Cause and effect can betray even the smartest amongst us!

When is C a cause of E?

Take this simple example: Pluto's barking causes Dick to wake up.

We need four steps:

1. The cause must precede the effect,

2. It's nearly impossible for the cause to happen and the effect not to happen. Another way of saying it: if the cause had not happened, the effect would not have happened. 

3. The cause makes a difference (without the cause, there's no effect),
4. There's no common cause. Think of a person suffering from depression. You could frame their depression using the common-cause relationship as well. Depression leads to a lack of motivation AND a lack of appetite.

   
So, we have:

1. The barking precedes Dick's waking up, 
2. It's nearly impossible for Pluto to bark and Dick not to wake up,

3. Without the barking, there's no waking up, 
4. Suppose both the barking and waking up are caused by a person jumping Dick's fence and making a noise which causes Pluto to bark and Dick to wake up. 

Necessary, sufficient, and contributory causes:

Pluto's barking is a necessary cause of Dick's waking up if the barking precedes the waking, but it doesn't imply the latter will occur, i.e., Dick may not wake up (it's not guaranteed).      

Pluto's barking is a sufficient cause of Dick's waking up if the the barking necessarily imply the waking, although another cause may also contribute to Dick's waking (noise coming from the bathroom where Dick's wife was taking a shower). Here the presence of the waking doesn't guarantee the prior occurrence of the barking.

A cause is a contributory cause if it's one among several co-occurrent causes. In general, there is no implication that a contributory cause is necessary, though it may be so.

Reciprocally, a contributory cause is not sufficient for the effect, because it is by definition accompanied by other causes, which would not count as causes if they are sufficient, for your information, most causes are contributory, i.e., there are more than one. 

In distinguishing the strength of evidence for causation from causation itself one gets:

“Probably causal” & “potentially causal”. They describe how confident we should be from the evidence given.

Potentially causal: There is a plausible causal connection, but the information given is insufficient to establish that C made a difference to E.

Probably causal: The evidence described gives us strong grounds for thinking that C did make a difference to E, even though causation is rarely demonstrated with absolute certainty in ordinary cases.

Here is the spectrum:

mere coincidence → possible causal relationship → probable causal relationship → well-established causal relationship

The counterfactual is what moves us along that spectrum.

Suppose: Maria drinks coffee → Maria can't sleep. 

We initially have only temporal succession.

Then we discover: On evenings when Maria doesn't drink coffee, she sleeps normally.

The counterfactual becomes much stronger: Without the coffee, the insomnia would probably not occur. That gives us evidence that the coffee made a difference.

Want one paramount example of contributory causation?  

Climate change, with all its contributory causes: sun, orbital variations of the earth, low cloud cover, oceans, albedo effect, man-made C0₂, etc.

REMEMBER, VERY IMPORTANT...

¡CORRELATION DOESN'T MEAN CAUSATION!