You’re free to reject the Omphalos hypothesis based on your own philosophical grounds (there are plenty of excellent philosophical arguments against it), but you can’t prove that it isn’t true because it is unfalsifiable. We can prove the age of the universe so long as we assume the hypothesis is false. This is completely fine for many problems, since physical models depend on physics being stable.

Also, I don’t mean to present the Omphalos hypothesis as the correct solution; it is just one example of a solution to a problem that cannot be solved empirically.

You’re free to reject the Omphalos hypothesis based on your own philosophical grounds, but you can’t prove that it isn’t true because it is unfalsifiable. We can prove the age of the universe so long as we assume the hypothesis is false. This is completely fine for many problems, since physical models depend on physics being stable.

Also, I don’t mean to present the Omphalos hypothesis as the correct solution; it is just one example of a solution to a problem that cannot be solved empirically.

You’re free to reject the Omphalos hypothesis based on your own philosophical grounds, but you can’t prove that it isn’t true because it is unfalsifiable. We can prove the age of the universe so long as we assume the hypothesis is false. This is completely fine for many problems, since physical models depend on physics being stable.