Nicely put! If a theist announces their revelation that pi is 3, and demands of me what
two integers I take as pi’s numerator and denominator, the best response is a proof
that no such pair exists.
I do agree with AlexMennen that for an optimization problem this isn’t adequate.
One doesn’t have to display an optimal solution, but one at least needs to show that
there is something like a direction in which one can move which is clearly an improvement.
To address SarahC’s example of government corruption—It isn’t sufficient to show
that the corruption does damage. One also has to show that, for instance, more
vigorous enforcement of anti-corruption laws won’t do more damage.
Right. It seems like to synthesize your point and the post we would need to say that, in evaluating a criticism, we should consider not:
Do we know of a solution to this problem?
but
Can we prove that there is no solution to this problem?
The second type of problem, we must live with. The first type, we should devote some resources to thinking about.
Nicely put! If a theist announces their revelation that pi is 3, and demands of me what two integers I take as pi’s numerator and denominator, the best response is a proof that no such pair exists.
I do agree with AlexMennen that for an optimization problem this isn’t adequate. One doesn’t have to display an optimal solution, but one at least needs to show that there is something like a direction in which one can move which is clearly an improvement. To address SarahC’s example of government corruption—It isn’t sufficient to show that the corruption does damage. One also has to show that, for instance, more vigorous enforcement of anti-corruption laws won’t do more damage.