It's not analytic (true by definition) that cats are animals. But it is metaphysically necessary: there is no possible world containing a cat that is not an animal.
I disagree with this. First, to make sure I know what you mean, you're basically saying that "that cat-like thing I see" is not, by definition, a cat. If we took a full description of a cat's biology to be the definition then it would be an animal by definition. Did I get all that right?
I don't think it's possible to prove a statement to be synthetic (the opposite of analytic - do LessWrongians know these words?) unless you prove that there is no possible way to show something by definition. In this case, it seems that we have just failed to show that the statement was analytic rather than proving it to be synthetic.
I'm not sure I follow your objection. In natural language, the meaning of 'cat' is fixed by ostention, not descriptive stipulation. We (most of us, at least) mean something like "that cat-like thing I see". If it turns out that the cat-like creatures of our worlds are cleverly disguised robots, rather than animals, we would conclude that cats are robots, not that our world contains no cats. Hence the meaning of our word 'cat' does not include their animality.
You could, of course, introduce a new term 'shcat' which you stipulate means "ca...
Philosophy is notorious for not answering the questions it tackles. Plato posed most of the central questions more than two millennia ago, and philosophers still haven't come to much consensus about them. Or at least, whenever philosophical questions begin to admit of answers, we start calling them scientific questions. (Astronomy, physics, chemistry, biology, and psychology all began as branches of philosophy.)
A common attitude on Less Wrong is "Too slow! Solve the problem and move on." The free will sequence argues that the free will problem has been solved.
I, for one, am bold enough to claim that some philosophical problems have been solved. Here they are: