Either this problem can be formalized, in which case such a theorem is possible to formulate (whether or not it is possible to prove), or it cannot, in which case it is pointless to argue about it.
So, what ought one do when interested in a problem (decision theory or otherwise) that one does not yet understand well enough to formalize?
I suspect “go do something else until a proper formalization presents itself” is not the best possible answer for all problems, nor is “work silently on formalizing the problem and don’t express or defend a position on it until I’ve succeeded.”
How about “work on formalizing the problem (silently or collaboratively, whatever your style is) and do not defend a position that cannot be successfully defended or refuted”?
Fair enough. Is there a clear way to distinguish positions worth arguing without formality (e.g., the one you are arguing here) from those that aren’t (e.g., the one you are arguing ought not be argued here)?
You check the arguments using mathematical intuition, and you use them to find better definitions. For example, problems involving continuity or real numbers were fruitfully studied for a very long time before rigorous definitions were found.
You check them using mathematical intuition, and you use them to find better definitions.
Indeed, you use them to find better definitions, which is the first step in formalizing the problem. If you argue whose answer is right before doing so (as opposed, say, to which answer ought to be right once a proper formalization is found), you succumb to lost purposes.
For example, “TDT ought to always make the best decision in a certain class of problems” is a valid purpose, while “TDT fails on a Newcomb’s problem with a TDT-aware predictor” is not a well-defined statement until every part of it is formalized.
[EDIT: I’m baffled by the silent downvote of my pleas for formalization.]
[EDIT: I’m baffled by the silent downvote of my pleas for formalization.]
If I had to guess, I’d say that the downvoters interpret those pleas, especially in the context of some of your other comments, as an oblique way of advocating for certain topics of discussion to simply not be mentioned at all.
Admittedly, I interpret them that way myself, so I may just be projecting my beliefs onto others.
My general impression of you(1) is that you consider much of the discussion that takes place here, and much of the thinking of the people who do it, to be kind of a silly waste of time, and that you further see your role here in part as the person who points that fact out to those who for whatever reason have failed to notice it.
Within that context, responding to a comment with a request to formalize it is easy to read as a polite way of expressing “what you just said is uselessly vague. If you are capable of saying something useful, do so, otherwise shut up and leave this subject to the grownups.”
And since you aren’t consistent about wanting everything to be expressed as a formalism, I assume this is a function of the topic of discussion, because that’s the most charitable assumption I can think of.
That said, I reiterate that I have no special knowledge of why you’re being downvoted; please don’t take me as definitive.
(1) This might be an unfair impression, as I no longer remember what it was that led me to form it.
My general impression of you(1) is that you consider much of the discussion that takes place here, and much of the thinking of the people who do it, to be kind of a silly waste of time, and that you further see your role here in part as the person who points that fact out to those who for whatever reason have failed to notice it.
It’s too easy for this to turn into a general counterargument against anything the person says. It may be of benefit to play the ball and not the man.
Or it’s hard to formalize.
It’s pointless to argue about a decision theory problem until it is formalized, since there is no way to check the validity of any argument.
So, what ought one do when interested in a problem (decision theory or otherwise) that one does not yet understand well enough to formalize?
I suspect “go do something else until a proper formalization presents itself” is not the best possible answer for all problems, nor is “work silently on formalizing the problem and don’t express or defend a position on it until I’ve succeeded.”
How about “work on formalizing the problem (silently or collaboratively, whatever your style is) and do not defend a position that cannot be successfully defended or refuted”?
Fair enough.
Is there a clear way to distinguish positions worth arguing without formality (e.g., the one you are arguing here) from those that aren’t (e.g., the one you are arguing ought not be argued here)?
It’s a good question. There ought to be, but I am not sure where the dividing line is.
You check the arguments using mathematical intuition, and you use them to find better definitions. For example, problems involving continuity or real numbers were fruitfully studied for a very long time before rigorous definitions were found.
Indeed, you use them to find better definitions, which is the first step in formalizing the problem. If you argue whose answer is right before doing so (as opposed, say, to which answer ought to be right once a proper formalization is found), you succumb to lost purposes.
For example, “TDT ought to always make the best decision in a certain class of problems” is a valid purpose, while “TDT fails on a Newcomb’s problem with a TDT-aware predictor” is not a well-defined statement until every part of it is formalized.
[EDIT: I’m baffled by the silent downvote of my pleas for formalization.]
If I had to guess, I’d say that the downvoters interpret those pleas, especially in the context of some of your other comments, as an oblique way of advocating for certain topics of discussion to simply not be mentioned at all.
Admittedly, I interpret them that way myself, so I may just be projecting my beliefs onto others.
Wha...? Thank you for letting me know, though I still have no idea what you might mean, I’d greatly appreciate if you elaborate on that!
I’m not sure I can add much by elaboration.
My general impression of you(1) is that you consider much of the discussion that takes place here, and much of the thinking of the people who do it, to be kind of a silly waste of time, and that you further see your role here in part as the person who points that fact out to those who for whatever reason have failed to notice it.
Within that context, responding to a comment with a request to formalize it is easy to read as a polite way of expressing “what you just said is uselessly vague. If you are capable of saying something useful, do so, otherwise shut up and leave this subject to the grownups.”
And since you aren’t consistent about wanting everything to be expressed as a formalism, I assume this is a function of the topic of discussion, because that’s the most charitable assumption I can think of.
That said, I reiterate that I have no special knowledge of why you’re being downvoted; please don’t take me as definitive.
(1) This might be an unfair impression, as I no longer remember what it was that led me to form it.
Thank you! I always appreciate candid feedback.
It’s too easy for this to turn into a general counterargument against anything the person says. It may be of benefit to play the ball and not the man.
Anything the person says? In respect to most things it would be a total non-sequitur.
Yes, I agree. Perhaps I shouldn’t have said anything at all, but, well, he asked.