What I Believe

A Twitter user writes: "I've never heard a single atheist explain to me What exactly they believe."

I think this is a good question, we all should ask ourselves what are our most basic belief. For myself, I can identify a few beliefs that are so basic that it's hard for me to imagine a world in which they wouldn't hold true. Here they are:

1. Mathematics and logic are correct.

2. The world is explainable and simpler explanations are more likely to be true.

3. My feelings are real.

4. Suffering is bad.

Each one of these statements requires some qualification and explanation, so I'll expand them in the following sections.

I can't think of any instance in my life where I acted based on any beliefs that contradict the ones that I list above and I am absolutely sure I will not act against these beliefs in the future.

For each belief, it would be interesting to examine, which of them are falsifiable, i.e. for which of them I could theoretically conceive of a sequence of events that would convince me that I'm wrong on that point. It turns out that I can imagine a way in which beliefs 1 and 2 can be falsified, though I strongly believe that in practice that will never happen. I can't imagine such scenarios for beliefs 3 and 4, though this doesn't mean that those beliefs are in any way stronger or weaker.

If I were to be asked how much money I would bet against $1 that each one these beliefs is true, I would answer something like $1000 for each of them, which would represent the probability 0.1% that I assign to me being completely mad and delusional to the point that I can't follow a coherent train of thought.

1. Mathematics is correct

Mathematics is the basic language of the world. At its core, it describes the relationships so fundamental that it's difficult to imagine them not being true. Suppose you have two piles of apples. In the first pile you put 2 apples and then 2 more. In the second pile you put 3 apples and then 1 more. The piles will have the same number of apples: you can arrange the apples side-by-side with one apple from each pile corresponding to the one from the other. This is a mathematical statement, and all of the mathematical statements are somewhat like this: they represent tautological propositions that can't possibly be false.

If you happen to have studied Math, you might ask me, what specific mathematical theory I believe. Do I believe Zermelo–Fraenkel set theory? Axiom of choice? Something else?

The remainder of this section is a bit technical, and if you are not asking these questions, you can freely skip until the next section.

At the very minimum I believe constructive mathematics: a mathematical theory operating statements about finite and countably infinite sets that could be either verified or falsified in the finite amount of steps by a Turing machine.

Consider Riemann hypothesis. It can't necessarily be verified by a Turing machine, but if it is untrue, it can certainly be falsified in a finite number of steps: given a non-trivial root with Re (real part) other than 1/2, we can find its neighborhood that separates it from the line Re z = 1/2 and prove that the neighborhood contains at least one root following Rouché's theorem. It means that not only can we falsify Riemann's hypothesis if we already know the counter-example, but we also can find the counter-example in a finite number of steps if it exists. Hence Riemann hypothesis is constructive.

The opposite example would be Banach-Tarski paradox — a proof that we can split a ball into several subsets that can be recombined into two balls of the same size. There is no way to formulate or prove it in a constructive, finite way.

Do I think that Axiom of Choice is untrue or uncountable sets do not exist? Not necessarily. I think mathematics with them is almost certainly consistent and can produce valid results. However we can't directly interact with any uncountable set. According to Bekenstein bound, a limited volume of space can contain only a finite amount of information before collapsing into a black hole. With this in mind, even if you or I live forever and somehow avoid the heat death of the universe, in our infinite lives we'll be able to interact only with a countably infinite amount of information.

For this reason, I don't have any unconditional faith in say Axiom of Choice. If tomorrow someone would find a contradiction in ZFC, it would be very exciting, but wouldn't shatter my life views. If on the other hand, tomorrow I put into a pile 2 apples and another 2 apples, and then manage take from it 3 apples and 3 more, it would completely blow my world apart. I can't imagine what I would feel or do if that were to happen. I probably just conclude that I went mad.

2. The world is explainable and simpler explanations are more likely to be true

This is the basis of the inductive empirical reasoning. You can think of it as a version of Occam's Razor, or if you wish of Bayesian reasoning. In its core, it's a belief that you can use your previous observations to predict the results of the future observations.

More specifically, if you have a number of observations in some domain, you can build a model and use this model to predict the results of future observations. The model doesn't necessarily have to be deterministic, it could include randomness.

For example, a model for throwing a coin would be: "The coin lands randomly, half the time heads and half the time tails". This is not the only model that would explain the past coin tosses. Another model would be "The coin landed on heads, heads, tail, heads, heads, heads, tail, tail, heads and next time it will land on tails". Both models explain all of the previous tosses and both make predictions for the next toss. The first model makes the following prediction: P(tails) = 0.5. The second model's prediction is: P(tails) = 1. My belief is that the first model is more likely to be true by virtue of being simpler.

While above I mentioned the "future" observations, this approach doesn't really have anything to do with time. If someone were to throw a coin in your presence and would conceal one coin toss from you, but show the subsequent ones, you could just as well use the model to predict the past toss as you would the future tosses.

There's a few more moving parts here that require further explanations. They include the meanings of the words "simpler", "explain" and "more likely". (I don't want to be like Jordan Peterson here and question the meaning of every single word, I promise.)

Suppose it's not you who does the tossing, but your friend, and on every third toss, he uses another coin that always falls heads. Consider the following three models:

1. P(heads) = 0.5

2. P(heads) = 1 for every thirds shot, P(heads) = 0.5 for other shots

3. HHHHTHHHHTHHHTHTHH and after that always heads.

Every next one of these models is more complex than the previous and is better at explaining the past observations. If we are looking for the simplest explanation, shouldn't we pick the first one? The answer is that the simplicity is not the only thing that we are looking for. We are also looking at the precision of prediction.

But then, what about the third model? Isn't its absolute precision in explaining the past tosses a good enough reason to use it despite additional complexity? The traditional answer to this is as follows: suppose we fix these three hypotheses and do some more experiments (i.e. coin tosses). After a few tosses we'll get a counter-example that will invalidate the third hypothesis.

This is not the whole story though. Suppose you are studying paleontology, and all you have are some limited number of bones. You simply can't run new experiments at will. Does it mean that if you have only limited amount of data, then there's no way to exclude hypotheses like 3? Not necessarily.

We can objectively measure both the complexity of a hypothesis and its predictive power. For the complexity, you could literally count the number of bits that are required to formulated it (or more precisely to build a Probabilistic Turing machine that would generate the model). This is called Kolmogorov complexity.

For the quality of the prediction, you can use Cross-entropy, which measures the amount of randomness in the results, conditional on your model: for the hypothesis 1 you need 1 bit of randomness per toss, for hypothesis 2 you need 2 bits per 3 tosses, while hypothesis 3 is fully deterministic — you don't need any additional randomness.

Using Kolmogorov complexity, Cross-entropy and the Bayes theorem it is possible to formulate specific criteria which will tell you if some model is better than the other. I do not subscribe to any such specific formula as my core belief (maybe if I give it more thought I will), but I do believe some version of it is true. Also I believe that the following two weaker statements are definitely true:

1. Out of two models of equal explanatory power the simpler one is more likely to be true.

2. Out of two models of equal complexity the one with more explanatory power (cross entropy closer to 0) is more likely to be true.

To finish this section, I want to highlight, that while I absolutely don't believe it possible, I can still imagine how I could find this belief untrue. Suppose I keep using inductive reasoning to predict various outcomes and I keep getting them wrong. This would mean that either inductive reasoning is wrong, or I myself am unreliable and I can't trust my beliefs anyway.

3. My feelings are real

The third belief stated in the intro to this article is less about what my feelings are, than about what it means to be real or to exist.

To talk about anything other than Math, we need to postulate the existence of something. Following Descartes and Locke, the absolute basic things about the existence of which we can be sure are our own thoughts and feelings.

Fortunately, given the belief 2, described in the previous section, postulating just the reality of your own thoughts and feelings seems sufficient to prove existence of many other things.

When I'm pressing keys on my keyboard right now, I see letters appearing on the screen. When I turn away, and then back to the monitor, the letters are still there (unless my cat decides to walk in front of the monitor). If I hit the wall with my fist, I feel pain. If I lift a coin and release it, I see it falling and than making a metallic sound that happens when it hits the surface.

Consider two hypotheses: a) those are figments of my imagination, and b) there's a thing called physical world, operating according to a limited set of laws, that preserves the consistency of my senses. The second hypothesis is a bit more complex than the first one, but it has so much more predictive power that it should be preferred.

So far, we don't have any evidence that this "physical world" is a thing that is external to us, rather than a part of our brain that just "emulates" the consistent external state. But let's move on.

In my life I've met other people than me. These people certainly feel different than I feel: if I prick someone else with a needle, I don't feel pain, while if I prick myself, I do. But there are similarities: if I ask someone to describe the feeling of being pricked with the needle, and then describe this feeling myself, the descriptions will be very similar. The same goes to the feeling of warmth from being in the sun, the thoughts about kittens being cute and the feeling of love. If all of the other people were just figments of my imagination, there wouldn't be any definite reason for it to be so.

Furthermore, there are other people that know more and are more skilled than I in many ways. The most damning of all is that there are other people that have expressed an idea that I might be a figment of their imagination. Putting it all together, it seems that the simplest explanation for these observations is that there are other people similar to me, and we all live in the same physical world external to our minds.

One important caveat about the reality of feelings is that, while all feelings are real in some sense, not every feeling corresponds to a real external event or entity. Some of the feelings could be dreams, hallucinations or delusions.

If we are initially agnostic about which feelings correspond to "real" external things and which do not, how can we separate ones from the others? The obvious answer is: by checking whether some entity that you are experiencing fits into the external world. Suppose you see a demon sitting on your right shoulder. How to determine if he is real or not? Ask yourself questions: Could anyone else see it? Could it help you cheat at cards by telling you others' hands? Could it affect anything in the external world, that you aren't touching, in a way noticeable to other people? If the answers to all of these questions are "no", the demon is likely not real, or at least not real beyond the reality of the impulses in your brain.

Unlike the previous two sections, I can't imagine a scenario which would convince me that this belief is not true, i.e. that I don't exist.

4. Suffering is bad

The previous beliefs that I wrote about are mostly epistemological and ontological in nature. This one is ethical and it's the most basic ethical belief that I can think of. In a few more words, to make it more precise, I believe that:

Everything else being equal, the situation where any conscious entities experience more suffering is less desirable.

Before we move on, let me define what exactly I mean by "suffering". Suffering is a situation that a conscious being would actively try to avoid. Pain is a biological process, subjective experience of pain is an example of suffering. A body of an unconscious or fully anesthetized person can have some processes associated with pain, i.e. neural impulses from the pain receptors and possibly some simple reflexes. However if the person is unconscious, there no one to "feel" the pain and act in a way to avoid it, hence there is no suffering in this scenario.

A conscious being is any entity that is capable of subjective experiences, i.e. something that can feel its feelings rather than mechanically respond to them. I know that this definition of consciousness is frustratingly imprecise, but I don't think the modern philosophy of mind has any better definition that capture the meaning of the word.

According to modern neuroscience, all mammals and birds are conscious (unless they are knocked out or are fetuses or are in a vegetative state). Octopuses are probably conscious. It's unclear whether fish and any insects are conscious and if yes, then to what degree. Trees aren't conscious.

Getting back to the belief stated above, "everything else being equal" part bears a lot of weight in it. I do believe that some suffering is ok provided it has benefits:

• Running a marathon involves a fair bit of suffering, but the self-esteem and physical benefits that you are drawing from it are worth it.

• Killing or banishing a mouse that lives on the field where a new house will be built is probably worth the utility that the people living in that house will draw.

There are many situations in which I am more or less agnostic about whether the suffering is justified or not:

• A predator killing its prey in the wild.

• Growing farm animals for food (under various conditions).

There are situations that aren't exactly covered by the above belief, but which I still believe are undesirable, the clearest one being somebody hurting someone else for fun (e.g. bullying, hunting animals for sport). Technically, this doesn't fall under the above definition, since there is a party that draws pleasure from the the process, but I still think that this is wrong.

Speaking of pleasure, as you might have noticed, the statement above only applies to suffering, but not to pleasure which is its opposite. I do think that usually, everything else being equal, more pleasure is good. However I'm not equally certain about this statement as I am about suffering. I can imagine that maximizing pleasure beyond some point can be if not negative, then at least neutral. For that reason, I don't treat this belief as fundamental.

5. Other beliefs

The four principles described above are my fundamental beliefs, something I can't imagine changing. Beyond these beliefs I do have more mundane or less certain beliefs.

When it comes to epistemology and experiencing the world, I think the beliefs 1-3 are more or less complete: these beliefs in themselves are enough to explain or discover anything in the physical world. This statement in itself is a belief, which I don't hold as fundamental. I think that it is enough to apply inductive and deductive reasoning to discover every empirical truth in the world, but I am not sure this is true. It is possible that I am mistaken and in fact I need some additional belief about the nature of the world or some such.

My relationship with ethics is a bit more uncertain. As I wrote in the previous section, my most basic belief about ethics is quite minimalistic. In real life I believe that we should follow some combination of Kantian and utilitarian ethics. However neither of them is precise enough that I could formulate it as some fundamental law that I would believe unquestionably.

What is fundamental though is game theory (as part of Math, i.e. belief 1). I think it is very likely that most of ethics can be derived from the natural selfishness via the application of game theory. The repeated prisoner's dilemma shows that cooperation is better than confrontation for one's own self interest. I believe that this principle might well be enough to base all of ethics upon it. I might though be wrong on this point.

Conclusion

I don't know how many readers will reach this point in the article. Kudos to all of you.

It is very possible that many would consider my 4 basic beliefs as something self-evident that is not worth writing down. Perhaps you are right. However one thing that I learned from my work as an engineer is that it is valuable to write down your very basic most obvious assumptions. In the worst case you'll waste a few pages of text. In the best case you'll find a crux of your disagreement with other people that will allow you to better understand each other's perspective.

I hope this article will be useful for this. In any case at the very least I will be able to link next time someone asks me what I believe in.