We probably underestimate the value of improving our arguments, and are overconfident in apparently-solid logical arguments. What can you do to improve a complex argument?
If an argument contains 20 inferences in sequence, and you’re wrong about such inferences 5% of the time without noticing the misstep, then you have about a 64% chance of being wrong somewhere in the argument. If you can reduce your chance of mistakes to 1% per inference, then you only have an 18% chance of being wrong, somewhere. Improving the reliability of the steps in your arguments, then, has a high value-of-information – even though 1% and 5% both feel like similar amounts of uncertainty.
So, if being wrong about an argument is highly costly – if you would stand to lose by believing incorrectly, or win by believing correctly – then it is well worth spending some real effort to ensure that long arguments are correct, before you act on them. This is even true if that argument appears to be very solid, and hangs together tightly.
Writing an argument in detail is a good way to improve the likelihood that your argument isn’t somewhere flawed. Consider:
- Writing allows reduction. By pinning the argument to paper, you can separate each logical step, and make sure that each step makes sense in isolation.
- Writing gives the argument stability. For example, the argument won’t secretly change when you think about it while you’re in a different mood. This can help to prevent you from implicitly proving different points of your argument from contradictory claims.
- Writing makes your argument vastly easier to share. Like in open source software, enough eyeballs makes all bugs trivial.
So, if you can spot non-sequiturs in your writing, and you put a lot of weight on the conclusion it’s pointing at, it’s a really good idea to take the time to fill in all the sequiturs.