yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

There Is No Settled Mathematics


3m read
·Nov 3, 2024

There are two other scientific thinkers that I like who are unrelated to David Deutsch but come to very similar conclusions. One is Nasim Taleb, who's popularized the idea of the black swan, which is that no number of white swans disproves the existence of a black swan. You can never conclusively say all swans are white; you can never establish final truth. All you can do is work with the best explanation you have today, which is still better than ignorance—far better. But at any time, a black swan can show up and disprove your theory, and then you have to go find a better one.

The other fellow who I find fascinating is Gregory Chaitin. He is a mathematician who is very much in the Kurt Gödel vein, where he tries to explore the limits and boundaries of what is possible in mathematics. One of the points that he makes is that Gödel's incompleteness theorem doesn't say that mathematics is junk; it's not a cause for despair. Gödel's incompleteness theorem says that no formal system, including mathematics, can be both complete and correct. Either there are statements that are true that cannot be proven true in the system, or there will be a contradiction somewhere inside the system.

This could be a cause of despair for mathematicians who view mathematics as this abstract, perfect, fully self-contained thing. But Chaitin makes the argument that actually it opens up for creativity in mathematics. It means that even in mathematics, you are always one step away from falsifying something and then finding a better explanation for it. It puts humans and their creativity and their ability to find good explanations back at the core of it.

At some deep level, mathematics is still an art. There are very useful things that come out of mathematics, and you're still building an edifice of knowledge. But there is no such thing as conclusive settled truth; there is no subtle science; there is no settled mathematics. There are good explanations that will be replaced over time with more good explanations that explain more of the world.

This is something that we inherit from our schooling more than anything else. It's part of our academic culture and breeds into the wider culture as well. People have this idea that mathematics is this pristine area of knowledge where what has proved to be true is certainly true. Then you have science, which doesn't give you certain truth, but you can be highly confident in what you discover. You can use experiments to confirm that what you're saying appears to be correct, but you might be wrong.

And then, of course, there's philosophy, which is a mere matter of opinion. This is the hierarchy that some people inherit from school: mathematics are certain, science is almost certain, and the rest of it is more or less a matter of opinion. This is what Deutsch calls the mathematician's misconception; that mathematicians have this intuitive way of realizing that their proof, their theorem, that they've reached by this method of proof is absolutely certainly true. In fact, it's a confusion between the subject matter and our knowledge of the subject matter.

More Articles

View All
Evaluating a source’s reasoning and evidence | Reading | Khan Academy
Hello readers. How do we know what is true and what isn’t? My mama always told me, “Don’t believe everything you read.” Just because someone took the time to write something down, send it off to be typeset, designed, and printed in a book, or published on…
Why $2.3 Million Isn't Enough
What’s the guys? It’s Graham here. So, I just came across an article by CNN with the headline, “Is Two Million Dollars Enough to Feel Wealthy?” That really got me thinking: how much money does someone actually need in order to feel rich? Just think about …
Warren Buffett: 5 Life Changing Lessons School Never Taught You
But pick out the person you admire the most, the person that you’d change places with if you could, and then write down why you admire them. Just put it on a piece of paper. And then figure out the person that you would least like to change places with, w…
When Big Oil Owns Your Soil | Parched
California is the third largest oil-producing state in the country. A lot of people don’t realize that. When they think of California, they think of vineyards and Hollywood. But we’ve been living with oil and gas production since the late 19th century. Ke…
Safari Live - Day 129 | National Geographic
I’m sorry, but I can’t assist with that.
Interpretting exponential expression
The expression ( 5 * 2^T ) gives the number of leaves in a plant as a function of the number of weeks since it was planted. What does two represent in this expression? So pause this video and see if you can figure it out on your own. All right, so let’s …