Some explanations require a lot of text. You want to say something simple, such as “a security model built on distrust amongst its users doesn’t really make you feel secure, instead you transfer trust to a set of machines and regulations, and the people responsible for them, instead of taking it into your own hands. Taking it into your own hands requires feedback loops, openness, the ability of the infrastructure to adapt to all its user instead of just a chosen few, and so on.”

And somebody will come and think: What was this guy thinking? It makes no sense at all!

And you’ll have to start digging deeper. Explain what you mean by security. Talk about passwords, and audit trails, delegations of responsibility, and so on. Basically you’re making an argument, that rests on the shoulders of more arguments that you will also have to make. And they in turn, rest on other points you will have to make. It’s a pyramid! It’s what we call the “argument pyramid”.

On a Wiki

The way to structure an argument pyramid on a wiki is by creating various pages. Start with the first page, and make links to issues you want to explain on a separate page for those who need more explanations. Try to make a small number or even just one important point per page. Move the underlying arguments out to supporting pages.

If you pick interesting names for the pages where the underlying arguments are, then you can reuse them by linking to them from elsewhere!

The net result is what we call a LinkLanguage: Concepts have pages of their own, and names of their own, and you can reuse them by simply writing their name. The result will be a link to their full text, allowing everybody to skim or to drill down.

Longer explanation

Arguments, explanations, stories, rest on a base, a ground, a substrate.

By “argument,” here, we don’t mean two people fighting.

What we mean is just about any explanation, reasoning, rational, or story. 1

Arguments are made of ThoughtChunks. Here’s one: “The reason you pay for gas, is because we believe in treating people fairly.”

But those ThoughtChunks are composed of simpler parts. “We need gas to drive our car. Fair is treating people equitably. Someone went to the work to bring us the gas, and so we want to give them something, to respond in kind.”

Those ThoughtChunks are composed of still simpler parts. “Cars move because the engine drives them. The engine runs on gasoline. One part of fairness is egalitarianism: When you consider people equal, then you don’t want one person to gain at another’s expense. It takes work and exposure to risk to set up a gas station.”

You can keep going down, down, down, answering the little kid’s “Why, Why, Why?”

The top of the pyramid is the short explanation of the whole story: “The reason you pay for gas, is because we believe in treating people fairly.” The middle of the pyramid is the support for that, and the base of the pyramid is the support for the supports.

(And so on, and so forth: The pyramid can just keep going down.)

If you have something you’re saying, then the thing and all the things beneath it are, together, can be called: “The argument pyramid.”


When someone says an argument that you disagree with, then you can undercut the argument.

The way you do that, is that you expose a difference in one of the underlying elements- something that people (whoever you are trying to persuade) will find persuasive.

How will it be persuasive? It will be persuasive if the listener thinks it’s better supported than the other story.

Undercuts can themselves be undercut.

The kind of reasoning where people present arguments and counter-arguments (undercuts) and then counter-counter-arguments (undercuts to the undercuts) is called “defeasible reasoning.”

See also: this great explanation from an Economics textbook, and perhaps this Defeasible Reasoning pge from Stanford.

We also talk about defeasible reasoning on “PersuasiveContent.”


A mathematical theorem, provided that it is correct and that the axioms are accepted, is a special kind of argument.

If the axioms are accepted, and if the rules of logic are accepted, and if the logic is correct (without flaw,) then the conclusion of the mathematically formed argument must be accepted.

A theorem may have a structure that looks like this:

If you can find a flaw in the logic of the Lemma, then you can show that the top level stuff is not proven. Note that: Sometimes, someone spots a flaw in a lemma. Then someone says, “Oh, wait- we can cover that case,” apply another lemma to complement it, patch up the top, and the whole thing still works. This may sound “dodgy,” but it’s really not: It’s just someone forgot to cross a “t” at the bank. The bank teller said, “wait, doesn’t your name have a ‘t’ in it?”, and then you said: “Oh, wait- that’s quite right,” and dashes the “t.”

Sometimes, though, someone spots what appears to be a minor problem in a lemma, and then they investigate it, and then they realize: “Oh no, this isn’t going to work at all,” and they have to retract the whole proof. It’s just wrong.

It’s actually possible to mathematically show that theorems are provably true, using special algebras. Then the question is: “Did the person carry out the algebra correctly?” You can submit the algebra to review before others, and they can hunt for mistakes. You can teach a machine to look for mistakes. You can teach a machine the steps to take, and have it perform the checks. There are all these verifying things you can do. But at the end of the day, basically, you can very rigorously prove these things, to any degree of certainty you want.

Finally, it’s possible that the axioms are just wrong. Those are the things that everyone agrees are true, at the bottom level of the pyramid. “Oops: The shortest distance between two points might not be a straight line between them!” Maybe our space has a curve to it, and it’s quicker to draw a line that walks around a steep mountain. If the surface (or space) you’re working on has a curve in it, you may need to play by some other rules.

non-mathematical argument The vast majority of the time, people are thinking about things that they are unable to mathematically prove (or mathematically disprove).

There may be some parts that they can prove, but they rely on something else to bring those parts together. We don’t know exactly what this “something” is, but around here we’ve been calling it “ThinkingGoo”.

See Also

CategoryReasoning CategoryInformationManagement


1. If we said “Little Red Riding Hood is going down the forest,” it’s a story, but not an argument, so I suppose there needs to be an element of trying to convince someone of something.

Define external redirect: LanguageInThoughtAndAction

EditNearLinks: ThoughtChunks