The lies

Sam Harris came on his show, prefacing an episode full of logical leaps and genetic fallacies, and stated, “People don’t want to hear that intelligence is a real thing, and that some people have more of it than others. They don’t want to hear that IQ tests really measure it. They don’t want to hear that differences in IQ matter because they’re highly predictive of differential success in life. And not just for things like educational attainment and wealth, but for things like out of wedlock birth and mortality. People don’t want to hear that a person’s intelligence is in large measure due to his or her genes, and there seems to be very little we can do environmentally to increase a person’s intelligence — even in childhood. It’s not that the environment doesn’t matter, but genes appear to be fifty to eighty percent of the story.”

And then the discussion turned to race.

This is the scene in which the podcast lives. It’s painted very metaphorically because it is not a podcast about actual models and formal details, which allows Charles Murray to make several logical leaps that do not go challenged. I feel it was the lack of challenging that lead to a feeling that Harris was an apologist for these genetic fallacies, leading to the Turkheimer at al. responses and ultimately the Ezra Klein discussion with Harris. And honestly, his stubborn refusal to understand the formal objections so clearly explained makes me lean more toward the assumption he is a knowing racial propagandist, or at least should be treated as such as a caution.

This is a topic that has reached a large audience in recent times due to various reverberations in the global discussion. Obviously, Very Bad Wizards had to follow up on the trends set by their benefactor Harris and do their own show on intelligence that again repeats this 50 to 80% claim. Gregory Clark on Julia Galef’s Rationally Speaking stated “there’s actually good evidence from a variety of sources that the majority of a people’s social status is actually genetically determined”. Later when she had Stuart Richie on there was an explicit “there is a lot of evidence that variation in IQ scores is explained to some quite substantial extent by variation in genetics”, and then a dive into heritability that makes the genetic assumption, later diving full in to defense of twin studies and the refrain “the constellation of evidence we have got, not just from twin studies but no, these days, from DNA as well — from direct testing of DNA — showing those twin studies were really on the right track all along. So nowadays we have evidence where we can take people that are completely unrelated or as unrelated as any randomly selected humans are, and give them a DNA array that checks the variation at 4 or 6 hundred thousand points along the DNA and give them an IQ test and essentially say are the people that are more similar in the DNA more similar in their intelligence and that gives a positive heritability number as well, so you get that a good chunk of the variation is associated with the genetic differences…”. I felt that there may be a wider misunderstanding effecting even scholars and the studied that needed a clear model to talk facts about.

This is a discussion that needs to live near the actual models. Formally, this discussion is all about heritability. Heritability is what Harris means when he points to the 50–80% genetics claim for IQ. It is this where the subtle implication of futility rests, that foundation of hopelessness on which the racial IQ gap wears it’s hideous supremacist robes. Throughout history, there has been this continued propagandizing of the unreachability of equality, and it is this that needs a proper scientific address.

There are two main “kinds” of heritability measurements: broad-sense (H) and narrow-sense (h). Broad sense heritability seeks to measure the proportion of variance in a trait due all genetic sources to the variance of the total trait. Narrow sense heritability wants to measure the proportion of only the additive genetic sources of trait variance to full trait variance, which describes those sources that are “selectable” from a breeder theoretic meaning. In a certain meaning of the terms, broad sense heritability wants to be the objective or innate proportion of variation due to genes, and narrow sense the external “usable” proportion for selection processes.

But these metrics actually don’t measure genetics in the causal way implied.

There is a horrible error that permeates the Harris episode on Charles Murray which can only be corrected by getting a better understanding of heritability. I hope this paper starts to give this better understanding, along with pointing out a handful of minor logical fallacies which frequent these racist circles. I feel all earnest researchers in trait heritability need to have a better understanding of these metrics and what they actually measure.

I call the “Murray Fallacy” the mistaken belief that bias is an environmental effect in heritability studies (and so high heritability means bias cannot be strongly affecting the variability of the trait). It is caused by a greater mistaken belief in the zeroness of the covariance of genetics and environment, and a whole panoply of causal errors that lead to this very convenient fiction for the rising white nationalism.

Bias measures as heritable when the trait on which the bias is based is heritable — for instance, skin color. Racism is heritable. This is because these measures only separate out the correlation of the effect with the gene variability — they do not determine whether the effect difference is due to genetic expression or due some cultural structure of bias against people that demonstrate some unrelated genetic expression. That this is possible is a critical part of the misunderstanding.

Understanding that much of the reason for this confusion is from the use of very informal and hand wavy descriptions, I put together a formal model to describe the actual phenomenon. Although people like Turkheimer clearly have pointed out this objection previously in their work, I was unable to find a formal model to pull statistics off of. So I pieced together a stable enough design to illustrate the interplay of uncorrelated environment, bias, and genetic skill. I will demonstrate this result and, in the process, show numerically an implication which I have not found pointed out elsewhere, but which is pretty obvious from understanding the above issue:

As bias increases, the broad-sense heritability increases.

The narrow-sense heritability metric measures a proportion of the biased trait through an additivity metric. This proportionality makes the narrow-sense heritability have some really interesting views into the additivity relationships between skills and biases. This is described in more detail below.

The model

My model first needed a population dynamics that I could do genetic statistics on. I wasn’t deeply concerned with population sizes and growth rates to begin with, as I first just wanted some tunable parameters and something stable. It turns out that my early config was fine for my needs, so it’s not an area I’ve altered much, though the theory of population dynamics is a rich theory with many model parameters for study.

I started by assigning the People a state machine evolution with the following states:

· Childhood — This is the initial state of each new Person. Childhood is 20 years in this sim.

· Mature / Single — Once they mature, they are available for possible coupling

· Coupled — If fortunate, a pair of Single People may Couple. Every year afterward, there is a chance of child.

· Widowed — A lifetime in this sim is a fixed 70 years, so the older of a couple will leave the younger in this state towards the end. This widowing state is not left in the lifetime in this sim.

· Deceased — People accumulate in this state for running test stats on after year 70.

A central time loop iterates the population over a yearly cycle that:

· Increases the age

· Checks if Deceased by age increase

· Opportunities to increase skill are executed.

· Checks if Matured by age increase

· Gives all Coupled pairs the chance for child (even twins). There is a procreation chance (5%) for any couple to have a birth. Of births, a twin proportion (5%) of them will be twins.

· Gives all Single people the chance to couple. There is a set coupling chance (10%) for any person to choose to couple, and they pick uniformly from all remaining single if they succeed. Note, a person may couple the same year that they Mature.

The model for the genetics was built into this state machine in several ways. First, there were two genes tracked in each Person: a Group gene and a Skill gene. The group gene had a matrix that split half of the combinations of alleles into Ingroup and Outgroup classifiers pseudoadditively. The skill gene expresses some number from (1 — SKILL_MODIFIER_SPAN) to 1 by simply using an additive allele system (so 7 tiers from 0+0 to 3+3), discretely and uniformly distributed in the span.

The procreation mentioned above gave children 1 allele randomly from each parent. Parent/child relationships were tracked as a tree to walk for statistical transformation.

The skill is simply a level advanced in a binomial process by each person. Everyone starts at level 0. Then they have some chance to advance in level 5 times a year. The chance to advance is given by

chance = expression(skill) * (1 — bias(group)) * environment

The environment was a number established when a pair couples, which is a random shared environment number among all kids in a family (chosen randomly from the interval [ENVIRONMENTAL_MODIFIER_LOW, ENVIRONMENTAL_MODIFIER_HIGH]). Bias is a fixed external handicapping of Outgroup People (BIAS_MODIFIER).

That’s the basic model.

VBW: “These are fairly uncontroversial findings at least if all you care about is facts, but.. One way in which you can tell that this is a sort of robust individual difference that is heritable, and heritable has a specific meaning that I’ll get into in a second, is that when you look at studies like on twins — so the very common way of doing this is by looking at identical twins and fraternal twins. Identical twins share all of their genes, fraternal twins don’t but they were both the same age raised in the same environment, the correlation between the identical twins is much higher than the correlation between the fraternal twins. So, you can do the fancy math and you can see what percentage of intelligence is due to heritable factors by kind of — doing this very abstract description of it but — subtracting sort of the variance of the environment which fraternal twins share and the heritable aspects which fraternal twins share less of than identical twins, and by doing that math you can see that, in fact, these traits are heritable.”

I ended up choosing 5 different heritability metrics to show differences in their behavior across the simulation. An interesting thing about the heritability metrics is that they all have different semantics — sometimes subtly, sometimes starkly. Heritability metrics are often not described from a mature mathematical viewpoint that gives a complete statistical semantics. Instead, there is a lot of argument from similarity to give the two metric types (broad-sense/narrow-sense) above. But they aren’t the same things, so it is important in any good model investigation to calculate multiple metrics that are used in the literature, to provide specific information on the individual metrics important to others. From my, admittedly limited, reading of the literature, these 5 metrics were very common.

1.

Falconer’s heritability — Uses the Pearson correlations between monozygotic (identical twin) pairs and between dizygotic (sibling) pairs to calculate heritability. Falconer’s formula

Is described online in several places (see Wiki and http://www.cureffi.org/2013/02/04/how-to-calculate-heritability/ for a description with the next formula).

2.

In “The Genetics of Human Populations” by L. L. Cavalli-Sforza and W. F. Bodmer, a slightly different calculation is given.

(I use H² instead of their H’ as that seems to be the consensus that this is a square estimator. I think C-S/B is not fully consistent with other literature here).

I have also calculated this metric to compare with Falconer’s. In a sense, this is a “more faithful” translation of the variance definition to correlations. They are similar when r_dz is near 0.5 but when r_dz is smaller, the multiplier is lower than 2 and thus the heritability is smaller.

3.

In the same C-S/B book, there is a calculation of the same kind as 2 using the means of the squares of the differences between pairs (both monozygotic and dizygotic). Again, switching out to use a square identifier instead of their single H, the equation is:(I use H² instead of their H’ as that seems to be the consensus that this is a square estimator. I think C-S/B is not fully consistent with other literature here).

Note the mapping implied: V_dz -> (1 — r_dz), V_mz -> (1 — r_mz). This describes the regions of overlapping validity and how the two metrics can diverge.

4.

Breeder’s heritability — a selection experiment where parent subgroup is chosen with mean away from the global mean. The offspring mean difference from global mean (R) and selected parent group difference from global mean (S) obey

(see page 684, eq. 6 of Hartl, Jones). This is a favorite equation of eugenicists because it transforms, via the causal fallacy, into a blunt instrument of genocide in the face of bias.

5.

Regression to the mean — when you graph average of parent’s skill levels (x) to offspring skill level (y)

A trait is additive when the likely expression in offspring is midway between parents. When parental traits away from mean give the offspring improved chances to be away from mean in the same way, that force is the selectable heritability of the narrow sense. We can see this as a passive version of the Breeder’s heritability, which differs where mean proportion does not predict regression slope.

In addition to these metrics, there are two important internal metrics we should also calculate to better understand the causal deviation:

I1.

The Causal Internal Heritability is just the ratio of the actual skill variance in the model to the sum of the component variance in the selection score.

Here, we have

This metric captures a simple comparison of size effects that obeys a sum-to-1 model of all effects. Since the skill gene is the only causal expression-path influence on level attainment in this model, this describes the actual “genetic” proportion as implied by fallacies of innateness.

I2.

The Correlated Internal Heritability is the measure of all expression effects that correlate with genetics, including those where genetics is not the causal factor for the change in expression.

Again, this is summative for effect size comparison and sum-to-1 proportionality — it is not an implication that the actual effects were due to summation (as they were not — they were multiplicative). It is interesting to compare these to effect heritabilities to see exactly how behavior differs.

The results

Here is a view of the broad-sense heritability metrics.

And here are the narrow-sense heritability metrics.

And here are the internal heritability metrics.

The model demonstrates quite clearly the following general properties of the heritability metrics:

· With a fixed environment and bias, the greater the skill gene variance, the greater the heritability metrics

· With a fixed skill and bias, the greater the environmental variance, the lower the heritability metrics

· With a fixed skill and environment, the greater the variance due to bias, the greater the broad-sense heritability metrics

· Narrow-sense heritability metrics demonstrated additive detection, where bias contributes the additive proportion of it’s group-identifying gene. The group expression matrix in this simulation is ~0.63 additively heritable. It is interesting how this illustrates how additive heritability handles non-additive heritability — it does not exclude it, as one might expect from some textbook accounts. There appears to be a measure of “matrix diagonal linearity” that the heritability metric measures, which even gives dominant/recessive expression types some additivity. This is discussed in a little more detail below.

· All external heritability metrics show heritability which is purely due to bias.

These results all show clearly the error of the causal fallacy. It shows that heritability metrics include (genetic, environment) covariance in which the entire causal chain lies in the environment. It is wrong to read off a heritability metric through it’s original definition on genotypic variance because this is not directly measured. Only correlations are measured, so the causal source is not established and covariance effects can be large, even dominating.

Heritability is not “proportion genetic”.

Turkheimer has been stressing this conclusion for quite some time.

“A group difference is genetic when there is a causal mechanism (not a heritability or a polygenic risk score) linking a gene or genes to a phenotypic outcome across a known, wide domain of contexts, and the causal gene or genes is distributed unequally across the groups.” Turkeheimer (Heritability and Malleability in Individuals and Groups) (http://www.geneticshumanagency.org/gha/heritability-and-malleability-in-individuals-and-groups/) “Heritability is not a special property of certain traits that have turned out to be genetic; it is a description of the human condition, according to which we are born with certain biological realities that play out in complex ways in concert with environmental factors, and are affected by chance events throughout our lives.” Turkheimer, Harden, Nisbett (Charles Murray is once again peddling junk science about race and IQ) (https://www.vox.com/the-big-idea/2017/5/18/15655638/charles-murray-race-iq-sam-harris-science-free-speech)

People often need these validations of biological determinism during abusive cycles of racial nationalism because it brings the air of scientific validity to outgroup abuse. Racial policy can focus on pretending the effects of racial oppression are natural and unbending and thus the system can remain — which is how it has been used, time after time, in our history of racism in America. Ezra Klein even suggested to Harris that he read Ibram X. Kendi’s “Stamped from the Beginning” to understand what harm he was causing by allowing this causal fallacy to propagate unchecked. From the discussion, it felt like Harris had taken this suggestion as tiresome and misguided, but I have to stress that this book is extremely relevant to this discussion. It goes into quite a lot of the scientific detail on the spread of racist ideas in scientific communities, including the eras when evolutionary theory and genetics were forming. It talks about much the same kinds of causal fallacies propagated to oppress African Americans.

Oppressed groups have been blamed for the effects of their oppression for millenia. It’s one of the easiest causal fallacies, and the cycle of effects of oppression -> blame -> oppression -> … has had many brutal consequences. Biologists, historians, and mathematical modelers should all understand the severe danger that lies in making claims of where fault lies in the world’s disparities without a very solid foundation for such claims. Heritability assertions in genetics are not “a very solid foundation”. Quite the opposite, it works explicitly to hide bias in the most pernicious way.

Honestly, I am far more deeply disturbed by the actions of people like Stuart Richie and Charles Murray, who portray themselves as having some kind of intellectual understanding of the field than I am by popularizers like the guys at Very Bad Wizards, or Sam Harris, or Julia Galef — all who make far less of a claim of authority in the field (and at least for Julia there was some natural questioning back). But I am concerned about the platform these ideas are given, where many who are curious about such details could come away with wrong and dangerous notions that are refuted by simple mathematical models. There is a sickness growing in society, a sickness that needs biological reductionism to feed abuse structures the legitimacy to majoritise. We need to vet ideas at an intellectual maturity that belies the actual seriousness and lives at stake.

Minutiae

There were actually some other cool pieces of information I could pull off the model concerning the mathematical and semantic behavior of the metrics.

The Falconer excess

There are regimes where the Falconer heritability calculation, due to the linearization, produces values greater than 1. It seems this metric tends to overshoot others and does not map to the standard interpretation very well at one extreme. However, it is also much more responsive to environmental variation and offers more accurate response in these regions. I would have hoped to have seen more cautions about regions of accuracy and the use of the different heritability metrics in the literature, as it is always dangerous in the hands of bigots to overestimate heritability.

There are a few places where we did find negative values pop up for heritabilities. These were all very small in magnitude and well within expectations of noise near 0 (where fluctuations can produce negative correlations), all in regions where 0 was the expected measure.

The cross-correlations of heritabilities and the causal/correlative summative measures

Some interesting things to note from this:

· The Falconer heritability is more closely correlated to narrow-sense heritability than the CS-B broad-sense metrics. It appears this is due to the more accurate shape of the environment response.

· The CS-B broad-sense metrics formed a closely related group of almost perfect cross correlation.

· The narrow-sense metrics were also very well cross correlated.

· None of the metrics did a good job of correlating with the internal causal genetic heritability in the model.

· The internal correlative heritability correlates best with Falconer’s, then the narrow-sense metrics, and then C-SB last. The lowest correlation was still high (>0.68).

Location of variance in gap

I ran the simulation in two different modes because I was curious of the different effects the choice had: the probability span of the distribution either grew down from certainty [1 — span, 1] or it grew from 0.5 outward [0.5 — span/2, 0.5 + span/2]. In the former there is this nice feature that you look the binomial natural variance is 0 at the origin. However, as the span grows, the average value decreases, so this model introduces variation across different first moments. In the latter model, the average is always 0.5 on all the metrics, but there is also then always the Binomial variance at p=1/8 present in the background. With the former, there were edge effects seen with bunching near level 350, so you could inspect hard statistical boundaries behavior. In the latter, the results were just “softer” — edge effects were less discernable.

Interestingly, both runs produced very similar landscapes. The behavior of heritabilities and bias had the same large-scale features and shapes, and I’ve stuck to the top-down run for reporting here.

Bias detection

Just because heritability metrics only access correlative external information does not mean that there are no metrics that can distinguish causative information. The effects of bias have a number of features over the possibility landscape that can be used to identify region and give indirect measurement of likely proportions (environment, skill, bias) of a 3-effect model like this. Metrics of additivity provide subtle identifiers in the narrow-sense regimes, which can be tied to the specific additivities of traits known to have biases against.

But this cannot be a means to the detection of bias for the same logical reasons underlying the causal fallacy: these models aren’t actually modeling bias. They are modeling an effect of a gene on the total level advancement in a binomial process whose semantic causality is actually not addressed in the model. It makes no difference if we switch the skill and bias genes, and say the skill is a bivalent gene — you got it or you don’t according to the additive matrix — and the bias group gene reveals 7 different levels of bias on this one additive group feature. The equation would be the same. They might both be “kinds of bias”. They might both be genetically causal in some direct trait expression. Nothing measurable to this model can determine actual causal links.

Bias detection is still possible, though. It’s just done externally. Social scientists have been measuring it for decades, using things like explicit criteria analyses of choices. For instance, when the criteria are quantifiable (like resume data), choices provide relevance metrics over the different data. When the data ought to be irrelevant to the choice if unbiased, like name, and is found to have relevance, that relevance is bias. These measurements can be used to establish model decompositions where the assertions of causality do have semantic meaning. I would love to explore this more at some point.

Interpretations of narrow-sense heritability

As seen in the results, narrow-sense heritability measures traits that are not perfectly additive by contributing proportionally according to some metric of additivity on the expression matrix. I think this indicates that additivity is probably defined in the wrong direction in traditional texts: instead of a specific type of expression, additivity should be a measure of expression “selectable heritability” which describes a measure over all types of expression.

The concept given by regression-to-the-mean is probably an important place to start. How much will two parents away from the mean pull their children away from the mean? Can you create stable populations with different means? But as with broad-sense heritability, this cannot be assumed to come from genetic expression, and this requires a much more conscious understanding of controllability in these models. Many traits and behaviors have additively heritable expression, many that even have no genetic component.

For traits that obey a genetic model of partial parent contribution and two component expression matrices, you can build the additive metric on the matrix in the standard way. For traits with more complicated inheritance models, the return to controllability should provide the path.

The meaning of IQ in the presence of bias

I think it should be absolutely clear how the model portrays IQ here. The binomial process has bias as a control, and when used, the same amount of skill reaches two different outcomes. If an individual suffering under bias were brought into an environment where they were suddenly free of bias, they would achieve better advancement rates than a number of those who had in the past outpaced them. IQ miscalculates potential in the face of bias. It suppresses our views of the outgroup.

An honest view of IQ must recognise that it measures the resulting skill attainment from a whole variety of forces, each pulling and pushing on what is reachable in the environment we have created. When we know bias exists, when we measure it in research and see it revealed in trends, we have to account it in our interpretations of the metric. Failing to do so is simply a scientific lie meant to prop up bigotry.

The population distribution, gen 1 to equilibrium

The initial 10,000 play an important component to the population over the first 70 years. First, the population is all precoupling. They transition to mature and single and quickly start coupling and producing the second gen precoupling population. At the age of 70, the first generation all dies off, leaving a core population which has already spread itself over the different life states. The second generation is still clustered enough that it’s rolling death is still noticeable in the data to 140, but afterwards, the population quickly blended to equilibrium distributions.

This is a Markov process with a clear equilibrium. It interested me a little to explore the different kinds of initial population algorithms and try out ideas that weren’t so brute as a single-aged gen1, but it was clear from the data that refinement wasn’t necessary.

Looking at the breakdown by age proportions, we can see just how quickly equilibrium is reached. The initial generation is 100% of the population for the first 20 years. There is a shadow of twenty years where no new people arrive. Then, the initial generation’s proportion starts decreasing as the next generation begins to be born, and we continue to feed each year with new births until the first generation’s end. There is some second generation clustering effects from the large influence of the first generation, and then the age distribution calms down.

At equilibrium, the ages are distributed near 1/70 per age, with a noticeable slope induced by population growth, where younger ages increase proportion slightly from older. There is noise from the random processes of coupling and birth around the clear linear trend.

The reasons for a multiplicative model of effect and the deformation in additive variance models

This model and my previous one on career bias effects show a common use of binomial processes with multiplicative effect on the transition probabilities. This is really a very intuitive and natural model for these kinds of processes, but one it may help to explain some because it is actually different than the conceptual decomposition used by metrics like heritability.

Let’s say you have several components that can both cause wide variability in expression such that they both have a particular expression that is “worst case”, and if you get either one, your total expression is lowest tier. But they all have more subtle effects, and there is some combination that gives “best case”. For numbers in [0, 1], abc… = 0 implies ThereExists(­x in a, b, ..) (x = 0) and abc… = 1 implies ForAll(x in a, b, ..) (x=1).

Summative effects have a strange behavior. When you try to do something similar in summation, great settings on some of the components mean that the effects are bloated to be somewhat good even if one component is 0. They all have to be bad to reach 0 and they all have to be best to reach 1. No component can control the range beyond it’s proportional influence.

It is common to represent these kinds of relationships multiplicatively because of the logical AND structure interpreting the possibility space of evolutionary processes. This is why, for instance, the Drake equation is also multiplicative. Binomial processes interpret these ANDs in an accumulator, so they represent the semantics faithfully.

Detecting the bias source of the IQ gap

In this model, the only source of ingroup / outgroup IQ gap was through bias (as the skill gene was independent to the group).

Since IQ gets redefined from absolute level attainment to a 100 mean, 15 sd scale, different regions of the simulation map the bias differently to IQ gap, and we can see that the correlation detected here is not perfect. However, it is quite strong and clearly indicates the relation.

Also, we can see some of the statistical effects of the bias effects on outgroup statistics in the standard deviation. This has even clearer correlation, though it would be expected for any gap effect.

These help show why the correlations are such blunt tools of relationship. Sometimes control parameters that are exclusive to an effect can show imperfect correlation due to nonlinear model effects, and sometimes indirect relationships that are not perfect can appear more so due to response consistencies.

Fallacy list

Finally, I want to end with a recap of the primary fallacies encountered in building this report. This is mostly for myself, as I want to eventually flesh out the full forms of fallacious reasoning in heritability and expand upon their formal structure.

1. Bias is an environmental effect in heritability (the Murray fallacy)

This is just a lack of understanding of heritability. Every effect that has parental correlations in the manner measured by heritability metrics is heritable. Things passed down in families are heritable. Opinions externally about families are heritable. When heritability talks about “environment” they actually mean “variation uncorrelated across family lines”, and it doesn’t have anything like the semantics it is normally talked about with.

2. Environment and Genetic contributions have 0 covariance

This is one of the first assumptions taken in developing the textbook model of heritability. It is usually mentioned that “with the right experimental setup, this can be ensured”. This is a slight variation of the first fallacy and is mostly due to the incorrect semantics of environment. The true statement is “variation uncorrelated across family lines” has 0 covariance with genetics, but this is more a tautological restatement than a positive assertion.

3. The environmental variation in an experiment matches all variation possible

This is a critical component to the futility argument, when a racist comes forth and, with heavy heart, must “admit” that we just know that equality can never be achieved and we have proof of it’s impossibility simply by looking at the known variability. Social observation is limited by the social structures that enforce regularity in society, and where there are questions of populations unnaturally constrained, one cannot take their variation as the limits of the natural.

4. The bigotry fallacy

And this is one that is infecting our society at large. It is one Harris regularly partakes in for his anti-Muslim campaign. Acts and behaviors of individuals in a group are not indicative of all individuals in a group. You can logically talk about individuals and their actions, and their implications for those individuals. Or you can talk about group statistics and discuss group dynamics. You cannot use group correlations to make logical implications between group individuals. Semantically, this is a version of the causal / correlative conflation that is particularly pernicious in racism, sexism, and other bigotries.