Picked this book up on a raving review from a friend, without knowing anything about it. Put it down again after slogging through the first 15%. DIM falls into the same problem as every philosophical treatise, namely that it argues by authority. "Plato thought this, but Aristotle thought that!" The argument is mainly one of linguistic games: "the OED says $x means this, and therefore we can deduce $y." Although it was pretty funny watching a philosopher trying REALLY HARD to grapple with the everyday ideas of mathematical composition and abstraction.
I didn't really understand the point that Peikoff was trying to make --- but I think it might have been "building models of systems is good." He makes the claim that Aristotle should be our role model in this endeavor, because he wanted to build, and... uhh.. believed in science? The argument is definitely that Plato believed too much and Kant too little, so I suppose it's that Aristotle believed just right.
Unfortunately, there is no predictive power here. Plato is wrong because he believed in some form of idealistic naturalism. Kant is wrong because he argued that arguments don't hold water (why does society take this guy seriously?). Aristotle is right because he built systems in exactly the right way, but right because he liked that we can reason from our subjective experiences and because he liked science (as best I can tell --- I was skimming at this point!). Some examples and counter examples would have really helped sell the idea he was hustling here.
I came away from this book with the feeling that Peikoff doesn't know what he's talking about, and furthermore that he's so tangled up that he has no idea that he doesn't know what he's talking about. The book comes off as intentionally dense; as in, if you don't understand it, you must be stupid. This is my best explanation for why everyone seems to rave about this book. Of course, I might just be missing something, but Peikoff really didn't try very hard to help me understand.