Three enigmas at the heart of our reasoning
Financial status: This is independent research supported by a grant. I welcome additional support.
Epistemic status: Reflections from personal experience.
What can we ultimately trust as a foundation for our reasoning?
As we go about our lives, we often trust reasoning that is based in empirical, mathematical, and ethical frameworks. Trust in these systems seems well justified. But what exactly is it justified by, and does this question have any practical relevance to our lives, or is it merely the domain of frivolous dorm-room discussion?
In this essay I am going to focus on the question of practical relevance. I will not ask you to take radical skepticism more seriously than you have. I will actually ask you not to take it seriously, but to take seriously the question of why it need not be taken seriously.
Here is why: at a day-to-day level, most of us do in fact trust empirical, mathematical, and ethical reasoning quite a bit. Yet when we question their foundations and come up empty-handed, we also in fact continue our day-to-day work unabated. Why is that possible?
This question, I believe, strikes at the heart of an issue of enormous practical importance, which is: how can we go about our work without being hindered by self-doubt? I am not talking about some small emotional thing or a mere personality quirk when I refer to “self-doubt”. I am talking about deep doubt concerning the fundamental reasoning systems upon which we predicate our lives.
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 is as if we were stuck in a kind of awkward middle ground: on the one hand we are, for good reason, not quite willing to surrender into radical skepticism and put our whole lives on hold in order to work through a deep ontological crisis, yet on the other hand we are not able to put these questions aside, either, and so although we do get up from our philosophical armchair and get to work, we do so with incomplete confidence, and so we proceed with some doubt in our hearts, quietly hoping that we haven’t gotten life completely wrong.
OK, now for the three enigmas.
The first enigma
Look, in order to justify our reasoning about the physical world, we often start with the assumption that simpler hypotheses are more likely to be true than complicated hypotheses, or that we should set our credence in hypotheses proportional to the inverse exponential of the shortest computer program that expresses them, or that the world operates on lawful principles that do not suddenly change, or that the methods of reasoning that have proven effective as a means to getting things done in the past will continue to do so in the future. These foundational principles can each be used to justify each other, can each be used to justify the whole edifice of empirical reasoning, and have no deeper justification within empiricism. The system of empiricism provides no empirical basis for believing in these foundational principles.
To doubt that methods of reasoning that have worked in the past will continue to work in the future is radical skepticism, but you don’t have to be a radical skeptic to see that the foundational principles of empiricism cannot be justified within empiricism. This is not a strike against the trustworthiness of empiricism, but it should be a strike against any sense that the reason empiricism is trustworthy lies within empiricism. I hope my wording does make out that this is some terribly deep point. I am really not trying to say any more than the literal here.
Now you might say that empiricism has given us houses that really stand upright, crops that really produce yields, power plants that really produce electricity, and dog collars that really play Christmas carols. This is true. But thus we have observed in the past; on what basis do we conclude that methods of reasoning that have worked in the past will continue to work in the future? 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.
Now you might say that methods of reasoning that have worked in the past are likely to continue working in the future because it would be a strange and unwieldy to hypothesize a world that operates according to one set of lawful principles for a long time and then unexpectedly changes just at the moment that you make an important inference about the future. Indeed that would be strange and unwieldy, and obviously we should not believe strange and unwieldy things. But why is it that we should not believe strange and unwieldy things? I am not asking you to start believing strange and unwieldy things! Please continue to disbelieve in strange and unwieldy things, but, as you do, please do not carry any sense that your disbelief in strange and unwieldy things can be justified empirically.
Now, Ray Solomonoff proved that a machine learning system using the universal prior would come to make predictions more or less as quickly and accurately as any other estimator and prior, but only on the assumption that the real world is Turing-computable. Why should we believe that the real world is Turing-computable? Well, we can appeal to the empirical laws of physics, but where does our trust in those laws come from? I am not asking you to stop believing that the world is Turing-computable, but I don’t think it’s feasible to say that the reason you believe that the world is Turing-computable lies within empiricism.
David Deutsch says that the Turing-computability of the universe should be taken as an observed property of physics in which we can place greater confidence than in any particular laws of physics, much as we can have greater confidence in the time-reversibility and conservation-of-energy principles than in any particular laws of physics. But now that we’re talking about inferring properties of the world from observations of the world, we’re just back to empiricism. Why should we believe in empiricism? I am not actually asking you to doubt empiricism. I am asking you to inquire into your seemingly-to-me well-justified non-doubt in empiricism.
You might say that any game of “but why should I believe that?” will eventually bottom out, and that we ultimately have to get up from our armchairs and actually build houses, actually plant crops, actually design power plants, and that when we do that we will easily shrug off the folly of our armchair skepticism. And here I wholeheartedly agree, but as you are shrugging off armchair skepticism through practical engagement with real-world problem-solving, do not imagine that you are doing so in a way that is justified by some well-founded principles of empiricism. The point of this essay is not to call into question the practical efficacy of real-world problem solving, it is in fact to highlight the practical simplicity of real-world problem solving, and to call to attention the fact that it is not founded in empiricism. Neither does it refute empiricism. It does not conflict in any way with empiricism, yet it cannot be ultimately justified by empiricism. And it does not seem that it needs to be. Why? This is what I will call the first enigma at the heart of our reasoning.
The second enigma
In mathematics, we begin with a system of logic and add to it a system of axioms. A system of logic is a rule for generating new logical sentences from an existing finite list of logical sentences, and a system of axioms is a set of logical sentences to start the whole process with. An example of a system of logic is first-order logic, and an example of a system of axioms is the nine axioms of Peano Arithmetic. Now there was a time when mathematics was expressed in natural language with little regard for rigorous systems of deduction, and then mathematicians began to ask whether they were allowing themselves to get away with too much, and were engaging in frivolous poetry rather under the guise of rigorous mathematics. In reaction to this, mathematics was formalized, with the intention that every mathematical theorem could, in principle, be derived formally from some suitably well-grounded system of logic plus axioms.
But why do we believe that a simple logic plus a small set of formal axioms is a sturdy foundation for mathematics? Why is this the basis on which we claim that our mathematics is non-frivolous? It was once hoped that we might find a foundation so sturdy that it could prove its own sturdiness, and then Kurt Gödel showed that this can never happen. But suppose we were living before Gödel proved his famous theorems. We might still ask why, if some mathematical theory were to assert its own soundness, would we believe it?
And once again we can go around and around with the “why should I believe it?” game. 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. We will never find a satisfying conceptual answer to “why should I believe it?” within the systems that we are questioning. And yet none of this matters at all to someone calculating the tensile strength of a beam in a house, or predicting the energy that will be released in a nuclear fission reaction, or, for that matter, squinting in awe at the beauty of algebraic geometry. We can question the foundations of mathematics all day long, but when we get up from that armchair and simply do mathematics, it matters not at all. This essay is not a call to stop doing mathematics and start worrying about the lack of a satisfying foundation for mathematics. Quite the opposite! But while we are happily doing mathematics, we should not imagine that the whole thing is based in some framework that can be justified all the way down by mathematics, or by empiricism. 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.
The third enigma
And finally we come to ethics, in which we have systems for reasoning about what we ought to do. We have virtue ethics. We have deontology. We have consequentialism. Perhaps we ought to cultivate virtue, or perhaps we ought to adhere to our moral duties, or perhaps we ought to select actions on the basis of their consequences. Why?
We can choose to place ethics in dependence upon empiricism and logic, and take as primary that we should act in service of the welfare of sentient beings, and then use empiricism and logic to work out which actions will lead to the welfare of sentient beings. Or we can take ethics as primary, and view the act of holding certain empirical or logical beliefs as moral actions, to be justified on the basis of their ethical consequences. In either case, we will not find an answer to the “why should I believe it?” game within the systems of ethics or mathematics or empiricism.
And yet we must act. We simply must. And we do, every day, without all too much of a problem. I am not asking you to doubt ethics. I am asking you to doubt that your reason for correctly (in my estimation) not doubting ethics can be found within ethics.
In our real lives out in the real world beyond the confines of this short essay, these questions are of no small practical importance. 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 is as if we were stuck in a kind of awkward middle ground: on the one hand we are, for good reason, not quite willing to surrender into radical skepticism and put our whole lives on hold in order to work through a deep ontological crisis. Yet on the other hand we are not able to put these questions aside, either, and so although we do get up from our philosophical armchair and get to work, we do so with incomplete confidence, and so we proceed with some doubt in our hearts, quietly hoping that we haven’t gotten life completely wrong.
In the year that I spent in a monastery, I was given the time and tools to deeply investigate these kinds of questions. I was in an environment where severe ontological crises were okay, where howls of despair were to be heard echoing from the interview room, where the rhythms of the daily schedule were practiced so deeply into our bones that we could become deeply confused without getting lost.
Many people think that meditation is about relaxation, or destroying the ego, or some kind of otherworldly magical something. It’s not like that. It’s about the questions that already haunt us, that have been haunting us for so long that we have grown used to living a haunted existence. It’s about leaning into those questions, and then getting to work without being haunted by doubt.
In my year in the monastery, I did not take this task to completion. I regret this very much. But I got a sense of it, so I’m writing about what I did discover.
In order to put doubt to rest, we might work on a question such as “what can really be trusted?”. In order to answer such a question, we have to concentrate our attention on it for a little while. In order to concentrate on such a question for a little while, we have to let go of the defense mechanisms that we have quite reasonably assembled in order to not be set adrift by investigating such a question from within a society that will not take good care of us during an ontological crisis. In order to let go of those defense mechanisms, we need to put ourselves in a place that demonstrably will take care of us during an ontological crisis. The place I found most able to take care of me was a monastery, where the leaders had already spent time struggling deeply and so were not easily spun out by students going through crises.
Many people do not understand why monastic containers are so rigid. It is so that the whole group can go through such crises without falling apart. When the world in which you’ve lived your whole life stops making sense, it is only the messages that you’ve left for yourself deep inside your own bones that carry you through. In the monastery, we practiced living the same simple day over and over, so that when it finally really mattered, we could do it without thinking.
I aspire to create the kind of community where people can do long-termist research in the context of such safety. It may or may not look anything like a monastery. The point is not to be a monastery, but to be a safe place where one can lean into important research questions and work through the ontological crises that sometimes result. I hope that this safety will make it possible to lean in exactly as deeply as each person wishes to. I hope that as a result, a wholehearted group ethos of simplicity and determination will emerge. I hope that within this container we can put to rest not just the doubts that haunt us personally, but also some of the unresolved technical and philosophical questions that haunt us as a society.
See also: G Gordon Worley on the problem of the criterion