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Silver_Swift comments on The Number Choosing Game: Against the existence of perfect theoretical rationality - Less Wrong Discussion

-1 Post author: casebash 29 January 2016 01:04AM

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Comment author: Vaniver 07 January 2016 04:45:59PM 0 points [-]

You seem to be arguing that there must be some solution that can solve these problems. I've already proven that this cannot exist, but if you disagree, what is your solution then?

I think you're misunderstanding me. I'm saying that there are problems where the right action is to mark it "unsolvable, because of X" and then move on. (Here, it's "unsolvable because of unbounded solution space in the increasing direction," which is true in both the "pick a big number" and "open boundary at 100" case.)

In fact, if you read the comments, you'll see that many commentators are unwilling to accept this solution and keep trying to insist on there being some way out.

Sure, someone who is objecting that this problem is 'solvable' is not using 'solvable' the way I would. But someone who is objecting that this problem is 'unfair' because it's 'impossible' is starting down the correct path.

then declared that you've found a reductio ad absurdum.

I think you have this in reverse. I'm saying "the result you think is absurd is normal in the general case, and so is normal in this special case."

Comment author: Silver_Swift 08 January 2016 11:21:33AM *  0 points [-]

I think you're misunderstanding me. I'm saying that there are problems where the right action is to mark it "unsolvable, because of X" and then move on. (Here, it's "unsolvable because of unbounded solution space in the increasing direction," which is true in both the "pick a big number" and "open boundary at 100" case.)

But if we view this as an actual (albeit unrealistic/highly theoretical) situation rather than a math problem we are still stuck with the question of which action to take. A perfectly rational agent can realize that the problem has no optimal solution and mark it as unsolvable, but afterwards they still have to pick a number, so which number should they pick?

Comment author: RichardKennaway 08 January 2016 03:03:10PM 3 points [-]

But if we view this as an actual (albeit unrealistic/highly theoretical) situation

There is no such thing as an actual unrealistic situation.

A perfectly rational agent can realize that the problem has no optimal solution and mark it as unsolvable, but afterwards they still have to pick a number

They do not have to pick a number, because the situation is not real. To say "but suppose it was" is only to repeat the original hypothetical question that the agent has declared unsolved. If we stipulate that the agent is so logically omniscient as to never need to abandon a problem as unsolved, that does not tell us, who are not omniscient, what that hypothetical agent's hypothetical choice in that hypothetical situation would be.

The whole problem seems to me on a level with "can God make a weight so heavy he can't lift it?"

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