E is evidence if it should update our beliefs about a hypothesis H: P(H|E)≠P(H).
We can then expand a bit:
P(H|E)=P(H)P(E|H)P(E)=P(H)P(E|H)∑H′P(E|H′)P(H′)
If we have only a single hypothesis H’ = H such that P(H)=1, then the sum in the denominator reduces to P(E|H), which cancels out with the numerator and gives us P(H|E)=P(H), preventing E from being evidence.
Wikipedia used to present both an environmental and a hereditarian perspective, but eventually the hereditarian perspective got deleted by being declared fringe. You should feel encouraged to show how recent science disproved hereditarianism, but I don’t think the change represents a change in evidence base, but instead a change in political power. Of course it might also be that the political change was well justified because you think wikipedia used to be biased in favor of hereditarianism but now no longer is. If so I would be interested in what brings you to this conclusion.
Anyway I would respond to the claims of wikipedia but the page is 100 thousand characters long, so it might be more efficient if you mention whether there is some part that you find particularly convincing or insightful.
More importantly, it’s important not to neglect seeing what’s really going on—people who, despite there being no scientific evidence for it, innocently suggest (the link talks about the fallacy, not about intelligence) that maybe the racial differences in intelligence, assuming they exist, might be genetic, have obviously a not-so-hidden and malicious agenda, or have been misled by such people.
After that meta is clearly stated, then we can talk about whether, despite there being no scientific evidence for that, there is >0% epistemic probability of >0% of the portion of racial IQ test result differences being genetically caused.
Well we first need to agree on whether there is no scientific evidence for it. I’m not sure about that, though it is easier to understand in the context of some alternate theory/worldview of race and IQ, if you have one that you would endorse. As then we can look at various pieces of evidence and see if there’s any pieces that have a likelihood ratio favoring the hereditarian position over your position.
More importantly, you’re missing some hypotheses there (you’re comparing no racial differences in intelligence to racial differences in intelligence being nonzero and also being genetic (that’s what I assume you mean by innate), which is pointless).
Yes, I acknowledged that and discussed it in my comment, with a followup question asking for clarification on your position.
Why would P(H)=1? Did you mean, in your previous comment, that evidence is only meaningful when I have at least two hypotheses (e.g.H and ¬H)? If so, that’s obvious.
The two hypotheses here are “the differences in IQ testing are partially or completely genetically caused” and “the differences in IQ testing aren’t genetically caused at all.”
Wikipedia used to present both an environmental and a hereditarian perspective, but eventually the hereditarian perspective got deleted by being declared fringe. You should feel encouraged to show how recent science disproved hereditarianism, but I don’t think the change represents a change in evidence base, but instead a change in political power.
You should feel encouraged to show the Wikipedia article is a result of political power rather than evidence. Good luck.
Yes, I acknowledged that and discussed it in my comment
That’s not good enough, because you were still being highly misleading. If I say there is strong evidence for you shooting Fred compared to the null hypothesis of Fred not being shot at all, it might still be a true statement, but it’s still connotatively misleading (even if I explicitly say so).
The two hypotheses here are “the differences in IQ testing are partially or completely genetically caused” and “the differences in IQ testing aren’t genetically caused at all.”
So there’s a sort of distinction to be made between two notions of hypothesis. One notion of hypothesis covers just about any proposition at all. But there’s a narrower notion of hypothesis which covers something which makes a positive description of the world.
For instance, Bayesianism is usually phrased in terms of measure theoretic foundations, where you have an outcome space containing the different ways that the world could be. Each such outcome could be considered a hypothesis in itself. There are other alternatives to the measure-theoretic foundations too.
But the problem is that “the differences in IQ testing aren’t genetically caused at all” is not a hypothesis in any sense like the above, because it doesn’t specify what alternative cause there is. Depending on the evidence a person has seen, they might have different things in mind for what the causes of the differences in IQ are, and that makes it hard to directly respond to them.
You should feel encouraged to show the Wikipedia article is a result of political power rather than evidence. Good luck.
Well, my evidence for it being a result of political power is that if it was a result of evidence, then I’d have thought that you as the expert in the evidence disproving genetic race differences in IQ would point at the relevant novel evidence that changed the Wikipedia consensus.
That’s not good enough, because you were still being highly misleading. If I say there is strong evidence for you shooting Fred compared to the null hypothesis of Fred not being shot at all, it might still be a true statement, but it’s still connotatively misleading (even if I explicitly say so).
Ehm, if anyone is being highly misleading, it is you. You said that there is “no scientific evidence the racial group differences in IQ are genetic”, yet if that’s true then how do you explain this?
But there’s a narrower notion of hypothesis which covers something which makes a positive description of the world.
Anything can be phrased as a positive description of the world—it only depends on the language used.
But the problem is that “the differences in IQ testing aren’t genetically caused at all” is not a hypothesis in any sense like the above, because it doesn’t specify what alternative cause there is.
It is a hypothesis in that sense as well—the rest of the outcome space is the other hypothesis.
Well, my evidence for it being a result of political power is that if it was a result of evidence, then I’d have thought that you as the expert in the evidence disproving genetic race differences in IQ would point at the relevant novel evidence that changed the Wikipedia consensus.
So, the evidence of your (evidenceless) hypothesis being right is that I haven’t pointed at the evidence that would contradict it. I see. I’m glad we cleared that up.
Ehm, if anyone is being highly misleading, it is you. You said that there is “no scientific evidence the racial group differences in IQ are genetic”, yet if that’s true then how do you explain this?
That’s an interesting one study. I don’t have time to learn the concepts enough to write about whether there are any other explanations than what the study suggests (for example, how did they control for environmental racism?, etc.).
Anything can be phrased as a positive description of the world—it only depends on the language used.
...
It is a hypothesis in that sense as well—the rest of the outcome space is the other hypothesis.
The simplest explanation of the problem:
In order to evaluate evidence (and to apply the model!), we need to be able to make predictions, i.e. to compute P(E|H).
This is possible for a hypothesis H which makes a positive claim for how the world works—just turn the gears of the hypothesis, and predictions pop out.
However, it is not possible for a hypothesis that is defined purely by negative of a positive hypothesis, because then in order to make the predictions, one needs to have a collection of alternative positive claims to turn the gears for.
So, the evidence of your (evidenceless) hypothesis being right is that I haven’t pointed at the evidence that would contradict it. I see. I’m glad we cleared that up.
My model can be approximated as there being two possibilities:
You have a detailed understanding of the evidence cited on wikipedia, the history of wikipedia’s trustworthyness, etc.. If that was the case, then I would expect that after writing a query, you would have an idea for what of the evidence you’ve seen is relevant for that query, and would be capable of and interested in pointing at that evidence.
You do not have a detailed understanding of the evidence, and your initial declaration that “There is no scientific evidence the racial group differences in IQ tests are genetic” is mainly due to trusting various authorities (like wikipedia) to fairly summarize the topic.
While I kept both possibilities in mind, while responding to you, I was mainly writing the response while conditioning on possibility 1. Conditional on 1, the fact that you aren’t pointing out counterevidence is evidence that such counterevidence doesn’t exist, which in turn is evidence for my original claims.
However, 1 might be false, and I’m well aware that it might be false. Does this make me disingenuous to condition on it? It might? Maybe I should have started the conversation by asking which of the possibilities apply? I think that asking about that would usually be considered rude, though maybe that is just because I haven’t been creative enough with the phrasing.
Though I did in fact ask about some aspects of your perspective in my very first comment. In the future to make these sorts of conversations go more smoothly, if something more like possibility 2 is true, when someone asks for your detailed perspective, it would probably be best if you wrote something like “I haven’t researched it in depth, so I just trust outspoken academics and wikipedians on it” to clarify your epistemic position.
However, it is not possible for a hypothesis that is defined purely by negative of a positive hypothesis, because then in order to make the predictions, one needs to have a collection of alternative positive claims to turn the gears for.
If I have three hypotheses “At least one swan is black,” “It’s not true at least one swan is black” and “All swans reflect EM waves on the wavelengths of the visible light,” which ones are negations of other hypotheses and which ones are positive?
On their own, none of these are positive in the sense I’m talking. They are propositions that describe properties of the world, but they don’t sketch out what that world looks like overall. This means that they generally can’t predict P(E|H) for arbitrary E, so they don’t have enough structure to be compared with other hypotheses for Bayesian updating.
If we negate them, the first two hypotheses just swap while the third hypothesis turns into “Not all swans reflect EM waves on the wavelengths of the visible light”, which also is a proposition that describes a property of the world but doesn’t sketch out what the world looks like overall, and so it too is not a positive hypothesis.
In summary, none of them are positive and none of them are negations of positive hypotheses.
Obviously that is not very helpful in practice, so there are a few things that can be used to improve the situation. First, we might assume that we have a lot of background knowledge W about what swans are like, such that this W can handle predictions on all other questions than the ones specifically dependent on these questions of swan blackness. In that case for each of the hypotheses H, we can form the hypothesis H∧W which conditions W on H.
The trouble is in the case of race is that what you get depends a lot on the shape of W. So for instance for you, ‘‘Thereisnogeneticracedifferenceinintelligence"∧W might be that race differences in IQ are caused by lead poisoning and test bias, whereas for me, since I have a different W than you, ‘‘Thereisnogeneticracedifferenceinintelligence"∧W might be that there are social network differences where black people are not getting sufficiently integrated into intellectual social groups. If I then start defending “The racial difference in IQ is genetic” with reference to evidence that there’s not much of interest going on with social network relations, then that is going to seem pointless to you because I am ignoring the real alternative hypothesis of lead poisoning and test bias.
Another approach than H∧W is to narrow the space of evidence under consideration. For instance if we assume that the observations we get is a set of indicators for an IID population of swans for whether or not those swans are black, then “It’s not true that at least one swan is black” does in fact predict P(E|H) for all E. Specifically, it permits observing that no swans are black but it does not permit observing that any swans are black. In fact for any fixed proportion p, “swans are black p of the time” is a positive hypothesis, which predicts an observation of n black and k white swans with probability pn(1−p)k.
Bringing the analogy to IQ-world, a hypothesis which breaks down the IQ gap, e.g. saying that there’s 2 points of gap due to lead, 1 point due to books, 2 points due to school quality, etc., would be sufficiently positive that I could engage with it. Like it wouldn’t predict everything about the world, but it would make predictions about the sorts of social science data that we would see (especially when augmented with other knowledge that is available).
More generally/abstractly, in the Bayesian framework, a hypothesis is not simply a proposition. There’s a few different ways to model what a hypothesis is instead depending on the flavor/mathematical foundations of Bayesianism one is using; e.g. one can model it as an event in an event space, or as a probability distribution over observations.
A third approach other than H∧W or restricting the evidence-space is to go non-Bayesian:
Scientific and logical inductor analysis:
Bayesianism basically requires a hypothesis to predict everything, which is computationally intractable and also kind of weird. There’s two alternate approaches, known as science and logical induction, which do not require hypotheses to make predictions on everything.
Rather than having the hypothesis predict all conceivable evidence, a hypothesis is an algorithm that only makes predictions in some areas that it happens to “care about”. So for instance, if the question comes up “Is this swan black?”, maybe “It’s not true at least one swan is black” would make a strong prediction that it isn’t, and gain credibility for that.
In science and logical induction, hypotheses get credit for making predictions on questions that no other hypotheses have made predictions on yet. So for instance if “black people are just genetically less intelligent” came first as a hypothesis for why black people did worse on certain cognitive tasks, then “black people are just genetically less intelligent” gets the credit for that prediction and gets considered a plausible hypothesis. If later other hypotheses such as “black people are not genetically less intelligent” come along, then they might not get any credit at all, due to not making clear predictions. On the other hands, “black people are less intelligent due to environmental lead pollution” may possibly get credit as a competitor once data on lead and IQ is collected, depending on what exactly that data says.
I left this one a long time without response while I gathered the energy to.
If I then start defending “The racial difference in IQ is genetic” with reference to evidence that there’s not much of interest going on with social network relations, then that is going to seem pointless to you because I am ignoring the real alternative hypothesis of lead poisoning and test bias.
All three are real alternative hypotheses. But what I had in mind was scientific evidence specific enough that would single that one hypothesis out from all possible reasonable hypotheses.
In the mathematical sense of “evidence,” not observing any different social network relations is evidence for black people being less intelligent for genetic reasons (under the assumption that they are, in fact, less intelligent, which itself remains to be shown). But that’s not the kind of evidence that I had in mind.
If someone (not me, because I’m not interested) asks you what scientific evidence do you have for black people being genetically less intelligent, and you have specific evidence to disconfirm the hypotheses that they (even though not you) believe to be the alternative ones (like lead poisoning or test bias), you can bundle that evidence to the evidence you were going to give them, compensating for the fact that each of you have different alternative hypotheses.
In other words, what you’re writing seems to me technically correct, but practically irrelevant (as far as converging to the truth goes).
It sounds to me like you are endorsing the possibility I bought up at first here?
Playing hypothesis whack-a-mole assumes that we have a small number of feasible hypotheses, but maybe really we have an exponential area of unexplored territory.
E is evidence if it should update our beliefs about a hypothesis H: P(H|E)≠P(H).
We can then expand a bit:
P(H|E)=P(H)P(E|H)P(E)=P(H)P(E|H)∑H′P(E|H′)P(H′)
If we have only a single hypothesis H’ = H such that P(H)=1, then the sum in the denominator reduces to P(E|H), which cancels out with the numerator and gives us P(H|E)=P(H), preventing E from being evidence.
Wikipedia used to present both an environmental and a hereditarian perspective, but eventually the hereditarian perspective got deleted by being declared fringe. You should feel encouraged to show how recent science disproved hereditarianism, but I don’t think the change represents a change in evidence base, but instead a change in political power. Of course it might also be that the political change was well justified because you think wikipedia used to be biased in favor of hereditarianism but now no longer is. If so I would be interested in what brings you to this conclusion.
Anyway I would respond to the claims of wikipedia but the page is 100 thousand characters long, so it might be more efficient if you mention whether there is some part that you find particularly convincing or insightful.
Well we first need to agree on whether there is no scientific evidence for it. I’m not sure about that, though it is easier to understand in the context of some alternate theory/worldview of race and IQ, if you have one that you would endorse. As then we can look at various pieces of evidence and see if there’s any pieces that have a likelihood ratio favoring the hereditarian position over your position.
Yes, I acknowledged that and discussed it in my comment, with a followup question asking for clarification on your position.
Why would P(H)=1? Did you mean, in your previous comment, that evidence is only meaningful when I have at least two hypotheses (e.g.H and ¬H)? If so, that’s obvious.
The two hypotheses here are “the differences in IQ testing are partially or completely genetically caused” and “the differences in IQ testing aren’t genetically caused at all.”
You should feel encouraged to show the Wikipedia article is a result of political power rather than evidence. Good luck.
That’s not good enough, because you were still being highly misleading. If I say there is strong evidence for you shooting Fred compared to the null hypothesis of Fred not being shot at all, it might still be a true statement, but it’s still connotatively misleading (even if I explicitly say so).
So there’s a sort of distinction to be made between two notions of hypothesis. One notion of hypothesis covers just about any proposition at all. But there’s a narrower notion of hypothesis which covers something which makes a positive description of the world.
For instance, Bayesianism is usually phrased in terms of measure theoretic foundations, where you have an outcome space containing the different ways that the world could be. Each such outcome could be considered a hypothesis in itself. There are other alternatives to the measure-theoretic foundations too.
But the problem is that “the differences in IQ testing aren’t genetically caused at all” is not a hypothesis in any sense like the above, because it doesn’t specify what alternative cause there is. Depending on the evidence a person has seen, they might have different things in mind for what the causes of the differences in IQ are, and that makes it hard to directly respond to them.
Well, my evidence for it being a result of political power is that if it was a result of evidence, then I’d have thought that you as the expert in the evidence disproving genetic race differences in IQ would point at the relevant novel evidence that changed the Wikipedia consensus.
Ehm, if anyone is being highly misleading, it is you. You said that there is “no scientific evidence the racial group differences in IQ are genetic”, yet if that’s true then how do you explain this?
Anything can be phrased as a positive description of the world—it only depends on the language used.
It is a hypothesis in that sense as well—the rest of the outcome space is the other hypothesis.
So, the evidence of your (evidenceless) hypothesis being right is that I haven’t pointed at the evidence that would contradict it. I see. I’m glad we cleared that up.
That’s an interesting one study. I don’t have time to learn the concepts enough to write about whether there are any other explanations than what the study suggests (for example, how did they control for environmental racism?, etc.).
The simplest explanation of the problem:
In order to evaluate evidence (and to apply the model!), we need to be able to make predictions, i.e. to compute P(E|H).
This is possible for a hypothesis H which makes a positive claim for how the world works—just turn the gears of the hypothesis, and predictions pop out.
However, it is not possible for a hypothesis that is defined purely by negative of a positive hypothesis, because then in order to make the predictions, one needs to have a collection of alternative positive claims to turn the gears for.
My model can be approximated as there being two possibilities:
You have a detailed understanding of the evidence cited on wikipedia, the history of wikipedia’s trustworthyness, etc.. If that was the case, then I would expect that after writing a query, you would have an idea for what of the evidence you’ve seen is relevant for that query, and would be capable of and interested in pointing at that evidence.
You do not have a detailed understanding of the evidence, and your initial declaration that “There is no scientific evidence the racial group differences in IQ tests are genetic” is mainly due to trusting various authorities (like wikipedia) to fairly summarize the topic.
While I kept both possibilities in mind, while responding to you, I was mainly writing the response while conditioning on possibility 1. Conditional on 1, the fact that you aren’t pointing out counterevidence is evidence that such counterevidence doesn’t exist, which in turn is evidence for my original claims.
However, 1 might be false, and I’m well aware that it might be false. Does this make me disingenuous to condition on it? It might? Maybe I should have started the conversation by asking which of the possibilities apply? I think that asking about that would usually be considered rude, though maybe that is just because I haven’t been creative enough with the phrasing.
Though I did in fact ask about some aspects of your perspective in my very first comment. In the future to make these sorts of conversations go more smoothly, if something more like possibility 2 is true, when someone asks for your detailed perspective, it would probably be best if you wrote something like “I haven’t researched it in depth, so I just trust outspoken academics and wikipedians on it” to clarify your epistemic position.
If I have three hypotheses “At least one swan is black,” “It’s not true at least one swan is black” and “All swans reflect EM waves on the wavelengths of the visible light,” which ones are negations of other hypotheses and which ones are positive?
Bayesian analysis:
On their own, none of these are positive in the sense I’m talking. They are propositions that describe properties of the world, but they don’t sketch out what that world looks like overall. This means that they generally can’t predict P(E|H) for arbitrary E, so they don’t have enough structure to be compared with other hypotheses for Bayesian updating.
If we negate them, the first two hypotheses just swap while the third hypothesis turns into “Not all swans reflect EM waves on the wavelengths of the visible light”, which also is a proposition that describes a property of the world but doesn’t sketch out what the world looks like overall, and so it too is not a positive hypothesis.
In summary, none of them are positive and none of them are negations of positive hypotheses.
Obviously that is not very helpful in practice, so there are a few things that can be used to improve the situation. First, we might assume that we have a lot of background knowledge W about what swans are like, such that this W can handle predictions on all other questions than the ones specifically dependent on these questions of swan blackness. In that case for each of the hypotheses H, we can form the hypothesis H∧W which conditions W on H.
The trouble is in the case of race is that what you get depends a lot on the shape of W. So for instance for you, ‘‘Thereisnogeneticracedifferenceinintelligence"∧W might be that race differences in IQ are caused by lead poisoning and test bias, whereas for me, since I have a different W than you, ‘‘Thereisnogeneticracedifferenceinintelligence"∧W might be that there are social network differences where black people are not getting sufficiently integrated into intellectual social groups. If I then start defending “The racial difference in IQ is genetic” with reference to evidence that there’s not much of interest going on with social network relations, then that is going to seem pointless to you because I am ignoring the real alternative hypothesis of lead poisoning and test bias.
Another approach than H∧W is to narrow the space of evidence under consideration. For instance if we assume that the observations we get is a set of indicators for an IID population of swans for whether or not those swans are black, then “It’s not true that at least one swan is black” does in fact predict P(E|H) for all E. Specifically, it permits observing that no swans are black but it does not permit observing that any swans are black. In fact for any fixed proportion p, “swans are black p of the time” is a positive hypothesis, which predicts an observation of n black and k white swans with probability pn(1−p)k.
Bringing the analogy to IQ-world, a hypothesis which breaks down the IQ gap, e.g. saying that there’s 2 points of gap due to lead, 1 point due to books, 2 points due to school quality, etc., would be sufficiently positive that I could engage with it. Like it wouldn’t predict everything about the world, but it would make predictions about the sorts of social science data that we would see (especially when augmented with other knowledge that is available).
More generally/abstractly, in the Bayesian framework, a hypothesis is not simply a proposition. There’s a few different ways to model what a hypothesis is instead depending on the flavor/mathematical foundations of Bayesianism one is using; e.g. one can model it as an event in an event space, or as a probability distribution over observations.
A third approach other than H∧W or restricting the evidence-space is to go non-Bayesian:
Scientific and logical inductor analysis:
Bayesianism basically requires a hypothesis to predict everything, which is computationally intractable and also kind of weird. There’s two alternate approaches, known as science and logical induction, which do not require hypotheses to make predictions on everything.
Rather than having the hypothesis predict all conceivable evidence, a hypothesis is an algorithm that only makes predictions in some areas that it happens to “care about”. So for instance, if the question comes up “Is this swan black?”, maybe “It’s not true at least one swan is black” would make a strong prediction that it isn’t, and gain credibility for that.
In science and logical induction, hypotheses get credit for making predictions on questions that no other hypotheses have made predictions on yet. So for instance if “black people are just genetically less intelligent” came first as a hypothesis for why black people did worse on certain cognitive tasks, then “black people are just genetically less intelligent” gets the credit for that prediction and gets considered a plausible hypothesis. If later other hypotheses such as “black people are not genetically less intelligent” come along, then they might not get any credit at all, due to not making clear predictions. On the other hands, “black people are less intelligent due to environmental lead pollution” may possibly get credit as a competitor once data on lead and IQ is collected, depending on what exactly that data says.
I left this one a long time without response while I gathered the energy to.
All three are real alternative hypotheses. But what I had in mind was scientific evidence specific enough that would single that one hypothesis out from all possible reasonable hypotheses.
In the mathematical sense of “evidence,” not observing any different social network relations is evidence for black people being less intelligent for genetic reasons (under the assumption that they are, in fact, less intelligent, which itself remains to be shown). But that’s not the kind of evidence that I had in mind.
If someone (not me, because I’m not interested) asks you what scientific evidence do you have for black people being genetically less intelligent, and you have specific evidence to disconfirm the hypotheses that they (even though not you) believe to be the alternative ones (like lead poisoning or test bias), you can bundle that evidence to the evidence you were going to give them, compensating for the fact that each of you have different alternative hypotheses.
In other words, what you’re writing seems to me technically correct, but practically irrelevant (as far as converging to the truth goes).
It sounds to me like you are endorsing the possibility I bought up at first here?