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.
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?