The Art of Logic

It’s not just that both are right in this case. Both are right in every case.

Even as “hard” a science as physics tells us light is both a particle and a wave. Quantum mechanics tells us electrons can be both here and millions of miles away at the same time. How can we be so hubristic to think that only higher taxes (or lower taxes) will save the economy, only a Democrat (or Republican) can save the country.

It’s not just that both are right in this case. Both are right in every case.

So I have told myself within the confines of my own brain when considering two sides of an issue. Even as I have articulated the thought, though, I have been forced to acknowledge that, logically, the assertion cannot be wholly true. Indeed, it might well be wrong.

It was in this spirit of radical doubt that I approached Eugenia Cheng‘s new book, The Art of Logic in an Illogical World. I was cheered by sentences such as the following: “Admitting the possibility of being wrong and having ways of detecting it is an important part of being a rational human being, I am sure. (But I could be wrong.)” And these two, a few pages later: “In reality, most people do some good things and some bad things. In fact, most things are themselves partly good and partly bad.” (The final sentence being, probably, a more convincing way of stating my italicized assertion above.)

Where did my radical doubt come from? By nature, surely, in the first instance. That is: I am my father’s child. We called him “middle-of-the-road” for never being able to commit to a position. He was by disposition unable to state a preference for either the steak or the potatoes. Instead, he would struggle to extol the virtues of both and express reluctance to deny either its due. In short: I came by my moderation honestly. (For the record, my mother was inveterately black-and-white. Gray did not exist for her, and she showed little patience for her husband’s affinity for it.)

Yet my moderation comes by nurture, too. Or, perhaps better, by the contingent byways of my intellectual development: books. William Damon’s Greater Expectations helped my thirty-three-year-old self collapse the false dichotomies that plagued my chosen profession (education). Child-centered vs. adult-led, progressive vs. traditional, whole language vs. phonics: these were all false dichotomies, Damon assured me. He gave me permission to give up either-or thinking for a more accommodating and mentally healthy both-and way of seeing. It was liberating.

It was not news to me to read in Cheng’s book, “A false dichotomy is when you think the options are perfectly cleanly split between A and B, but in reality they are not.” On the other hand, her formal rendering of the topic extended my thinking. She admonishes against arguing that “A is equivalent to ‘not B’ and B is equivalent to ‘not A.'” The truth could be found in the overlapped section of circles A and B in the Venn diagram. On the other hand, the truth might be outside both circles: neither A nor B is correct. (There goes my italicized assertion at the top!)

In my early-to-mid forties, I discovered Jennifer Michael Hecht’s Doubt: A History. The book gave religious/philosophical doubt/skepticism a respect (not to mention an acknowledgement) that it had previously been denied. It gave my natural predilection toward moderation, inherited from my father, some intellectual heft. Epicurus, Lucretius, Montaigne, Hume: doubt comes from an esteemed line of thinkers. I was becoming sure of myself, intellectually as well as psychologically. Andrew Sullivan’s The Conservative Soul extended the importance of doubt to the political realm for me. (Which is not to say I became a conservative, but I became more comfortable in my claim to being “independent.”)

Cheng is a mathematician, not a scientist. Evidence is less integral to her skepticism than logic. Yet it is one of the central aims of her book to show the limits of logic. The Law of the Excluded Middle may state that ‘true’ and ‘not true’ are the only options under consideration, but Cheng understands this will not help us solve problem in the real world? Gray areas are all around us, inhabiting every issue under discussion, whether it be sexual preference or the percentage of cocoa needed to make chocolate. Where do we draw the line? Between black and not-black? White and not-white? White, black, and the lost middle? White(ish) and black(ish)? White, gray, and black? In life, “really we’re all living somewhere on that gray bridge.” Cheng encourages us to make our line-drawing choices explicit. She acknowledges that “for some people it feels unsettling to take positions of nuanced uncertainty,” but she spends a good portion of her book encouraging readers to get comfortable with it.

Nuanced uncertainty. In my mid-to-late forties, I performed an in depth study of Keynes, inspired by the world recession that was being compared to the earlier depression his seminal work sprang from. Keynes was obsessed with the idea of uncertainty. It was central to his Treatise on Probability of 1921, his General Theory on Employment, Interest, and Money of 1936, and probably everything in between. I added “uncertainty” (in economics and all human affairs) as another form of doubt.

As rigorous and rule-bound as logic is, Cheng argues, it cannot (and must not) be used to erase uncertainty. Two people can both be logical and reach different conclusions. This usually happens when they start from different places. For no matter how exacting one’s logic it has to start from somewhere, else another could, like a four-year-old, keep asking “but why?” farther and farther back. At some point the logician as much as the everyday person must say, for example, “Because I believe humans are obliged to treat each other as we wish to be treated.” For this person, the Golden Rule is axiomatic. Again, Cheng encourages us to be clear about our axioms and to push them far enough back they can be truly universal principles. (Not just, “Because the Bible says so,” but perhaps, “I believe humans were made to follow the word of God.”)

Cheng applies the tools of her trade–category theory, fuzzy logic, paradoxes, analogies–to real world issues, quandaries, and dilemmas. After three hundred pages, it becomes apparent that the material for this book came as much from discussions with friends over coffee as it did from lessons with her students at the Art Institute of Chicago. Cheng’s struggle against the allure of treats and the insidiousness of weight gain serves as an ongoing context for explaining the principles of logic.

As often, Cheng dips into more divisive political issues we all face: race, gender and sexual preference, social services and the role of government. To her credit, Cheng states clearly that many of the arguments she examined “come down to tensions between the idea of individuals and the idea of groups.” Certain readers might dismiss her as overly group-oriented and biased toward a multiculturalist worldview. But Cheng is not seeking to win arguments; she is showing how they break down. She gives her readers, whatever their political beliefs, critical logical tools to debate with her, or anyone, on equal footing: to understand their differences, to find bridges of disagreement, and to feel comfortable agreeing to disagree.

For explanations of those tools: go to the source.

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