The condition for the difference to be observable in principle is much weaker than you seem to imply.
It might be, but whether or not it is seems to depend on, among other things, how much randomness there is in the laws of physics. And the minutiae of micro-physics also don’t seem like the kind of thing that can influence the moral value of the world, assuming that the psychological states of all actors in the world are essentially indifferent to these minutiae.
Can’t we resolve this problem by saying that the moral value attaches to a history of the world rather than (say) a state of the world, or the deductive closure of the information available to an agent? Then we can be consistent with the letter if not the spirit of consequentialism by stipulating that a world history containing a forgotten lie gets lower value than an otherwise macroscopically identical world history not containing it. (Is this already your view, in fact?)
Now to consider cousin_it’s idea that a “proper” consequentialist only cares about consequences that can be seen:
Even if all information about the lie is rapidly obliterated, and cannot be recovered later, it’s still true that the lie and its immediate consequences are seen by the person telling it, so we might regard this as being ‘sufficient’ for a proper consequentialist to care about it. But if we don’t, and all that matters is the indefinite future, then don’t we face the problem that “in the long term we’re all dead”? OK, perhaps some of us think that rule will eventually cease to apply, but for argument’s sake, if we knew with certainty that all life would be extinguished, say, 1000 years from now (and that all traces of whether people lived well or badly would subsequently be obliterated) we’d want our ethical theory to be more robust than to say “Do whatever you like—nothing matters any more.”
It might be, but whether or not it is seems to depend on, among other things, how much randomness there is in the laws of physics. And the minutiae of micro-physics also don’t seem like the kind of thing that can influence the moral value of the world, assuming that the psychological states of all actors in the world are essentially indifferent to these minutiae.
Can’t we resolve this problem by saying that the moral value attaches to a history of the world rather than (say) a state of the world, or the deductive closure of the information available to an agent? Then we can be consistent with the letter if not the spirit of consequentialism by stipulating that a world history containing a forgotten lie gets lower value than an otherwise macroscopically identical world history not containing it. (Is this already your view, in fact?)
Now to consider cousin_it’s idea that a “proper” consequentialist only cares about consequences that can be seen:
Even if all information about the lie is rapidly obliterated, and cannot be recovered later, it’s still true that the lie and its immediate consequences are seen by the person telling it, so we might regard this as being ‘sufficient’ for a proper consequentialist to care about it. But if we don’t, and all that matters is the indefinite future, then don’t we face the problem that “in the long term we’re all dead”? OK, perhaps some of us think that rule will eventually cease to apply, but for argument’s sake, if we knew with certainty that all life would be extinguished, say, 1000 years from now (and that all traces of whether people lived well or badly would subsequently be obliterated) we’d want our ethical theory to be more robust than to say “Do whatever you like—nothing matters any more.”