Ladders and impossibility clouds
2 min read

Ladders and impossibility clouds

This is niche topic but I want to write about it because it’s something that I’ve found useful. Syllogistic reasoning is sequential reasoning from premises to a conclusion, and it’s the type of reasoning most people use. For example:

  1. If the tax plan will increase jobs then it’s worth passing
  2. The tax plan will increase jobs
  3. Therefore it’s worth passing the tax plan

We can think of syllogistic reasoning as a ladder we climb towards a conclusion. I prefer to use a variant of syllogistic reasoning, which I’ll call ‘impossibility clouds’. To use impossibility reasoning, you take every premise in an argument like the one above and you negate the conclusion and put it all into a set. If the original argument was valide, this is a set of things that you can’t have: you can’t have all of the premises and also have the negation of the conclusion.

In other words, the argument above is saying that the following is an impossibility cloud (we’re not reasoning sequentially so the order doesn’t matter):

  • It’s not worth passing the tax plan
  • If the tax plan will increase jobs then it’s worth passing
  • The tax plan will increase jobs

If you can look at this set and see some way to make all of the things in it true then you know that the original argument is invalid. If you notice that the member of the set you find least plausible is one of the original premises then you can pick that out and argue against the original argument, e.g. arguing that the argument above is unsound because it's not true that if the tax plan will increase jobs then it’s worth passing. In doing so, you've identified your point of disagreement with the original author. ("Actually, I don’t agree that if the tax plan will increase jobs then it’s worth passing - that’s only true if the cost per job created isn’t too high.")

This might seem like a very minor adjustment, especially in an example this simple, but I find it much easier to work with impossibility clouds than with sequential arguments. I also like presenting arguments as impossibility clouds because it lets people explicitly see the trade-offs they have to make. Underneath it all, arguments are just statements of the form "you can’t have all of these things". I think it’s good to present them as such and make your case, but let your reader decide what they want to give up.