The Inverted Pyramid: What Bertrand Russell Can Teach Us About The Limits of Logic


“To refute the solipsist…all that you have to do is take him out and throw a rock at his head: if he ducks he’s a liar. His logic may be airtight but his argument, far from revealing the delusions of the living experience, only exposes the limitations of logic.” – Edward Abbey

Something in Betrand Russell’s a History of Western Philosophy caught my eye recently. At first I noticed it because it’s basically Russell badly dissing another philosopher. But after I thought about it more I realized his point is really relevant to the way we think about the world and the way we make decisions.

In the passage that I’ll quote Russell wants to outline the differences between analytic and continental philosophy.

It’s difficult to define the exact differences between the two schools (they’re both terms that encompasses lots of different philosophers and world-views) but, roughly, analytic philosophy tends to try to break down philosophical problems into tiny pieces (like the definitions of words) and take a careful and considered look at each of the pieces and their relation to one another. Continental philosophy, on the other hand, is a bit more literary – it’s less concerned with the definitions of words and more concerned with broad synthesis.[^1]

Here’s how Lord Russell talks about the distinction:

“There is first of all a difference of method. [Analytic] philosophy is more detailed and piecemeal than that of the Continent; when it allows itself some general principle, it sets to work to prove it inductively by examining its various applications.”

By this he means that analytic philosophers don’t generally talk about broad, general principles. Instead, they like to build up their world-view in a more piecemeal fashion – considering one little question at a time. And when they do accept some general principle as true, they do so only when they can prove it by considering lots of empirical evidence in favor of the fact that it is true. They try not to make any large logical leaps that aren’t backed by experience.

By contrast, he says, Continental philosophers prefer deduction from first principles. As an example he talks about Gottfried Leibniz – the man who invented calculus[^2].

He chooses to examine how Leibniz argues for monadology – which is a theory of the nature of matter. The basic gist is that matter is made up of infinitely many “monads” – somewhat similar to geometrical points in that, by themselves, they don’t have “extension” or mass but when you get a lot of them together you can get a substance like wood or metal or dirt.

Lord Russell writes:

“When Leibniz wants to establish his monadology, he argues, roughly as follows: Whatever is complex must be composed of simple parts; what is simple cannot be extended[^3]; therefore everything is composed of parts having no extension. But what is extended is not matter. Therefore the ultimate constituents of things are not material, and, if not material, then mental. Consequently a table is really a colony of souls.”

Whoa! What just happened here? It seems like we went from some very simple basic propositions to an outlandish conclusion: “A table is really a colony of souls.”[^4]

How did that happen? Russell answers:

“The difference of method, here, may be characterized as follows: In Locke or Hume [both of whom are analytic philosophers], a comparatively modest conclusion is drawn from a broad survey of many facts, whereas in Leibniz a vast edifice of deduction is pyramided upon a pin-point of logical principle. In Leibniz, if the principle is completely true and the deductions are entirely valid, all is well; but the structure is unstable, and the slightest flaw anywhere brings it down to ruins. In Locke or Hume, on the contrary, the base of the pyramid is on the solid ground of observed fact, and the pyramid tapers upward, not downard; consequently the equilibrium is stable, and a flaw here or there can be rectified without total disaster.”

Russell’s problem with Continental philosophers is that they start with an axiomatic principle – something like “Whatever is complex must be composed of simple parts” – and they use it to deduct the rest of their worldview.

This is actually a valid method of figuring things out. For example, Euclid’s entire system of geometry is deducted from a few axiomatic principles. Pretty much any mathematical system works like this.

But what Russell is saying is that this system of thinking, while incredibly powerful, is also incredibly brittle.

This is generally not bad when you’re dealing with something like math because it doesn’t have to comport with experience – the axioms are true because we say they are. But when you’re reasoning about the real world it becomes a huge problem: it’s often impossible to tell if your axioms are correct. And equally difficult to know whether each of your deductions are valid.

And, if you’re reasoning in this way, if your starting axioms are wrong, or any of your deductions are invalid, all of your conclusions are totally wrong. It’s not robust to error at all. It’s a system of thought built like an upside down pyramid – the whole thing rests on one single point of balance.

Russell argues that a better way to do philosophy (or figure things out about the world in general) is to construct your pyramid right-side up. Start with known, observed facts about the world and construct your argument based on those. This will allow you to build a base of thought with strong foundations; one that’s much more robust to small errors than a purely deductive system of thought because it won’t come crashing down if one little piece is wrong.

There’s a common expression among programmers that goes, “Garbage in, garbage out.” And this is exactly how logic works. It’s a powerful tool that’s only as good as the person that uses it. And when we’re reasoning about things in the real world we want our system of thought to be like a right-side up pyramid – logic based on a robust foundation of experience – rather than a long chain of deduction that’s vulnerable to error and easy to tip over.

[^1]: If this still seems hopelessly unclear that’s because it is. To actually understand the differences you need to read some of the philosophers in question.

[^2]: he and Newton both independently came up with it around the same time

[^3]: Again this means, roughly, that it doesn’t have mass

[^4]: There’s a question about whether Bertie is really being fair to Leibniz here, but we’ll let it slide to hammer home the point.

31 Dec 2014, 5:09am | 2 comments

Writing and Running: Haruki Murakami

I’ve never read one of Murakami’s novels, but I recently picked up his memoir What I Talk About When I Talk About Running. I just finished Stephen King’s On Writing, so when I spotted it in a bookstore it seemed like a logical thing to read next.

Murakami’s prose is simple and his attitude is unassuming. Basically the entire book is spent talking about running (his main pastime aside from writing). The way he writes sets up a kind of hypnotic rhythm that he builds over the course of the book. Mostly he talks about marathons: training for marathons, running in marathons, competing in triathlons, etc. But every so often the book is also interspersed with these great nuggets about writing and life.

One parallel that Murakami draws between writing and running is that both act as a sort of alchemy for the events and emotions in his life. Both writing and running allow him to take what happens to him – events, emotions, feelings – and transmute them in to another, useful, form.

“When I’m criticized unjustly (from my viewpoint, at least), or when someone I’m sure will understand me doesn’t, I go running for a little longer than usual. By running longer it’s like I can physically exhaust that portion of my discontent. It also makes me realize again how weak I am, how limited my abilities are. I become aware, physically, of these low points. And one of the results of running a little farther than usual is that I become that much stronger. If I’m angry, I direct that anger toward myself. If I have a frustrating experience, I use that to improve myself. That’s the way I’ve always lived. I quietly absorb the things I’m able to, releasing them later, and in as changed a form as possible, as part of the story line in a novel.”

One thing that I noticed reading Murakami he has very deep, zen-like thoughts on the nature of the mind and the meaning of life, but he says them so matter-of-factly that you might miss them:

“The thoughts that occur to me while I’m running are like clouds in the sky. Clouds of all different sizes. They come and they go, while the sky remains the same sky as always. The clouds are mere guests in the sky that pass away and vanish, leaving behind the sky. The sky both exists and doesn’t exist. It has substance and at the same time doesn’t. And we merely accept that vast expanse and drink it in.”

He talks a lot about things that are constantly changing in form: clouds, the sky, and the water in the river where he runs. And he uses it to place himself in the broader picture of the world:

“The surface of the water changes from day to day: the color, the shape of the waves, the speed of the current. Each season brings distinct changes to the plants and animals that surround the river. Clouds of all sizes show up and move on, and the surface of the river, lit by the sun, reflects these white shapes as they come and go, sometimes faithfully, sometimes distortedly…In the midst of this flow, I’m aware of myself as one tiny piece in the gigantic mosaic of nature. I’m just a replaceable natural phenomenon, like the water in the river that flows under the bridge to the sea.”

A lot of writers talk about pain as the engine behind the creative process. Someone like Dostoevsky comes to mind. Murakami is in this camp as well. Here he talks about emotional pain:

“As I’ve gotten older, though, I’ve gradually come to the realization that this kind of pain and hurt is a necessary part of life. If you think about it, it’s precisely because people are different from others that they’re able to create their own independent selves. Take me as an example. It’s precisely my ability to detect some aspects of a scene that other people can’t, to feel differently than others and choose words that differ from theirs, that’s allowed me to write stories that are mine alone. And because of this we have the extraordinary situation in which quite a few people read what I’ve written. So the fact that I’m me and no one else is one of my greatest assets. Emotional hurt is the price a person has to pay in order to be independent…”

Aside from just emotional pain, Murakami also talks about physical pain, which is a key part of his routine as a serious marathon runner.

“Of course it was painful, and there were times when, emotionally, I just wanted to chuck it all. But pain seems to be a precondition for this kind of sport. If pain weren’t involved, who in the world would ever go to the trouble of taking part in sports like the triathlon or the marathon, which demand such an investment of time and energy? It’s precisely because of the pain, precisely because we want to overcome that pain, that we can get the feeling, through this process, of really being alive…Your quality of experience is based not on standards such as time or ranking, but on finally awakening to an awareness of the fluidity within action itself. If things go well, that is.”

By the end of the book, he’s sort of established the rhythm of his life for us: he writes, he trains for marathons, he runs marathons. Rinse and repeat. He’s consistently doing things, but not always making visible progress.

He likens it to pouring water in to an old pan with a hole at the bottom: there’s always water running through it, but the pan never fills up. But the message he leaves us with, is that despite pouring tremendous effort in to these seemingly inefficient activities, it’s these very activities that have borne the most fruit in his life.

“Even if, seen from the outside, or from some higher vantage point, this sort of life looks pointless or futile, or even extremely inefficient, it doesn’t bother me. Maybe it’s some pointless act like, as I’ve said before, pouring water in to an old pan that has a hole in the bottom, but at least the effort you put into it remains. Whether it’s good for anything or not, cool or totally uncool, in the final analysis what’s most important is what you can’t see but can feel in your heart. To be able to grasp something of value, sometimes you have to perform seemingly inefficient acts. But even activities that appear fruitless don’t necessarily end up so. That’s the feeling I have, as someone who’s felt this, who’s experienced it.”

14 Dec 2014, 9:04pm | 8 comments


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