“To live, man must hold three things as the supreme and ruling values of his life: Reason—Purpose—Self-esteem.” It is not surprising that neither Rand nor any of her followers ever tried to provide evidence for this statement. Taken literally, the statement is palpably false. For it suggests anyone who does in fact "live" must hold reason, purpose, and self-esteem as his ruling values. Do Objectivists really believe that? Probably not. Here we have an example of Objectivists refusing to face up to the empirical implications of one of Rand's assertions.
“There has never been a philosophy, a theory or a doctrine that attacked (or 'limited') reason, which did not also preach submission to the power of some authority.” Given that Rand was not exactly very well read and had huge gaps in her knowledge, how could she know whether this assertion is true? As a matter of fact, it is not true. Even worse, Rand was probably should have known it not to be true, since she read two writers who attacked (or ridiculed the pretensions of) "reason" and authority: namely, Friedrich Nietzsche and H. L. Mencken. And if there be any doubts on the score of these two radical individualists, one need only add Vilfredo Pareto to the list, who remained, even in his late anti-ideological phase, a radical libertarian at heart who explicitly attacked "reason" in his sociological treatise, The Mind and Society.
None of the traditional theories of concepts regards concepts as objective. Rand never made any serious attempt to demonstrate this assertion. In fact, it's not even clear that she understood any of the "traditional" theories of concepts, or that she deeply read and studied any of the philosophers espousing them. Her interpretations of Hume and Kant are so distorted and eccentric (see Seddon and Walsh for more info) that, in the absence of clear, exhaustive, documented evidence, she is not to be trusted on such issues.