Nitpicking: Modus ponens is not about “deriving”. It’s about B being true. (Your description matches the provability relation, the “|-” operator.)
It’s not clear how “fundamental” modus ponens it is. You can make up new logics without that connective and other exotic connectives (such as those in modal logics). Then, you’d ask yourself what to do with them…
Speaking of relevance, even the standard connectives are not very useful by themselves. We get a lot of power from non-logical axioms, with a lot of handwaving about how “intuitively true” they are to us humans. Except the Axiom of Choice. And some others. It’s possible that one day an alien race may find our axioms “just plain weird”.
The never-learn-anything example that you quoted looks a bit uselessly true to me. The fact that once can have as prior knowledge the fact that the monkey generates perfect 1⁄4 randomness is utopia to begin with, so then complaining about not being able to discern anything more is like having solved the halting problem, you realize you don’t learn anything more about computer programs by just running them.
I’m not well versed on YEC arguments, but I believe people’s frustrations with them is not due to the lack of universally compelling arguments against them. Probably they’re already guilty of plain old logical inconsistency (i.e. there’s a valid chain of reasoning that shows that if they doubt the scientific estimates, then they should turn off their television right now or something similar), or they possess some kind of “undefeatable” hypothesis as prior knowledge that allows for everything to look billions of years old despite being very young. (If so, they should be very much bothered by having this type of utopic prior knowledge.)
I’m not well versed on YEC arguments, but I believe people’s frustrations with them is not due to the lack of universally compelling arguments against them. Probably they’re already guilty of plain old logical inconsistency (i.e. there’s a valid chain of reasoning that shows that if they doubt the scientific estimates, then they should turn off their television right now or something similar), or they possess some kind of “undefeatable” hypothesis as prior knowledge that allows for everything to look billions of years old despite being very young. (If so, they should be very much bothered by having this type of utopic prior knowledge.)
Well, if they’re logically inconsistent, but nothing you can say to them will convince to give up YECism in order to stop being logically inconsistent… then that particular chain of reasoning, at least, isn’t universally compelling.
Or, if they have an undefeatable hypothesis, if that’s literally true… doesn’t that mean no argument is going to be compelling to them?
Maybe you’re thinking “compelling” means what ought to be compelling, rather than what actually convinces people, when the latter meaning is how Eliezer and I are using it?
I am at a loss about the true meaning of a “universally compelling argument”, but from Eliezer’s original post and from references to things such as modus ponens itself, I understood it to mean something that is able to overcome even seemingly axiomatic differences between two (otherwise rational) agents. In this scenario, an agent may accept modus ponens, but if they do, they’re at least required to use it consistently. For instance, a mathematician of the constructivist persuasion denies the law of the excluded middle, but if he’s using it in a proof, classical mathematicians have the right to call him out.
Similarly, YEC’s are not inconsistent in their daily lives, nor do they have any undefeatable hypotheses about barbeques or music education: they’re being inconsistent only on a select set of topics. At this point the brick wall we’re hitting is not a fundamental difference in logic or priors; we’re in the domain of human psychology.
Arguments that “actually convince (all) people” are very limited and context sensitive because we’re not 100% rational.
Nitpicking: Modus ponens is not about “deriving”. It’s about B being true. (Your description matches the provability relation, the “|-” operator.) It’s not clear how “fundamental” modus ponens it is. You can make up new logics without that connective and other exotic connectives (such as those in modal logics). Then, you’d ask yourself what to do with them… Speaking of relevance, even the standard connectives are not very useful by themselves. We get a lot of power from non-logical axioms, with a lot of handwaving about how “intuitively true” they are to us humans. Except the Axiom of Choice. And some others. It’s possible that one day an alien race may find our axioms “just plain weird”.
The never-learn-anything example that you quoted looks a bit uselessly true to me. The fact that once can have as prior knowledge the fact that the monkey generates perfect 1⁄4 randomness is utopia to begin with, so then complaining about not being able to discern anything more is like having solved the halting problem, you realize you don’t learn anything more about computer programs by just running them.
I’m not well versed on YEC arguments, but I believe people’s frustrations with them is not due to the lack of universally compelling arguments against them. Probably they’re already guilty of plain old logical inconsistency (i.e. there’s a valid chain of reasoning that shows that if they doubt the scientific estimates, then they should turn off their television right now or something similar), or they possess some kind of “undefeatable” hypothesis as prior knowledge that allows for everything to look billions of years old despite being very young. (If so, they should be very much bothered by having this type of utopic prior knowledge.)
Well, if they’re logically inconsistent, but nothing you can say to them will convince to give up YECism in order to stop being logically inconsistent… then that particular chain of reasoning, at least, isn’t universally compelling.
Or, if they have an undefeatable hypothesis, if that’s literally true… doesn’t that mean no argument is going to be compelling to them?
Maybe you’re thinking “compelling” means what ought to be compelling, rather than what actually convinces people, when the latter meaning is how Eliezer and I are using it?
I am at a loss about the true meaning of a “universally compelling argument”, but from Eliezer’s original post and from references to things such as modus ponens itself, I understood it to mean something that is able to overcome even seemingly axiomatic differences between two (otherwise rational) agents. In this scenario, an agent may accept modus ponens, but if they do, they’re at least required to use it consistently. For instance, a mathematician of the constructivist persuasion denies the law of the excluded middle, but if he’s using it in a proof, classical mathematicians have the right to call him out.
Similarly, YEC’s are not inconsistent in their daily lives, nor do they have any undefeatable hypotheses about barbeques or music education: they’re being inconsistent only on a select set of topics. At this point the brick wall we’re hitting is not a fundamental difference in logic or priors; we’re in the domain of human psychology.
Arguments that “actually convince (all) people” are very limited and context sensitive because we’re not 100% rational.