It’s strange that these pebblesorters can be convinced by “a heap of 103 pebbles and a heap of 19 pebbles side-by-side” that 1957 is incorrect, yet don’t understand that this is because 19 * 103 = 157. Admittedly I didn’t notice this myself on first reading, but I wasn’t looking for a pattern.
I don’t think your analogy holds up. Your pebblesorters all agree that prime numbered piles are correct and composite ones incorrect, yet are unreflective enough not to realize that’s how they are making the distinction and bad enough mathematicians that they can’t reliably tell whether or not large numbers are prime. If only they were smarter, all their disagreements would go away. The question of why prime piles are correct, or why piles should be made at all, would be forever unanswerable, but it wouldn’t matter much.
I think with human beings the moral disagreements are fundamental. There is no equivalent of a universal belief that primality = goodness. It’s not just that we make calculational errors (although of course we do). It’s not just that we aren’t consciously aware of the fundamental criteria by which we as individuals evaluate things as morally “good” or “bad” (although of course we aren’t). Something like a universal agreement as to what these fundamental criteria are just isn’t there. Not consciously, not unconsciously, not waiting to emerge, just not.
It’s strange that these pebblesorters can be convinced by “a heap of 103 pebbles and a heap of 19 pebbles side-by-side” that 1957 is incorrect, yet don’t understand that this is because 19 * 103 = 157. Admittedly I didn’t notice this myself on first reading, but I wasn’t looking for a pattern.
I don’t think your analogy holds up. Your pebblesorters all agree that prime numbered piles are correct and composite ones incorrect, yet are unreflective enough not to realize that’s how they are making the distinction and bad enough mathematicians that they can’t reliably tell whether or not large numbers are prime. If only they were smarter, all their disagreements would go away. The question of why prime piles are correct, or why piles should be made at all, would be forever unanswerable, but it wouldn’t matter much.
I think with human beings the moral disagreements are fundamental. There is no equivalent of a universal belief that primality = goodness. It’s not just that we make calculational errors (although of course we do). It’s not just that we aren’t consciously aware of the fundamental criteria by which we as individuals evaluate things as morally “good” or “bad” (although of course we aren’t). Something like a universal agreement as to what these fundamental criteria are just isn’t there. Not consciously, not unconsciously, not waiting to emerge, just not.
At least, I don’t think it is.