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A Holiday gift for someone thoughtful in your life? Consider the New York Times Best-selling graphic novel Logicomix. It’s a beautiful story about the death of the 2,400-year-old dream of creating a system of logic that wasn’t founded on the shaky ground of intuitive assumptions. The central character is Bertrand Russell. Though he failed, his Herculean effort did contribute to the invention of the computer.

It also led to mathematician Kurt Godel’s major revelation: It wasn’t just Bertie’s logic system that failed. No matter how they’re built, any and all systems of logic will be built on shaky unprovable intuitions. In other words, it is possible to build great sturdy towers of thought, but they’ll all have loose foundations.

The philosopher Richard Rorty applies this to everyday life. If some smart alec responded to every assertion you made by asking “yes, but why?”, within the limits of your patience you could reason your way to answers:

Why do you work?
Because that’s how I earn a living.
Why do you earn a living?
Because that’s how I pay for the things I need and want.
And why do you pay for the things you need and want?
Because it’s good to have them.
And why is it good to have them?

At some point you would be unable to explain. Your response would be tautological, in other words circular, where the answer is just a restatement of the question: “It’s good because it’s good!”

Rorty calls this your “final vocabulary.” At the edge of your powers of explanation, you’ve got no logical traction. What you say is unfounded and yet final. All you can say is, “It just is.”

With Godel’s discovery of logic’s limits, a final vocabulary isn’t optional. We all have one. Every great scientific theory has one.

Our thoughts and conversations are thus like explorations around an expanse of blacktop surrounded on all sides by sand. We have traction up to the edge, but if we go over our wheels spin.

In this context, a debate can become like a game of chicken, with two people trying to drive each other off the edge. The smart alec asks question after question until you fall onto your final vocabulary. She can then say, “Look at you. You’re a joke. You believe things without a strong foundation. You’re making assumptions!”

Socrates is remembered as a humble, inquiring man but he famously confronted self-certain Athenians with their own final vocabularies. By question alone he drove his fellow citizens into the sand.

A few of his students became infamous smart alecs. By imitating Socrates, they made others look dumber and themselves look smarter. Two ended up with so much confidence in their own assumptions they became tyrants.

Socrates himself meant well. He believed that with more inquiry comes more careful thought. Inquiry is how you build out the blacktop to where you have traction everywhere in all directions. When I say that the dream of building a system of logic not founded on shaky ground is 2,400 year-old, I’m dating it to Socrates.

And now that dream is dead.

But the smart alec isn’t. Plenty of people still use what I’ll call the ad laxus (against the looseness) fallacy: It’s the smart alec’s fallacious assumption that because she can drive you into your own traction-less final vocabulary, her own reasoning must be solid.

You’ve got to watch out for that. Don’t let anyone take you down saying, “You don’t know that for sure.” No one knows anything for sure.

And as with all fallacies, this one has an opposite: Just because nothing can be known for sure, it doesn’t necessarily mean your assumptions are as good as hers. In my next article I’ll suggest a way of thinking about how to evaluate ideas given that they’re all bordered by sand.

In the mean time here’s a quick exercise for reducing your own potential for exploiting the ad laxus fallacy.

There’s a fabled Jewish village called Chelm inhabited by numbskulls. The tradition is to laugh not at, but with these numbskulls because they are us. We are all satisfied with unsatisfactory answers. To help inoculate yourself against the ad laxus fallacy, read about these Chelmites stuck in the sand. It’s about you, me and all of us.

A group of citizens in the town of Chelm were busily engaged in digging a foundation for the new synagogue, when a disturbing thought occurred to one of the laborers.

“What are we going to do with all this earth we’re digging up? “ he asked. “We certainly can’t just leave it here where our Temple will be built.”

There was a hubbub of excitement as the men rested on their spades and pondered the question. Suggestions were made and just as quickly rejected.

Suddenly one of the Chelmites smiled and held his hand up for silence.” I have the solution,” he proclaimed. “We will make a deep pit, and into it we’ll shovel all the earth we’re digging up for the synagogue!”

A round of applause greeted this proposal until another Chelmite raised his voice in protest.” That won’t work at all! What will we do with the earth from the pit?”
There was a stunned silence as the men tried to cope with this new problem, but the first Chelmite soon provided the answer.

“It is all very simple,” he said. “We’ll dig another pit, and into that one we’ll shovel all the earth we’re digging now, and all the earth we take out of the first pit. The only thing we must be careful about is to make the second pit twice as large as the first one.”

There was no arguing with this example of Chelmic wisdom, and the workers returned to their digging.