Because either you are not updating credence (which I have no objection to), or you can’t distinguish between hypotheses without assuming simplicity as an axiom (which, feel free to do so, but I already argued it doesn’t need to be assumed). But I think this train of thought seems less important than the necessity of induction discussion in the other threads.
Why is that interesting to me?
It doesn’t need to be. I just found it more compelling.
forming conjectures without any attempt to refute or support them is not knowledge generation.
Totally agree. So I think we may have talked past each other a bit because I was only comparing induction to conjecture, not the full knowledge-generation process. Sure (b) alone is simpler than (a), (b), and (c) collectively, but that’s not what I was arguing against.
I’m stipulating that b) is a simple inductor.
Okay, well that’s a bit of a bedrock of disagreement then.
No, it’s just doing something in a hard coded way. Not generating an English level description of what to do, interpreting it, and executing it.
Sure, so what is your sufficient condition for conjecture to be present, and what is your necessary condition for induction to be present?
can’t distinguish between hypotheses without assuming simplicity as an axiom (which, feel free to do so, but I already argued it doesn’t need to be assumed).
So have I.:-
There are more complex conjectures than simple ones. So if you conjecture something complex, it is less likely to be the right conjecture. Also, you have only a finite amount of time to consider conjectures, so you can’t start at the end an infinite list..But you can start with th the simplest conjecture. Of course, that’s roughly how Solomonoff induction works.
(Also, it is completely unclear why “having to assume simplicity” amounts to “not working”. You could argue, as Vasrani does that Bayes without simplicity doesn’t work: I have argued that no real Bayesian ignores simplicity).
but that’s not what I was arguing against
Why not? An aircraft without wing s or engine is sim ple, but it can’t fly.
Okay, well that’s a bit of a bedrock of disagreement then
Because you think I was stipulating something else? Because you think there are no simple inductors?
Sure, so what is your sufficient condition for conjecture to be present, and what is your necessary condition for induction to be present
You can tell that a algorithm is making predictions on a black box basis , and you can tell it’s an inductor if it does immediately on boot up.
A conjecture-and-refutation machine has to be complex enough to form high level representations, and make inferences from them.
I think in each of these threads, we’ve started to go in circles, so if it’s any consolation I’m interested in following your future posts, and if I post anything in the future I would be interested to see your critiques.
Because either you are not updating credence (which I have no objection to), or you can’t distinguish between hypotheses without assuming simplicity as an axiom (which, feel free to do so, but I already argued it doesn’t need to be assumed). But I think this train of thought seems less important than the necessity of induction discussion in the other threads.
It doesn’t need to be. I just found it more compelling.
Totally agree. So I think we may have talked past each other a bit because I was only comparing induction to conjecture, not the full knowledge-generation process. Sure (b) alone is simpler than (a), (b), and (c) collectively, but that’s not what I was arguing against.
Okay, well that’s a bit of a bedrock of disagreement then.
Sure, so what is your sufficient condition for conjecture to be present, and what is your necessary condition for induction to be present?
So have I.:-
(Also, it is completely unclear why “having to assume simplicity” amounts to “not working”. You could argue, as Vasrani does that Bayes without simplicity doesn’t work: I have argued that no real Bayesian ignores simplicity).
Why not? An aircraft without wing s or engine is sim ple, but it can’t fly.
Because you think I was stipulating something else? Because you think there are no simple inductors?
You can tell that a algorithm is making predictions on a black box basis , and you can tell it’s an inductor if it does immediately on boot up.
A conjecture-and-refutation machine has to be complex enough to form high level representations, and make inferences from them.
I think in each of these threads, we’ve started to go in circles, so if it’s any consolation I’m interested in following your future posts, and if I post anything in the future I would be interested to see your critiques.