Rand’s argument against Positivism is false.
Rand’s philosophy rejects falsification, saying on pg. 159 that falsification is to: “evade the facts of experience and arbitrarily to invent a set of impossible circumstances that contradict these facts.”
According to http://plato.stanford.edu/entries/popper/ , The Positivist process of falsification evaluates theories by how well they predict what we then observe. If what we observe contradicts the prediction then the theory is falsified.
A) Since what we observe is a fact of experience, facts of experience are not being evaded. Rand’s argument is false.
B) Since the observed facts will be used to confirm or contradict the proposition, facts are not being contradicted by the proposition. Cart before the horse. Rand’s argument is false.
Ayn Rand, An Introduction to Objective Epistemology, Signet Edition, New American Library. Also Ch. 2, the Analytic/Synthetic Dichotomy by Leonard Piekoff.
http://plato.stanford.edu/entries/popper/ is the source for my paraphrasing of the practice of falsification.