I think it’s just wrong that “H1′: If it is not black, it is not a raven” predicts that you will observe non-black non-raven objects, under the assumption/prior that the color distributions within each type of object (chairs, ravens, bananas, etc.) are independent of each other.
The intuition comes from implicitly visualizing the observation of an unknown non-black object O; then, indeed, H1 predicts that O will turn out to not be a raven. Then point is, even observing that O is non-black would decrease your credence in H1; and then increase it again when you saw that O was not a raven. Since H1 is only about ravens, by the independence assumption, H1 says nothing about non-ravens and whether you will see non-black ones. (I.e., its likelihood ratio for “observe a non-black non-raven object” is 1.)
This model of independence between shapes is what I’m calling the implicit model that people use to say that the conclusion of the raven paradox is absurd.
Right, I should have written, “I agree. Also, …”. I just wanted to find the source of the intuition that seeing non-black non-ravens is evidence for “non-black → non-raven”.
I think it’s just wrong that “H1′: If it is not black, it is not a raven” predicts that you will observe non-black non-raven objects, under the assumption/prior that the color distributions within each type of object (chairs, ravens, bananas, etc.) are independent of each other.
The intuition comes from implicitly visualizing the observation of an unknown non-black object O; then, indeed, H1 predicts that O will turn out to not be a raven. Then point is, even observing that O is non-black would decrease your credence in H1; and then increase it again when you saw that O was not a raven. Since H1 is only about ravens, by the independence assumption, H1 says nothing about non-ravens and whether you will see non-black ones. (I.e., its likelihood ratio for “observe a non-black non-raven object” is 1.)
This model of independence between shapes is what I’m calling the implicit model that people use to say that the conclusion of the raven paradox is absurd.
Right, I should have written, “I agree. Also, …”. I just wanted to find the source of the intuition that seeing non-black non-ravens is evidence for “non-black → non-raven”.