I have always leaned towards Peikoff’s view that probabilities have to be grounded in certainties, but that was only based on intuition, and I could never quite concretize it to my satisfaction. However, I recently realized that I am well acquainted with a perfect example of Peikoff’s point: modern academic philosophy.
If you take a class in philosophy in most universities, you will be presented with an array of mutually exclusive theories and a baffling list of arguments for and against each of them. Each of these theories is presented as “plausible” or “having some evidence in its favor,” but no theory is ever presented as certain. The overall tone of a typical philosophy class is “maybe A is true, and maybe B is true, and maybe C is true, but who knows?”
Peikoff’s principle cuts all of this down by pointing out that if no theory in philosophy is certain, we have no idea what even counts for or against any philosophical theory, because we have nothing to compare them to. We could compare them to other theories that are uncertain, but then we would have no way of ruling out the possibility that both theories being compared are completely wrong. We cannot even compute the probability of both theories being wrong to delimit our doubts, because we have nothing certain to compare them to.
Something similar happens in science, when scientists compare theories that are under scrutiny with well established theories like Newton’s laws or the theory of evolution. They basically say, “the theories that have been established so far have tended to be testable and based on observational evidence (and so on), so those qualities are virtues in a theory in our field and their absence from a theory in our field is a vice.” In the absence of established theories, there could be no criteria for judgment.
Edit: Upon rereading my post I realized that it could be taken to imply that I think that there is no certainty in philosophy. That is not what I was saying. Rather, my point was that academic philosophy’s insistence that no theory in philosophy is certain is internally inconsistent, so they should adopt a specific philosophy as certain, like Ayn Rand’s philosophy. Indeed, I think that many tenets of Ayn Rand’s philosophy qualify as certain.