I'll assume that you do not hold fast to a rigorous system of metaphysics, in which case I think you can fancy me and accept that, if I so desire to struggle, I could reduce the concept of causality to one (or a chain of) probabilistic relationships between events.

Here's a naive definition of causality: P(E) ~= 1 | C (where "|" stands for "given"). If I can say this, I can most certainly say that C causes E, at least in a system where a thing such as "time" exists and where C happens before E.

It should be noted this doesn't imply P(C) ~= 1 | E.

Obviously, this definition doesn't cover all or even most of the things we call causal and can be taken into an extreme context where it holds in spite of no causal relationship. I'm just starting with it because it's a point from which we can build up to a better one. Let's roll with it and look at an example.

1. Hypothetical number one

Human height can be viewed as a function of haplogroup alleles + shoe size, that is to say, we can predict h fairly well given those 2 parameters.

Height can also be viewed as a function of mTORC1 expression + HGH blood levels. Let's say some assay that tells us the levels of mTORC1 and HGH predicts height equally well to haplogroup alleles + shoe size.

But I think most scientists would agree the later are to some extent "causal" for height while the former aren't. Why?

Well consider 2 hypothetical experiment:

1. Take a 30yo human of average height and use a saline solution pump to inflate their feet to 1.5x their size. Then use {magical precision nucleotide addition and deletion vector} to remove all his haplogroup alleles and insert those most associated with increased height.
2. Take a 30yo human of average height and then use {magical precision nucleotide addition and deletion vector} to overexpress the heck out of mTORC1 and HGH.

In which case do we expect to see an increase in height? That might indicate causality.

Trick question, of course, in neither.

We'd expect to see increased height in the second case if the human was, say, 13 instead of 30.

The causality here is P(E) given C under some specific conditions. Where C has happened before P(E), even if C happened 10 years ago and C happening again now would not affect E.

Also, see physics for situations where that doesn't quite cut it either because the temporal relationship "seems" inverted [citation needed].

Causality is what we call P(E) ~= 1 | C happened in the past in a world where we have "intuitive" temporal relationships AND we can be pretty certain about the environment.

Hit glass with a hammer and it breaks, except for the fact that this only happens in a fairly specific environment with some types of glass and some types of hammer. Move the environment 300 meters underwater, make the glass bulletproof, make the hammer out of aluminum or let an infant wield it and we lose "causality", even though the event described is still the same.

But even that doesn't cut it in terms of how weird causality is.

2. Causality and effect size

Now let's move onto the idea of "cause" that doesn't fall into the whole P(E) ~= 1 | C. This is not so easy because there are two different ways by which this could happen.

The easy one involves E as a continuous value rather than a binary event. In the previous height example, E could have been an increase as counted by a % of the subject's initial height or in centimeters.

But this is easy because we can just abstract away E as something like "and increase in height by between 10 and 25%", basically strap some confidences ranges on a numerical increase and it's back to being a binary cause.

The hard one involves events that happen due to a given cause only very seldom.

For example, if we are traveling through a mountain pass after a heavy snowstorm and our friends start yodeling very loudly we might say something like:

Shut up, you might cause an avalanche

But this seems like the exact kind of situation where we'd be better suited saying:

Shut up, there's a very spurious correlation between loud singing and avalanches and I'd rather not take my chances.

Well, maybe we say "cause" only for the sake of brevity? Doubtfully.

I think the reason we say "cause" here rather than "correlate with" is that we seem to have some underlying intuition about the laws of the physical world, that allows us to see the mechanism by which yodeling might put in motion a series of events (using the "naive" strong definition of causality) which end up being "causal" of an avalanche using the naive definition used before (e.g. some to do with very strong echos + very unstable snow covering on a steep slope).

Conversely, if we saw a black cat jump out of the snow and just realized today is Friday 13th we might start being a bit afraid of an avalanche happening, maybe even more so than if our friends start yodeling. But I think even the most superstitious person would shy away from calling black cats in random places and certain dates "causal" of avalanches.

But then again, if yodeling can cause an avalanche by this definition, so can the butterfly flapping its wings in China the action of which snowballed into a slight direction of current in your mountain pass which (coupled with the yodeling) could cause the avalanche.

Heck, maybe the slops were avalanche secure for some obtuse reason, but then someone moved some medium-sized rocks a few weeks ago and accidentally really harmed the avalanche-related structural stability.

3. Causality order, time and replication

Ok, this section could be expanded in an article on its own, but I don't find it as interesting as the last, so I will try to keep it brief. To patch up our previous model we need to introduce the idea of order, time, and replication.

Why is the wind causal of an avalanche but not the butterfly flapping its wings?

Well, because of the order those events happened in. Given P(E) = x | C1 and P(E) = x | C2 but P(E) = x | C1 & C2 the "cause" of E will be whicever of the two causes happened "first".

Sometimes we might change this definition in order to better divert our action. If you push someone on a subway track and he is subsequently unable to climb back in time and gets hit by a subway, you could hardly say to a judge:

Well, your honor, based on precedence, I think it's fair to say that it was his failure to get off the tracks that caused him to be hit. Yes, my pushing might have caused him to fail at said task... But if we go down that slippery slope you could also place blame on my boss, for making me angry this morning and thus causing the pushy behavior.

Similarly with the yodeling causing the avalanche, rather than the yodeling causing some intermediary phenomenon chain which ends up with one of them causing the avalanche.

We say yodeling causes the avalanche because "yodeling" is an actionable thing, the reverberation of sound through a valley once it leaves the lips, not so much.

A cause is defined based on how easy it is to replicate (or, in the case of the track-pushing, how easy it is to avoid it ever again be replicated).

Barring ease of replication, some spatiotemporal ordering of the events seems to be preferred.

We usually want the cause to be the "simplest" (easy to state and replicate) necessary and sufficient condition to get the effect (Okams Razor + Falsifiability).

That is to say, crossing the US border is what "causes" one to be in the USA.

Taking a plane to NYC also causes one to be in the USA, but it explains fewer examples and is a much more complex action. So I think we prefer to say that the border crossing is the "cause" here.

Introducing spatial-temporal order via appealing to the scientific method doesn't make a lot of sense, but it's quite an amazing heuristic once you think about it.

Two causes seem linked and equally easy to replicate, what is a good heuristic by which we can get the least amount of experimental error if our replication assumption is wrong?

Well, replicating the one that's closest in space and time to the event observed (harder if one is close in space and the other in time, but this is so seldom the case I'd call it an edge case, and heuristic aren't made for that).

Or, what if we can't decide on how easy they are to replicate? Or think they are linked but can't be sure?

Well, again, the spatial-temporal heuristic cleaves through the uncertainty and tells us we are most likely to observe the desired effect again (or stop it) by acting upon the cause closest to it in space and time.

Interesting... and getting more complex.

But at this point causality still sounds kinda reasonable.

Granted, we haven't gotten into the idea of ongoing cause-effect relationships. I've kind of assumed very complex cause-effect relationships can be split into hundreds of little "naive" causations and that somehow hundreds of naive causations can add up to a single bigger cause.

But those things aside, I think there's one final (potentially most important ?) point I want to consider:

4. (Partially real) Hypothetical number two

Assume we have 5 camps that argue about what is the causes of human violence, from people attacking their spouse to sadomasochism, to mass shootings, to drunken fistfights, to gang wars.

• The blankslateist: Violence is caused by a lack of education and a society that perpetuates it. Raise kids in a non-violent environment, educate them about the uselessness of violence and improve their empathy and we'd basically get rid of all the violence.
  
• The economist: Violence is caused by monetary and social status motivated causes. The robber threatens people with a gun because he wants money. The drunk fistfighter is motivated by some fake ideal of "masculine social status", in a runaway-erroneous way even the school shooter might be viewed as such. A gang threatens to kill business owners for protection taxes and engages in war with rival gangs as to not lose it's "customers". Provide economic and social incentives which always make violence an obviously suboptimal choice and you'd get rid of it.
  
• The genetic deterministic: Violence is caused by genetic, it's baked into human nature, it goes down because of evolutionary circumstances not favoring it and increases for the same reasons. There's no cure to violence other than figuring out how to genetically engineer non-violent humans.
  
• The Freudian: Violence is caused by our deeper animal self, our subconscious animal feeling castrated by the pact our conscious self has to sign with modern society. Violence is just a form of psychosis, and outburst harkening back to times immemorial. Treat psychosis using therapy that allows people to explore and understand their mind and you get rid of violence.
  
• The Statistician: Violence is mainly caused by lead. Get rid of lead pollution and you've solved most cases of violence.
  

In the first 4 cases, we see an example of what we recognize as causality.

The blankslateist seems to correctly figure out some strong causes, but he's much too idealist in hoping one can design the cultural context and education systems that would rid us of violence. After all, we've been at it for a long while and no matter how much money one throws at education it doesn't seem to stick.

The economist has found some causes, but they are high-level causes he uses for everything and his solution is too vague to be applicable.

The genetic determinist seems to have cause and effect backward. He doesn't understand the fact that humans self-segregate into communities/tribes based on phenotype, and some communities are forced into situations that promote violence. His solution seems to us morally abhorrent and likely not to work unless you literally engineer a population of identical humans. Even then, they'd likely find ways to make tribes and some of those tribes would be forced or randomly stumble into a corrupt equilibrium that promotes violence.

The Freudian's explanation is outright silly to modern ears, but again, he seems to be getting at something like a cause, even though it's so abstract he might have well pointed to "God" as the cause. Conversely, since his cause is so vague, so is his solution.

But the statistician seems to not even understand causality. He's confusing a correlation for causation.

Lead is not a cause of violence, maybe it's a proxy at best, an environmental hazard that encourages certain behavior patterns, but a cause, nah, it's...

1. Lead level (even if we only track measures in the air) correlated with aggravated assault more so then antibiotics are with bacterial infection survival. [link]
2. Strongly correlated (both high p-value and large effect size) with violent crime as far back as the 20th century and the lowering of crime rates as the centuries progress match its decrease. [link]
3. Lifetime exposure is strongly correlated (both high p-value and large effect size) with violent criminal behavior. [link]
4. Strongly correlated in a fairly homogenous population with small variations in lead exposure (same city) with gun violence, homicide, and rape. [link]

Huh, I wonder if the other 4 can claim anything similar. And this is just me searching arbitrary primary sources on google scholar.

You can find hundreds of studies looking at lead levels in the environment and body and their correlation with crime. Including at the fact that decreasing lead levels seem to decrease violence in the same demographic and area where violence proliferated when lead levels were high.

The lead blood level in a toddler tracks violent crime so well it's almost unbelievable. Most drug companies or experimental psychologist can't hack their way into something that looks 1/3rd as convincing as this graph.

Did I mention the interventions that remove lead by replacing the pipe or banning leaded gasoline and see a sharp drop in crime rate only a few years afterward?

To my knowledge, what little correlation education has with violence vanishes when controlling for socioeconomic status.

Poverty is surprisingly uncoupled from violence when looked at in the abstract (e.g. see rates of violence in poor Asian countries vs poor European countries and poor vs rich cities), when it can be considered a proxy for violence, the lead-violence correlation would eat it up as just a confounder.

Psychoanalyst therapy doesn't seem whatsoever related to violence, though due to the kind of people that usually get it, it's hard to deconfound past a point.

One could argue genes are related to violence from a snapshot at a single point in time, but looking at violence dropping in the same population over just a single generation this doesn't seem so good.

So, if we could cut violent crime by 50% in a population by reducing serum lead levels to ~0 (a reasonable hypothesis, potentially even understated)... then why can't most people declare, with a straight face and proud voice, that lead is the single most important cause of violence? Why would anyone disagree with such a blatantly obvious C => P(E) ~= 1 statement? (Where E is something like "reduction in violent crime by between 30 and 80%)

What if I make my hypothesis stronger by adding some nutritional advice to the mix? Something like: reduce lead blood level to ~0, reduce boron blood level to as little as possible, increase iodine and omega-3 intake to 2x RDA in every single member of a population.

If, this intervention reduced violence in all populations by ~90%, would I be able to claim:

Hey guys, I figured out the cause of human violence, apparently, it has to do with too much residual lead and boron in the body coupled with lack of iodine and omega-3. Good news, with a 5-year intervention that costs less than 1% of the yearly US budget we can likely end almost all crime and war.

I'd wager the answer is, no and I think it's no mainly for misguided reasons. It has to do with the aesthetics we associate with a cause. It's the same reason why the butterfly effect sounds silly.

Violence seems like such a fundamental human problem to us that it seems silly beyond belief that the cause was just some residual heavy metal all along, or at least for the last 200 years or so.

Yet... I see no reason not to back up this claim. It seems a much stronger cause than anything else people have come up with based on the scientific evidence. It respects our previous definition of causality, it gets everything right. Or, at least, much more so than any other hypothesis one can test.

So really, P(E) ~= 1 | C is not enough even if we use the scientific method to find the simplest C possible. Instead, it has to be something like P(E) ~= 1 | C where C respects {specific human intuition that reasons about the kind of things that are metaphysically valid to be causes for other things}.

This is where we get into issues because "{specific human intuition that reasons about the kind of things that are metaphysically valid to be causes for other things}" varies a lot between people for basically no reason.

It varies in that a physicist, chemist and biologist might think different of what a valid cause is. It also varies in that a person that grew up disadvantaged their whole life might have a fundamentally different understanding of "what a human can cause" than someone that grew up as the son of a powerful politician.

It varies based on complex taxonomies of the world, the kind that classifies things into levels of "importance" and tells us that a cause which is too many levels of importance bellow an effect cannot be a "real cause".

If e.g. love, violence, and death are "intuitive importance level 100", then education, economics, and social status might be "intuitive importance level 98". On the other hand, lead blood levels, what we eat for breakfast, or our labrador's ownership status are closer to "intuitive importance level 10".

To say that something that's "intuitive importance level 98" can cause something that's "intuitive importance level 100" sounds plausible to us. To say that something that's "intuitive importance level 10" can cause something that's "intuitive importance level 100" is blasphemy.

5. Why I find causality harmful

I admit that I can't quite pain a complete picture of causality in ~3000 words, but the more edge cases I'd cover, the leakier a concept causality would seem to become.

Causality seems like a sprawling mess that can only be defined using very broad statistical concepts, together with a specific person's or groups intuition about how to investigate the world. And all of that is coupled protected by a vague pseudo-religious veil that dictates taboos about what kind of things are "pure enough" or "important enough" to serve as causes to other things on the same spectrum of "importance" or "purity".

I certainly think that causality is a good layman term that we should keep using in day to day interactions. If my friend wants to ingest a large quantity of cyanide I want to be able to tell them "Hey, you shouldn't do that, cyanide causes decoupling of mitochondrial electron transport chains which in turn cause you to die in horrible agony".

But if a scientist is studying "cyanide's effects upon certain mitochondrial respiratory complexes" I feel like this kind of research is rigorous enough to do away with the concept of causality.

On the other hand, replacing causality with very strict mathematical formulas that are tightly linked to the type of data we are looking at doesn't seem like a solution either. It might be a solution in certain cases, but it would make a lot of literature pointlessly difficult to read.

However, there might be some middle ground where we replace the ideas of "cause" and "causality" with a few subspecies of such. Subspecies that could also stretch the definition to include things like lead causing violence or butterflies flapping their wings causing thunderstorms.

Maybe I am wrong here, I certainly know it would be hard for me to stop using causal language. But I will at least attempt to reduce my usage of such and/or be more rigorous when I do end up using it.