Induction-blindness

There's a particular trap I fall into at times, particularly when I've agreed or planned to do something without really thinking the consequences through. What happens is I intend to, say, reply to an email, but I don't intend to reply to it right now. However, later on I still don't intend to reply to it right now. In fact, through a series of decisions to not do the action now, I don't do it at all, and all the while I'm still convinced that I'll do it. I call this paradoxical state of affairs induction-blindness.

Induction, in the mathematical sense, was best described to me as a three-step dance as follows: if I eat one banana [1], and every time I eat a banana I eat another banana [n->n+1], then I will eat all the bananas [all n]. It's a kind of sister to recursion, in the sense that you can build a proof for any n by recursively applying the second step. What makes induction interesting is that it's more than just repeatedly applying that step, it's a proof from the fact that you could. In a sense it's a kind of meta-proof, a statement about the system itself.

So, applied to a goal, induction-blindness is a failure to go meta. It's thinking about the goal and the steps, but not realising that your system for getting to the goal from the steps doesn't work. If I don't feel like replying now [1], and later I'll still feel like I do now [n->n+1], then I will never write the email [all n]. Despite those steps being trivial and obvious, I often miss that crucial step and fail to induct appropriately.

Perhaps this is an inevitable weakness caused by the mismatch between formal logic and fleshy brain reasoning, but I still think there are ways to recognise it. Most crucial is the inductive step, the n->n+1. Notice that it is perfectly reasonable to put off the email if I'm currently being eaten by an alligator. Trying to write an email then would be distracting and counterproductive. But the difference is that the alligator situation doesn't recurse. There's no reason to think that one alligator attack will mean another alligator attack, unless you're some kind of alligator farmer or in one of those infinite Greek mythological punishments.

The key, then, is to recognise when a situation is self-perpetuating in that same way. Induction-blindness is caused by the mistaken belief that change means difference. But if tomorrow is going to be the same as today, then anything you don't do today you're not going to do ever.