautologies;
the denial of any of them would result self-contradiction.
In other words, none of them is synthetic. A is A,
cats are cats,
you can't be both here and not here at the same time, cats are mammals (since being a mammal is one of the defining characteristics of being a cat), and so on. I don't deny that all these statements are necessary, and it would be foolish indeed to feel that you had to verify them by observing the world. The reason that we don't have to test them by observation of the world is simply that they are empty of any factual content: they are all analytic. This is quite obvious in the examples just given but it holds also of not-so-obvious cases like "Everything that has shape has size." This statement, of course, is necessarily true, and we don't have to go around testing things of various shapes to see whether they all have size, But the reason for this is that the statement is really analytic: just analyze the concepts of shape and size. Whether something is two-dimensional like a square or three-dimensional like a cube, its shape is only the total configuration of the boundary of its spatial extension, and its size is only the amount of this spatial extension. You can't have an amount of something (at least if it's of finite size) without its coming to an end somewhere, and wherever it comes to an end is its boundary. The two concepts are logically interconnected. A mathematical point, of course, has no shape, but then, it point has no size either - although the little dot we write on paper to represent a point has both shape and size. So I agree that the statement is necessarily true, but only because it's analytic.