In this series on definitions, I have sought to show why Rand's theory is erroneous. Rand tacitly thought of meaning as being something different than the concept. So if an individual ascribed the wrong meaning to a specific concept, they were in effect using the wrong definition. However, if I define tomatos as a fruit with an orange rind, I am not actually guilty of using a wrong definition; I'm guilty of improper word usage. Fruit with an orange rind is itself a concept, as is any meaning whatsoever. That's essentially all that a concept is: a meaning. What word is connected to a specific meaning is a matter of convention. A specific meaning can neither be true or false. It merely is. Nor does it matter one jot whether a proposed meaning accords with anything in reality. The meaning/concept of unicorn is every bit as "valid" as the meaning/concept of horse. What is important is what we assert of a specific meaning within the confines of a proposition. The proposition Unicorns exist is false; the proposition Horses exist is true.
Following Aristotle, Rand bases her theory of definition on classical essentialism. But this doctrine has been decisively refuted by Wittgenstien.
Consider … the activities that we call "games". I mean board-games, card-games, ball-games, Olympic Games, and so on. What is common to them all?—Don't say: "There must be something common, or they would not be called 'games' "—but look and see whether there is anything common to all.—For if you look at them you will not see something that is common to all, but similarities, relationships, and a whole series of them at that. To repeat: don't think, but look !—Look for example at board-games, with their multifarious relationships. Now pass to card-games; here you find many correspondences with the first group, but many common features drop out, and others appear. When we pass next to ballgames, much that is common is retained, but much is lost.—Are they all 'amusing'? Compare chess with noughts and crosses [i.e. tic-tac-toe]. Or is there always winning and losing, or competition between players? Think of patience [i.e. solitaire]. In ball games there is winning and losing; but when a child throws his ball at the wall and catches it again, this feature has disappeared. Look at the parts played by skill and luck; and at the difference between skill in chess and skill in tennis. Think now of games like ring-a-ring-a-roses; here is the element of amusement, but how many other characteristic features have disappeared! And we can go through the many, many other groups of games in the same way; can see how similarities crop up and disappear.
And the result of this examination is: we see a complicated network of similarities overlapping and criss-crossing: sometimes overall similarities, sometimes similarities of detail.
Rand made no effort to respond to Wittgenstein beyond the following verbal perslifage:
As reporters, linguistic analysts were accurate: Wittgenstein's theory that a concept refers to a conglomoration of things vaguely tied together by a "family resemblance" is a perfect description of the state of a mind out of focus. [IOTE, 78]
As a refutation of Wittgenstein's theory, this simply will not do. Rand begs far too many questions. She assumes that unless every word we used can be perfectly summarized in a defining formula, the only alternative is that our minds are out of focus. But this only establishes that Rand did not understand Wittgenstein's theory. If Rand had been serious about refuting Wittgenstein's theory, she would have provided a defining formula for the concept game that was not open to any of Wittgenstein's objections. Since Rand was (apparently) incapable of providing such a refutation, she resorted to her usual ad hominem and ad consequentiam tactics.
If it be argued that the concept game is merely one of those "exceptions that prove the rule," and that, in fairness, one should concentrate on simpler, easier to define concepts, then let us glance at a simpler concept — say, the concept bachelor. Google defines bachelor as "A man who is not and has never been married." How well does this definition apply in reality? Hardly with immaculate precision. In some contexts, it begins to break down. Is the pope a bachelor? Is a young man who has been in an irreversible coma since childhood a bachelor? What about a Eunuch? Or an elderly senile gentleman who has never been married? What determines the usage of the word bachelor is far more subtle and nuanced than can be limned in a mere definition.
It would, therefore, appear that Wittgenstein is right: words generally cannot be squeezed into simple, defining formulas. There are no essences defining what a concept is. Language is more complicated than that. The complexity of language is required for the mind to adequately grasp and communicate the complexities and nuances of the real world.