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This explanation ignores the two perspectives of probability - assertions on states of the world (the "frequentist" view) vs. states of the mind (the "bayesian"

by acchow 13y ago

This explanation ignores the two perspectives of probability - assertions on states of the world (the "frequentist" view) vs. states of the mind (the "bayesian" view). See also http://lesswrong.com/lw/oj/probability_is_in_the_mind/ http://lesswrong.com/lw/oj/probability_is_in_the_mind/

klodolph 13y ago
It has nothing to do with frequentist versus bayesian statistics this is really just a pure probability theory problem.
- ggreer 13y ago
  This exact puzzle is discussed in http://lesswrong.com/lw/ul/my_bayesian_enlightenment/ http://lesswrong.com/lw/ul/my_bayesian_enlightenment/: I responded—note that this was completely spontaneous—"What on Earth do you mean? You can't avoid assigning a probability to the mathematician making one statement or another. You're just assuming the probability is 1, and that's unjustified." While the equations of probability theory are agreed upon, there are multiple interpretations[1]. In some ways, it's like QM.[2] 1. http://en.wikipedia.org/wiki/Probability_interpretations#Philosophy http://en.wikipedia.org/wiki/Probability_interpretations#Phi... 2. http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics http://en.wikipedia.org/wiki/Interpretations_of_quantum_mech...
javert 13y ago
As far as I can tell, that blog post contains a "bait and switch." Here it is: > But suppose that instead you had asked, "Is your eldest child a boy?" and the mathematician had answered "Yes." Then the probability of the mathematician having two boys would be 1/2. Since the eldest child is a boy, and the younger child can be anything it pleases. No, it cannot be "anything it pleases." That is the whole point of the blog post that we are all commenting about here on HN, which is re-told on the blog post you are linking to. Since the post you are linking to is misrepresenting one side of the "argument," I strongly suggest that there is no actual apparentl contradiction here that needs to be resolved. Yes, you can talk about the actual probability of something vs. making the best possible prediction you have. A good example raised in this post is the point about a biased coin; you know it is biased but not which way, so you assign odds of .5 for heads and .5 for tails. Fine. This is not some massive philosophical conundrum. The fact is that actual knowledge is neither purely "out there" (e.g. "in the cards") nor purely "in here" (in the mind). This is the classic rationalism vs. empiricism debate, which was settled by Ayn Rand's theory of objective knowledge, where she answers that knowledge is in man's mind, but it is knowledge of external reality. So, "both." Not understanding this, and other basic epistemological errors, seem to plague lesswrong.com. It is embarassing to see them supposedly championing "reason" under a non-objective epistemology. They come to bizarre conclusions, and that is, at least partially, why.
- tarblog 13y ago
  Ayn Rand settled the age-old epistemology debate? I don't think so.
  - javert 13y ago
    Well, there are only five reasonable ways to disagree. (1) Do you hold that concepts and principles are purely "in" the referents? (2) Do you hold that they are purely "in" man's mind? (3) Do you hold that they are "in" man's mind, but refer to properties of the referents? (Rand's conclusion) (4) Do you hold that Rand's argument and conclusion is correct, but somebody else made it earlier? (5) Do you hold that there is insufficient evidence to answer the question (which then raises questions about why you would even engage in an intellectual discussion)? For example, you could "argue" for a subjectivist view of knowledge. An actual answer along the lines of 1-5 would be useful, but stating "I don't think so" does not provide any reasoning, and thus is utterly devoid of intellectual content. You seem to be dismissing a theory without considering and responding to its evidence, which is fraudulent science. Nobody wants to see that kind of "argument," even people who nonetheless do agree with the conclusion. I do think you have the intellectual right to merely state that you disagree, but you have to say that you don't intend to defend it, or let yourself be subject to having it pointed out by someone, as I am. That is because too many people today hide behind the assumption that agreement or disagreement without evidence presented is enough to establish or disestablish truth. As I said before, that is fraudulent science.

by acchow 13y ago

klodolph 13y ago

It has nothing to do with frequentist versus bayesian statistics this is really just a pure probability theory problem.

ggreer 13y ago
This exact puzzle is discussed in http://lesswrong.com/lw/ul/my_bayesian_enlightenment/ http://lesswrong.com/lw/ul/my_bayesian_enlightenment/: I responded—note that this was completely spontaneous—"What on Earth do you mean? You can't avoid assigning a probability to the mathematician making one statement or another. You're just assuming the probability is 1, and that's unjustified." While the equations of probability theory are agreed upon, there are multiple interpretations[1]. In some ways, it's like QM.[2] 1. http://en.wikipedia.org/wiki/Probability_interpretations#Philosophy http://en.wikipedia.org/wiki/Probability_interpretations#Phi... 2. http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics http://en.wikipedia.org/wiki/Interpretations_of_quantum_mech...

javert 13y ago

As far as I can tell, that blog post contains a "bait and switch." Here it is: > But suppose that instead you had asked, "Is your eldest child a boy?" and the mathematician had answered "Yes." Then the probability of the mathematician having two boys would be 1/2. Since the eldest child is a boy, and the younger child can be anything it pleases. No, it cannot be "anything it pleases." That is the whole point of the blog post that we are all commenting about here on HN, which is re-told on the blog post you are linking to. Since the post you are linking to is misrepresenting one side of the "argument," I strongly suggest that there is no actual apparentl contradiction here that needs to be resolved. Yes, you can talk about the actual probability of something vs. making the best possible prediction you have. A good example raised in this post is the point about a biased coin; you know it is biased but not which way, so you assign odds of .5 for heads and .5 for tails. Fine. This is not some massive philosophical conundrum. The fact is that actual knowledge is neither purely "out there" (e.g. "in the cards") nor purely "in here" (in the mind). This is the classic rationalism vs. empiricism debate, which was settled by Ayn Rand's theory of objective knowledge, where she answers that knowledge is in man's mind, but it is knowledge of external reality. So, "both." Not understanding this, and other basic epistemological errors, seem to plague lesswrong.com. It is embarassing to see them supposedly championing "reason" under a non-objective epistemology. They come to bizarre conclusions, and that is, at least partially, why.

tarblog 13y ago
Ayn Rand settled the age-old epistemology debate? I don't think so.
- javert 13y ago
  Well, there are only five reasonable ways to disagree. (1) Do you hold that concepts and principles are purely "in" the referents? (2) Do you hold that they are purely "in" man's mind? (3) Do you hold that they are "in" man's mind, but refer to properties of the referents? (Rand's conclusion) (4) Do you hold that Rand's argument and conclusion is correct, but somebody else made it earlier? (5) Do you hold that there is insufficient evidence to answer the question (which then raises questions about why you would even engage in an intellectual discussion)? For example, you could "argue" for a subjectivist view of knowledge. An actual answer along the lines of 1-5 would be useful, but stating "I don't think so" does not provide any reasoning, and thus is utterly devoid of intellectual content. You seem to be dismissing a theory without considering and responding to its evidence, which is fraudulent science. Nobody wants to see that kind of "argument," even people who nonetheless do agree with the conclusion. I do think you have the intellectual right to merely state that you disagree, but you have to say that you don't intend to defend it, or let yourself be subject to having it pointed out by someone, as I am. That is because too many people today hide behind the assumption that agreement or disagreement without evidence presented is enough to establish or disestablish truth. As I said before, that is fraudulent science.