I disagree with Ishaan’s approach of taking anything on faith, even logic itself.
Let me unpack “faith” a little bit, then, because it’s not like regular faith. I only use the word “faith” because it’s the closest word I know to what I mean.
I agree with the postmodern / nihilist / Lesswrong’s idea of “no universally compelling arguments” in morality, math, and science. Everything that comes out of my mind is a property of how my mind is constructed.
When I say that I take logic “on faith”, what I’m really saying is that I have no way to justify it, other than that human minds run that way (insert disclaimers about, yes, I know human minds don’t actually run that way)
I don’t have a word to describe this, the sense that I’m ultimately going to follow my morality and my cognitive algorithm even while accepting that is not and cannot be justification for them outside my own mind. (I kinda want to call this “epistemic particularism” to draw an analogy from political particularism, but google says that term is already in use and I haven’t read about it so I am not sure whether or not it means what I want to use it for. I think it does, though.)
Suppose I got up one morning, and took out two earplugs, and set them down next to two other earplugs on my nighttable, and noticed that there were now three earplugs, without any earplugs having appeared or disappeared
I think there would exist a way to logically describe the universe Eliezer would find himself in.
(There are redefinitions, but those are not “situations”, and then you’re no longer talking about 2, 4, =, or +.) But that doesn’t make my belief unconditional.
I disagree with Eliezer here. If the people in this universe want to use “2”, “3“, and “+” to describe what is happening to them, then their “3” does not have the same meaning as our “3” We are referring to something with integer properties, and they are referring to something with other properties. I think Wittgenstein would have a few choice words for Eliezer here (although I’ve only read summaries of his thoughts, I think he’s basically saying what I’m saying).
I don’t think Eliezer should be interpreted as admitting that the territory might be illogical. I think he just made a mistake concerning what definitions are. (I’m not saying your interpretation is unreasonable. I’m saying that the fact that your interpretation is reasonable is a clue that Eliezer made a logical error somewhere, and this is the error I think he made. (I’d be curios to know if he’d agree with me that he made an error in saying 2+2=3 is not a re-definition. Judging from his other writing I suspect he would.)
(And again, it’s circular because it has to be. The fact that your perfectly logical interpretation of Eliezer basically just invoked the Principle of Explosion indicates the statements themselves contain a logical error, but none of this works if you don’t buy into logic to begin with. You’re throwing out logic, and I’m convincing you that this is illogical—which is a silly thing to do, but still.)
Eliezer’s weird universe is still in the space of logic-land. We’ve just constructed a different logical system, where 2+2=3 because they are different;y defined now. It’s not like Eliezer is simultaneously experiencing and not experiencing three earplugs or something. An illogical world isn’t merely different from our world—it’s incomprehensible and indescribable nonsense insofar as our brain is concerned. If you’re still looking at evidence and drawing conclusions, you’re still using logic. (Inb4 paraconsistent and fuzzy logic, the meta rules handling the statements still use the same tautology-contradiction structure common to all math)
Let me unpack “faith” a little bit, then, because it’s not like regular faith. I only use the word “faith” because it’s the closest word I know to what I mean.
I agree with the postmodern / nihilist / Lesswrong’s idea of “no universally compelling arguments” in morality, math, and science. Everything that comes out of my mind is a property of how my mind is constructed.
When I say that I take logic “on faith”, what I’m really saying is that I have no way to justify it, other than that human minds run that way (insert disclaimers about, yes, I know human minds don’t actually run that way)
I don’t have a word to describe this, the sense that I’m ultimately going to follow my morality and my cognitive algorithm even while accepting that is not and cannot be justification for them outside my own mind. (I kinda want to call this “epistemic particularism” to draw an analogy from political particularism, but google says that term is already in use and I haven’t read about it so I am not sure whether or not it means what I want to use it for. I think it does, though.)
I think there would exist a way to logically describe the universe Eliezer would find himself in.
I disagree with Eliezer here. If the people in this universe want to use “2”, “3“, and “+” to describe what is happening to them, then their “3” does not have the same meaning as our “3” We are referring to something with integer properties, and they are referring to something with other properties. I think Wittgenstein would have a few choice words for Eliezer here (although I’ve only read summaries of his thoughts, I think he’s basically saying what I’m saying).
I don’t think Eliezer should be interpreted as admitting that the territory might be illogical. I think he just made a mistake concerning what definitions are. (I’m not saying your interpretation is unreasonable. I’m saying that the fact that your interpretation is reasonable is a clue that Eliezer made a logical error somewhere, and this is the error I think he made. (I’d be curios to know if he’d agree with me that he made an error in saying 2+2=3 is not a re-definition. Judging from his other writing I suspect he would.)
(And again, it’s circular because it has to be. The fact that your perfectly logical interpretation of Eliezer basically just invoked the Principle of Explosion indicates the statements themselves contain a logical error, but none of this works if you don’t buy into logic to begin with. You’re throwing out logic, and I’m convincing you that this is illogical—which is a silly thing to do, but still.)
Eliezer’s weird universe is still in the space of logic-land. We’ve just constructed a different logical system, where 2+2=3 because they are different;y defined now. It’s not like Eliezer is simultaneously experiencing and not experiencing three earplugs or something. An illogical world isn’t merely different from our world—it’s incomprehensible and indescribable nonsense insofar as our brain is concerned. If you’re still looking at evidence and drawing conclusions, you’re still using logic. (Inb4 paraconsistent and fuzzy logic, the meta rules handling the statements still use the same tautology-contradiction structure common to all math)