"because men vary in height considerably, and women too, and because the average difference in height between men and women isn’t are large as these differences between men or between women, it doesn’t follow that induction has lied to us and that men aren’t taller than women. Of course, nobody does make this mistake regarding height differences. The error is usually made on more politically or socially charged questions."
B-b-but surely this could lead to the denial not just of height differences but also of the categories 'men' and 'women'! No such mistake could ever be made!
1. All models (deduction) are wrong. Some are useful (induction).
2. I'd say P(George wears a hat) $\neq 0.5$. Instead, it's $\in \{0, 1\}$; we're just not sure which.
3. Popper's logic of science strikes me as parochial, focusing on clean, simple models in physics. It leads him to some crazy places in trying to apply physics-type logic and modeling to the kinds of messy, hopelessly complex problems in statistics-based fields. That said, he does have some fantastic insights and can be wonderfully quotable.
4. I'm a huge fan of science, but it is definitely not the answer (depending on the question, of course).
William, are you a G-man?
Great stuff as always!
Thank you for this lesson. I appreciate it very much.
I'm reading for sure.
The only proper attitude.
"because men vary in height considerably, and women too, and because the average difference in height between men and women isn’t are large as these differences between men or between women, it doesn’t follow that induction has lied to us and that men aren’t taller than women. Of course, nobody does make this mistake regarding height differences. The error is usually made on more politically or socially charged questions."
B-b-but surely this could lead to the denial not just of height differences but also of the categories 'men' and 'women'! No such mistake could ever be made!
Great stuff, Matt.
A few quick comments...
1. All models (deduction) are wrong. Some are useful (induction).
2. I'd say P(George wears a hat) $\neq 0.5$. Instead, it's $\in \{0, 1\}$; we're just not sure which.
3. Popper's logic of science strikes me as parochial, focusing on clean, simple models in physics. It leads him to some crazy places in trying to apply physics-type logic and modeling to the kinds of messy, hopelessly complex problems in statistics-based fields. That said, he does have some fantastic insights and can be wonderfully quotable.
4. I'm a huge fan of science, but it is definitely not the answer (depending on the question, of course).
Thanks, Dan. It will turn out we get into each of these later.
For instance, it will turn out that I disagree with #1 - in a way. Depends on those tacit premises!