So here’s an interesting example of what I mean. I woke up this morning and realised that there is indeed a rather strong refutation of my binary chop argument below, namely “don’t bother, just use X+Y - one doesn’t need to take exactly the minimum amount of time needed, only enough".I object to the concept of a "strong refutation". I don't think there are degrees or quantities of refutation.
A reason "strong refutation" seems to make sense is because of something else. Often what we care about is a set of similar ideas, not a single idea. A refutation can binary refute some ideas in a set, and not others. In other words: criticisms that refute many variants of an idea along with it seem "strong".
People have some ability to guess whether it will be easy or hard to proceed by finding a workable close variant of the criticized idea. And they may not understand in detail what's going on, so it can seem like a hunch, and be referred in terms of strong or weak criticism.
- Refuting more or fewer variant ideas is different than degrees of strength. Sometimes the differences matter.
- Hunches only have value when actually there's some reasonable underlying process being done that someone doesn't know how to put into words. Like this. And it's better to know what's going on so one can know when it will fail, and try to improve one's approach.
- People can only kinda estimate the prospects for CLOSE variants handling the criticism and continuing on similar to before. This gives NO indication of what may happen with less close variants.
- This stuff is pretty misleading because either you're aware of a variant idea that isn't refuted, or you aren't. And you can't actually know in advance how well variants you aren't aware of will work.
But consider: yesterday I came up with the binary chop argument and it intuitively felt solid enough that I thought I’d spent enough time looking for refutations of it by the time I sent the email. I was wrong - and for sure I’ve been wrong in the same way many times in the past. But was I wrong to be sure enough of my argument to send the email? I’d say no. That’s because, as I understand your definition of a refutation, I can’t actually fix on a finite Y, because however large I choose Y to be I can always refute it by a pretty meaningful argument, namely by reference to past times when I (or indeed whole communities) have been wrong for a long time.There are never any guarantees of being correct. Feeling sure is worthless, and no amount of that can make you less fallible.
We should actually basically expect all our ideas to be incorrect and one day be superseded. We're only at the BEGINNING of infinity.
The ways to deal with fallibilism are doing your best with your current knowledge (nothing special), and also specifically having methods of thinking which are designed to be very good at finding and correcting mistakes.
You've acknowledged your approach having some flaws, but think it's good enough anyway. That seems contrary to the spirit of mistake correction, which works best when every mistake found is taken very seriously.
I realize you also think something like one can't do better (so they aren't really flaws since better isn't achievable). That's a dangerous kind of claim though, and also important enough that if it was true and well understood, then there ought be books and papers explaining it to everyone's satisfaction and addressing all the counter-arguments. (But those books and papers do not exist.)
Since we agreed some time ago that mathematical proofs are a field in which pure CR has a particularly good chance of being useful,I consider CR equally useful in all fields. Substitute "CR" for "reason" in these sentences – which is my perspective – and you may see why.
I direct you to the example of the “Lion and Man” problem, which was incorrectly “solved” for 25 years. It seems to me that the existence of cases where people can be wrong for a long time constitutes a very powerful refutation of the practicality of pure CR, since it means one cannot refute the argument that there is a refutation one hasn’t yet thought of. Thus, we can only answer “yes stop now” in finite time to "Have I done enough effort? Should I do more effort or stop now?” if we’ve already made a quantitative (non-boolean), and indeed subjective and arbitrary, decision as to how much risk we’re willing to take that there is such a refutation.The possibility of being mistaken is not an argument to consider thinking about an issue indefinitely and never act. And the risk of being mistaken, and consequences, are basically always unknown.
What one needs to do is come up with a method of allocating time, with an explanation of how it works and WHY it's good, and some understanding of what it should accomplish. Then one can watch out for problems, keep an ear open for better approaches known to others, and in either case consider changes to one's method.
This is a general CR approach: do something with no proof it will work, no solidity, no feeling of confidence (or if you do feel confidence, it doesn't matter, ignore it). Instead, watch out for problems, and deal with them as they are found.
And here is a different answer: You cannot mitigate all the infinite risks that are logically possible. You can't do anything about the "anything is possible" risk, or the general risks inherent in fallibility. What you can do is think of specific categories of risks, and methods to mitigate those categories. Then because you're dealing with a known risk category, and known mitigation methods – not the infinite unknown – you can have some understanding of how big the downsides involved are and the effectiveness of time spent on mitigation. Then, considering other things you could work on, you can make resource allocation decisions.
It's only partially understood risks that can be mitigated against, and it's that partial understanding that allows judging what mitigation is worthwhile.
Continue reading the next part of the discussion.