H proves that it can't decide the question one way or the other.

`H`

is literally defined as either returning true or false. Or it can run forever, if it can't find a proof. It's possible to create another program which does return "UNDECIDABLE" sometimes. But that is not `H`

.

The point is that the behavior of `H`

is paradoxical. We can prove that it can't return `true`

or `false`

without contradiction. But if that's provable, that also creates a contradiction, since `H`

can prove it to.

Not only can `H`

not decide, but we can't decide whether or not `H`

will decide. Because we aren't outside the system, and the same logic applies to us.

Let's say I wanted to solve my dating issues. I present the following approaches:

I endeavor to solve the general problem of human sexual attraction, plug myself into the parameters to figure out what I'd be most attracted to, determine the probabilities that individuals I'd be attracted to would also be attracted to me, then devise a strategy for finding someone with maximal compatibility.

I take an iterative approach: I devise a model this afternoon, test it this evening, then analyze the results tomorrow morning and make the necessary adjustments.

Which approach is more rational? Given sufficient time, Approach 1 will yield the optimal solution. Approach 2 has to deal with the problem of local maxima and in the long run is likely to end up worse than Approach 1. An immortal living in an eternal universe would probably say that Approach 1 is vastly superior. Humans, on the other hand, will die well before Approach 1 bears fruit.

While rationality can lead to faster improvement using Approach 2, a rationalist might try Approach 1, whereas a non-rationalist is unlikely to use Approach 1 at all.

Simple amendments to the general problem such as "find the best way to get the best date for next Saturday" will likely lead to solutions making heavy use of deception. If you want to exclude the Dark Arts from the solution space, then that's going to limit what you can accomplish. The short-term drawbacks of insisting on truth and honesty are well-documented.