What, specifically, is “damning” about those quotes?
Suppose creationists took over a formerly respected biology journal. Wouldn’t you expect to find quotes like the above (with climate sceptics replaced by creationists) from the private correspondence of biologists?
Inspired by reading this blog for quite some time, I started reading E.T. Jaynes’ Probability Theory. I’ve read most of the book by now, and I have incredibly mixed feelings about it.
On one hand, the development of probability calculus starting from the needs of plausible inference seems very appealing as far as the needs of statistics, applied science and inferential reasoning in general are concerned. The Bayesian viewpoint of (applied) probability is developed with such elegance and clarity that alternative interpretations can hardly be considered appealing next to it.
On the other hand, the book is very painful reading for the pure mathematician. The repeated pontification about how wrong mathematicians are for desiring rigor and generality is strange, distracting and useless. What could possibly be wrong about the desire to make the steps and assumptions of deductive reasoning as clear and explicit as possible? Contrary to what Jaynes says or at least very strongly implies (in Appendix B and elsewhere), clarity and explicitness of mathematical arguments are not opposites or mutually contradictory; in my experience, they are complementary.
Even worse, Jaynes makes several strong claims about mathematics that seem to admit no favorable interpretation: the are simply wrong. All of the “paradoxes” surrounding the concepts of infinity he gives in Chapter 15 (*) are so fundamentally flawed that even a passing familiarity of what measure theory actually says dispels them as mere word-plays caused by fuzzy or shifting definitions, or simply erroneous applications of the theory. Intuitionism and other finitist positions are certainly consistent philosophical positions, but they aren’t made appealing by advocates like Jaynes who claim to find errors in standard mathematics while simply misunderstanding what the standard theory says.
Also, Jaynes’ claims about mathematics that I know to be wrong make it very difficult to take him seriously when he goes into rant mode about other things I know less about (such as “orthodox” statistics or thermodynamics).
I’m extremely frustrated by the book, but I still find it valuable. But I definitely wouldn’t recommend it to anyone who didn’t know enough mathematics to correct Jaynes’ errors in the “paradoxes” he gives. So.. why haven’t I seen qualifications, disclaimers or warnings in recommendations of the book here? Are the matters concerning pure mathematics just not considered important by those recommending the book here?
(*) I admit I only glanced at the longer ones, “tumbling tetrahedron” and the “marginalization paradox”. They seemed to be more about the interpretation of probability than about supposed problems with the concepts of infinity; and given how Jaynes misunderstands and/or misrepresents the mathematical theories of measure and infinities in general elsewhere in the book, I wouldn’t expect them to contain any real problems with mathematics anyway.