Rhetorica:
The Fourth Ditch of Fraud
By Gabriel Blanchard
Mark Twain is known for having said that "There are three kinds of lies: lies, damned lies, and statistics."
A Virgilian Admonition
Speaking of the damned, in the Inferno, the ghost of the Roman poet Virgil guides the still-living Dante through hell, showing him the punishments of the damned—that is, he shows him their sins, experienced without illusion. In the eighth of hell’s nine circles, simple fraud1 is punished, under ten subdivisions contained in distinct bowges (meaning ditches or pockets). As the title indicates, it is with the fourth that we are momentarily concerned; this is the part of hell in which sorcerers, oracles, and diviners are punished.
When they reach the bowge full of those who tried, by methods either ridiculous or horrific,2 to foresee the future—and, thus, to pervert the free will of others and escape the sovereignty of God—Dante sees that their heads have been twisted around to face backwards. He is horrified, but Virgil warns him (as Sayers renders it), “Here pity, or here piety, must die”. In other words, one must do exactly one of two things: Stand with the holiness of God and the dignity of one’s fellow man, which sorcery tries to violate for person gain; or, feel sorry for the poor sorcerers who are enduring nothing they did not try to inflict on the rest of mankind.
Anyway, this post is part of our larger discussion of induction as an element in rhetorical logos. We dealt with the scientific method last week; this post is about probability and statistics.
More Like “Problem-bility”
Probability has some strange qualities—and we’re not even going to get into the math. It is one of those fields that, on analysis, seems like an impossibly stupid thing for any sane person to pursue … and yet every one of us lives by making (at minimum) probabilistic judgments about nearly everything, every day.
The topic has come up at the Journal before, in our series on fallacies, when we discussed the famous puzzle colloquially known as the Monty Hall problem. In the name of credibility, however, let us begin with a professional: the late Bruno de Finetti, an Italian actuary born in Austria-Hungary (which he outlived by sixty-six years). He wrote the following in his 1970 book, Theory of Probability.
My thesis, paradoxically, and a little provocatively, but nonetheless genuinely, is simply this:
PROBABILITY DOES NOT EXIST.
The abandonment of superstitious beliefs about the existence of phlogiston …, or fairies and witches, was an essential step along the road to scientific thinking. Probability, too, if regarded as something endowed with some kind of objective existence, is no less a misleading misconception, an illusory attempt to exteriorize or materialize our true probabilistic beliefs.
This is not too difficult to work out for ourselves, really. Probabilities are calculated in three circumstances, and three circumstances only:
- When we are discussing what will—to be more exact, what may—happen in the future.
- When we are discussing things already past or present, but about which we have incomplete information.
- When we are discussing hypothetical events that may never happen, are not happening, and have not happened (as far as we know).
Rephrased, 1 and 2 are circumstances in which we have incomplete information, while 3 has only a tenuous relationship to reality itself. Probability is an attempt to balance out, or cope with, our own ignorance; it does not study things in themselves, but what we know about them. It tries to quantify exactly how ignorant we are—except really, it doesn’t even do that, for you only use it when your topic is unknown or unknowable. Really, what probability tells us is how ignorant we should feel.
Surprisingly, this does not necessarily mean probability is a useless concept. It is based on the assumptions that the future will resemble the past, and that the more consistently we have observed something thus far, the more likely that same thing is to occur (at least under similar circumstances) in the future. To be fair, this assumption does seem reasonably sound.
So far.
O Fortuna velut luna
statu variabilis,
semper crescis aut decrescis;
vita detestabilis
nunc obdurat et tunc curat
ludo mentis aciem,
egestatem, potestatem
dissolvit ut glaciem.
Lady Fortune, like the Moon
dost thou change and change thy tune,
wax or wane, forever strife.
Lo, this is a loathsome life,
now 'tis cruel, then softens o'er
playing with the mind's self-war;
poverty and power as one
Fortune melts, like ice the Sun.
Think About Thirty-Seven Elephants
But let’s talk about statistics. It shares a certain more or less indispensable usefulness with probability, and indeed, the former is a chief tool used by students of the latter; yet both fields are afflicted with similar epistemological problems that make them tricky to use well, on any but the simplest questions.
Statistics can be regarded either as a science or as a branch of mathematics. Descriptive statistics is the more strictly mathematical type; it records and analyzes data points and discerns strictly factual relationships among them.4 Inferential statistics is the other branch, more resembling experimental science, in that it hopes to draw conclusions about how things work—not only to record facts, but to advance theories that explain the facts.
Consider Hannibal’s herd of thirty-seven elephants (if for some reason you weren’t already). Descriptive statistics will tell us, for example what the mean height of these elephants is—say, 220 cm. To please statisticians and make our own jobs easier, we shall assume a normal distribution of height among said elephants, which means that if you plot their heights on a graph, they more or less form a bell curve.
In analyzing normal distributions, another key term is the standard deviation. Again, we aren’t getting into the nitty-gritty; for our purposes, what matters is that this defines what we might call “normal amounts of abnormality” (if we have our hearts set on glibness). If we also know the standard deviation in height among these elephants, then we can make two predictions: first, whether the elephants are mostly similar or quite variable in height; and second, what the range of difference among them is likely to be. If the heights of thirty-seven elephants have a standard deviation of one centimeter, then most of them are either 220 cm tall or within a centimeter of that height; if, however, the standard deviation is eighty centimeters, then Hannibal apparently has some wooly mammoths and some teacup elephants on his hands.5
The Statistician in the Room
Inferential statistics, on the other hand, try to draw conclusions about causality based on statistical studies. Of course, one of the very few statisticians’ maxims familiar to a much broader public is that correlation does not prove causation, and any statistician worth her salt knows this. This is often why statisticians tend to be so hesitant to say things in categorical, simple terms, and so frequently urge further study of a problem—they don’t want their expertise misinterpreted or misused. A single statistical study practically never demonstrates the truth or falsehood of a theory; dozens, even (if practicable) hundreds, are preferable.
Now, the sharp reader will note that even in discussing the descriptive branch we assumed a normal distribution; he may then have wondered whether there are also abnormal distributions. There are. Sometimes, discovering that your data set is abnormally distributed tells you that your sample is flawed, and probably does not represent the world in general. On the other hand, it may be telling you that you’ve run into a different kind of pattern. A normal, i.e. bell-curved, distribution of “elephants that are still alive after being kept underwater for a week” would be extremely confusing and somewhat worrisome (if only because elephants never forget and you’ve just kept some of them underwater for a week, which they can’t have enjoyed). The distribution that would be normal to find, on the other hand, would be a flat line rather than a bell curve; in its way, this would be telling you something, albeit something you knew already—elephants need to breathe.
With Virgil, Hand in Hand
This in turn illustrates one of the difficulties about statistics: In order to analyze them properly, you often need to have some notion of what you’re going to discover. As probability is largely a measurement of our own ignorance, statistics is largely a rearrangement of things we knew already.
Again, this does not mean that these fields have no uses, or no honest uses. It does mean that they’re extremely difficult to use without training. It also means they are apt to throw a lot of abrupt and bizarre, if not downright paradoxical, obstacles in your intellectual path.
The great point here is simply this. If you’re going to use these disciplines to try and learn anything worth knowing, do yourself a favor and study them. Don’t take your statistics from the news; even honest journalists are forced, by the marketing demands of their profession, to leave out nearly all of the context that gives these numbers their significance—and not all journalists are honest. Learn how to reason properly; you can do it, and there’s a great deal at stake.
A great place to start, as it happens, is a book on statistics by a pair of journalists—The Tiger That Isn’t: Seeing Through a World of Numbers, by Michael Blastland and Andrew Dilnot. However, they’re Brits, so it may be a little while before it arrives; in the meantime, BBC Bitesize has an excellent guide to elementary probability reasoning right here.
1“Fraud Simple” contrasts with “Fraud Complex,” or treachery. The latter preys on the good will of those who had a special reason to trust us (family members, guests, etc.); the former preys merely on the good will and trust of humanity in general.
2Or at any rate, this was the opinion of the Medieval Church, which on the whole found the same things vile that we do, and found other sorceries ridiculous because she maintained pretty firmly that magic was not real. If this prompts you to wonder why, if the Church felt that way about it, she burned all those witches, the answer is that she didn’t. Executions for witchcraft were in truth quite uncommon in the Middle Ages; they were, rather, an overwhelmingly Early Modern (sixteenth to seventeenth century) phenomenon. By the time we reach executions like those of St. Joan of Arc and Gilles de Rais, the Medieval period is coming to an end.
3Carmina Burana means “songs from Buria.” Buria is the Latin name of Benediktbeuern, a Bavarian city very close to the border with Austria which has been home to a Benedictine monastery since the mid-eighth century; though famed for the dramatic musical setting to which they were put by Carl Orff, which premiered in 1937, most of the poems are about everyday matters—many are drinking songs.
4For instance, it is strictly factual that ice cream consumption and the murder rate are correlated. Theories about why this is the case (including the theory “for no reason”) properly belong to the other branch of statistics, and of course to other sciences, e.g. thermodynamics and psychology.
5You’re telling me you’ve never heard of teacup elephants? Next you’ll be saying you suspect me of inventing them myself for purposes of philosophic illustration. Bless me, what do they teach children in these schools …
An uncle to seven nephews, Gabriel Blanchard has a baccalaureate in Classics from the University of Maryland, College Park. He serves as CLT’s staff writer and editor at large; he lives in Baltimore, MD.
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Published on 22nd May, 2025. Page image of a sketch by Gustave Doré, illustrating the fourth bowge of the Eighth Circle.