Counterfactuals of Causality

Explain the counterfactual analysis of causation. Is it correct?

Causality is generally thought of as one thing leading to another, e.g. x so then y so then z. This is stated as an actuality, and there are several things to note about it. One, there are limited items under consideration. Two, there is a relation between the items. Three, there is a structured concept of time. Four, it is final. Counterfactuals offer us a path for a more in-depth analysis of causation by allowing us to vary each of these items, and thus work with possibility.

If x happens and then y happens, how do we know that x caused y? Even if this sequence of events repeats, we can only know that we have found a correlation (Hume). The proposition “x causes y” is true if and only if x actually causes y (Tarski). We can use the idea of a counterfactual to help us explore the issue, i.e. a proposition counter to the facts. If x were to not happen, and that means that y would therefore also not happen, then this would show that x is necessary for y, therefore x makes the difference in whether or not y happens, and thus we can say that x causes y. This idea of causation according to counterfactuals leads to many possibilities and difficulties.

Let’s work with an example and see how the complexity grows, we’ll start with the proposition “Jack painted the room red, so then the room was red.” Now we can use a counterfactual and say that “If Jack hadn’t painted the room red then the room wouldn’t be red.” The alternative possible state of the world appears to give us an explanation of causality, that Jack painting the room red was necessary for the room to be red. However, saying that the room is red because Jack painted it is different than saying that the room wouldn’t be red if Jack didn’t paint it.

If we add to our known context that Mary hired Jack to paint the room then we have an added layer of complexity, which can quickly show how the data for determining the difference between a sufficient and a necessary cause grows exponentially. Let our proposition now be, “Mary hired Jack to paint the room, so Jack painted the room red, so then the room was red.” Let’s use a counterfactual, “If Mary hadn’t hired Jack to paint the room, then Jack wouldn’t have painted the room red, then the room wouldn’t be red.” The possibilities that are being ignored in this counterfactual are greater than the variables that are accounted for.

The room being red is contingent on an ever-widening set of potential causes. For instance, “If Mary hadn’t hired Jack to paint the room, then she would have hired Bob, then Bob would have painted the room blue, so then the room would be blue.” If we take this counterfactual “Mary not-Jack, Bob, Bob blue, room blue” we see that it doesn’t contradict the counterfactual “Mary not-Jack, Jack not-red, room not-red”. Indeed, we can combine them without contradiction, “Mary not-Jack, Bob, Jack not-red and Bob blue, room not-red and room blue”. From this it would seem that multiple counterfactuals have converged with supporting evidence for the conclusion that Jack painting the room red was necessary for the room to be red.

However, a conflicting conclusion can be generated by using a counterfactual. For instance, “If Mary hadn’t hired Jack to paint the room, then she would have hired Peter, then Peter would have painted the room red, so then the room would be red.” Now, if we take “Mary not-Jack, Jack not-red, room not-red” and combine it with “Mary not-Jack, Peter, Peter red, room red” we end up with “Mary not-Jack, Peter, Jack not-red and Peter red, room not-red and room red”. This seeming contradiction at the end is really no contradiction, we can simply end with “room red” because the abstract idea of non-existence is used as a mental conceptual tool for thinking and doesn’t exist. But, this does contradict our previous conclusion that Jack painting the room red was necessary for the room to be red, because the room can be red because Peter painted the room red.

Therefore, we hadn’t previously found a necessary cause. We found one potential cause out of a set of potential necessary causes of unknown number that can generate a sufficient causal context through emergent interaction and spatial-temporal convergence. Jack painting the room red isn’t necessary, but it can potentially be part of a sufficient causal context. The number of potential necessary causes for a said conclusion is unknown, unknowable, and potentially infinite, or at least infinite in comparison to our ability and capacity to know.

It is possible to reduce the number of potential necessary causes to infinite minus n. For instance, “Mary hired Jack to paint the room, so Jack painted the room red, the house burned down, so then the room was red.” This doesn’t work. We can use the counterfactual that if the house didn’t burn down then the room would be red. Since to achieve the result we know that it’s necessary that the house not burn down, we know that the house burning down is not a potential necessary cause for the room being red. We therefore have infinite minus one potential necessary causes. This can be repeated an unknown, unknowable, and potentially infinite, or at least infinite in comparison to our ability and capacity to know, number of times. We can therefore falsify a causal sequence, but never fully verify it (Popper).

Counterfactuals reveal the emergent complexity of causality. For an organism with a limited capacity for information processing and total information capacity across space and time this presents a problem for knowledge and action based on that knowledge, requiring a reduction of all potential data to the limited set of useful, useable, and accessible information necessary for appropriate action in a given context. This is not a refutation of counterfactuals, rather an acknowledgment of their utility for the revelation of the complex nature of causality and our understanding of it.

A Simplified Reference List:

Alfred Tarski’s truth theorem

David Hume’s idea of all causation actually only being correlation

Karl Popper’s falsifiability versus verificationism

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