A less formal way of putting the same thought process, in case it helps it click into place for anyone, might be “Every observation I make has some possibility of being contradictory evidence. That this observation, of a green apple, isn’t contradictory means that my [All ravens are black] theory has faced another opportunity to be disproved and survived unscathed”
Does an observation of a black herring or black apple reduce the claim of all ravens are black—or somehow be less forceful a failure to disprove the claim? What about a blackberry?
I think by default, anything that isn’t a non-black raven would carry the same weight of “I made an observation and it wasn’t a contradictory example”
I guess unless maybe you had a somewhat contrived prior, saying that there must be a certain number of ravens, and also that there can only be a certain number of black things in total. Then seeing a black non-raven would deplete the number of remaining black things and raise the odds that some of the number of ravens would spill outside that category.
There are choices of hypotheses and assumptions about probability distributions.
Good’s choice was the hypothesis family “there are i non-black ravens in the universe”, uniform prior over these, and an assumption that there are N objects in the universe and observations were drawn uniformly at random from these.
For these assumptions, anything that isn’t a non-black raven does carry the same weight for updating the posterior distribution. But the assumptions are obviously false and the hypothesis family doesn’t seem very efficient. I wouldn’t use these by default.
I don’t think what you’re saying makes sense in general. For one thing, you’re assuming (as does the model in the post) that non-ravens being black is anti-correlated with all ravens being black. Maybe more interestingly, you’re assuming something about the process that presented you with a green apple. If the process is “look for a non-black object”, then yeah, we’ve probably gotten evidence in favor of all ravens are black—this corresponds to “trying and failing to disprove the hypothesis”. If the process is “look for a non-raven object” or just “look for an object”, then we’ve probably gotten very little evidence about ravens, and the direction of the evidence depends on our prior.
A less formal way of putting the same thought process, in case it helps it click into place for anyone, might be “Every observation I make has some possibility of being contradictory evidence. That this observation, of a green apple, isn’t contradictory means that my [All ravens are black] theory has faced another opportunity to be disproved and survived unscathed”
Yup, the “update based on the magnitude of your surprise” heuristic matches this pretty well.
Does an observation of a black herring or black apple reduce the claim of all ravens are black—or somehow be less forceful a failure to disprove the claim? What about a blackberry?
I think by default, anything that isn’t a non-black raven would carry the same weight of “I made an observation and it wasn’t a contradictory example”
I guess unless maybe you had a somewhat contrived prior, saying that there must be a certain number of ravens, and also that there can only be a certain number of black things in total. Then seeing a black non-raven would deplete the number of remaining black things and raise the odds that some of the number of ravens would spill outside that category.
There are choices of hypotheses and assumptions about probability distributions.
Good’s choice was the hypothesis family “there are i non-black ravens in the universe”, uniform prior over these, and an assumption that there are N objects in the universe and observations were drawn uniformly at random from these.
For these assumptions, anything that isn’t a non-black raven does carry the same weight for updating the posterior distribution. But the assumptions are obviously false and the hypothesis family doesn’t seem very efficient. I wouldn’t use these by default.
I don’t think what you’re saying makes sense in general. For one thing, you’re assuming (as does the model in the post) that non-ravens being black is anti-correlated with all ravens being black. Maybe more interestingly, you’re assuming something about the process that presented you with a green apple. If the process is “look for a non-black object”, then yeah, we’ve probably gotten evidence in favor of all ravens are black—this corresponds to “trying and failing to disprove the hypothesis”. If the process is “look for a non-raven object” or just “look for an object”, then we’ve probably gotten very little evidence about ravens, and the direction of the evidence depends on our prior.