For example, Peikoff's piece on the analytic-synthetic distinction shows that he is completely unaware of contemporary philosophy: he begins by saying that the analytic-synthetic distinction "is accepted, in some form, by virtually every influential contemporary philosopher". But this is clearly false. The most cited paper in 20th century philosophy is Quine's "Two Dogmas of Empiricism" (1953, available in From A Logical Point of View) which famously (and, I think, quite effectively-much more effectively than Peikoff) attacks the distinction. Though there have been many criticisms of the paper and defenses of the distinction, many agree with Quine and he is one of the most famous philosophers of the 20th century, especially within Anglo-American philosophy.

Peikoff must have been completely removed from the philosophical community and not reading any contemporary philosophy in order to not be aware of this. And this kind of ignorance and refusal to make citations to important philosophical works being drawn on or criticized shows up throughout the book. This is an interesting read for those with little philosophical background, but frustratingly vague, ignorant, and thus arrogant--not accurately prideful--to anyone with such a background.

My biggest question after reading this, was how was this not included in my (and everyone's) schooling? It's one thing for schools not to present Ayn Rand's epistemology, but no school (before college) I am aware of presents ANY epistemology. That more than any other statement shows the poor state of modern academia.

The author's intent was to summarize the "Objectivist theory of concepts" as a prelude to a future book on Objectivism, the latter name the author has given to her philosophy. Since it is a summary, and since it is philosophy (which usually eschews any need for empirical validation), one perhaps should not expect the details of all the assertions made in the book. The problem with this work though is that the author implicitly draws on fields such as child psychology and neuroscience, but no citations are given and therefore its credibility is suspect.

Some examples of the parts in the book that need reworking include: 1. The author's assertion that the human mathematical and conceptual abilities develop simultaneously. Not only is the author assuming that these abilities are indeed different, she offers no studies to support her assertion concerning the time development of these abilities in a child. What studies influenced her thinking on these matters? It is doubtful that the author has conducted the careful experimental work needed to reach her conclusions. Considering the amount of research that has been done in child and cognitive development in the past fifty years, this research involving many individuals, the author's claims on the cognitive development of a child are most astounding. 2. In her discussion on concept formation, the author explains the process, as she sees it, of the forming of the simplest concept, the concept of a single attribute. She does not define or have a criterion for "simplicity" of a concept, but as an example gives the concept of "length" as being one of the simplest. For the author, the child forms the concept "length" by observing objects of different length, noting that the length is the attribute they have in common, but the actual measurements are omitted. The author does not give any empirical evidence supporting this claim of concept formation, and she asserts that this process does not involve words. The lack of words to form concepts is not by itself troubling, but the lack of evidence to support both of these claims is. Again, there are many researchers who are very curious about the processes of learning and cognition, and much work in these areas has been done. The author's claims are extraordinary in this regard, and require much more substantiation if they are to be accepted from a scientific standpoint. 3. It is very apparent throughout the book that the author's knowledge of mathematics is very limited, and her limitations here cause problems in many of the discussions in the book. For example, when she describes the process of a child forming the concept of "table", she claims that it is the "shape" of the tables that forms the distinguishing characteristic. However, "shape" is a more complicated concept than the author realizes from a mathematical standpoint. A classification of objects by "shape" would not necessarily be the rigid geometric one which she clearly wants to use in the book. As another example, she discusses integral calculus as being a method for calculating the area of circles. It does this of course, but this is perhaps its most elementary application, and it goes far beyond this in its ramifications. The author's case for the importance of mathematics in her theory of concept formation would be much more credible if she would have obtained a more in-depth understanding of modern mathematics. 4. In the book the terms "complexity" and "random" are used very loosely. Since these notions are important in her epistemology, and of course very important from the standpoint of modern computer science and complexity theory, they need more careful consideration in this book. Indeed, her assertion that as a child's knowledge grows the complexity of the definitions of his concepts increases may if taken at face value completely invalidate her theory of concept formation. This is because some theories of concept formation that are based on knowledge trees can run into the problem of a "combinatorial explosion" or if based on first order logic may be "undecidable". The author's definition of complexity is completely absent though, and so one cannot analyze her works in the context of modern notions of complexity. Her notion of randomness too is left undefined, but she makes use of the notion frequently in the book, as for example in her assertion that concepts cannot be formed "at random". But randomness is a notion that requires careful elucidation in many different fields of endeavor, and especially in the field of neuroscience, the latter of which is also very concerned with developing a successful theory of concept formation.

It is readily apparent while reading the book that the author was completely isolated from the mathematical and scientific community while the book was being written. The lack of references, the extraordinary claims made, and the overall tone of the book make it almost useless to those readers who are actively involved in developing theories of cognitive development or those who are curious about such developments. If the book had included what was needed, its size would be many times over what it is now. Its status as a book on epistemology is typical of philosophical treatises: lots of speculation and arm-chair reasoning, but little or no empirical content.

Every sentence in Ayn Rand's "Introduction to Objectivist Epistemology" has the precision, economy, and practicality of a mathematical theorem. I have been reading it for years,
and yet I still find ideas that are unebelievably penetrating and important. I have learned how to introspect and examine the progress of my thoughts, how to condense increasingly large amounts of knowledge, and how to call upon them at will to solve problems, the importance of definitions for the end of organizing this knowledge, the step-by-step reduction of knowledge to sensory evidence thus guaranteeing certainty, and much more.

Now let me sweep aside that category of comments made by schoolboys who think that evaluating a philosopher consists of grafting her ideas onto their accepted premises and then condemning the result, as though one could blame a horse for not being able to run a race after its head has been planted on the body of a pig. It is unbelievable to me that someone would read this work, then criticize it by saying, in effect: "This does not solve the problem of the universals, because what we are looking for is something that either demonstrates that there is 'horseness' out there in reality, in horses, or something that shows that 'horseness' is arbitrarily made up". This amounts to treating philosophy as a 'ruler-and-compasses' sort of game, in which facts of reality are replaced by chess-like conventions. Geometers tried for centuries to "square the circle" using ruler and compasses, until it was proven that their basic assumption was wrong, and that such a thing could not be done.

Unanswerable objections have historically been posed to the main existing viewpoints on universals. He who says that "animality" and "planthood" exist in reality cannot say exactly where animality ends and planthood begins (consider some primitive organisms), and will also have trouble separating out "horseness" from the horses, since no two horses are exactly alike in any respect. The other that claims that "animality" is created by convenience, cannot account for why both the 19th-century Central African and the 17th-century Chinese arrive at and appear to *require* mostly the same concepts, if their "animal", "plant", and so on are just "groupings by convenience" (and let me leave aside the kind of intellectual chaos that will befall anyone tries to practice this viewpoint, as I did once).

Ayn Rand's "Introduction" is the first successful attempt at the problem because it does not begin by accepting any of these stale premises, but instead it begins by by taking *nothing* for granted, and then asking: what are the facts of the case? Step by step.

First there is the fact of "similarity". A light blue table and a dark blue television set are similar in one respect, in their being shades of blue. It is immediately clear that there is no single thing contained in both of them (after all one is light blue, and the other is dark blue), but a *relationship* that exists *between* them that does not exist between either and a yellow banana. Goodbye to the "no two horses are exactly alike" argument. Further, we find that the relationship is *closeness on a spectrum*, and that given the neccessity of *some* classification, we can choose within limits where light blue begins and dark blue ends, where indigo ends and blue begins, etc. Goodbye to the "animality ends and plant begins" problem.

But a similarity, by itself, is not a universal! They are only used to create universals, although some universals correspond directly to a single similarity, such as "blue". What if we used only these primitive universals? It is easy to see that you would not be able to understand much of the world from using only ideas such as "blue", "long", "wide", "many", "few", and so on (some of the ancients appear to have tried this, with ludicrous results). What we wish to understand are not *similarities*, but *things*, i.e. the entities between which these similarities exist, such as men, horses, solar systems, gravitational pulls, etc. By grouping men, horses, etc. based on a large number of similarities in shape, height, width, color, texture, number (e.g., of feet), we are able to apply all these similarities to each new man we meet without having to know it of him individually and directly. Imagine if a doctor had no concept of "man", and therefore, faced with a patient, could not apply a certain similarity that exists among all men, the posession of an organ within a certain range of shape, color, size, and periodic motion, within a certain range of position (the left side of the ribcage), i.e. a heart.

There is much more than even this in this book. And the above is one might almost say an oversimplification, and there is no substitute for approaching it more technically. But to summarize, it is quite a remarkable achievement.