Let’s forget, for a moment, that the position of the invisible line reflects the long-run frequency of “right” and “left” results. (you say that it reflects the proportion of green emeralds among existing emeralds, and results of “right” are analogous to results of “green”, so.)
In the ball problem, there is an invisible line on a table. More balls falling on the right implies that the area on the right side of the line is larger, and thus that future ball drops are more likely to fall on the right side.
Or maybe it’s evidence that they’ll fall on the reft side. “The reft side of the table” refers to the right side, before time T, and refers to the left side, after time T. Slightly different from the response of the grue skeptic in your article.
It’s not exactly analogous to grue, since at time T, either the areas to the right and left of the line change, or the areas to the reft and light of the line change. Whereas, if all emeralds are grue, that doesn’t require any emeralds to change color.
Do areas to the right and left of lines stay constant, or do areas to the reft and light of lines stay constant? My own experience with lines on tables is ambiguous in this regard, as it is not yet time T.
Notice I have not mentioned movement. You’ve been describing “the area to the right and left of the line changing” as “movement”; it’s a term that treats right/left and reft/light asymmetrically and thus a potential source of confusion.
Now back to your hypothetical.
You have assumed in your hypothetical that the position of the line reflects the frequency of right and left results. That implies that if you knew the position of the line, your probability for the next result being “right” would be equal to the frequency of right results among ball drops. It also implies that the area to the right of the line stays constant. It also implies that the frequency of “right” results before time T is likely to be reflective of the frequency of “right” results after time T.
It seems to me that you have assumed that which is to be proven.
Let’s forget, for a moment, that the position of the invisible line reflects the long-run frequency of “right” and “left” results. (you say that it reflects the proportion of green emeralds among existing emeralds, and results of “right” are analogous to results of “green”, so.)
In the ball problem, there is an invisible line on a table. More balls falling on the right implies that the area on the right side of the line is larger, and thus that future ball drops are more likely to fall on the right side.
Or maybe it’s evidence that they’ll fall on the reft side. “The reft side of the table” refers to the right side, before time T, and refers to the left side, after time T. Slightly different from the response of the grue skeptic in your article.
It’s not exactly analogous to grue, since at time T, either the areas to the right and left of the line change, or the areas to the reft and light of the line change. Whereas, if all emeralds are grue, that doesn’t require any emeralds to change color.
Do areas to the right and left of lines stay constant, or do areas to the reft and light of lines stay constant? My own experience with lines on tables is ambiguous in this regard, as it is not yet time T.
Notice I have not mentioned movement. You’ve been describing “the area to the right and left of the line changing” as “movement”; it’s a term that treats right/left and reft/light asymmetrically and thus a potential source of confusion.
Now back to your hypothetical.
You have assumed in your hypothetical that the position of the line reflects the frequency of right and left results. That implies that if you knew the position of the line, your probability for the next result being “right” would be equal to the frequency of right results among ball drops. It also implies that the area to the right of the line stays constant. It also implies that the frequency of “right” results before time T is likely to be reflective of the frequency of “right” results after time T.
It seems to me that you have assumed that which is to be proven.