Eliezer Yudkowsky wrote this article about the two things that rationalists need faith to believe in: That the statement “Induction works” has a sufficiently large prior probability, and that some single large ordinal that is well-ordered exists. Are there any ways to justify belief in either of these two things yet that do not require faith?
Explain. Are you saying that since induction appears to work in your everyday like, this is Bayesian evidence that the statement “Induction works” is true? This has a few problems. The first problem is that if you make the prior probability sufficiently small, it cancels out any evidence you have for the statement being true. To show that “Induction works” has at least a 50% chance of being true, you would need to either show that the prior probability is sufficiently large, or come up with a new method of calculating probabilities that does not depend on priors. The second problem is that you also need to justify that your memories are reliable. This could be done using induction and with a sufficiently large prior probability that memory works, but this has the same problems mentioned previously.
Not exactly. MIRI and others have research on logical uncertainty, which I would expect to eventually reduce the second premise to induction. I don’t think we have a clear plan yet showing how we’ll reach that level of practicality.
Justifying a not-super-exponentially-small prior probability for induction working feels like a category error. I guess we might get a kind of justification from better understanding Tegmark’s Mathematical Macrocosm hypothesis—or, more likely, understanding why it fails. Such an argument will probably lack the intuitive force of ‘Clearly the prior shouldn’t be that low.’
Eliezer Yudkowsky wrote this article about the two things that rationalists need faith to believe in: That the statement “Induction works” has a sufficiently large prior probability, and that some single large ordinal that is well-ordered exists. Are there any ways to justify belief in either of these two things yet that do not require faith?
You can justify a belief in “Induction works” by induction over your own life.
Explain. Are you saying that since induction appears to work in your everyday like, this is Bayesian evidence that the statement “Induction works” is true? This has a few problems. The first problem is that if you make the prior probability sufficiently small, it cancels out any evidence you have for the statement being true. To show that “Induction works” has at least a 50% chance of being true, you would need to either show that the prior probability is sufficiently large, or come up with a new method of calculating probabilities that does not depend on priors. The second problem is that you also need to justify that your memories are reliable. This could be done using induction and with a sufficiently large prior probability that memory works, but this has the same problems mentioned previously.
Wouldn’t that be question begging?
Not exactly. MIRI and others have research on logical uncertainty, which I would expect to eventually reduce the second premise to induction. I don’t think we have a clear plan yet showing how we’ll reach that level of practicality.
Justifying a not-super-exponentially-small prior probability for induction working feels like a category error. I guess we might get a kind of justification from better understanding Tegmark’s Mathematical Macrocosm hypothesis—or, more likely, understanding why it fails. Such an argument will probably lack the intuitive force of ‘Clearly the prior shouldn’t be that low.’