Implies both ways

I wrote a while back about the idea of the brain as an association machine. The main point I made then was that it makes disassociation very difficult, and it's hard for us to forget things or break existing habits. However, there's another aspect I've been meaning to write about, which is the way that association machines can (and can't) do logic.

Implication is a fairly foundational part of logic, and it's just statements of the form "if X is true, then Y is true", which you write X → Y. For example, you could write "all humans are mammals" as "human → mammal". However, it would be incorrect to assume that because all humans are mammals, then all mammals are humans. That is to say, X → Y doesn't mean Y → X. That's a different thing, sometimes called equivalence: rich people have lots of money, people with lots of money are rich, rich ↔ lots of money. This is also sometimes said to "imply both ways", and mixing up one-way and two-way implication is a very common error.

But why is it so common? It's not like we often confuse addition and subtraction, or up and down. And it's tough to imagine that an artificial intelligence, for example, would make the same mistake, even if it wasn't very clever. However, presented with a situation where every murderer plays videogames (murderer → gamer), there's no end of people lining up to say that gamer → murderer. As in that example, it has the distinction of being a very harmful and common mistake. So for us to keep making it there must be a fairly compelling reason.

My proposition is that the association machine doesn't do one-way implication. By its very nature, an association is two-way; if you hear about gamers and murderers together a lot, you don't intuitively tease out the causation there, you just think about one whenever you hear about the other. The main theory for why conditioning works is exactly this. If every time you get fed a bell is rung, you have food → bell, but for some reason that turns into food ↔ bell and you end up slobbering whenever a bell rings. Two-way implication is natural to our associative machinery.

This can sometimes have disastrous effects on your understanding of success. For example, if being a famous musician → going to parties and dressing like a rock star, that's a very different thing than being a famous musician ↔ going to parties and dressing like a rock star. If you mistakenly think the latter, you're going to spend a lot of time working on your dancing and wardrobe skills, and very little time working on music. Quite often the trappings of success can feel like real success, but easier.

Another popular one is acting as if something is true. Let's say you have to finish an assignment and then you won't have to think about it anymore. Finished assignment → not thinking about assignment, except... uh oh... finished assignment ↔ not thinking about assignment. Now if you ignore the assignment, it feels like you're done with it. Amusingly, things like acting as if you're confident in order to become confident do work, but only because you're tricking the very same two-way associative machinery in your own head.

But just because two-way implication is natural and intuitive doesn't mean we're doomed. Obviously people manage to use one-way implication both in and out of logic, it just takes a bit more effort to do. Maybe we can't rely on all our associations being rigorously constructed, but we can take the time to reason through the ones that are important and make sure we've got the right implication.