What you should do is say specifically what I got wrong (just one thing is fine). Then you’ll be making a substantive statement!
Ok, here’s one. You criticize Bayesian updating for invoking infinitely many hypotheses, as a fundamental problem. In fact, the problem of infinite sets is an issue, but it’s resolved in Jaynes’ book by a set of rules in which one never deals with infinities directly, but rather with convergent limiting expressions, which are mathematically well-behaved in ways that infinities aren’t. This ensures, among other things, that any set of hypotheses (whether finite or infinite) has only finite total plausibility, and lets us compute plausibilities for whole sets at once (ideally, picking out one element and giving it a high probability, and assigning a low total probability to the infinitely many other hypotheses).
What predictions? It is a philosophical theory.
Both theories make predictions about the validity of models using evidence—that is, they predict whether future observations will agree with the model.
Your conception of epistemology is different than ours. We seek things like explanations that help us to understand the world.
No, our conceptions of epistemology are the same. Math does help us understand the world, in ways that natural language can’t.
Ok, here’s one. You criticize Bayesian updating for invoking infinitely many hypotheses, as a fundamental problem.
No, I didn’t say that. I invoked them, because they matter. You then claims Jaynes’ deals with the problem. Yet Yudkowsky concedes it is a problem. I don’t think you understood me, rather than vice versa.
Both theories make predictions about the validity of models using evidence
Popper never made a prediction like that. And this rather misses some points. Some models for using evidence (e.g. induction) are literally incapable of making predictions (therefore people who do make predictions must be doing something else). Here Popper was not making a prediction, and also was pointing out prediction isn’t the right way to judge some theories.
No, our conceptions of epistemology are the same. Math does help us understand the world, in ways that natural language can’t.
Can you write philosophical explanations in math? Of course math helps for some stuff, but not everything.
Ok, here’s one. You criticize Bayesian updating for invoking infinitely many hypotheses, as a fundamental problem.
No, I didn’t say that. I invoked them, because they matter. You then claims Jaynes’ deals with the problem. Yet Yudkowsky concedes it is a problem
Here’s where you’ve really gone astray. You’re trying to figure out math by reading what people are saying about it. That doesn’t work. In order to understand math, you have to look at the math itself. I’m not sure what statement by Yudkowsky you’re referring to, but I’ll bet it was something subtly different.
Both theories make predictions about the validity of models using evidence
Popper never made a prediction like that.
Uh, wait a second. Did you really just say that Popper doesn’t provide a method for using evidence to decide whether models are valid? There must be some sort of misunderstanding here.
The only way evidence is used is that criticisms may refer to it.
Please reread what Jim wrote. You seem to be in agreement with his statement that evidence is used.
I’m not trying to figure out math, I’m trying to discuss the philosophical issues.
Unfortunately, they are interrelated. There’s a general pattern here: some people (such as Jaynes and Yudkowsky) are using math as part of their philosophy. In the process of that they are making natural language summaries and interpretations of those claims. You are taking those natural language statements as if that was all they had to say and then trying to apply your intuition of on ill-defined natural language statements rather than read those natural language statements in the context of the formalisms and math they care about. You can’t divorce the math from the philosophy.
Ok, here’s one. You criticize Bayesian updating for invoking infinitely many hypotheses, as a fundamental problem. In fact, the problem of infinite sets is an issue, but it’s resolved in Jaynes’ book by a set of rules in which one never deals with infinities directly, but rather with convergent limiting expressions, which are mathematically well-behaved in ways that infinities aren’t. This ensures, among other things, that any set of hypotheses (whether finite or infinite) has only finite total plausibility, and lets us compute plausibilities for whole sets at once (ideally, picking out one element and giving it a high probability, and assigning a low total probability to the infinitely many other hypotheses).
Both theories make predictions about the validity of models using evidence—that is, they predict whether future observations will agree with the model.
No, our conceptions of epistemology are the same. Math does help us understand the world, in ways that natural language can’t.
No, I didn’t say that. I invoked them, because they matter. You then claims Jaynes’ deals with the problem. Yet Yudkowsky concedes it is a problem. I don’t think you understood me, rather than vice versa.
Popper never made a prediction like that. And this rather misses some points. Some models for using evidence (e.g. induction) are literally incapable of making predictions (therefore people who do make predictions must be doing something else). Here Popper was not making a prediction, and also was pointing out prediction isn’t the right way to judge some theories.
Can you write philosophical explanations in math? Of course math helps for some stuff, but not everything.
Here’s where you’ve really gone astray. You’re trying to figure out math by reading what people are saying about it. That doesn’t work. In order to understand math, you have to look at the math itself. I’m not sure what statement by Yudkowsky you’re referring to, but I’ll bet it was something subtly different.
Uh, wait a second. Did you really just say that Popper doesn’t provide a method for using evidence to decide whether models are valid? There must be some sort of misunderstanding here.
I am pretty sure it was this one—where: Yudkowsky goes loopy.
The only way evidence is used is that criticisms may refer to it.
I’m not trying to figure out math, I’m trying to discuss the philosophical issues.
Please reread what Jim wrote. You seem to be in agreement with his statement that evidence is used.
Unfortunately, they are interrelated. There’s a general pattern here: some people (such as Jaynes and Yudkowsky) are using math as part of their philosophy. In the process of that they are making natural language summaries and interpretations of those claims. You are taking those natural language statements as if that was all they had to say and then trying to apply your intuition of on ill-defined natural language statements rather than read those natural language statements in the context of the formalisms and math they care about. You can’t divorce the math from the philosophy.