Thanks for this post, but I don’t feel like I have the background for understanding the point you’re making. In the pingback post, Demski describes your point as saying:
an agent could reason logically but with some looseness. This can fortuitously block the Troll Bridge proof.
Could you offer a high level explanation of what the main principle here is and what Demski means by looseness? (If such an explanation exists. )Thanks.
The key piece that makes any Lobian proof tick is the “proof of X implies X” part. For Troll Bridge, X is “crossing implies bridge explodes”.
For standard logical inductors, that Lobian implication holds because, if a proof of X showed up, every trader betting in favor of X would get free money, so there could be a trader that just names a really really big bet in favor of the X (it’s proved, after all), the agent ends up believing X, and so doesn’t cross, and so crossing implies bridge explodes.
For this particular variant of a logical inductor, there’s an upper limit on the number of bets a trader is able to make, and this can possibly render the statement “if a proof of X showed up, the agent would believe X” false. And so, the key piece of the Lobian proof fails, and the agent happily crosses the bridge with no issue, because it would disbelieve a proof of bridge explosion if it saw it (and so the proof does not show up in the first place).
Thanks for this post, but I don’t feel like I have the background for understanding the point you’re making. In the pingback post, Demski describes your point as saying:
Could you offer a high level explanation of what the main principle here is and what Demski means by looseness? (If such an explanation exists. )Thanks.
The key piece that makes any Lobian proof tick is the “proof of X implies X” part. For Troll Bridge, X is “crossing implies bridge explodes”.
For standard logical inductors, that Lobian implication holds because, if a proof of X showed up, every trader betting in favor of X would get free money, so there could be a trader that just names a really really big bet in favor of the X (it’s proved, after all), the agent ends up believing X, and so doesn’t cross, and so crossing implies bridge explodes.
For this particular variant of a logical inductor, there’s an upper limit on the number of bets a trader is able to make, and this can possibly render the statement “if a proof of X showed up, the agent would believe X” false. And so, the key piece of the Lobian proof fails, and the agent happily crosses the bridge with no issue, because it would disbelieve a proof of bridge explosion if it saw it (and so the proof does not show up in the first place).