You’re pointing to a concept represented in your brain, using a label which you expect will evoke analogous representations of that concept in readers’ brains, and asserting that that thing is not something that a human brain could represent.
The various mathematical uses of infinity (infinite cardinals, infinity as a limit in calculus, infinities in nonstandard analysis, etc.) are all well-defined and can be stored as information-bearing concepts in human brains. I don’t think there’s any problem here.
You’re pointing to a concept represented in your brain, using a label which you expect will evoke analogous representations of that concept in readers’ brains, and asserting that that thing is not something that a human brain could represent.
It looks like we agree but you either misread or I was unclear:
I’m not asserting that the definition of infinity I mentioned at the beginning (“a number that is big enough for its smallness to be negligible for the purpose at hand”) is not something a human brain could represent. I’m saying that if the speaker considers “infinity” to be something that a human brain cannot represent, I must question what they are even doing when they utter the word. Surely they are not communicating in the sense Eliezer referred to, of trying to get someone else to have the same content in their head. (If they simply want me to note a mathematical symbol, that is fine, too.)
I also agree that various uses of concepts that could be called infinity in math can be stored in human brains, but that depends on the definitions. I am not “anti-infinity” except if the speaker claims that their infinity cannot be represented in anyone’s mind, but they are talking about it anyway. That would just be a kind of “bluffing,” as it were. If there are sensical definitions of infinity that seem categorically different than the ones I mentioned so far, I’d like to see them.
In short, I just don’t get infinity unless it means one of the things I’ve said so far. I don’t want to be called a “finitist” if I don’t even know what the person means by “infinite.”
You’re pointing to a concept represented in your brain, using a label which you expect will evoke analogous representations of that concept in readers’ brains, and asserting that that thing is not something that a human brain could represent.
The various mathematical uses of infinity (infinite cardinals, infinity as a limit in calculus, infinities in nonstandard analysis, etc.) are all well-defined and can be stored as information-bearing concepts in human brains. I don’t think there’s any problem here.
It looks like we agree but you either misread or I was unclear:
I’m not asserting that the definition of infinity I mentioned at the beginning (“a number that is big enough for its smallness to be negligible for the purpose at hand”) is not something a human brain could represent. I’m saying that if the speaker considers “infinity” to be something that a human brain cannot represent, I must question what they are even doing when they utter the word. Surely they are not communicating in the sense Eliezer referred to, of trying to get someone else to have the same content in their head. (If they simply want me to note a mathematical symbol, that is fine, too.)
I also agree that various uses of concepts that could be called infinity in math can be stored in human brains, but that depends on the definitions. I am not “anti-infinity” except if the speaker claims that their infinity cannot be represented in anyone’s mind, but they are talking about it anyway. That would just be a kind of “bluffing,” as it were. If there are sensical definitions of infinity that seem categorically different than the ones I mentioned so far, I’d like to see them.
In short, I just don’t get infinity unless it means one of the things I’ve said so far. I don’t want to be called a “finitist” if I don’t even know what the person means by “infinite.”