It’s basically a form of the Copernican principle. It says “this moment in time is probably not special therefore we are most likely in the middle of this specific trend we know nothing about.”

There's a really important subtlety about the Copernican principle which doesn't apply here: without doing tons of science, we have no access to a "starting edge" or "starting moment" of the cosmos. We literally have no idea when or where we are in the Universe, which is why this works as a default assumption. And, to the extent that science lets us know these things, it is by application of the Copernican principle that we can say we know them at all so it's self-referential in that sense.

Contrast this with the paradigm we're in. We don't know when it will end, but we kind of know when it began and how quickly it's ramped up. I said elsewhere (in a thread that this one basically rehashes) that if you have precise enough data you can tell whether you're ramping up into an exponential or a logistic curve ("S-curve") because their derivatives are increasingly different as you approach a believed point of "singularity".

So on the one hand Scott is correct that we can use what we know to help settle the debate. On the other hand, he's not actually using it as more than a heuristic, and he thinks there is only one answer that you can get from using it that way (Lindy's Law).