Personally, I think Doug Self represents a radical extreme in the objectivist camp, and he's putting his evidence through a contradictory-fact-removing-filter worthy of Fox News. I don't have the listening experience to judge any of his conclusions, but I can certainly critique his logic.
Overall, his book seems to have one underlying theme: "I think all amplifiers sound the same, but some people don't, so here's how you can swindle more customers by advertising a really low THD measurement that you and I both know doesn't make a bit of difference." So should it surprise us if his arguements don't hold much water?
The most obvious rebuttal to objectivism is just that amplifiers are bulit for listening, and all that matters in the end is the subjective perception of the listener. Perhaps in Futurama they could have a THD-analyzing robot that loves nothing more than to listen to beautiful undistorted sine waves, but that's not me.
Which brings us to another clear mistake: his near-total reliance on THD measurements as the final word on amplifier quality. In Part 1 of this article:
http://peufeu.free.fr/audio/memory/
you can see a great example of where THD measurements specatcularly fail to predict the behavior of the system. What Self really needs to remember is that distortion residuals will fully characterize a memoryless nonlinear system, and the various linear ODE tools (state-space, Laplace, Fourier) will fully characterize an LTI system. But to analyze a real amplifier which is neither memoryless nor linear, none of those tools are theoretically appropriate. In fact, there IS no general theory that allows one to analytically predict the behavior of such a system. Even proving stability requires you to "guess" a Lyapunov function.
Another fatal flaw is his lack of respect for human hearing. It's true, we can only percieve a 10% step change in amplitude or a 0.2% step change in frequency, but those measurements have little to do with how we actually use our hearing. We can nevertheless perform a myriad of feats that not even the best microphones and DSP algorithms can match...like picking a voice we recognize out of a room full of people. Also relevant is the fact (which I unfortuneately know only from anecdotes) that a difference in volume that's not directly perceptible will nonetheless make a louder amplifier sound better.
So to conclude, I don't disparage mathematical analysis as a way to better sound quality...it's just essential to have the right tools. Doug Self does not have those tools, and furthermore he seems to have given up looking.