I really empathize with being troubled by such questions. I was amused by them a decade or so ago and I've found a way to actually make peace with them before I discovered Less Wrong, which in turn gave me so crucial insights, allowing to solve these enigmas to my own satisfaction. 

The way I originally made peace with these questions was through embracing the doubts rather than running from them. To, as you put it, "surrender to radical skepticism" Suppose that the questions are indeed unsolvable. That there is no ultimate justification, that everything is doubtful, that no absolute truth can ground our knowledge. Why would that be bad? How would we navigate in such a world?

The first impulse may be to fall for the fallacy of gray. It's understandable. But notice that some things are still easier to doubt than the others. You may doubt in you sensory inputs and you whole reasoning process. Allow it to yourself. Try it for a while and notice how much harder it is than to doubt the existence of invisible pink unicorn. There is no rule that compell you to doubt so hard in some specific cases but not the others. If such rule existed it would be so easy to doubt it. And notice that when you approach everything with the same level of doubt it all adds up to normality. 

The questions aren't answered yet. Why is it easier for me to doubt in X than in Y? But no more they are torturous, when you try to ground your knowledge in doubt rather than in certanity. Why did you think that absolute certanity is necessary in the first place? Isn't this idea really weird? How would it even work?

Yeah, it's hard to imagine how "why regress" can be escaped.

Ontological: why is there something rather than nothing? To any answer, reply "why" again.

Epistemological: why is something true? To any answer, reply "why" again.

Moral: why is something good? To any answer, reply "why" again.

Maybe our trouble with these questions has to do with our conviction that everything must have a reason? An interesting perspective on this is Chaitin's: "Some mathematical facts are true for no reason, they're true by accident!" He gives a specific infinite sequence of questions about natural numbers, such that the sequence of their yes/no answers is provably indistinguishable from a fair coin by any algorithm (including our finite minds). Maybe this could teach us something about how to deal with "why regress" in other areas.

The first enigma seems like it's either very closely related or identical to Hume's problem of induction. If that is a fair-rephrasing, then I think it's not entirely true that the key problem is that the use of empiricism cannot be justified by empiricism or refuted by empiricism. Principles like "don't believe in kludgy unwieldy things" and "empiricism is a good foundation for belief" can in fact be supported by empiricism - because those heuristics have worked well in the past, and helped us build houses and whatnot.

I think the key problem is that empiricism both supports and refutes the claim "I know empiricism works because empirically it's always worked well in the past". This statement is empirically supported because empiricism has worked well in the past, but it's also circular, and circular reasoning has not generally worked well in the past.

This can also be re-phrased as a conflict between object-level and meta-reasoning. On the object level, empiricism supports empiricism. But on the meta level, empiricism rejects circular reasoning.

We will never find a satisfying conceptual answer to "why should I believe it?" within the systems that we are questioning.

Satisfying to whom? Plenty of people are perfectly well satisfied with various answers to this question within all sorts of systems.

Other people have some doubts, and I strongly suspect that a large fraction of those always will.

Personally, I nearly always reserve some sliver of weight to the possibility that my senses, memory, and thought processes cannot be trusted. There's not much I can do about it, so it has little practical application except to make me slightly more risk-averse in some situations.

That aside, I think that on theoretical grounds empiricism is a bit more well-founded than the "first enigma" section makes it sound. While fundamentally there is no reason for the future to follow the same rules as the past, there does seem to be some reasonable justification that it's unlikely to suddenly change right now. Okay, maybe it didn't happen while you were reading that last sentence, but maybe it will happen right now instead.

While there's nothing fundamentally wrong with supposing that things may well change right now when they don't appear to have changed in at least the past few billion occasions of right now, it does seem to privilege the observer almost to the point of solipsism.

It is as if we were stuck in a kind of awkward middle ground

Throughout this post I was thinking about the phrase "starting from the middle" as where we are, with neither perfect knowledge of reasoning nor of our goals, but having something to go on and having to build from there.

It also reminds me of Abram's post An Orthodox Case Against Utility Functions which is about getting started from the point of view of an agent, created in motion, not the point of view of the universe (or some other omniscient sort of position).

Regarding the first enigma, the expectation that what has worked in the past will work in the future is not a feature of the world, it's a feature of our brains.  That's just how neural networks work, they predict the future based on past data.

Regarding the third enigma, ethical principles are not features of the world, they are parameters of our neural networks, however those parameters have been acquired.

Regarding the second enigma, I am less confident, but I think something similar is going on.  Here my metaphor is not the ML branch of AI, but the symbolic processing branch of AI.  Or System 2 rather than System 1, to use a different metaphor.   Logic and math are not features of the world, but features of our brains.

I know I keep leaving comments pointing to this post of mine (I would stop if I felt like its contents had entered the collective consciousness, but they haven't and I wrote the post to change that so here we are), but all three of these enigmas are instances of the problem of the criterion. Reading through the comments, I feel like most of them come down to folks continuing to struggle to come to terms with the problem and its implications.

These three enigmas are all instances of the same enigma, the impossibility of finding ultimate justification for anything, respectively knowledge of how to observe, how to think, and how to act; alongside the necessity to carry on with life anyway. Why not just recognise the impossibility of finding ultimate justification for anything, and carry on with life anyway, while studying these things at your leisure?

My house is not going to fall down just because I start thinking about why it has not.

I greatly enjoyed this, thanks for writing it. I matched it to one of the questions in my own personal pantheon of mysteries.

What does it mean for a belief to be self-evident?

It seems self evidently true that I exist, that I am conscious, suffering is bad, wellbeing is good, and the next moment of experience will be the nesesary consequence of this moment.

I can point to the raw justification for these facts in my experience, and I just assume that other people have similar justifications embedded within their subjective perspective. But it's still an intellectual mystery to me why "it's self evident" feels like a satisfying justification. As you say maybe that too is self evident ad infinitum

justify our reasoning

It seems more practical to develop reasoning systems that work well enough to explain what the confusing systems that were never designed happen to be doing. The useful sense of justification is not about describing what's already happening, but about choosing well, making use of what you have available. There is no point in figuring out if what you have available is well-designed, apart from an act of redesign.

Awesome. I feel a strong resonance with many thoughts and ideas and its beautiful cadence and phrasing touch me. While reading I was at the same time thinking that meditation has some (un-)answers and wondering whether you would give answers or not.

When you mentioned your monastery year it made sense that the prose felt a bit like the parts of the Satipathana Sutta that I know. Very wholesome; I hope it will be appreciated (earlier or later).

Please elaborate or foster elaboration on this. Talk more about the safe space you have in mind. I have the feeling that it is subtly different from what Jacob Falkovich touches on in The Treacherous Path to Rationality.  

Having doubts is crucial for better investigations. How you address those doubts and to what extend you address them dictate the success and practicality of your investigations. Some doubts are more easily solvable than others, but doubts are usually not really the direct focus of your investigations but of supplementary materials that can potentially change the course of of your methodology. It can affect how you value your work and what areas you think would be worthwhile to focus on in your future work.

I firmly believe that having doubts is better than not having them. It's one of the core component of thinking outside of the box so to speak. Everything in moderation suggests that there can be a breaking point in having too many unrelated doubts that would hinder your own progress as you get lost in the sea of possibilities. Doubts essentially guide us in whether we think of our own pursuits as something that's fruitful or futile. How we deal with the importance of certain doubts vs others is an art in and of itself.

I am not asking you to doubt that things that have worked in the past will continue to work in the future, but you cannot claim that your non-doubt is founded in empiricism.

Can't I though? I can empirically observe that for any year N between N=1800 (or less) and N=2000, general laws that held before N usually held after N, and further, we can empirically find heuristics for what kinds of laws tend to hold up (starting, obviously, with the laws of physics).

Our ability to observe history is limited, though, and maybe that's a big problem?

An "ontological crisis" is treated well enough when you note your perception as a belief. If it's literally impossible to not have a best working model of reality in its entirety that undermines profound doubt.

Have you read the Sequences, or Sean Carrol's 'The Big Picture'? Both talk about these questions. For example:

We can appeal to empiricism to provide a foundation for logic, or we can appeal to logic to provide a foundation for empiricism, or we can connect the two in an infinitely recursive cycle.

See explain-worship-ignore

and more generally

mysterious-answers

The system of empiricism provides no empirical basis for believing in these foundational principles.

See no-universally-compelling-arguments-in-math-or-science

and more generally

mind-space

simpler hypotheses are more likely to be true than complicated hypotheses

I'm not sure if this appeared in the Sequences or not, but there's a purely logical argument that simpler hypotheses must be more likely. For any level of complexity, there are finitely many hypotheses that are simpler than that, and infinitely many that are more complex. You can use this to prove that any probability distribution must be biased towards simpler hypotheses.

We need not doubt all of mathematics, but we might do well to question what it is that we are trusting when we do not doubt all of mathematics.

"All of mathematics" might not be as coherent as you think. There's debate around the foundations. For example:

• Should the foundation be set theory (ZF axioms), or constructive type theory?
• Axiom of Choice: true or false?
• Law of excluded middle: true or false?

(I'm not a mathematician, so take this with a grain of salt.)

There are two very different notions of what it means for some math to be "true". One is that the statement in question follows from the axioms you're assuming. The other is that you're using this piece of math to model the real world, and the corresponding statement about the real world is true. For example, "2 + 2 = 4" can be proved using the Peano axioms, with no regard to the world at all. But there are also (multiple!) real situations that "2 + 2 = 4" models. One is that if you put two cups together with two other cups, you'll have four cups. Another is that if you pour two gallons of gas into a car that already has two gallons of gas, the car will have four gallons. In this second model, it's also true that "1/2 + 1/2 = 1". In the first model, it isn't: the correspondence breaks down because no one wants a shattered cup.

I'm actually very interested to see what assumptions about the real world correspond to mathematical axioms. For example, if you interpret mathematical statements to be "objectively" true then the law of the excluded middle is true, but if you interpret them to be about knowledge or about provability, then the law of the excluded middle is false. I have no idea what the axiom of choice is about, though.

the-simple-truth

I am asking you to doubt that your reason for correctly (in my estimation) not doubting ethics can be found within ethics.

Have you read about Hume's is-ought distinction? He writes about it in 'A Treatise of Human Nature'. It says that ought-statements cannot be derived from is-statements alone. You can derive an is-statement from another, for example by using modus-ponens. And you can derive one ought-statement from another ought-statement, plus some is-statement reasoning, for example "you shouldn't punch him because that would hurt him, and someone being hurt is bad". But you can't go from pure is-statements to an ought-statement. Yudkowski says similar things. Once you instinctively see this distinction, it's not even tempting to look for an ultimate justification of ethics or within empiricism, because it's obviously not there.

The problem, I suspect, is that these questions of deep doubt in fact play within our minds all the time, and hinder our capacity to get on with our work.

It's always dangerous to put thoughts in other people's minds! These questions really truly do not play within my mind. I find them interesting, but doubt they're of much practical importance, and they do not bother me. I'm sure I'm not alone.

It seems like you are unhappy without having "a satisfying conceptual answer to 'why should I believe it?' within the systems that we are questioning." Why is that? Do you not want to strongly believe in something without a strong and non-cyclic conceptual justification for it?

Wanting compressions to be universalizable makes sense, it would be an additional compression bonus to be able to throw out all the contextual data about when the compression isn't a good fit for part of reality. I think it's mostly incoherent as a principle even though as a process it can be a good intuition to follow (E=MC^2 and Natural Selection sure are useful). We don't actually need a ground to push off of, we create our own control surfaces, like wingsuits.

" In order to let go of those defense mechanisms, we need to put ourselves in a place that demonstrably will take care of us in an ontological crisis."

While I agree with statement by itself. In relationship to the Monastic Academy which is here called the monastery, this is laughable at best and at it's worst deeply untrue and dangerously misguided. This does not track with my own experience; or over a dozen other testimonies from former residents and apprentices that have left the monastery over the last 2-3 years in traumatic states whom have not been cared for or even followed up with to see if they are ok by the organization you are speaking about. While some speak to the positive benefits they received via simple living, community, and meditation practice as you've described here; many have also had suffering significant pschological challenges and needed professional support to heal and deprogram the unhealthy beliefs and behaviors they learned within the organization. So should you or any other person consider the Monastic Academy trustworthy in the face of an ontological crisis? Especially when the environment itself, more often than not drives one into a state ontological crisis that is neither normal or healthy.

So how do we decide what and whom is trustworthy? How much evidence do we need? Do we trust our own direct experience, first and foremost? Do we ignore others direct experiences when they don't align with ours? Do we trust the data? Do we trust reasoning, mathematics, and ethics to show us what's ethical?

The question of " what is trustworthy?" Is of incredible importance. All too often those whose view of things has been skewed by the privileges given to them by society or within a group(I.e class, race, gender, wealth and social influence) miss the mark entirely on this question because they have never had the good fortune of learning the true nature of the people who surround them, and too often they have not even learned there own. The only way to know someone's true nature is to watch how they treat others from whom they have nothing to gain but their humanity. Few recognize that this is the most valuable gift of all.