When it comes to evidence, I don't believe Bayes' theorem deals with the real-world problems that arise when considering a hypothesis. For example, it doesn't deal with the "garbage in, garbage out" problem.
If you mean things like the base rate fallacy, then yes it does. If you mean that putting in random numbers for your priors doesn't solve your problems, then there isn't any method of considering evidence that fixes that in principle.
If you mean things like the base rate fallacy, then yes it does.
In the paragraph after the one you quoted, I gave an example of what I was discussing.
If you mean that putting in random numbers for your priors doesn't solve your problems, then there isn't any method of considering evidence that fixes that in principle.
You can check the source of the evidence and try to make sure that you're not putting in random numbers but reliable data.
When considering hypotheses in the real world -- like "Does God exist?" or "Is my wife cheating on me?"-- Bayes' theorem doesn't encapsulate all the skills you need to arrive at a trustworthy answer. You must clearly understand what it is you're trying to establish -- Aquinas's conception of God is very different from your average Christian's. You must be willing to question beliefs that you are attached to or identify with -- maybe your wife is sleeping with anything that moves, or maybe you're a needlessly jealous, insecure husband. You must gather as much evidence as possible, including the evidence that you might initially deem to be irrelevant. You must be diligent, fastidious, and detached when performing the investigation -- not hiding behind "Oh, my wife would never do that" or allowing your emotions to effect your judgment.
People will have done all the above and still arrived at erroneous conclusions. Such is the difficulty of testing a hypothesis.
Explaining the way one uses a word isn't a statement about maths or the laws of probability either.
It is, actually. It's the Bayesian definition that evidence for X is something more likely to be true in a universe where X than in a universe where -X.
Part of the point of Bayes' Theorem is that correction for the base rate fallacy is baked in. That's a large part of what separates Bayesian rationality from irrationality,
It is, actually. It's the Bayesian definition that evidence for X is something more likely to be true in a universe where X than in a universe where -X.
What you're saying here is that you use Bayes' theorem to inform your definition of "evidence".
If I used a different definition of evidence, that doesn't mean I'm saying something about Bayes' theorem. That simply means I use the word differently.
When it comes to evidence, I don't believe Bayes' theorem deals with the real-world problems that arise when considering a hypothesis. For example, it doesn't deal with the "garbage in, garbage out" problem.
As I said, we might plug the number of calls Uri Geller got into Bayes' theorem and because of the answer believe that supernatural events did actually occur. But that would be an incorrect conclusion because we have based our conclusion on the faulty premise that more calls means supernatural events are more likely to have occurred.
I don't think a less abstract example will solve a dispute over word usage.
This is really a dispute over maths. The laws of probability are the law, they don't depend on word usage.
And even if they did receive a statistically significant number of calls, perhaps people lied, grouped together and phoned in supernatural events that hadn't actually occurred.
Of course people can mock up evidence of things that are not in fact true. It's still evidence from the perspective of people who are not in on the plot. All of our evidence for everything could in theory have been mocked up by the architects of the Matrix and it would still all be evidence, from our perspective.
I'm not clear how this is relevant to the base rate fallacy though.
How relevant a piece of evidence truly is might not become apparent even after significant consideration. This is why, for important matters, I explore as much evidence as possible, even the seemingly irrelevant evidence.
Strictly speaking what's going on there is that you are collecting facts which might later turn out to be evidence for a hypothesis you have not articulated yet. This is an entirely rational approach to solving certain classes of problems. It doesn't change the definition of evidence though,
This is really a dispute over maths. The laws of probability are the law, they don't depend on word usage.
Explaining the way one uses a word isn't a statement about maths or the laws of probability either.
I'm not clear how this is relevant to the base rate fallacy though.
It's not. I was riffing on what you said.
Strictly speaking what's going on there is that you are collecting facts which might later turn out to be evidence for a hypothesis you have not articulated yet.
I was discussing ascertaining the trustworthiness of evidence concerning a hypothesis you are currently considering. Like an investigation into whether Uri Gellers phone calls were genuine reports of supernatural events, for example.
It doesn't change the definition of evidence though,
Of course not. I'm not trying to suggest that my usage of "evidence" is somehow better or superior than yours. I do think mine is more common, but that's a matter of opinion.
I think our disagreement is to do with our differing usage of "evidence", not a misconception. I'd say that a sole anecdote of someone seeing Russell's teapot can be considered evidence for its existence, even though it's not credible evidence.
Perhaps a less abstract example would help. Uri Geller used to claim he was projecting his psychic powers over the TV or the radio and invite people to phone in if something "spooky" happened in their home. Inevitably people phoned in to report clocks stopping or starting, things falling off shelves and so on. It was pretty convincing stuff for people who believed in that sort of thing, but it turned out that when skeptics with no psychic powers whatsoever pretended to be psychic on the radio and invited people to phone in they got exactly the same flood of calls. Odd things happen all the time and if you get a large enough sample of people looking about the house for odd things to report you get a fair number of calls.
What would have been evidence for Uri Geller having psychic powers is if he got more calls than normal people when he did that stunt. Just getting the base rate of calls anyone else would proves nothing. As you said yourself, you have to look at all the evidence.
You might be thinking "I read this Bayes theorem essay, and it said evidence for X was whatever was more likely to be true in a universe where X was true. In a universe where Russell's teapot existed I'd be more likely to hear someone say they saw Russel's teapot, right? So it's evidence! Bayes says so". That line of reasoning only works if you don't have all the evidence to look at so you can't determine the base rate. If you can determine the base rate then it's probably going to turn out that the number of claimed teapot-sightings is consistent with the base rate of stupid noises humans make.
If all you have is the one anecdote then it does count as evidence, but only in a strictly philosophical or mathematical sense. Not in any practical sense though since the shift in the relevant p value isn't going to be visible in the first twenty or thirty decimal places and I doubt anyone alive has that level of precision in their decision-making. (The odds of someone having seen Russell's teapot could be said, very conservatively, to be lower than the odds of someone winning the lotto twice in a row).
Perhaps a less abstract example would help
I don't think a less abstract example will solve a dispute over word usage.
What would have been evidence for Uri Geller having psychic powers is if he got more calls than normal people when he did that stunt.
And even if they did receive a statistically significant number of calls, perhaps people lied, grouped together and phoned in supernatural events that hadn't actually occurred.
If all you have is the one anecdote then it does count as evidence, but only in a strictly philosophical or mathematical sense. Not in any practical sense though since the shift in the relevant p value isn't going to be visible in the first twenty or thirty decimal places and I doubt anyone alive has that level of precision in their decision-making.
I don't have a problem with dismissing evidence if it truly is highly irrelevant. I think the problem is that in some cases evidence that at first seems irrelevant turns out to be important.
How relevant a piece of evidence truly is might not become apparent even after significant consideration. This is why, for important matters, I explore as much evidence as possible, even the seemingly irrelevant evidence.
I think I might have to write something specifically addressing this misconception because a few people seem to have picked it up.
It's only evidence for the existence of Russell's teapot if more people say they have seen it than you would expect in a universe where Russell's teapot does not exist.
(That's ignoring the fact that Russell's teapot is by stipulation non-observable and hence in that artificial situation we can skip Bayesian updating and just go straight to p=1 that anyone claiming to have observed it is lying or deluded).
I think I might have to write something specifically addressing this misconception because a few people seem to have picked it up.
I think our disagreement is to do with our differing usage of "evidence", not a misconception. I'd say that a sole anecdote of someone seeing Russell's teapot can be considered evidence for its existence, even though it's not credible evidence.
It's only evidence for the existence of Russell's teapot if more people say they have seen it than you would expect in a universe where Russell's teapot does not exist.
I would add that different situations require different standards of evidence, depending on how willing we are to accept false positives. The fire service only requires one phone call before they respond.
No, just as there is no evidence for Russell's teapot.
There is only one historical document from the time of Jesus' supposed life which even resembles evidence of a teacher called Jesus (or Yeshua or whatever), and that is just a reference to a rabbi with the right name who had one brother with the right name. Given that Jesus supposedly had four named brothers and multiple sisters, at least one of whom is also named, there's plenty of scope for that to be a false positive. Taking it as strong evidence would be like taking the discovery of a journalist named Clark who worked with a journalist named James in the 1920s as strong evidence that those two were the historical basis for the story of Superman.
There could have been a historical Yeshua so boring that none of his contemporaries, including the Romans, wrote anything about him during his life or for decades after he died. Or the character could have been entirely made up. Evidence to differentiate these two possible universes does not currently exist.
No, just as there is no evidence for Russel's teapot.
As the word evidence is commonly used, there is evidence for Russell's teapot -- just not evidence that you or me believe in. If someone says "Russell's teapot exists! I've seen it!", that is anecdotal evidence for its existence. Anything that suggests something is true or false is evidence, no matter how flawed that evidence may be.
It is by considering all the evidence, for and against our beliefs, that we progress towards truth.
It seems to me that Adam Frank doesn't do himself any favors in this debate by linking "spiritual endeavor" to religion. While one can argue that "spiritual endeavor" is the basis on which most religions are founded, if one wishes to debate the subject with an atheist it is probably better to not bring up religion at all.
You're more likely to have a fruitful conversation if you discuss "understanding the true nature of subjective reality" rather than "spiritual endeavor", "the overview effect" rather than "religious experiences", and neurological research rather than the Bible.
But even then it is probably pointless. The Buddha says that a student only obtains proof of the validity of his teachings when he becomes a Sotāpanna. Before that, the Buddha's teachings must be taken on blind faith -- not something any self-respecting skeptic is going to do.
Atheists may not believe in God, but I think they mostly adhere to the 10 commandments.
I think you're just trying to say that atheists follow moral expectations of modern Christian-influenced culture, but taken literally, the statement's nonsense.
I mean, look at the Ten Commandments:
- Thou shalt have no other gods before me.
- Thou shalt not make unto thee any graven image (...).
- Thou shalt not take the name of the Lord thy God in vain (...).
- Remember the sabbath day, to keep it holy. (...)
- Honour thy father and thy mother (...).
- Thou shalt not kill.
- Thou shalt not commit adultery.
- Thou shalt not steal.
- Thou shalt not bear false witness against thy neighbour.
- Thou shalt not covet thy neighbour's house, (...) nor his ass, nor any thing that is thy neighbour's.
The first 4 are blatantly ignored, 6 is famously problematic, 9 and 10 are mostly ignored (via gossip, status seeking, greed and so on) and finally 7 and 8 might be typically obeyed, but minor theft (especial anonymous) is common and adultery has at least 10% base rates.
How is this a "mostly adhered"? (Obviously, Christians and atheists don't really differ in their behavior here.)
I'll have to concede that atheists moral beliefs don't mostly adhere to the 10 commandments.
The point I wished to make was that many of the moral philosophies of rationalists are very similar to their Christian counterparts. I believe the similarity is mostly due to the culture they were brought up in rather than whether they believe God exists or not. You might even consider God to be irrelevant to the issue.
I was actually just trying to say that Eliezer gave a bad example of a disguised query.
As for moral philosophy, it can be considered a science. So atheists that believe in morality should value it as any other science (for it's usefulness etc). Well, hm, atheists need not be fans of science. So they can be moral because they enjoy it, or simply because "why the heck not".
I wouldn't call moral philosophy a science.
If we both independently invented an imaginary creature, neither would be correct. They are simply the creatures we've arbitrarily created. There is no science of moral philosophy anymore than there is a science of inventing an imaginary creature.
I'd say to be science there needs to be the ability to test whether something is valid. There is no such test for the validity of morals anymore than there is a test for the validity of an imaginary creature.
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Absolutely. Otherwise I can't exclude from the domain of "evidence of X" all things which should not incline a rational person to amend their views about X, and I very much want to do that.
Note that something can be "evidence" without being "evidence of X" where X is one specific something. Someone calling in to say their watch stopped is evidence that someone called in and evidence that a watch stopped and so on, just not evidence that Uri Geller has radio-propagated psychic powers.
I agree with you to the extent that Bayes' theorem is not a magic wand that cures all epistemological ills. You don't have to browse this site for too long to come across people advancing silly ideas under the banner of Bayesian inference because they are using it incorrectly. However while it's not a magic wand it's a mathematical truth about how the universe works, and any time you deliberately deviate from Bayes' theorem you are deliberately going wrong as a matter of mathematical fact.
What is actually going on here, assuming you are applying Bayes correctly, is that the prior probability of Uri Geller having radio-propagated psychic powers should be seen as astoundingly low. Far lower than the odds of me winning the lotto twice in a row, for example - let's say one on ten to the fourteenth as a very generous prior probability. If Uri Geller got a lot more phone calls than a skeptic pretending to be a psychic that should tip the scales a little in his favour but nowhere near enough to get P(Uri Geller has psychic powers) up to a level we should take seriously.
The premise "more calls makes psychic powers more likely" is not flawed at all. If we lived in a bizarre universe where Uri Geller really could reach out through your radio and stop your watch then we would indeed see more calls coming in, and if we lived in that bizarre world we should want to believe we lived in that bizarre world. I'm very sure we do not live in that world but that's because the evidence is against it, not because I would dismiss that evidence if it supported it.
If someone believes the Bible is central to question of whether God exists, you can challenge that without having a definition of "evidence" that is informed by Bayes' theorem.
It could be flawed if there are things that effect the number of phone calls other than Geller's proposed psychic powers. One show might get more calls but also have more viewers, and that obviously doesn't make Geller more likely to be psychic during that particular show.
But I am in agreement with you generally with the Uri Geller example. I don't think phone calls to a television show would alone change my mind, but if we did live in a world where he truly did have psychic powers, I would hope that such evidence would lead me to investigate the matter further.