I, too, believe that a thorough grounding in metaphysics, epistemology, and ethics is important. I will concede a touche on not having studied enough Aristotle. However, regarding the central issues of ARI/TOC, I think we can consider the arguments directly.
I want to advance a sketch of an argument against Peikoff's stated theory of "Certainty as Contextual" in OPAR. I think this has been one of my main intellectual sticking points with Peikoff from the beginning. It is, I believe, of more consequence than his true/false/arbitrary trichotomy, which I also believe to be flawed. It is also another example of Peikoff's overreliance on the coherence theory of truth.
In OPAR page 171:
In the previous chapter, I stressed the importance of relating a new idea
to the full context-- of seeking to reduce the idea to the data of sense and
to integrate it with the rest of one's conclusions. Now I want to develop a
further point: once these logical requirements have been met, the idea has
been validated. If a man evades relevant data: or if defaulting on the process
of logic, he jumps from the data to an unwarranted conclusion; then of course
his conclusion does not qualify as knowledge. But if he does consider all the
available evidence, and he does employ the method of logic in assessing it,
then his interpretation must be regarded as valid.
Logical processing of an idea within a specific context of knowledge is
necessary and sufficient to establish the idea's truth.
Now, the last sentence of this passage is just plain false. The truth of an idea is its relationship to the facts of reality, my reasoning about it or logical processing of an idea within my context of knowledge has no bearing on its truth. Peikoff's argument conflates the idea of validity, which is an epistemological term designating a best effort standard for an argument (i.e. I have considered the available evidence and made no logical or inferential errors) with the idea of truth which represents the relationship between an idea and the facts of reality independent of anyone's apprehension of it.
This passage that I quoted is not an isolated instance. Throughout Peikoff's writings he seems more concerned with how an idea fits together with what he already knows than gathering additional data. In fact, there is always an epistemological tension between gathering new data and integrating the knowledge we have and it is a difficult balance. The standard I use concerning the rigor of an argument is the maintenance of that balance. Are the counterarguments considered? What are the sources of evidence of which I may be in ignorance? Is there any disconfirming evidence? The process of continuing to consider these questions is key in maintaining objectivity.