Comment by godelski
5 days ago
> I don’t think it’s just (or even particularly) bad axioms
IME most people aren't very good at building axioms. I hear a lot of people say "from first principles" and it is a pretty good indication that they will not be. First principles require a lot of effort to create. They require iteration. They require a lot of nuance, care, and precision. And of course they do! They are the foundation of everything else that is about to come. This is why I find it so odd when people say "let's work from first principles" and then just state something matter of factly and follow from there. If you want to really do this you start simple, attack your own assumptions, reform, build, attack, and repeat.
This is how you reduce the leakiness, but I think it is categorically the same problem as the bad axioms. It is hard to challenge yourself and we often don't like being wrong. It is also really unfortunate that small mistakes can be a critical flaw. There's definitely an imbalance.
>> The smartest people I have ever known have been profoundly unsure of their beliefs and what they know.
This is why the OP is seeing this behavior. Because the smartest people you'll meet are constantly challenging their own ideas. They know they are wrong to at least some degree. You'll sometimes find them talking with a bit of authority at first but a key part is watching how they deal with challenging of assumptions. Ask them what would cause them to change their minds. Ask them about nuances and details. They won't always dig into those can of worms but they will be aware of it and maybe nervousness or excited about going down that road (or do they just outright dismiss it?). They understand that accuracy is proportional to computation, and you have exponentially increasing computation as you converge on accuracy. These are strong indications since it'll suggest if they care more about the right answer or being right. You also don't have to be very smart to detect this.
IME most people aren't very good at building axioms.
It seems you implying that some people are good building good axiom systems for the real world. I disagree. There are a few situations in the world where you have generalities so close to complete that you can use simple logic on them. But for the messy parts of the real world, there simply is not set of logical claims which can provide anything like certainty no matter how "good" someone is at "axiom creation".
I don't even know what you're arguing.
How do you go from "most people aren't very good" to "this implies some people are really good"? First, that is just a really weird interpretation of how people speak (btw, "you're" not "you" ;) because this is nicer and going to be received better than "making axioms is hard and people are shit at it." Second, you've assumed a binary condition. Here's an example. "Most people aren't very good at programming." This is an objectively true statement, right?[0] I'll also make the claim that no one is a good programmer, but some programmers are better than others. There's no contradiction in those two claims, even if you don't believe the latter is true.
Now, there are some pretty good axiom systems. ZF and ZFC seems to be working pretty well. There's others too and they are used to for pretty complex stuff. They all work at least for "simple logic."
But then again, you probably weren't thinking of things like ZFC. But hey, that was kinda my entire point.
I agree. I'd hope I agree considering my username... But you've jumped to a much stronger statement. I hope we both agree that just because there are things we can't prove that this doesn't mean there aren't things we can prove. Similarly I hope we agree that if we couldn't prove anything to absolute certainty that this doesn't mean we can't prove things to an incredibly high level of certainty or that we can't prove something is more right than something else.
[0] Most people don't even know how to write a program. Well... maybe everyone can write a Perl program but let's not get into semantics.
I think I misunderstood that you talking of axiomatization of mathematical or related systems.
The original discussion are about the formulation of "axioms" about the real world ("the bus always X minutes late" or more elaborate stuff). I suppose I should have considered with your username, you would have consider the statement in terms of the formulation of mathematical axioms.
But still, I misunderstood you and you misunderstood me.
3 replies →
If you mean nobody is good at something, just say that.
Saying most people aren't good at it DOES imply that some are good at it.