Surely, you've heard the phrase "correlation does not equal causation" or "correlation does not imply causation". I despite that notion, because, it's not entirely true.
Walk up to a light switch, and toggle it. You'll notice the light turns on or off accordingly. Toggle it a few more times, and with (hopefully, depending on your electric wiring) 100% correlation, the status of the light will change as well.
You are not irrational or illogical for concluding that correlation does imply causation, in this case. If some guy comes bursting through the wall, insisting that it's not, punch him in the face and throw him back out through the wall hole.
This insipid phrase is a cautionary tale against prematurely jumping to a conclusion, which is fine. Lots of scenarios exist where the correlation doesn't equal causation. Prayer comes to mind.
You have a headache, and you pray for it to go away. It fades, and you credit prayer for working - it was a clear correlation. The causation may have been something else. You wanted the prayer gone, so you prayed and took some Tylenol. The correlation was established because you wanted to rid yourself of the headache so bad that you attempted multiple cures... and one of them worked. The causal mechanism was the Tylenol, not the prayer.
That's how we know that flipping the light switch isn't just a coincidence - that the 10 times you toggled it, the status of the light changed at the same time. We also have established the causal mechanism between the light switch and the light - the wires, the electricity, etc.
It's a good thing we have the ability to overcome the correlation/causation conundrum, because most of science works through establishing correlations. When we provide a new experimental drug to a group of patients, and some of them get better, we're establishing correlations. When we investigate CO2 versus global temperature, we're looking at a major correlation.
We work with correlations all the time, and if we kept dropping the efforts every time because "correlation does not equal causation", we'd never get anywhere.
The key is understanding that we investigate the causal mechanism for each correlation. We've investigated the greenhouse effect in laboratory conditions, and so we understand why the correlation between CO2 and global temperature indicates causation.
The problem with the above, is that each causal mechanism that's established is just recursively more instances of the correlation/causation issue. It may just be a coincidence that the temperature happened to rise in the gas test chamber with CO2 when it was exposed to light. It may just be a coincidence that the thermometer gauge just happened to indicate a higher temperature, and was actually changing due to something else.
We can keep regressing back, with each causal mechanism needing more correlations to establish that the parent correlation was actually causation.
This is where the Argumentum ad Infinitum Procedere emerges. We frequently get this from amateur apologists:
- Apologist: "If there is no god, where do you think you came from?"
- "Uh... my parents?"
- Apologist: "And where did they come from?"
- "... their parents?"
- Apologist: "And where did their parents come from? And their parents? And their parents?"
- "Going back far enough, we evolved from an ape common ancestor, which evolved from earlier ancestors, etc. But we don't know how abiogenesis happened, that started life."
- "AH HAH!" - and points excitedly at you.
- "Ah hah what?"
- "SO EVOLUTION CAN'T BE TRUE"
It's this notion that if you ever say "I don't know" at any point, everything you claim to know is false. These apologists often don't seem to get that, while life had to start existing (or always exist) in order for evolution to work, the fact we don't know how it happened does not falsify evolution. Why would it?
PZ Myers addressed a bunch of evolution questions that, frankly, I would have been clueless about. These were clearly engineered to be stumpers. For instance, "How can functional proteins form without ribosomes or ribosome-like machines?" It's a question about early evolutionary history, and the underlying argument intention is that if we don't know the answer, then "evolution major has problems", as opposed to a specific point in evolutionary history that isn't well understood yet (like 100% of modern evolutionary knowledge was at one point unknown). If we don't know the answer to the above question, then clearly, according to the apologist, we don't know anything about the evolutionary history of the whale, for example.
That's the point of the Gish Gallop, incidentally - to flood the opposing side with stumpers (or purely idiotic arguments), and any that aren't addressed or answered are considered failures against that side.
The Argumentum ad Infinitum Procedere works on this principle - find some point in a regression of knowledge where the person doesn't know the answer, and claim it invalidates their entire position.
The fact that I don't know where my truck was 5 years ago doesn't mean I don't know that it's in my driveway/bog right now. The fact that I don't know the exact history of the formation of the gasoline in its tank, doesn't mean we don't know its chemical makeup, or how to use it for fuel. The fact that we don't know where the matter "came from" that makes up the gasoline doesn't mean we don't know how it formed from decaying compressed dead plants untold millions of years ago.
... but that's the structure of the argument. It's not exactly the product of deep thinkers.
This leads me to my overall point of this post - we only need demonstrate one level of regression to demonstrate a causal mechanism, to demonstrate that the correlation isn't merely correlated - but caused. I'll explain.
Going back to the Tylenol/Prayer correlation. The fundamentalist theist would assert it was God's answered prayer that cured my headache, and the scientist would say that the Tylenol was the cure.
How do we know which one was actually the cure? The first level regression of causal mechanism. We can study the chemistry and biology behind what Tylenol does. Additionally, we establish control groups between praying patients and non-praying patients, to help eliminate what's not a causal mechanism.
Our establishing the causal mechanism of Tylenol isn't thwarted because we don't know where the matter, that constitutes the pill, came from. Why would it? We don't even need to know what store or manufacturer the pill came from. All we need to know is that we have it, and that it's chemically valid as Tylenol.
When establishing the causal mechanism between the light switch and the light, we don't need to know anything about quantum physics - just the fact electricity exists, and how to use it, is sufficient. To demonstrate that connection between the switch and the light, only requires us to demonstrate the sub-mechanisms one level deep.
Good science experiments may go a few more levels, for the sake of accuracy, ensuring that the thermometers and instruments are working properly.
... but they don't keep regressing forever. They'd never accomplish anything.