It seems like human philosophy is more effective than it has any right to be. Why?
and I said, “What? Huh? Not!” Then OP wrote:
To cite one field that I’m especially familiar with, consider probability and decision theory, where we went from having no concept of probability, to studies involving gambles and expected value, to subjective probability, Bayesian updating, expected utility maximization, and the Turing-machine-based universal prior, to the recent realizations that EU maximization with Bayesian updating and the universal prior are both likely to be wrong or incomplete.
If you want to call math philosophy, then, yes, philosophy is effective. But then the post doesn’t make any sense; the issues being raised don’t apply. The opening claims philosophy is effective by pointing to math and economics and calling them philosophy. The rest of the post contrasts philosophy with math, and talks about how hard philosophy is, and how non-useful it appears to be; the only example provided is ethics.
I recommend Wei Dai try to rewrite the post, being more specific about what philosophy and meta-philosophy are (and what the main point of the post is), providing many more examples of “philosophy”, and paying careful attention that they mean the same thing in all parts of the post.
And I’ll say it again: Being a tribal forager is much more intellectually demanding than city-folk think it is.
If you want to do math, you need some basic definitions, concepts, and motivations. Once philosophy has provided those, then you can start quantifying and proving theorems. See the history of economics, for instance.
Philosophy has never provided the basic definitions, concepts, or even motivations for math. The historical influence was the other way around: The successful use of math inspired the invention of philosophy as a rational discipline.
Mathematical logic grew out of the philosophical analysis of arguments. Mathematically rigorous analysis and calculus grew out of the concepts of motion and speed used in understanding physics (“natural philosophy”), which itself grew out of philosophy. Probability and statistics, as applied to controlled studies, grew out of the philosophy leading to the scientific method.
OP wrote:
and I said, “What? Huh? Not!” Then OP wrote:
If you want to call math philosophy, then, yes, philosophy is effective. But then the post doesn’t make any sense; the issues being raised don’t apply. The opening claims philosophy is effective by pointing to math and economics and calling them philosophy. The rest of the post contrasts philosophy with math, and talks about how hard philosophy is, and how non-useful it appears to be; the only example provided is ethics.
I recommend Wei Dai try to rewrite the post, being more specific about what philosophy and meta-philosophy are (and what the main point of the post is), providing many more examples of “philosophy”, and paying careful attention that they mean the same thing in all parts of the post.
And I’ll say it again: Being a tribal forager is much more intellectually demanding than city-folk think it is.
If you want to do math, you need some basic definitions, concepts, and motivations. Once philosophy has provided those, then you can start quantifying and proving theorems. See the history of economics, for instance.
Philosophy has never provided the basic definitions, concepts, or even motivations for math. The historical influence was the other way around: The successful use of math inspired the invention of philosophy as a rational discipline.
Mathematical logic grew out of the philosophical analysis of arguments. Mathematically rigorous analysis and calculus grew out of the concepts of motion and speed used in understanding physics (“natural philosophy”), which itself grew out of philosophy. Probability and statistics, as applied to controlled studies, grew out of the philosophy leading to the scientific method.