Thanks, you’re right that this isn’t self refuting. But with that P1, the argument seems invalid:
P1: For most predicates X: Not (For all minds m: X(m))
P2: UCMAs are X
C: Not UMCA
is like
P1: For most prime numbers n: (odd)n
P2: 2 is prime
C: 2 is odd
Edit: you might think that the conclusion is not that not ‘not UMCA’ but ‘UMCA is unlikely’, but this doesn’t follow either. I don’t know quite how ‘most’ quantifiers work, but I don’t think we can read a probabilistic conclusion off of them. I don’t think it follows from the above, for example, that 2 is likely to be odd.
Yes, the crucial issue in this conversation is the concept of ‘most’ and ‘probability’. What you can conclude from P1 is that a priori, a randomly selected predicate X probably does not satisfy X(m) for all m. If we had other reasons to believe that X(m) for all m, then we can update our beliefs. Similarly, we expect that a randomly selected prime number n is probably odd; but if we learn the further fact that n=2, then our belief changes.
So what do you make of this argument then? Suppose I were of the opinion that 2 is an even prime. You come to me with an argument to the effect that I should not believe 2 to be prime because a randomly selected prime number is very, very unlikely to be even. Should I be convinced by that? I may be convinced that in some sense, 2 is unlikely to be even, but I don’t think I should accept that 2 is not even, or that the evenness of 2 is questionable.
Similarly, suppose someone believes an argument to be universally compelling. It seems to me that EY’s argument should be unmoving: granting that it is unlikely for a randomly selected argument to be UC, but theirs is no randomly selected argument. And on DaFranker’s reading of this argument, the thesis that a given X is unlikely to hold for of all minds relies on the assumption that for most X’s, there is (something like) a 50% chance of its being true of some mind. But certainly a UCMAist won’t accept that this is true of UCMA’s. UCMA’s, they will say, are exactly those X’s for which this is not true.
The burden may be on them to justify the possibility of such an X, but that fact won’t save the argument.
As for your first paragraph, well, this is a straightforward application of Bayes’ theorem. If you’re sure that 2 is even, then learning that 2 was randomly selected from some distribution over primes should not be enough to change your credence very much.
As for your second and third paragraphs: Yes, the argument of Eliezer you’re talking about doesn’t refute the existence of universally compelling arguments; it merely means that you shouldn’t believe you have a universally compelling argument unless you have a good reason for believing so. If you think you have a good reason, then you don’t have to worry about this argument.
There’s a very simple argument refuting the existence of universally compelling arguments, and I believe it was stated elsewhere in this thread. It’s that argument you have to refute, not this one.
There’s a very simple argument refuting the existence of universally compelling arguments, and I believe it was stated elsewhere in this thread. It’s that argument you have to refute, not this one.
Please point this out to me if you get a chance, as I haven’t noticed it. And thanks for the discussion. I mean that: I can see that this wasn’t helpful or interesting for you, but rest assured it was for me, so your indulgence is appreciated.
You’re welcome! The refutation of universally compelling arguments I was referring to is this one. I see you responded that you’re interested in a different definition of “compelling”. On the word “compelling”, you say
On the one hand, we could mean ‘persuasive’ where this means something like ‘If I sat down with someone, and presented the moral argument to them, they would end up accepting it regardless of their starting view’. This seems to be a bad option, because the claim that ‘there are no universally persuasive moral arguments’ is trivial.
This is indeed the meaning of “compelling” that Eliezer uses, and Eliezer’s original argument is indeed trivial, which perhaps explains why he spent so few words on it.
If you wanted to defend a different claim, that there are arguments that all minds are “rationally committed” to accepting or whatever, then you’d have to begin by operationalizing “committed”, “reasons”, etc. I believe there’s no nontrivial way to do this. In any case the burden is on others to operationalize these concepts in an interesting way.
That I can’t argue with, though it wouldn’t follow from that that UCMAs are likely to be false.
EDIT: you edited your post, and so my reply doesn’t seem to make sense. In answer to your new question, I would say ‘I don’t, I just want some presentation of the argument on which its validity (or invalidity) is obvious’.
Or, more likely, I am confused by my syntax. If you were to formalize EY’s argument, how would you put it?
At the risk of prolonging an unproductive thread, I’d say P1 is like
P1: For most predicates X: Not (For all minds m: X(m))
This isn’t self-refuting.
Thanks, you’re right that this isn’t self refuting. But with that P1, the argument seems invalid:
P1: For most predicates X: Not (For all minds m: X(m))
P2: UCMAs are X
C: Not UMCA
is like
P1: For most prime numbers n: (odd)n
P2: 2 is prime
C: 2 is odd
Edit: you might think that the conclusion is not that not ‘not UMCA’ but ‘UMCA is unlikely’, but this doesn’t follow either. I don’t know quite how ‘most’ quantifiers work, but I don’t think we can read a probabilistic conclusion off of them. I don’t think it follows from the above, for example, that 2 is likely to be odd.
Yes, the crucial issue in this conversation is the concept of ‘most’ and ‘probability’. What you can conclude from P1 is that a priori, a randomly selected predicate X probably does not satisfy X(m) for all m. If we had other reasons to believe that X(m) for all m, then we can update our beliefs. Similarly, we expect that a randomly selected prime number n is probably odd; but if we learn the further fact that n=2, then our belief changes.
So what do you make of this argument then? Suppose I were of the opinion that 2 is an even prime. You come to me with an argument to the effect that I should not believe 2 to be prime because a randomly selected prime number is very, very unlikely to be even. Should I be convinced by that? I may be convinced that in some sense, 2 is unlikely to be even, but I don’t think I should accept that 2 is not even, or that the evenness of 2 is questionable.
Similarly, suppose someone believes an argument to be universally compelling. It seems to me that EY’s argument should be unmoving: granting that it is unlikely for a randomly selected argument to be UC, but theirs is no randomly selected argument. And on DaFranker’s reading of this argument, the thesis that a given X is unlikely to hold for of all minds relies on the assumption that for most X’s, there is (something like) a 50% chance of its being true of some mind. But certainly a UCMAist won’t accept that this is true of UCMA’s. UCMA’s, they will say, are exactly those X’s for which this is not true.
The burden may be on them to justify the possibility of such an X, but that fact won’t save the argument.
As for your first paragraph, well, this is a straightforward application of Bayes’ theorem. If you’re sure that 2 is even, then learning that 2 was randomly selected from some distribution over primes should not be enough to change your credence very much.
As for your second and third paragraphs: Yes, the argument of Eliezer you’re talking about doesn’t refute the existence of universally compelling arguments; it merely means that you shouldn’t believe you have a universally compelling argument unless you have a good reason for believing so. If you think you have a good reason, then you don’t have to worry about this argument.
There’s a very simple argument refuting the existence of universally compelling arguments, and I believe it was stated elsewhere in this thread. It’s that argument you have to refute, not this one.
Please point this out to me if you get a chance, as I haven’t noticed it. And thanks for the discussion. I mean that: I can see that this wasn’t helpful or interesting for you, but rest assured it was for me, so your indulgence is appreciated.
You’re welcome! The refutation of universally compelling arguments I was referring to is this one. I see you responded that you’re interested in a different definition of “compelling”. On the word “compelling”, you say
This is indeed the meaning of “compelling” that Eliezer uses, and Eliezer’s original argument is indeed trivial, which perhaps explains why he spent so few words on it.
If you wanted to defend a different claim, that there are arguments that all minds are “rationally committed” to accepting or whatever, then you’d have to begin by operationalizing “committed”, “reasons”, etc. I believe there’s no nontrivial way to do this. In any case the burden is on others to operationalize these concepts in an interesting way.
Okay, thanks for pointing that out.
Why would you want to formalize the argument?
That I can’t argue with, though it wouldn’t follow from that that UCMAs are likely to be false.
EDIT: you edited your post, and so my reply doesn’t seem to make sense. In answer to your new question, I would say ‘I don’t, I just want some presentation of the argument on which its validity (or invalidity) is obvious’.