If we hold our beliefs to the discipline of probability and evidence, some puzzles remain. For example, most thinkers are familiar with the problem of induction. How do you know the sun will rise tomorrow? Well, because it always has and we have precise theories that have always held up about how the world works which strongly predict tomorrow's sunrise. Pretty solid stuff as it goes. How do we know the future will be like the past? Well, it always has been.

That last bit is circular. It could easily be the case that what we have witnessed so far is a perversely long string of heads from a fair coin. And why not? Assuming nothing, that's as likely as any other possible world history. The no free lunch theorem in compression strongly establishes: to learn from patterns requires prior knowledge of likely patterns; a truly know-nothing prior also learns nothing. Thus the problem of induction. We have to take induction itself on faith, which is uncomfortable.

If we hold our beliefs to the lawful processes of information accumulation, and we believe we know that the universe is tractable to induction, where did we get that knowledge? You can't just "assume" things and then expect them to be true. If we have true knowledge of induction, we have it by some sound derivation.

Physically, induction is written in our genes like some nanoscale tablet from God. "Thou shalt have a brain. Thou shalt use it to notice patterns". The natural history of these nanotablets was given by Darwin: the animals with inductive priors (ie working brains) figured out the patterns of life reliably enough to turn a profit on the metabolic investment, and thus had more children on average over the last 500 million years.

By why should induction working in the past result in us believing in it now? Well, physically speaking again because evolution itself has an inductive prior. The genes associated with successful life are assumed to be able to cause it again, and passed down. Evolution is itself an inductive epistemic process, with us running around as its little hypotheses testing the knowledge that it accumulates in our genes. Why does evolution have an inductive prior? Because that's the kind of life that worked, and more deeply, because the natural world itself has enough of an inductive prior to "learn" life into existence to exploit its own regularities for fun and profit. So physically at least, we trace our belief in induction back to the beginning, to knowledge somehow baked in to the foundations of the world.

And where did that knowledge come from? Back there at dawn of nature we reach the limits of natural science, and can only speculate about simulation hypotheses, anthropic principles, and first and final causes. But the long and the short of is is that some process of design or selection produced this universe, with that knowledge already baked in. It was revealed to us, written like a message from God in the fabric of reality itself, by some loftier power inherently beyond the limits of our cognition. I feel I've heard this story before.

But that's just a natural history of our belief up to now, not a proof of it going forward. I believe there is no proof. All we can do is notice how existentially bound up we are to its truth, notice that whether we believe it or not we are doomed to take the leap of faith on induction, quake at the implications of deciding not to believe it at this point, and fatalistically accept that we must have faith in the apparent word of whatever or whoever created the world with an inductive prior.

So we're left where we started: we have to assume it on faith. But now we have a somewhat better idea what exactly is being taken on faith and why, and more importantly a schema by which such questions can be answered. In particular, can this story be extended to cover also revelations of value? If it can, maybe we have the beginnings of a moral rationality.

>>2206

I believe the No Free Lunch (NFL) Theorem for learning is profound, but that its implication is nearly the opposite of its naive interpretation.

It states that there is no effective algorithm for learning "across all possible universes." (You stated that as a "know-nothing prior." Same thing.)

But the critical point (usually missed in discussions of NFL) is that we don't live in all possible universes. We live in exactly one, with its very particular laws of physics. And in this particular universe, we observe that learning *does* work. Evolution does it. So do our ML algorithms, some of them surprisingly well.

I agree that it's a kind of faith to trust that our universe will keep being this way. But that's equivalent to trusting that the laws of physics won't suddenly change. I, for one, can muster that degree of faith without difficulty.

We aren't God. We don't need to solve problems across all universes. Only across our own. So I would say that the necessary faith can indeed be extended to revelations of value.

>>2207
It's not a particularly profound leap of faith to believe that the order we see in the universe is stable, that is true. But I think it's necessary to acknowledge that it is a revelatory leap of faith, so that we have a very solid and simple example as we go on to tackle the more speculative sorts of revelation.

> We don't need to solve problems across all universes. Only across our own.

Reminds me of the Jim.com classic:

> Utilitarian and relativist philosophers demand that advocates of natural law produce a definition of natural law that is independent of the nature of man and the nature of the world. Since it is the very essence of natural law to reason from the nature of man and the nature of the world, to deduce “should” from “is”, we unsurprisingly fail to meet this standard.

Our leap of faith is only the kind of animals we are and the kind of world we live in.