The Mathematical Case for Hypocrisy

It may be a bad trait, but it’s sometimes unavoidable.

Hypocrisy may be occasionally unavoidable.

Photo illustration by Lisa Larson-Walker. Photos by iStock/Thinkstock.

The present political and cultural climate seems to have led to an intensifying of the natural human tendency to hurl charges of hypocrisy at one another. Rather than partaking in this pleasant activity and pointing to the many current instances of political or personal hypocrisy, I’d like here to offer a partial defense of the notion.

Hypocrisy thrives on black-or-white, either-or thinking. Once we accept such dichotomies, we naturally look for the apostasies and hypocrisies of benighted people on the wrong side of the ethical or cognitive tracks but rarely for real understanding.

I have received my share of emails, for example, from people who have written (actually screeched in capital letters) that I’m a hypocrite because of some article, book, or column of mine that, let’s say, recommended a cost-benefit analysis of something they, and they thought I, held sacrosanct.

Conventional understandings would suggest that I hold liberal positions on most issues, but I’ve known many “liberals,” myself included, as well as many “conservatives” whose private actions and beliefs on some issues were on the opposite end of a spectrum (assuming that there is such a thing as a spectrum) from their public ones. As such, they are often judged to be hypocritical. Examples might be environmentalists who don’t recycle, libertines who rail against porn, gun-control advocates who have an arsenal of high-powered weapons in their basements, “pro-family” people with several marriages under their belts, etc. Are these people necessarily hypocritical, as commentators and biographers might be strongly tempted to say, or is it just easier to note their apparent conflicts than it is with other less “well-defined” people?

One common definition of hypocrisy is “the practice of professing beliefs, feelings, or virtues that one does not hold or possess.” (I wonder if one can be said to be hypocritical if one professes vices that one does not hold or possess.) Hypocrisy is usually considered to be a bad trait, and indeed it usually is, but it’s rarely considered to sometimes be a necessary one. I think hypocrisy is occasionally unavoidable, and one of my reasons for thinking this is mathematical.

Occupational obsessions bring to mind the decision problem (in German the Entscheidungsproblem) in mathematical logic. It is the question of whether there exists an algorithm, that is, a well-defined recipe, for deciding whether a statement or collection of statements in the spare formal language of predicate logic (using the simple quantifiers all and some) is universally valid. Short answer: Nope, this is not possible. In the 1930s it was proved by Alonzo Church and Alan Turing that there is no algorithm such that, if given a collection of statements, the algorithm will always respond yes if it is universally valid, or no if it is not.

Related limitations hold for the even sparer, more limited language of propositional logic. The problem here is whether, given some complicated combination of many simple propositions P, Q, R, … connected only by and, or, and not, there is any way at all to assign truth or falsity to the simple propositions in such a way that their complicated combination is true. This so-called Boolean satisfiability problem is decidable, but it remains an extraordinarily difficult logical problem.

Without the mathematical jargon, the point is that it’s not always easy or even possible to determine whether some large collection of statements is universally valid or whether it’s even satisfiable. We probably all subscribe to inconsistent or unsatisfiable collections of statements and hence are at times hypocritical—sometimes knowingly so, sometimes not. This is all the more the case when we go beyond the formal languages and rules of mathematical logic to natural languages that admit of connotation, vagueness, and intentionality that allow for people’s incommensurable ways of chopping up and organizing the world.

Sexual morality is one area particularly prone to hypocrisy. Inundated by sexual images, Viagra ads, and ubiquitous porn as well as by moralistic preaching and preening about fidelity, marriage, and “cheating,” we might be excused—at least sometimes—if we’re not sure how to avoid hypocrisy and achieve consistency. A similar example is the sometimes-futile attempt to reconcile libertarian beliefs, attitudes toward prostitution and feminism, (ir)religious convictions, and economic or political ideologies. If you dislike someone, you can probably find a rationale for a charge of hypocrisy; if you like that same person, you can probably find a way to describe his or her positions as nuanced and thoughtful.

We rightfully find hypocrisy repellent to varying degrees, but when we’re dealing with complex situations, we may also find it inevitable. Paraphrasing François de La Rochefoucauld, I think that hypocrisy is sometimes the homage that truthiness pays to truth.

Adapted from A Numerate Life: A Mathematician Explores the Vagaries of Life, His Own and Probably Yours.