By that logic, Rand is wrong, based on the evidence.
What evidence?
Hank
Evidence in nature, supporting the theory of evolution, for example.
Let's take one of Rand's biggies -- we can't sacrifice others to our own ends. By what logic can you prove that it's immoral to sacrifice others to my own ends? Evolutionary theory suggests that it can be just fine -- and we, as putative products of evolution, are subject to the same objective, "discoverable" rules as any other animal.
For example, if I'm a Pharaoh, who's to say that it's wrong to sacrice others to my own selfish ends? After all, it happens at all levels of nature, and has demonstrably good results for certain individuals who are, after all, "ends in themselves."
For objectivism to be valid, you have to prove that the Pharaoh is wrong, based on objective evidence. Knock yourself out.
At best, objectivist practice is merely one choice among many. Indeed, the arguments for it are often based on an alleged optimization of results. (Though the claims to optimality are themselves open to question.) But in that case, objectivism reduces to a merely relativist philosophy.