From Objectivism, the Philosophy of Ayn Rand, by Leonard Peikoff, p.164:
"An arbitrary idea must be given the exact treatment its nature demands. One must treat it as though nothing had been said. The reason is that, cognitively speaking, nothing has been said."
To see the nature of an arbitrary idea, think of the difference between "LA, CA," and "La, la, la." The first is an abbreviation for "Los Angeles, California." The second is a group of nonsense syllables. The abbreviation, in context, signifies the name of a place. The nonsense syllables signify nothing, but are used to vocalize a tone or a tune that might have significance in some context.
Nonsense syllables are interchangeable. One could use "la-la," or "ah-ah," or "la-ca." The meaning is always the same, because there is no meaning. They are arbitrary syllables, used only to make a sound. In fact, one could use words: mama, papa, gaga, and so on. What to notice is that using words as nonsense syllables does not give meaning to the nonsense syllables. They are still just sounds. Words are sounds used cognitively, to convey facts of reality.
How do people know if you are using "gaga" as nonsense syllables, or as a word referring to a state of mind? You make it plain by the context. You do not announce, "I was gaga," without any context. You say when you were gaga, and why you were gaga. You connect the word to reality by showing where it fits. You show that it is not arbitrary by relating it to objective reality.
The point to get is that arbitrary is the default value. Words uttered with no hint of a connection to reality are nonsense syllables, even if a pretence is made otherwise.
The entire difference between words and vocal sounds is that words refer to facts of reality—not automatically, but as shown by the context. If a word, or a statement, or an elaborate declaration, is uttered without indication of a place in reality, it is arbitrary noise, just as surely as are the words of a nonsense song.
The last of those statements is from an old nonsense song. It has the same cognitive status as the others: it is meaningless. It does not pretend to have a connection to reality, but the others do. However, the pretence is thin. "Everybody knows" does not connect rich men to reality as crooks; it just adds another arbitrary statement to the original. It is easy to see how meaningless the statement is by substitution: "All poor men are crooks; all fat men are crooks; all thin men are crooks." In the second statement, anything at all could be substituted for "ESP" without altering the meaning, since there is none. That is, there is no indication of how to connect the statement to objective reality.
Good people go wrong when they assume that any grammatical statement must be taken as rational, and either disproved or accepted. Imagine that I said arbitrarily, "You deserve to die." Would you say, "No I don't, because"? Or would you take measures to defend yourself against a high-handed threat? That is the true nature of the arbitrary: not cognitive, but simply high-handed.
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