Rand derived her doctrine of definitions from Aristotle. It is not however clear what she means by "logical order," or how definitions go about preserving it. What Rand seems to have in mind (although she's none too clear about it) is the ideal of knowledge as a complete "logical" structure (logical in this sense meaning: integrated without contradiction). In this, Rand is mirroring Aristotle's ideal of knowledge as (in the words of Karl Popper) "an encyclopaedia containing the intuitive definitions of all essences, that is to say, their names together with their defining formulae."
For better or worse, there exists no compelling evidence that knowledge works this way; nor does Rand (or her disciples) provide any evidence, or seem in the least interested in the empirical side of this issue. Yet there is a great deal of evidence that formal definitions are of little importance to understanding the meaning of words. Most words are learned unconsciously, without the aid of formal definitions or dictionaries. Moreover, it can easily be observed that many people understand the meaning of words without being able to provide formal definitions for them. Just ask anyone (besides a linguist or a grammarian) to define the word the and you'll see what I mean.
Now it could be argued that Rand's theory of definitions is not confined to mere formal definitions, but applies to "tacit" or "implicit" definitions as well (whatever those might be), and that when she declares that definitions preserve the logical order of conceptual hierarchies, she is not distinguishing whether those definitions are consciously formalized or are merely implicit and tacit. Yet if this is so, Rand needs to explain (1) how she knows this to be true; and (2) provide compelling evidence for her view.
“Words without definitions are not language but inarticulate sounds.” If by definitions, Rand means consciously formalized definitions (after Aristotle methods of essentialist definitions), this is a grossly implausible position, for the reasons provided above. If Rand means merely "tacit" or "implicit" definitions, in the absence of any evidence (none of which is provided by Rand), it is not clear that this is true (or if it is true, whether it has any significance). What would make a lot more sense would be Words without meanings are not language but inarticulate sounds. This suggests that Rand has confused the concept meanings with that of definitions. Definitions are explanations of what a word means; but this does not mean that a definition is identical with the meaning. The meaning of a term can be understood without defining it, because knowledge is largely tacit and intuitive, rather than formalized and logical, as Rand seems to assume.
“The process of forming, integrating and using concepts is not an automatic, but a volitional process.” Given how important this assertion is to some of Rand's claims about history and morality, Rand's unwillingness to provide any evidence for it is most unfortunate. I suspect it never occured to her that she needed to provide evidence, because empirical responsibility was not part of her basic MO. In any case, had she tried to find evidence for it, she almost certaintly would have realized that the statement is not true. Many concepts, perhaps even most concepts, are formed unconsciusly, without anything remotely describable as volition having anything at all to do with the process. Indeed, this is an obvious fact that can be gleaned merely by observing young children learning to speak. How Rand could have ignored and/or evaded these obvious facts is difficult to comprehend.
An animal cannot perform a process of abstraction. Really? How on earth did Rand know this? For it's not clear at all that this is true. Consider the testimony of two neuroscientists, Jorge Martins de Oliveira and Julio Rocha do Amaral:
Although there is no general agreement, we believe that other species are also capable to develop abstractions. Some primates and cetaceans, without any doubt, have abstract conceptions, but these must be very tenuous and, certainly, they never develop, as humans do, to a point of giving rise to high creativity. And, even if it so happened, it would be an innocuous creativity, since they lack the physical attributes to allow them to build up something that could be considered significant and concrete. In spite of these handicaps, the exercise of conscious and abstract thoughts, among dolphins and superior simians, has been widely evidenced.