The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us by Noson S. Yanofsky
My rating: 2 of 5 stars

Whatever Passes For Reason

“With understanding comes ambivalence.” This is an opening line that rates in concision and anticipatory depth with Dickens and Kafka. It also rings a suggestive note of intellectual honesty and reserve that gives the reader hope that what follows is tentative and provocative not an attempt to grind an intellectual axe. I was sympathetic with this Yarn0fsky from the start. Unfortunately, I found that as I began to understand Yanofsky, ambivalence about Yanofsky grew apace.

The book is really about logic despite its title and its stated ambitions about reason. It’s not a bad exposition of logical contradictions and how they occur. If the book were pitched as a popular introduction to this topic in logic, without pretending it had something to say about the philosophy of science, it might sit well in a certain niche for university undergraduates. But Yarnofsky and his publisher are after bigger game apparently. And there it fails to score.

“My goal is clarity,” Yanofsky says. And I think he succeeds. But at the cost of pedantry that is remarkable in its casual expression. He breezes from arbitrary definition to spectacularly prejudicial conclusion to sweeping implication with ease, confidence, and yes, great clarity. He is a university teacher after all, and apparently a teacher who takes no prisoners among his dissenting students. Neither nuance nor dialectic stands a chance in his class based on the contents of this book.

According to Yanofsky, “Rationality and reason are the methodologies used by a society to advance.” This is obviously meant to get the reader’s attention. But seriously? Does he mean by this broad claim to include those ancient societies of Asia, Middle, South and North America and Africa whose primary spurs to advance were often rather irrational and unreasonable (by today’s standards) religious beliefs. Or is the claim just a plug for scientistic boosterism, a nod to technology and material progress perhaps? In any case, whatever the “methodologies” employed by these societies, they were profoundly different from each other. So his claim that reason is the “tool of civilization” is tendentious as well as insulting to the intellectual traditions of most of the world.

But as his story unfolds, it becomes increasingly clear that Yanofsky really has no idea what he means by reason. He begins his exposition, arbitrarily and with a certain puerile insouciance, by choosing one among sixteen (his count) OED definitions of the term. No historical review, no comparisons, no explanation whatsoever except that he likes the definition he’s chosen. Ultimately, after conducting us on a grand tour of his real subject, contradictions, he concludes with his own re-considered definition: “Reason is the set of processes or methodologies that do not lead to contradictions and falsehoods.” One shudders. The circularity of this statement is apparent. Even Yanofsky recognises that it may not have any meaning at all except as a tautology: “The point I am making is that there are no exact rules to determine when some idea or process is part of reason or beyond its boundaries.” I don’t disagree. But so much for civilisation and its foundation in reason.

After he has trashed reason as an indeterminate process, then backtracks on his initial claims, Yarnofsky comes to a very narrow, very specific point. Despite the wide diversity of what constitutes reason among different scientific disciplines and among philosophers of science, he believes that “there is a property that most thinkers agree reason has: one cannot use reason to derive contradictions and false facts.” So, he continues, “We must keep such mental constructs [presumably theories] and language contradiction-free so as to describe the contradiction-free physical universe.” No discussion of which thinkers he has in mind or what their critiques might have said, or for that matter why the universe doesn’t choose to be contradictory. But Yarnofsky is quite sure that this is the Holy Grail of method that the world has overlooked.

So, here’s a fact: numerous experiments in quantum mechanics demonstrate entanglement, that is instantaneous action at (even great) distance, between paired photons. This contradicts much of modern physics. Is the issue factual (we’re measuring the wrong things) or theoretical (this actually happens and we can’t explain it)? Could be either. Could be both. Could be a presumption buried deeply in our logic of either our theoretical language or our physical technique (it may be some other issue entirely, for example: https://apple.news/AAWuNbce6RUGuiPjoM...). Yarnofsky’s discussion doesn’t get us any closer to pinpointing its locus much less solving the problem of entanglement. Or any other scientific problem. The logical technique of reductio ad absurdum, contradiction, is well-known to scientists in fields from physics to evolutionary anthropology. But to my knowledge it has never been of use in distinguishing factual from theoretical error. I don’t see how such a distinction is possible. And Yarnofsky’s not saying.

To be fair, Yarnofsky knows he’s got a problem with the self-referentiality of his preferred “tools of reason,” mathematics and logic. Neither of these is entirely rational. That is to say, their internal consistency cannot be demonstrated. All we (or at least he) can say is that no one has yet shown them to be inconsistent. He strengthens this empirical statement with one of a quasi-religious plea. “Do not worry,” he says as if he were a preacher addressing a room full of Sunday worshippers, “that modern mathematics or even basic arithmetic is inconsistent. I assure you that they are consistent.” Trust me, I’m a Doctor, is not really an acceptable piece of scientific evidence or reasonable argument.

Yarnofsky glosses over Gödel’s second incompleteness theorem, the one that really scuppers self-referentiality, as if it contributes to his thesis about intellectual limits: “one of the central themes of this book: any self-referential system, no matter how powerful, is somewhat limited.” Yet he rests his whole case - about contradiction, about method, about reason, about civilisation itself - on the integrity of mathematics and logic? The inability to demonstrate that integrity is fatal for his project from the start. Rephrase his project: “I want to demonstrate to you the limits of reason by using tools that are themselves limited in their reasonability,” to understand as my growing ambivalence turned into annoyance.

So, after building the case for reason and rationality, or at least a case for the usefulness of logical contradiction, and then retracting it, Yarnofsky goes into a sort of general intellectual meltdown and abjures what he has built entirely:

“Since we do not know what will and will not cause one to err, our definition of reason is somewhat time dependent. What was once considered reasonable, could, in the future, be shown to cause contradictions. In fact, throughout history, there have been many times that something was considered part of science and only later turned out to be false.”

So much for logic and method and reason, and civilisation.

“Reason”, as the philosopher, Charles Taylor, has said with pointed sarcasm about current thought patterns, “is whatever passes for reason.” Yarnofsky apparently agrees - without any sarcasm. If either of them could simply accept that the search for better methods of inquiry is a permanent part of inquiry, the world might be better off. It would certainly require less paper.

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