It is the year 2100 and physicists have narrowed down the search for a theory of everything to only two remaining plausible candidate theories, T1 and T2 (using considerations from super-duper symmetry). According to T1 the world is very, very big but finite, and there are a total of a trillion trillion observers in the cosmos. According to T2, the world is very, very, very big but finite, and there are a trillion trillion trillion observers. The super-duper symmetry considerations seem to be roughly indifferent between these two theories. The physicists are planning on carrying out a simple experiment that will falsify one of the theories.
...except the simple experiment won’t quite falsify one of the theories. You see, the experiment has a trillion different possible outcomes. If T1 is true, the outcome will be a specific possibility that scientists have already calculated. If T2 is true, the outcome will be a random one, distributed uniformly among all possibilities.
Well, the experiment is performed, and the result is the one that’s consistent with both theories. For whatever reason, anthropic reasoning is pretty standard in this hypothetical universe, so now, not before but after the experiment, the two theories are considered to be pretty much on par with each other. Enter the Other Presumptuous Philosopher: “Hey guys, we can stop experimenting now, because I can already show to you now, using non-anthropic reasoning, that T1 is about a trillion times more likely to be true than T2!”
My point: the Presumptuous Philosopher argument, though a good argument against certainty of either anthropic or non-anthropic reasoning, isn’t a good argument against anything else. It’s about as good an argument as “If you think that’s true, why don’t you bet your life on it?”
The Other Presumptuous Philosopher:
It begins pretty much as described here:
...except the simple experiment won’t quite falsify one of the theories. You see, the experiment has a trillion different possible outcomes. If T1 is true, the outcome will be a specific possibility that scientists have already calculated. If T2 is true, the outcome will be a random one, distributed uniformly among all possibilities.
Well, the experiment is performed, and the result is the one that’s consistent with both theories. For whatever reason, anthropic reasoning is pretty standard in this hypothetical universe, so now, not before but after the experiment, the two theories are considered to be pretty much on par with each other. Enter the Other Presumptuous Philosopher: “Hey guys, we can stop experimenting now, because I can already show to you now, using non-anthropic reasoning, that T1 is about a trillion times more likely to be true than T2!”
My point: the Presumptuous Philosopher argument, though a good argument against certainty of either anthropic or non-anthropic reasoning, isn’t a good argument against anything else. It’s about as good an argument as “If you think that’s true, why don’t you bet your life on it?”