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This is a question of terminology. I'm trying to distinguish words and ideas from reality itself. If you hold that a "fact is a type of claim" then you lose (or at least muddy) that distinction. What is a fact a claim of? What do you call the thing out there in reality? (A statement is a complete sentence, not just a noun. So if a statement is "factual," i.e., true, the underlying fact, out there in reality, must be more than just a "thing" like a rock or whatever, it has to be a thing doing (or being) something, even if only existing.) As evidence that my distinction here is not mine alone, I offer this: if I say something, and someone replies, "Is that a fact?" they're asking about the state of things "out there" in reality; they aren't asking for a mere categorization of my utterance (which could be determined entirely from the utterance itself, and from a knowledge of how to categorize utterances, as opposed to looking at whatever I'm talking about). If a fact were a type of statement then asking, "Is that [statement] a fact?" would be the same sort of thing as asking, "Is that statement using an intransitive verb?" Another thing to consider is context. All statements are made in a context. The context can be used to resolve ambiguities and to specify meanings. If I say, "That book is on the shelf over there," it would have to be the context that would make it clear which book and which shelf. Some contexts are broader than others. The broadest context available is the context of "all human knowledge," but smaller contexts are frequently useful and necessary, so you can have your own personal context, e.g., concerning whatever is in your immediate vicinity, and distinguish that from other contexts. A statement has to be put into a context in order to be judged as true, false, or arbitrary (or "possible," "probable," etc.). Further, the same statement can be true in one context, false in another, and arbitrary in yet another, although this might hinge on certain words that have different meanings in different contexts. (I should also point out that in the case of a "word salad" which isn't even grammatical, there's no use trying to put it in a context, because context doesn't make any difference...) I did make a distinction between a statement which is "arbitrary in a particular context" and one which "would be arbitrary in any context." The latter, I think, is what most people here mean when they state that something is "arbitrary." The examples of arbitrary statements given by Peikoff seem to be of that latter type; they seem to be those where the claimant is deliberately trying to insulate a claim from evidence. I think such a statement, "detached from the realm of evidence" as Peikoff describes it, is very different from a claim that merely lacks evidence. A claim that lacks evidence is merely useless; a claim that's impervious to evidence is another sort of beast -- and the statements Peikoff makes about the arbitrary being "an affront to reason and to the science of epistemology" would make more sense applying to the latter.