Rand’s philosophy misrepresents Positivism.
The Positivist process of falsification tries to identify and observe any possible evidence which contradicts the predictions of a theory, especially “predictions which are ‘risky’ (in the sense of being intuitively implausible or of being startlingly novel) and experimentally testable”. http://plato.stanford.edu/entries/popper/
Rand’s philosophy rejects falsification, pg. 159, claiming it requires us to: “evade the facts of experience and arbitrarily to invent a set of impossible circumstances that contradict these facts.”
“Risky, implausible and novel” are not the same as impossible. Their predictions must be testable, therefore not impossible. Her argument is false and misrepresents Positivism.
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 the quotes and my paraphrasing of the practice of falsification.