You shouldn’t take this post as a dismissal of intuition, just a reminder that intution is not magically reliable. Generally, intuition is a way of saying, “I sense similarities between this problem and other ones I have worked on. Before I work on this problem, I have some expectation about the answer.” And often your expectation will be right, so it’s not something to throw away. You just need to have the right degree of confidence in it.
Often one has worked through the argument before and remembers the conclusion but not the actual steps taken. In this case it is valid to use the memory of the result even though your thought process is a sort of black box at the time you apply it. “Intuition” is sometimes used to describe the inferences we draw from these sorts of memories; for example, people will say, “These problems will really build up your intuition for how mathematical structure X behaves.” Even if you cannot immediately verbalize the reason you think something, it doesn’t mean you are stupid to place confidence in your intuitions. How much confidence depends on how frequently you tend to be right after actually trying to prove your claim in whatever area you are concerned with.
Luke, I thought this was a good post for the following reasons.
(1) Not everything needs to be an argument to persuade. Sometimes it’s useful to invest your limited resources in better illuminating your position instead of illuminating how we ought to arrive at your position. Many LWers already respect your opinions, and it’s sometimes useful to simply know what they are.
The charitable reading of this post is not that it’s an attempted argument via cherry-picked examples that support your feeling of hopefulness. Instead I read it as an attempt to communicate your level of hopefulness accurately to people who you largely expect to be less hopeful. This is an imprecise business that necessarily involves some emotional language, but ultimately I think you are just saying: do not privilege induction with such confidence, we live in a time of change.
It might quell a whole class of complaints if you said something like that in the post. Perhaps you feel you’ve noticed a lot of things that made you question and revise your prior confidence about the unchangingness of the world...if so, why not tell us explicitly?
(2) I also see this post as a step in the direction of your stated goal to spend time writing well. It seems like something you spent time writing (at least relative to the amount of content it contains). Quite apart from the content it contains, it is a big step in the direction of eloquence. LWers are programmed to notice/become alarmed when eloquence is being used to build up a shallow argument, but it’s the same sort of writing whether your argument is shallow or deep. This style of writing will do you a great service when it is attached to a much deeper argument. So at the least it’s good practice, and evidence that you should stick with your goal.