I think V=â is logically possible when you aggregate over space and time, and I think we shouldnât generally assign probability 0 to anything thatâs logically possible (except where a measure is continuous; I think this requirement had a name, but I forget). Pascalâs wager and Dysonâs wager illustrate this.
We have reason to believe the universe is infinite in extent, and thereâs a chance that itâs infinite temporally. You might claim that our lightcone is finite/âbounded and we canât affect anything outside of it (setting aside multiverses), but this is an empirical claim, so we should give it some chance of being false. That we could affect an infinite region of spacetime is also not a logical impossibility, so we shouldnât absolutely rule it out.
Yep, weâve got pretty good evidence that our spacetime will have infinite 4D volume and, if you arranged happy lives uniformly across that volume, weâd have to say that the outcome is better than any outcome with merely finite total value. Nothing logically impossible there (even if it were practically impossible).
That said, assigning value âââ to such an outcome is pretty crude and unhelpful. And what it means will depend entirely on how weâve defined â in our number system. So, what I think we should do in such a case is not say V equals such and such. Instead, ditch the value function when youâve left the domain where it works. Instead, just deal with your set of possible outcomes, your lotteries (probability measures over that set), and a betterness relation which might sometimes follow a value function but might also extend to outcomes beyond the functionâs domain. Thatâs what people tend to do in the infinite aggregation literature (including the social choice papers that consider infinite time horizons), and for good reason.
we shouldnât generally assign probability 0 to anything thatâs logically possible (except where a measure is continuous; I think this requirement had a name, but I forget)
I think V=â is logically possible when you aggregate over space and time, and I think we shouldnât generally assign probability 0 to anything thatâs logically possible (except where a measure is continuous; I think this requirement had a name, but I forget). Pascalâs wager and Dysonâs wager illustrate this.
We have reason to believe the universe is infinite in extent, and thereâs a chance that itâs infinite temporally. You might claim that our lightcone is finite/âbounded and we canât affect anything outside of it (setting aside multiverses), but this is an empirical claim, so we should give it some chance of being false. That we could affect an infinite region of spacetime is also not a logical impossibility, so we shouldnât absolutely rule it out.
Yep, weâve got pretty good evidence that our spacetime will have infinite 4D volume and, if you arranged happy lives uniformly across that volume, weâd have to say that the outcome is better than any outcome with merely finite total value. Nothing logically impossible there (even if it were practically impossible).
That said, assigning value âââ to such an outcome is pretty crude and unhelpful. And what it means will depend entirely on how weâve defined â in our number system. So, what I think we should do in such a case is not say V equals such and such. Instead, ditch the value function when youâve left the domain where it works. Instead, just deal with your set of possible outcomes, your lotteries (probability measures over that set), and a betterness relation which might sometimes follow a value function but might also extend to outcomes beyond the functionâs domain. Thatâs what people tend to do in the infinite aggregation literature (including the social choice papers that consider infinite time horizons), and for good reason.
Youâre probably (pun not intended) thinking of Cromwellâs rule.
Yes, thanks!