Are you following the rules of life?

Imagine you’re out with some friends and you have to, for whatever reason, add up two numbers: 432 and 222. It’s easy, you think! You were great at calculus in school, and you won’t even need to get out your phone. In a confident voice, you say, “Oh, that’s 654.”

There’s a pause as everyone looks at you oddly. “You serious?” someone says. Of course you are. That’s how addition works, right?

Or is it? According to Saul Kripke, how do you know that you’re doing addition correctly?

The games people play

In everyday life, we all follow a series of rules, whether we know it or not. These can be the rules of etiquette, like “don’t burp in public” or “don’t cook fish in the office microwave,” but there are also unspoken rules that apply to our use of words and concepts. For instance, consider the words “anxious” and “scared.” The two are similar but there are also very specific rules for when we cannot use them interchangeably.

Sociologists, anthropologists, and linguists have varying names for these rules, but Austro-British philosopher, Ludwig Wittgenstein, called them our “form of life.” Although the term is a bit ambiguous, it’s taken to mean those rules that we accept to go about our public interactions. They’re a bit like the rules of a game before everyone plays — “don’t pick up the ball” or “start running when you hear the gun.”

We all belong to various forms of life, which give us the values we have and the language we use (which in turn influences how we think). It might be, for instance, that your family has a very particular word for the remote control that other families find odd. Or a certain country might have cultural norms that others do not. It’s curious how Scandinavians tend to eat their evening meal around 4 or 5pm, while Spaniards eat nearer 9 pm.

Let’s return to the opening example. Mathematics is no different. There are certain rules we have to learn and understand, and then we apply them to new situations. We have axioms, parameters, operators, coefficients, and so on, all of which constitute the “form of life” of mathematics.

Do any of us know what we’re doing?

Kripke was a card-carrying Wittgensteinian. He argued that while we go about applying these rules all the time, he raised the question of whether we can ever be entirely sure that we’re applying them correctly.

For example, if a child or a non-native speaker is learning a language, they will often be corrected by competent speakers. In fact, it’s important that they are corrected so that they can, themselves, become the ones who will enforce those rules later. As a speaker learns the proper rules of a language, they will recalibrate what Kripke calls their “rule following consideration.” And yet, it’s quite conceivable that someone could misunderstand a word, but use it correctly all the time, by luck, perhaps.

In my own case, I remember using the word “reprehensible” quite correctly for a long time, thinking it meant one (slightly off) thing. I was simply lucky enough to use the word only in the contexts that fit my understanding. I was never “caught out.” Most adults have a vocabulary of around 30,000 words, and most haven’t taken the time to look up even a fraction of those. And, even if you did, what would that prove? Lexicographers are always playing catch up — words morph and evolve as well as die, and new ones are born every day.

But, this skepticism is not limited to words. It applies, too, to things like mathematics. No one is ever shown “addition.” What happens is that we’re given a list of discrete examples of addition at work and are expected to just understand. We say, “2+2=4, 4+3=7, 9+7=16. You got it yet? Good, now go and do that on your own.”

A teacher or a group of people competent at math might correct us as we’re finding our feet, but it’s a wonder how we latch on to the principle of addition. And then we assume that we’re doing it right all along.

But what if addition isn’t what you think it is? In the opening example, what if addition works differently if the second addend is three repeated numbers? What if addition works differently after you reach a certain number? It might be that you’ve just never encountered this before.

I don’t care — it just works

There are some Wittgensteinians who think Kripke misses the point. They argue that when you are part of a form of life, or when you wholesale accept a system of rules, part of doing that means that you don’t question it. When you play chess you don’t spend all your time asking, “But why do the knights move this way? It makes no sense!” You just play the game.

Likewise, when we speak to each other, we’re not crippled by doubt that we might be choosing the wrong word. We just assume that we’re right and get on with it. So, too, with Kripke’s “rule following considerations.” To understand a rule is to accept it, not to doubt it. Addition is no different.

But, that being true, it’s still an interesting thought: How do you know that you’re doing anything properly? We all think that we’re competent and intelligent, but what if we’re just monumentally lucky? What if one day, we’re exposed as poseurs?

Jonny Thomson teaches philosophy in Oxford. He runs a popular Instagram account called Mini Philosophy (@philosophyminis). His first book is Mini Philosophy: A Small Book of Big Ideas