A review of Krzysztof Burdzy’s The Search For Certainty: On The Clash of Science and Philosophy Of Probability.

The first thing you have to get over in the book is the slightly rough ESL delivery. I also personally consider it a clear defect when every paragraph and section starts by declaring what grand things will be revealed in subsequent text - just say it already!

On to business, this book is written by someone who, like me, is not fully on board with all the accepted thinking about the nature of probability. That’s good and why I sought out the book. But early on the author presents his slightly cryptic theory, unappealingly named "(L1)-(L5)". Seriously. I kept thinking of it (referenced 100s of times) as some kind of weird ascii art. Could the author think of no better way to refer to his system of thought (like "frequentist", "Bayesian", "subjective")?

Digging into the author’s system, right away on "L1" I notice ambiguity. He says that "Probabilities are numbers between 0 and 1…." Since this is a very abstract thing which he doesn’t really relate to intuition, I feel free to assume he’s using his mathematician’s magic hat and wants to be very, very punctilious about things in only ways that mathematicians can. Mathworld defines "between" as a system of 3 distinct points, technically ruling out the possibility that a probability could be 0 or 1. But "L5" says "An event has probability 0 if…" Now, perhaps it seems I’m picking at details, but isn’t that the whole point of fancy math? I’m all for chilling out about the importance of fancy math, but you can’t just use this kind of extreme pedantry only when it suits you. If the author is making clearly ambiguous and contradictory statements in the core of his whole thesis, then how seriously am I going to want to figure out what else he has to say?

Even stepping back from the kind of problem that makes me skeptical about probability systems in general, I could make no sense out of the author’s grand "laws". They seem like some randomly chosen rules pulled out of any normal statistics book. I never did figure out what the conventional alternative would be like as a direct comparison. Instead he focuses on theories of de Finetti and Von Mises. It seems he really has an ax to grind with these two. For me the long exercise of reading the book was useful in that it tipped me off that these two guys had something to say about probability.

Most useful and interesting to me in the book was the occasionally clear exposure of isolated flaws of conventional probability thinking. Conventional probability works in many conventional situations to be sure, especially classes teaching conventional probability. But there are the unsettling corners where it fails comically.

I am interested in the philosophical aspects of probability and this book bumped into them here and there enough to be worth reading. Clearly the author knows the terrain of the weird hinterland of probability thought and I found the bibliography to be an interesting place to continue the exploration.

If you’re very, very interested in skepticism about conventional probability thinking and philosophy, this book might be worth a quick read. If you’re trying to discover a better calculus for making more accurate predictions, I don’t think this is it.