It's just nice to feel happy. It's axiomatic almost. But what the research in the last about 15, 20 years has discovered is that it's also useful to be happy. So I'm going to talk about three ways in which it's useful to be happy.
become become something I'd grown out of again so I I learned about uh Axiom axiomatic thinking self-justified statements now you can have axioms in logic that are very formal or you can have axioms in philosophy that are are much less
And nobody notices, and nobody really cares because these people are very old and near death. It's kind of axiomatic to us that the human body isn't that hackable.
And nobody notices, and nobody really cares because these people are very old and near death. And it's axiomatic that you live within a certain range of life, but it was also, in earlier stages of not just evolution,
bones that make up the human body. And it's axiomatic that right from day one, of all the various bones that you see preserved in graves and middens and so forth, it is the skull that occupies the pride of place.
choice is being used and they don't want to use the axiom of choice, so they work out the consequences that's- that are possible without the axiom of choice or with weakened - That's right - A consistent axiomatic system is that there are no contradictions.
There's a tendency, in particular, like in the Ted Talks where there's real selection for being provocative, to suggest that people are irrational because they don't follow the rules of formal or axiomatic rationality theory. However, every economic decision entails an optimization problem, and I feel like I'm on safe ground when I'm at Google talking about optimization problems.
alive in a variable and uncertain environment. So rather than the mathematicians' formal axiomatic rationality, people seem to use a procedural rationality, and this is a point that the great polymath economist Herbert Simon suggested in his scissors metaphor, that trying to understand decision-making is like trying to understand the way a pair of scissors work.
rather than specifying the way that they're expected to behave, but I think there's still a decent amount of baggage. What do I mean when I say "axiomatic ?" Standard economic theory generation starts from a series of axioms-- primitive assumptions are taken to be self-evident. Things like, you shouldn't reverse your preferences.
And nobody notices, and nobody really cares because these people are very old and near death. But all of these things that are axiomatic -- and that's what I started with.
original set, even in cases where the collection is infinite or where there is no natural way to specify a selection rule. So this was controversial and this was described before there's even a language for axiomatic systems. - That's right. So on the one hand, I mean, the axiom of choice principle is
The real thing about Euclidean geometry is not that he derived brand new results because most of his results had already been derived by other people. The great thing about it was that he turned it into an axiomatic system. You wrote down some axioms, and then you proved some theorems.
It's about "demand." Simply saying, we deserve rent control, that we deserve more fairness, that we deserve a city that everybody can live in, OK, so you explained that it's axiomatic that power concentrates, right?
set theory became the foundation of mathematics. All mathematics could now be built from sets, giving math its first truly rigorous foundation. The axiomatization of mathematics, the paradoxes forced mathematicians to develop ZFC and other axiomatic systems, and mathematical logic emerged. Gödel, Turing, and others created entire new fields. So can you explain what set theory is and, how does it serve as a foundation of modern mathematics and maybe even the
Where Rand, to some degree, we could say she's empirical in that she lives through the Russian Revolution and takes a very big lesson from that, but her style of thinking is really first principles, an axiomatic approach, going from the basic idea of rationality and then playing that out in different spheres.
Yeah, exactly. Real world stuff like the Death Star. And also, you run into the problem that when you're developing any axiomatic system, the early proofs are usually very technical, and about
genius and daring and tremendous effort and labor-- was inevitable. In the past, it seemed to me that cognitive psychology had been axiomatically fixed on foundations that were not useful.
to think about what's next. Yeah. Thanks, Rudy. I mean, I think we take as axiomatic that, sustainability is not achievable without, just processes and recognizing human dignity. And in fact, a lot of what we see as the current environmental crises, whether it's pollution crisis, the pollution crisis, biodiversity-
that what's called the axiom of choice implies the well-order principle. So he described his proof, and that was extremely controversial at the time. And there was no theory, there weren't any axioms there. Cantor was not working in an axiomatic framework. He didn't have a list of axioms in the way that we have for set theory now, and Zermelo didn't either. And his ideas were challenged so much with regard to the well-order theorem—
We open up a fresh ledger on ourselves essentially, the same way a business would open up a fresh ledger on a new quarter or a new year. So when they look at the research on when people begin behavior change-- and again, it's axiomatic . You're more likely to change your behavior if you begin to try to change your behavior.
And this isn't meant as a put-down. It's a statement of fact, and it's because the preferred and overwhelmingly-- the dominant mode of economic theory generation is axiomatic , and that's not the way the natural sciences proceed.
- Sure. - This infinity crisis led to a kind of rebuilding of mathematics. So it'd be nice if you lay out the things it resulted in. So one is set theory became the foundation of mathematics. All mathematics could now be built from sets, giving math its first truly rigorous foundation. The axiomatization of mathematics, the paradoxes forced mathematicians to develop ZFC and other axiomatic systems, and mathematical logic emerged. Gödel, Turing, and