Interview with Bertrand Russell: The Limits of Human Knowledge
Is there any knowledge so certain that no reasonable person could doubt it? This is one of the most difficult questions that can be asked.
So let’s answer it, with the help of my friend Bertrand Russell.
He’s a mathematician, philosopher, and one of the greatest minds of the 20th century.
(Read this on the web here)
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Russell: Are you sure that the table in front of you is real?
DKB: I’m pretty sure it is.
Russell: What color is it?
DKB: Light brown.
Russell: What about the fact that the parts reflecting light look brighter? If people look at the table from different angles, they’ll see different colors.
DKB: Sure there are differences that people see, but it’s objectively a specific color which we can measure scientifically.
Russell: Which color is the objective one? If the lighting in the room changes, the color changes. In a dark room, there’s no color at all. If someone’s wearing blue shades, they see a different color entirely.
It seems to me that the color isn’t inherent in the table, but dependent on the table, the person viewing it, and the way light falls on it.
When we talk about the color of the table in daily life, we mean the color it will seem to have to a normal person, from an average point of view, in average light conditions. But other colors that appear in other conditions have just as much of a right to be considered real.
To avoid favoritism, we have to deny that the table itself has any particular color.
Let’s use the phrase “sense data” to refer to things immediately known to us via sensation, like colors and sounds.
The real table, if it exists, we will call a “physical object”. And we’ll call the collection of all physical objects “matter”.
So what we really want to know is, does matter exist? And if so, what is its nature?
DKB: If we go down this rabbit hole, then can’t I doubt my knowledge of everything?
Russell: Descartes, the founder of modern philosophy, asked the same question. He invented the method of systematic doubt.
He would believe nothing that he didn’t see clearly to be true. Whatever he could doubt, he would doubt, unless he saw a reason for not doubting it.
He imagined that there could be a deceitful demon, presenting unreal things to his senses. That meant he had to doubt everything he experienced.
But he couldn’t doubt his own existence. Because if he didn’t exist, then no demon could deceive him. If he doubted, he must exist. Thus his own existence was an absolute certainty to him, leading to the famous “I think, therefore I am.”.
We can be certain of our own existence, and our subjective sense data, but is there something else that isn’t sense data, which persists when we leave the room?
DKB: There must be something right? Even though different people see the table slightly differently, they all see something fairly similar. So there must be some physical object that exists.
Russell: That argument assumes that other people besides you exist, which is the entire issue we’re trying to resolve. Other people are represented to me by sense data, so if I have no reason to believe in physical objects independent of my sense data, I have no reason to believe that other people exist.
DKB: So it’s possible that I’m the only one that exists, and all the physical objects around me are created in my mind?
Russell: Well, we can’t definitively prove that it isn’t all in your head, but there’s no reason to believe that’s the case. The simpler hypothesis is the common-sense view that there really are objects independent of us.
Consider the example where a cat appears in one part of the room, then at a later moment it’s in another part. It’s natural to assume that the cat moved from one place to another, passing over a series of intermediate positions.
If it is merely a set of sense data in your head, it can’t have ever been in any place where you didn’t see it. So you’ll have to believe that the cat didn’t exist while you weren’t looking, but suddenly sprang into being in a new place.
It’s a lot simpler to believe that the cat exists independently of us.
Either way, it’s not by argument that we originally start believing in an independent external world. This belief is ready in us as soon as we begin to reflect. It’s what we can call an “instinctive belief”. Since this belief doesn’t lead to any difficulties, and simplifies our explanation of things, there seems to be no good reason to reject it.
DKB: That’s kind of a weak argument. You’re saying that just because we naturally believe it, and it makes things simpler, that it’s true?
Russell: The argument is definitely weaker than we would want it to be, but it is typical of many philosophical arguments. All knowledge must be built upon our instinctive beliefs. If those are rejected, then nothing is left. We have to start our quest for knowledge somewhere.
Of course it is possible that all or any of our beliefs may be mistaken, and we should have some element of doubt about them. But we can’t have a reason to reject a belief except when it comes into conflict with some other belief.
DKB: Alright, so we instinctively believe that physical objects and matter exist. There is some real table, though it might not look like what our sense data gives us.
I don’t see why we can’t also assume that physical objects are basically the same as the sense data we get. The colors we perceive through sense data are similar from many points of view. So maybe the “real” color is an average color between all the possible points of view. Does that make sense?
Russell: While that theory can’t be definitively refuted, it can be shown to be baseless. The color we see depends only on the nature of the light waves striking the eye, and is modified by the air in between the object and the eye, as well as the manner in which the light is reflected.
The color we see is not just a property of the object. So it is quite gratuitous to assume that physical objects have colors. There’s no justification for that hypothesis.
DKB: Is there anything we can know about the nature of physical objects then?
Russell: Well we know we have our sense data, but that data is limited. It might be possible to know things about physical objects if we could draw inferences from our sense data somehow.
We need some general principle that enables us to come up with valid inferences. I can reveal the principle everyone uses by asking a simple question.
Do you think the sun is going to rise tomorrow?
DKB: Of course. It’s risen every day in the past, and there’s no reason to believe it won’t rise tomorrow. We know the laws of physics, and we know the motion of the earth and the sun.
Russell: Every day of its life, the thanksgiving turkey gets more data to prove that human beings are benevolent creatures that provide food and shelter. Right when it has the most confidence that it’s safe based on past data, it gets shoved into the oven.
DKB: I mean, sure, the earth could get hit by a giant asteroid which knocks it out of orbit or something. And then maybe the sun won’t rise. But the laws of physics would still be working as expected.
Russell: You still have the same problem though. Just because the laws of physics have worked in the past, does that mean they will always work in the future?
The only reason for believing the laws of physics will remain in operation is that they have operated this way for a long time. But do any number of cases of a law being fulfilled in the past give evidence that it will be fulfilled in the future?
If not then we have no grounds whatsoever for expecting the sun to rise tomorrow, or for expecting the bread we eat at our next meal not to poison us.
DKB: Well that’s not good…
Russell: Unfortunately we can’t get true certainty. The most we can hope for is that the more often things are found together, the more probable it becomes that they will be found together another time. This is called the principle of induction.
DKB: And how do we know the principle of induction is true?
Russell: All arguments which predict the future on the basis of past experience assume the principle of induction. We can never use experience to prove the principle of induction, because that would be a circular argument.
So we have to either accept the principle of induction on the grounds of its intrinsic evidence, or give up on predicting the future. Everything in our lives depends on the principle of induction, but we can’t prove that it’s true.
DKB: If we can’t prove that it’s true, then what reason do we have to believe in it?
Russell: We need some number of self-evident logical principles before any argument becomes possible. Once we assume some of them are true, others can be proven.
Take for example the following logical principle: “anything implied by a true proposition is true”.
This principle is involved in everything. Whenever one thing we believe is used to prove something else, this principle is relevant. If anyone asks us “Why should I accept the results of valid arguments based on true premisses”, we can only answer by appealing to our principle.
The truth of this principle is impossible to doubt, and it’s so obvious that it seems trivial. But it’s not trivial, because it shows that we may have indisputable knowledge that is not derived from sense objects.
DKB: But where do these self-evident principles come from? It’s not innate in us as human beings. We still have to learn them somehow.
I feel like the usual flow is that we have experiences, then come up with general laws based on those experiences.
Russell: It is true that babies aren’t born with an innate knowledge of these principles. So we don’t use the word innate, and prefer the phrase “a priori” to refer to this kind of knowledge.
All knowledge is caused by experience. But for a priori knowledge, the experience that makes us think of it doesn’t actually prove it. Experience merely directs our attention to the a priori knowledge, so that we see its truth without requiring any proof from experience.
DKB: In that case, how is a priori knowledge even possible? How can we know some underlying principle when we haven’t examined all the possible instances of it?
Russell: To understand that, let’s take a step back into ancient greek philosophy. Plato originally tackled a related problem, and came up with his “theory of ideas”.
Let’s consider the notion of justice. If we want to know what justice is, we can look at various just acts and see what they all have in common. They will all have some common nature found in just things and nothing else. This common nature will be justice itself. This pure essence is what Plato calls an “idea” or “form”.
The truly real world for Plato is the world of ideas. Whatever we can say about things in the world of sense, we can only succeed in saying that they participate in some ideas, which constitute their character.
But idea is a loaded word, so let’s use the word “universal” instead of “idea” to capture what Plato meant. Whatever we interact with through sensation is called a “particular”. A universal is anything which may be shared by many particulars.
DKB: Are universals just something we make up in our minds then? They clearly aren’t physical things.
Russell: Universals are not merely mental. Consider the proposition Canada is north of Mexico. We don’t cause the truth of the proposition by knowing it. The part of the earth’s surface where Canada is would be north of the part where Mexico is, even if there were no human beings to know about north and south, and even if there were no minds at all in the universe.
But the relation “north of” doesn’t seem to exist in the same sense that Canada and Mexico exist. There is no place or time where we can find the relation “north of”. It is neither in space nor in time. Neither material nor mental. Yet, it is something.
Let’s only call things “existing” when they are in the world of time. Thoughts, feelings, minds, and physical objects exist. But universals don’t exist in this sense. We can say that they have being. “Being” as opposed to “existence” is timeless. The world of universals is a world of being.
DKB: We’re starting to get a little mystical here. A timeless world of being makes me think of the way that Hindus describe the Unmanifested, or the way that Taoists describe the Tao. It’s that world beyond shape and form that all religions seem to talk about.
Russell: It does feel somewhat mystical, but the basis of the theory is in logic. Anyway, now we can return to your question about how a priori knowledge is possible. The answer is that all a priori knowledge deals exclusively with the relations of universals.
A priori knowledge is not the same as knowing a specific instance of a priori knowledge. We can know a priori that two and two are four. But we cannot know a priori that if Alicia and Akari are two, and Edward and Alphonse are two, then Alicia, Akira, Edward and Alphonse are four. We can’t understand the proposition at all because we don’t know that there are such people. That can only be known by experience.
The statement two and two are four deals exclusively with universals, and may be known by anyone acquainted with the universals concerned.
DKB: To have a priori knowledge, we have to know at least a few instances of it from experience so we can observe the general principle right?
Russell: No, we can know a general proposition even if we don’t know a single instance of it.
For example, we know that multiplication tables contain every product below 100. So take the following proposition: “All products of two integers, which have never been and never will be thought of by any human being, are over 100”. The truth is undeniable, yet we can never give an instance of it, by definition.
Our knowledge of physical objects depends on this possibility of general knowledge where no instance can be given. The same applies to our knowledge of other people’s minds, and any other thing which we can’t know directly.
DKB: Okay, but what if something that seems self-evident to us turns out to be false? Our knowledge is based on these intuitive general principles, but some of our principles may turn out to be garbage.
Russell: People like to think that everything we believe should be capable of proof. Most people would say that a belief that you can’t give a proper argument for is an unreasonable belief. But in reality, if we keep asking “why”, we end up at some self-evident general principle like induction, which we have no way of proving.
You are onto something though. Self-evidence has degrees. Truths of perception and some principles of logic have the very highest degree of self-evidence. Memories have diminishing self-evidence as they become remoter and fainter. The truths of logic and mathematics have less self-evidence as they become more complicated. Judgments of intrinsic ethical or aesthetic value have some self-evidence, but not much.
Degrees of self-evidence are important in the theory of knowledge. When we find a conflict between propositions, we can keep the more self-evident one.
DKB: So do we have to compare all the things we believe and look for conflicts? Is that how we finally solve this problem of knowledge?
Russell: The majority of what we call knowledge is actually “probable opinion”, because we can never be absolutely certain of it.
In order to deal with this sea of probable opinion, we can use the test of coherence, which is basically what you’re alluding to. A body of individually probable opinions, if they are mutually coherent, become more probable than any one of them would be individually.
This is how many scientific hypotheses acquire their probability. They fit into a coherent system of probable opinions, and become more probable than they would be in isolation.
But even though this test increases probability, it never gives us absolute certainty. The mere organization of probable opinion will never, by itself, transform it into indisputable knowledge.
We can organize our instinctive beliefs and their consequences, modifying or abandoning beliefs until they don’t clash, forming a harmonious system. Through this method we can arrive, on the basis of accepting as our sole data what we instinctively believe, at an orderly systematic organization of our knowledge.
Even though the possibility of error remains, its likelihood is diminished by the interrelation of the parts, and the critical scrutiny we have undertaken.
When we go down rabbit holes like this, we can’t always get definitive answers, but at least we have the power to ask questions which increase the interest of the world.
This type of inquiry shows the strangeness and wonder lying just below the surface, even in the most common things of everyday life.
Moving to Substack + Building community
Hello end-of-the-newsletter crew, and happy new year to you. I've decided to move the newsletter off my self-hosted site and on to Substack this year. All future posts will come from the Substack site: https://dkbshow.substack.com/.
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The main reason for this switch is that Substack supports community building. I get lots of nice emails from you all, but it's a shame that I'm the only one who sees them. With Substack, posts have comment sections, so you can share your thoughts with everyone, and we can all benefit.
I hope we can form a community of kind and curious people in the comments, and I look forward to seeing you there.
If you have any thoughts on the interview above, I'd love if you shared those thoughts in the Substack comments this time instead of replying to me.
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Thank you for your continued support,
Dmitri