Arbitrary assertion:- any claim made without any evidence whatsoever.
This is a start. It names two necessary elements of “arbitrary assertion.” The first is that there must be a claim, that is, a statement of alleged (claimed) fact. Second, the claimant presents no evidence.
The criteria list shouldn’t stop there, however. The reason is that every writer or speaker makes claims not backed by evidence at that time and place. The justification is clear: No writer, in a particular circumstance (such as a lecture or essay) can prove every statement he makes, as part of his presentation. If he tried to, his 10 page essay would swell to 100 pages; and then if he tried to prove all the elements of each proof statement, the essay would swell to 1000 pages, and so forth.
A speaker or writer, in his lecture or essay, is obligated to initially provide evidence only for the essentials of his claim. For example, in For the New Intellectual (hb p. 6, pb p. 12, or ARL, p. 225), Ayn Rand discusses professional intellectuals. In contrasting modern intellectuals to earlier ones, she says, “There were no professional intellectuals in the Middle Ages, there were only monks in monasteries.” She provides no evidence for this assertion. That does not mean her claim is arbitrary. It is not an essential of her essay. Trying to justify every justifying claim would lead to an unlimited progression of text – an impossibility.
Later, listeners or readers may question the speaker or writer about some of his secondary statements, asking for evidence for those too. Then the speaker or writer, if circumstances permit, can respond with the evidence he has for those secondary, supporting statements.
This is where the third element of the idea of “arbitrary” (assertion) comes in: An arbitrary claim is one for which the claimant refuses or fails to provide evidence when queried.
The example that Dr. Peikoff gives, if I recall correctly, is the claims made by the “channeler,” Shirley McClaine. She claimed that what she said under certain circumstances was actually spoken through her from the spirit of a Chinese sage living 5000 years ago. As such, this claim is not arbitrary – yet. Only when she is asked for evidence for the claim that there was such a sage and that he is now speaking through her, and when she responds by saying something such as, “Because that is the way I feel,” then the claim is arbitrary because she is refusing to provide evidence. (Emotions and feelings are not proofs.)
She has, thus, made verification or falsification of her statement impossible. She does not offer even a route for investigation. Rational investigation is impossible. Now her claims are arbitrary.
So, in summary, there are three elements that constitute an arbitrary assertion: It is a statement; it is about some supposed fact (aspect of reality); and when challenged the speaker refuses or fails to provide evidence.
Stated negatively, a claim is not arbitrary if the speaker has erred or is illogical in his argument (which can be an innocent mistake) or has initially not provided evidence. The speaker is arbitrary when he refuses or fails to provide evidence for his claim when challenged.
I welcome corrections and additions to my understanding of this concept of the arbitrary. It is central to a current, long-term project.