The Quantities of Everyday Language

Quantity is an ancient idea, so ancient that it appears at the core of every human language. Words like “less” and “every” are obviously quantitative, and lead to more complex concepts like “trend” and “significant.” Quantitative thinking starts with recognizing when you are talking about quantities.

Spot the quantitative ideas in this sentence from the article “Anti-Intellectualism is Killing America,” which appeared in Psychology Today:

In a country where a sitting congressman told a crowd that evolution and the Big Bang are “lies straight from the pit of hell,” where the chairman of a Senate environmental panel brought a snowball into the chamber as evidence that climate change is a hoax, where almost one in three citizens can’t name the vice president, it is beyond dispute that critical thinking has been abandoned as a cultural value.⁸

This is pure cultural critique, and we could take it many different ways. We could read this sentence as a rant, a plea, an affirmation, a provocation, a list of examples, or any other type of expression. Maybe it’s art. But journalism is traditionally understood as “nonfiction,” so let’s take this at face value and ask whether it’s true.

I see an empirical and quantitative claim at the heart of the phrase “critical thinking has been abandoned as a cultural value.” It’s empirical because it speaks about something that is happening in the world, something with observable consequences. It’s quantitative because the word “abandoned” speaks about comparing the amount of something at two different times. Something we never had can’t be abandoned.

For at least two points in time we need to decide whether or not “critical thinking is a cultural value.” This is the moment of quantification. “Abandoned” might have an all-or-nothing flavor, but it’s probably a lot more reasonable to define shades of gray based on the number of people and institutions that are embodying the value of critical thinking; or perhaps it makes sense to look at how many acts of critical thinking are occurring. Of course “critical thinking” is not an easy thing to pin down but if we choose any definition at all we are literally deciding which things “count” as critical thinking. The next step is to come up with a practical plan to count those things. If we can’t or won’t count in practice, there’s no quantitative way to test this claim against reality. It’s not that the sentence would then mean nothing, it’s just that its meaning couldn’t be evaluated by comparing the words with the world in a yes/no kind of way.

One way or another, testing the claim that “critical thinking has been abandoned as a cultural value” demands that we count something at two different points in time and look for a drop in the number. There are surely fights waiting to happen over what should be counted, whether it was correctly counted, and the numerical threshold for “abandoned.” But if you’re willing to make some choices, you can go out and find relevant facts. This is what the author’s given us:

• a sitting congressman told a crowd that evolution and the Big Bang are “lies straight from the pit of hell”

• the chairman of a Senate environmental panel brought a snowball into the chamber as evidence that climate change is a hoax

• almost one in three citizens can’t name the vice president

Even if these were all good examples of a failure of “critical thinking,” they still wouldn’t be good evidence for the idea that critical thinking has been abandoned. The problem is that the author is trying to say something about a very large group of people. These examples would need to be representative. Are these failures of critical thinking typical of the whole society? It seems just as easy to come up with counterexamples. Yeah, someone brought a snowball into Congress to argue against climate change, but the EPA also recently decided to start regulating carbon dioxide as a pollutant. That’s evidence against the representativeness of the author’s examples, but of course you could dig up a million more examples on each side. That’s where counting gets interesting: it’s a systematic way to grasp the whole of something, which can lead to much stronger statements.

That’s the logic behind historian G. Kitson Clark’s advice for making generalizations:

Do not guess; try to count. And if you cannot count, admit that you are guessing.⁹

The fact that “one in three citizens can’t name the vice president” is closer to the sort of evidence we need. This statement generalizes in a way that individual examples can’t, because it makes a claim about all U.S. citizens. It doesn’t matter how many people I can name who know who the vice president is, because we know (by counting) that there are 100 million who cannot. But this still only addresses one point in time. Were things better before? Was there any point in history where more than two-thirds of the population could name the vice-president? We don’t know.

In short, the evidence in this sentence is not the right type. The word “abandoned” has embedded quantitative concepts that are not being properly handled. We need something tested or measured or counted across the entire culture at two different points in time, and we don’t have that—none of which makes this a “bad” piece of writing. It might provoke the reader to think about the value of critical thinking. It might be emotionally resonant. It might draw attention to important examples. It might even be persuasive. Whether it’s good or not depends on what you want it to do. But in terms of empirical claims and the evidence provided for them, this is a weak argument. It doesn’t respect the quantitative structure of the language it uses.

Many words have quantitative aspects. Words like “all,” “every,” “none,” and “some” are so explicitly quantitative that they’re called quantifiers in mathematics. Comparisons like “more” and “fewer” are clearly about counting, but much richer words like “better” and “worse” also imply counting or measuring at least two things. There are words that compare different points in time, like “trend,” “progress,” and “abandoned.” There are words that imply magnitudes such as “few,” “gargantuan,” and “scant.” A series of Greek philosophers, long before Christ, showed that the meanings of “if,” “then,” “and,” “or,” and “not” could be captured symbolically as propositional logic. To be sure, all of these words have meanings and resonances far beyond the mathematical. But they lose their central meaning if the quantitative core is ignored.

We’re really taking language apart here, and no one could make it through a day if they had to fact check every sentence they read. Also, there are other ways of relating to a story. But this is a way of seeing that every journalist should have in their toolbox—and pass on to readers when helpful. The relation between words and numbers is of fundamental importance to the pursuit of truth. It tells you when you should be counting something.