The second sentence of the excerpt says that IOE is a summary of “one of its cardinal elements” (my emphasis). The referent of “its” is obviously Objectivism. “One of its cardinal elements” implies that Objectivism has other cardinal elements–at least one more, more likely at least two more–and that each of these cardinal elements is (trivially) an element of Objectivism. The most plausible reading of sentence 2, then, is that IOE is a summary of one of several unspecified cardinal elements of an as-yet incomplete Objectivist epistemology which, when completed, will become a complete (or minimally complete) Objectivist epistemology—but right now isn’t one. In “The Objectivist Ethics,” Rand makes reference to “cardinal values” that are the “means to and realization of” the ultimate value, life. Inferring from her use in the OE passage, we can say that a “cardinal X” is a crucial (essential, indispensable) identity-making constituent of X. Putting the point another way: any X is fundamentally or even fatally incomplete if it is missing the full suite of “cardinal X’s” that constitute it.
The implication here (I take it) is that the Objectivist epistemology, lacking its other (unspecified) cardinal elements, is itself radically incomplete, even on Rand’s own view. Rand gave the Objectivist epistemology (a summary of) one of its several cardinal elements, its theory of concepts. The other cardinal elements are missing. So are the non-cardinal elements, for that matter. It follows (without much trouble, I think) that most of the main elements of the Objectivist epistemology have yet to be supplied. That’s why the book Rand wrote is an introduction to Objectivist epistemology. It’s an introduction to an epistemology that had not, as of the publication date of IOE, yet been produced. The point of the book was to give guidance to “philosophy students” who chose, in the future, to discover and produce it.
The point—which seems obvious enough in itself—is worth dwelling on, if only because the pathologies of the contemporary Objectivist movement conceal its implications from view. An introduction to Objectivist epistemology implies the possibility of an Objectivist epistemology that is not itself introductory and yet fully Objectivist in content. The introduction to Objectivist epistemology serves as an introduction to this (as-yet non-existent) epistemology. Notice that it makes no sense to conflate the introduction to Objectivist epistemology with “Objectivist epistemology” as such, merely because Rand happened to write the introduction to the epistemology but not the epistemology to which the introduction serves as introduction.
Absurd as this seems, the closed-system conception of Objectivism literally tells us that an introduction to Objectivist epistemology cannot be an introduction to Objectivist epistemology. On the closed-system view, the introduction to Objectivist epistemology, qua written by Ayn Rand, has to be the whole Objectivist epistemology. Since “Objectivism” names Ayn Rand’s own achievement, and IOE is the only book of epistemology Ayn Rand wrote, then since official first edition text of IOE is the whole of Ayn Rand’s achievement, that text is the whole of Objectivist epistemology. On the other hand, Rand was the one who said IOE was an introduction to Objectivist epistemology—and the closed-system view of Objectivism requires fidelity to what she actually said. So, on the closed-system view, IOE is both the whole of Objectivist epistemology and an introduction to a whole epistemology that doesn’t yet exist. In other words, it must simultaneously be the whole epistemology and an introduction to that whole.
Put another way: on the closed-system view, IOE must function as an introduction to an Objectivist epistemology that is debarred from coming into existence because Ayn Rand did not (therefore cannot) write it—and is likewise debarred from coming into existence because (being her exclusive achievement) no one else is allowed to write it, either.*
What are the other cardinal elements of the Objectivist epistemology? Rand seems to suggest that one of them is the (Objectivist) theory of perception, but doesn’t explicitly say that. IOE (she tells us) is “presented outside of its full context,” where that omitted context includes “a discussion of the validity of man’s senses” (p. 3). She explains this decision on the grounds that “the arguments of those who attack the senses are merely variants of the fallacy of the ‘stolen concept’” (p. 3).
This omitted material on perception seems to be a candidate for a “cardinal element” of the Objectivist epistemology, but the claim itself is a bit puzzling. There is a discussion of “the validity of man’s senses” in IOE: the discussion of axiomatic concepts in chapter 6 of the book, but that discussion is specifically about axiomatic concepts, not about the senses as such. The chapter elaborates on the idea that perceptual skepticism involves a variant of the stolen-concept fallacy, but doesn’t discuss very many of the variants. I assume that Rand meant that the “full context” she omitted would consist of a theory that focused more specifically on the senses rather than on axiomatic concepts. But would it merely consist of a negative or quasi-polemical discussion/refutation of the variants of perceptual skepticism? Or would it have to involve a positive theory of the nature of perceptual evidence, in the manner of David Kelley’s The Evidence of the Senses?
She doesn’t say, but I think the latter is the more plausible claim: a positive theory of the nature of perceptual evidence would provide the most defensible basis for a refutation of the variants of perceptual skepticism. Rand didn’t produce such a theory, at least not in print (and as I’ve said above, if it’s not in print, it exists at best in potentia).
Suppose then that someone besides Rand were to write such a book, be it David Kelley or someone else. Suppose that the book’s contents are entirely true. Call this hypothetical book The Objectivist Theory of Perception (TOTP). If the claims of IOE is true, and those of TOTP are true, and IOE is a summary of one of the cardinal elements of Objectivism, and TOTP states another cardinal element of Objectivism (perfectly coherent with IOE), then TOTP’s content would be Objectivist, and the theory defended in it would be part of Objectivism. If Kelley’s The Evidence of the Senses is such a book, then what I’ve just said of TOTP would be true of The Evidence of the Senses. But if Michael Watkins’s Rediscovering Colors is a better instance of TOTP, then what I’ve said of TOTP would be true of it. If Watkins’s book were more coherent with IOE than Kelley’s (I haven’t read Watkins, so I don’t know), then Watkins’s book would have more of claim to being called Objectivist than Kelley’s (and vice versa).
How many cardinal elements does the Objectivist epistemology have? Since Rand doesn’t tell us how many cardinal elements the theory has, we ourselves would have to decide how many there are. Suppose someone decides on (true) theoretical grounds that there are six cardinal elements. Then there being six cardinal elements would have to become Objectivist doctrine, whether Rand realized it at the time of writing IOE or not.
Suppose more minimally that there is some third cardinal element of Objectivism, call it X. Suppose that someone writes a book defending a theory of X, and suppose further that this theory of X is true. Since X is ex hypothesi the third envisioned cardinal element of Objectivism, X is as much a part of Objectivism as the first and second parts, whether X stands for “induction” or anything else.
Rand says that IOE is a summary of one of the cardinal elements of Objectivism. A summary is the brief version of some longer exposition. In the case at hand, there is no such “longer exposition.” Suppose, then, that someone writes up the longer version of the theory of concepts summarized in IOE. In that case, the longer exposition would draw out the elements of the summary: that’s just what the longer exposition of a summary is. But then the longer exposition would have to be Objectivism, because the summary is a summary of it. If it isn’t Objectivism, the summary can’t be Objectivism. As long as the longer exposition is a faithful exposition of the claims of the summary, there’s nothing else for the longer exposition to be but a long and detailed exposition of the Objectivist theory of concepts.
*I re-wrote this sentence slightly after the initial posting of this annotation. It originally made the same claim, but in a slightly different form.
 Actually, I think “one of its” implies that there are at least two more cardinal elements. The more natural way of implying that there are exactly two cardinal elements is to say “one of its two cardinal elements.” It seems to me that if Rand was writing in a self-conscious way (as I think she was), and meant to suggest that there were precisely two cardinal elements, she would have said “one of its two cardinal elements,” not what she actually said. The phrase “one of its cardinal elements” most plausibly implies “one of several, i.e., three or more cardinal elements.”
 A passage at the bottom of p. 57 sounds to me like a parody of Schlick’s views, but that’s about it.
 There doesn’t have to be just one, of course.
 We would have to decide it even if we discovered in some archive that Rand said she thought that there were precisely six cardinal elements to the Objectivist epistemology, and enumerated them. For one thing, on my view, her saying something doesn’t make it so. For another, even on the Peikoff-type of view, her saying something outside of the official corpus can’t make that thing part of the content of Objectivism. So I wouldn’t worry too much about this possibility, much less ransack the archives for it.
 Personally, what I think IOE presents is less a summary than a research program. A ‘summary’ has to summarize something that already exists: you can’t summarize a theory that hasn’t yet been brought into being. Arguably, though, the Objectivist theory of concepts hasn’t been brought into being. IOE is an extremely dense monograph whose ramifications haven’t (in my view) fully been understood. (I say this because I’m surprised on each successive reading by what I obvious missed or failed to understand in the prior reading, and often find that standard criticisms of it are misunderstandings of the text.) “Haven’t fully been understood,” as I see it, is compatible with one or both of two possibilities: (1) there’s more there than anyone has fully grasped, (2) there’s less there than Rand advertised (and her more devoted followers have advertised). If (2) is the case, then, “it” can’t, strictly speaking, be ‘summarized’. I’ll ignore this for present purposes, but one can’t ignore it indefinitely.
 Presumably, then, the summary at the end of IOE is a summary of a summary of one cardinal element of Objectivism. I wonder if this tendency to summarize summaries is where the Objectivist habit of “essentializing” everything comes from—the tendency to offer summaries of summaries of delimited elements of a theory and then to treat the undigested meta-summary as the content of a whole discipline of philosophy. On a view of this sort, epistemology just becomes: summarizing a summary of a cardinal element of a theory as laid out in a short monograph, simply because that’s what Rand did.