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.
Moral people follow their moral philosophy because they believe it's the right thing to do, whether they are Christian or atheist or neither.
My point is that Christians believe their moral philosophy is correct because God told them so. Atheists don't have such an authority to rely on.
So what rational justification can an atheist provide for his moral philosophy? There is no justification because there is no way to determine the validity of any justification they may provide.
There is no rational foundation for moral beliefs because they are arbitrarily invented. They are built on blind faith.
How do people use the karma system here? If you agree vote up, if you disagree vote down? That will create a very insular community.
My five cents.
Direct counterargument: I would phrase my attitude to ethics as: "I have decided that I want X to happen as much as possible, and Y to happen as little as possible." I'm not "believing" anything - just stating goals. So there's no faith required.
Reflective counterargument: But even if God did say so*, why should we obey Him? There are a number of answers, some based on prior moral concepts (gratitude for Creation, fear of Hell, etc.) and some on a new one (variations on "God is God and therefore has moral authority") but they all just push the issue of your ultimate basis for morality back a step. They don't solve the problem, or even simplify it.
*Incidentally, what does it mean for an all-powerful being to say something? The Abrahamic God is the cause for literally everything, so aren't all instructions written or spoken anywhere by anyone equally "the speech of God"?
Direct counterargument: I would phrase my attitude to ethics as: "I have decided that I want X to happen as much as possible, and Y to happen as little as possible." I'm not "believing" anything - just stating goals. So there's no faith required.
I'd agree. By switching from morals to your individual preferences, you avoid the need to identify what is objectively good and evil.
I agree that religion isn't the source of morality. In my experience, atheists believe in good and evil just as much as religious people do.
To believe you can somehow make the world objectively better, even in a small way, you must still believe in some sort of objective good or evil. My position is the sacrilegious idea that there is no objective good or evil -- that the universe is stuff bouncing and jumping around in accordance with the laws of nature. Crazy, I know.
There is a difference between the universe itself and our interpretations of the universe. A moral is a judgement about the universe mistaken for an inherent property of the universe.
In order to establish that something is better than or superior to something else, we must have some criteria to compare them by. The problem with objective good and evil, if you believe they exist, is that there is no way to establish the correct criteria.
A lion's inclination to kill antelope isn't inherently wrong. The inclination is simply the lion's individual nature. Because you care about the antelope's suffering doesn't mean the lion should. The lion isn't wrong if it doesn't care.
We are all individuals with different wants and desires. To believe there is a one-size-fits-all moral code that all living creatures should follow is lunacy.
A point everyone seems to be missing here is that there ARE no scientific facts. There are only scientific theories. During any given era there may be what we "believe" to be proven scientific facts that have gone through rigorous, repeated testing by many in the scientific community. Then the next generation comes along and proves some of those well respected theories to be exactly that - theoretical. Phlogiston anyone? (Just one very small example of something that was accepted as scientific "law" - so much so it was at one time added to the periodic table of elements until it was finally proven it didn't even exist.) - A closed mind is a trap.
A point everyone seems to be missing here is that there ARE no scientific facts.
There are scientific facts, as the phrase is commonly understood. Anything that is independently verifiable is considered to be a scientific fact. Facts are not built upon theories; theories are built upon facts.
You would be right to say that that sensible scientists don't claim that they are definitely correct. They tentatively believe what the available evidence currently suggests. No more, no less.
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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.