| > 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. |
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| ▲ | godelski 7 days ago | parent [-] | | I don't even know what you're arguing. > you implying that some people are good building good axiom systems
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. > there simply is not set of logical claims which can provide anything like certainty no matter how "good" someone is at "axiom creation".
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. | | |
| ▲ | joe_the_user 7 days ago | parent | next [-] | | 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. | | |
| ▲ | godelski 7 days ago | parent [-] | | > you talking of axiomatization of mathematical or related systems.
Why do you think these are so different? Math is just a language in which we are able to formalize abstraction. Sure, it is pedantic as fuck, but that doesn't make it "not real world". If you want to talk about the bus always being late you just do this distributionally. Probabilities are our formalization around uncertainty.We're talking about "rationalist" cults, axioms, logic, and "from first principles", I don't think using a formal language around this stuff is that much of a leap, if any. (Also, not expecting you to notice my username lol. But I did mention it because after the fact it would make more sense and serve as a hint to where I'm approaching this from). | | |
| ▲ | joe_the_user 6 days ago | parent [-] | | Why do you think these are so different? Because "reality" doesn't have "atomic", certain, etc operations? Also, it's notable that since most reasonings about the real world are approximate, the law of excluded middle is much less likely to apply. If you want to talk about the bus always being late you just do this distributionally. Probabilities are our formalization around uncertainty. Ah, but you can't be certain that you're dealing with a given distribution, not outside the quantum realm. You can talk about, you can roughly model, real world phenomena with second order or higher kind of statements. But you can't just use axioms We're talking about "rationalist" cults, axioms, logic, and "from first principles", I don't think using a formal language around this stuff is that much of a leap, if any. Sure, this group used (improperly) all sorts of logical reasoning and so one might well formal language to describe their (less than useful) beliefs. But this discussion began with the point some made that their use of axiomatic reasoning indeed lead to less than useful outcomes. | | |
| ▲ | godelski 6 days ago | parent [-] | | > Because "reality" doesn't have "atomic", certain, etc operations?
That's not a requirement. The axioms are for our modeling, not reality. > but you can't be certain that you're dealing with a given distribution, not outside the quantum realm.
I guess I'll never understand why non-physicists want to talk so confidently about physics. Especially quantum mechanics[0]. You can get through Griffiths with mostly algebra and some calculus. Group theory is a big plus, but not necessary. I also suggest having a stiff drink on hand. Sometimes you'll need to just shut up and do the math. Don't worry, it'll only be more confusing years later if you get to Messiah.[0] https://xkcd.com/451/ |
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| ▲ | Dylan16807 7 days ago | parent | prev [-] | | 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. |
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