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July 2nd, 2025 (Permalink)

New Book: Proof

Quote: "Life is full of situations that can reveal remarkably large gaps in our understanding of what is true and why it's true. This is a book about those gaps. It is the story of the ideas that have helped scientists and societies discern between truth and falsehoods, improving decision-making and reducing dangerous errors. From medieval juries to modern scientific revolutions, it is about the methods people have used to accumulate evidence, negotiate uncertainty, and converge on proof. And, crucially, what happens when those methods fail."¹

Title: Proof

Subtitles: This book has different subtitles for its United Kingdom and United States editions:

UK: The Uncertain Science of Certainty²
Comment: This is certainly an intriguing subtitle, but I'm uncertain what it means. The science of certainty would seem to refer to formal logic, but what's uncertain about it?
US: The Art and Science of Certainty
Comment: What is meant by "the art…of certainty"? The invocation of certainty, like the word "proof", suggests the logical and mathematical, as opposed to more informal notions, of "proof". I'll have more to say about these ideas in the General Comments, below.

I wonder why it was thought advisable to have different subtitles for the US and UK. All of this, of course, may have little to do with the book or its author, since the subtitles may have been selected by the book's publisher. Was there some reason to think that the second subtitle would sell better here in the US than the first, or that the first would sell better in the UK?

Author: Adam Kucharski

Comment: Please don't hold it against him, or against me, but I'd never heard of Kucharski prior to this book. Based on the author's short biography at the end of the book, he is a mathematician and epidemiologist, and has written two previous books―The Perfect Bet and The Rules of Contagion―neither of which I've read.

Date: 2025

Summary: So far, I've read only the Introduction to the book, which lacks a summary of its structure, and the chapter titles are not very revealing, so I'm guessing as to the topics covered. Beside the Introduction, there are eight chapters. I suppose that the first chapter is an introductory one; the second appears to concern "proof" in the fullest sense, that is, in logic and mathematics; the third, in contrast, seems to deal with the weaker sense of "proof" used in the law and legal trials; the fourth would seem to concern the sense of "proof" in the statistical trials of medical and social research; the penultimate chapter may have something to do with computers; and the last may be a summing up since there is no afterword.

Given that Kucharski is an epidemiologist, I was curious whether he discusses the events of the last few years in the book. None of the chapter titles suggest a concern with the pandemic, though the fourth is a likely suspect. Thankfully, the index indicates that, unlike Marty Makary, author of a previous New Book³, Kucharski does treat the pandemic at some length.

The Blurbs: The book is positively blurbed by Tim Harford, author of The Data Detective, and Alex Bellos, who wrote Can You Solve My Problems?, both of which I've read.

General Comments: "Proof" has both a strong and a weak sense:

Strong: The strong sense of proof is that which occurs in deductive logical and mathematical contexts. In this sense, a proof is an argument that's valid. This means that if the premisses of the proof are true then the conclusion must also be true. It does not mean that the conclusion of the proof is true, let alone necessarily so, since one or more of the premisses might not be true. It would appear to be this sense of "proof" that's discussed in chapter four of the new book.
Weak: A proof in this weaker sense is one that makes its conclusion more likely to be true than false, but not necessarily so. This sense is weaker than the strong one in that the premisses of such a proof could be true and the conclusion false. For instance, the legal standard of "beyond a reasonable doubt" is not a proof in the strong sense since it does not mean beyond any doubt whatsoever, and it's possible that an innocent person might be convicted of a crime based on evidence that meets the standard. Similarly, the evidence supporting a theory in empirical science never amounts to a proof in the strong sense as there is always a possibility that new evidence will refute it. This sense would seem to be the subject of chapters three and four.

I plan to read this book and may have more to say about it in the near future.

Disclaimer: I haven't read this book yet, so can't review or recommend it, but its topic is right in the wheelhouse of my bailiwick, so I'm interested in it and thought that readers might be as well.

Notes:

↑ "Introduction", p. 3.
↑ For the UK cover with subtitle, see: "Proof: The Uncertain Science of Certainty", Adam Kucharski, accessed: 7/1/2025.
↑ New Book, 3/27/2025.

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