Our minds use the notions of cause and consequences all the time. It is, without a doubt, one of the fundamentals of human reasoning. However, when observed closely and formally, it becomes apparent that our concept is based rather on intuition and lacks strictness and connection to the real word. This post is intended as a quick introduction to causation from the philosophical point of view.

General thoughts

1. Where to establish the causal relation? We are going to use propositions, which represent quantitative properties of various systems in a given moment of time, that is, measurable properties. Events represents the changes in these properties. These events will be selected as causes and consequences. This way we are building an expressive language to construct statements of a scientific value. Contrary, people often think about events that can either happen or not. In our system such events are easily modeled as Boolean properties (taking value of either 0 or 1).
2. There exist two seemingly equally justified points of view on the place of causal relations in the world.
• There are common causation laws that rule the world; then they are instantiated in different situations with different events.
• Causes and consequences are an indispensable part of the world, all generalizations are secondary.

Hume’s arguments

The arguments we are going to study can partly be traced to XVIII century! Meet David Hume, a philosopher.

Hume’s account on causes and consequences is highly empiric. What an observer (even ideal one) can observe about two events A and B is:

• A occured before B.
• A and B are close in space and time. Or they are connected by a chain of events, where each link is a relation between two events which satisfies these properties.
• When we observe something resembling A again, something resembling B appears as well.

It is suspicious that these three observations sum up everything an observer can notice — even an ideal observer. There is no way this information might be of a foundation for a strict causal relation as we usually imagine it.

Adding causality changes absolutely nothing here, because it does not give us anything observable.

In fact the pattern above can describe many events not necessarily connected in any way. Hume’s opinion is a great starting point, but now let us also address some problems about it.

Three properties of (A,B) pinpointed above occur not only in cases where we want to establish the relation, but also:

1. When A and B have a common cause
2. Just by coincidence
3. By preemption. It means that there is an event C that occurred before A and would have caused B anyway.

These three major problems are addressed differently depending on how one sees causation in general, which features of the cause-consequence pair are really key. Let’s now speak about those ways.

Sufficiency

To this day people tend to think about causation as a deterministic beast. Our knowledge about micro world, however, contradicts it (as many things about micro world contradict common sense). Contrary to some traditional views on causation based on necessity of the cause to bring about its effect, their modern counterparts fit mostly in two categories:

1. Those who base on regular occurrences of A followed by B.
2. Those who reconstruct the events of real world in the other, purely logical world.

Let’s take a closer look at the second point. In order to construct our logical structures we can use certain sets of rules (they can represent f.e. the laws of nature) of form:

Here for an event a the expression  F a will be substituted by an event instance; G a  is the consequence. As for the arrow, we can substitute it for either a material conditional (think simple implication) or something stronger like a subjunctive conditional (“If Oswald hadn’t killed Kennedy, someone else would have”).

Necessity

You know, sufficiency is not sufficient for causation. Even if we stick to determinism, the overdetermination (multiple causes) alone is a valid reason to question it. Let us say, A and B can both equally cause C and they occurred simultaneously. What caused C?

Basing on sufficiency of cause we can deduce:

• If A was the cause, then C would not have occurred without A. So A is not the cause.
• If B was the cause, then C would not have occurred without B. So B is not the cause.

Some people tend to think that it’s rather the cause’s necessity for the consequence that forms a casual relation between them. This way A caused B if and only if:

• A and B occurred.
• We can assert: “If A had not occurred, than B would not have occurred” (we will refer to it as sine qua non, because, well, its  what it is).

I guess it should look like: $A \land B \land ( \neg A \rightarrow \neg B)$.

It is but a foundation of a longer talk I intend to give in the next post based on arguments of Lewis and maybe Mackie (if I do have time for his book).

Probabilistic approach

Reasoning about sine qua non is not easy as long as you abandon determinism. Non-determinism, however, goes in pair with probabilities. The general idea of this approach is that causes increase probabilities of consequences in a large variety of contexts:

Here Z should take into account:

• Common causes of A and B.
• Preemptive causes of B.

This way preemption problem and common cause problem are addressed, and A and B become probabilistically independent.

The hard thing is to choose Z and a good definition of probability.

For example, take relative frequencies for probability. This way we should exclude from Z all causal consequences of B for which B is necessary. If we do not do it, we just get a wrong inequality 1 > 1 (check it!). However, look at it again: to calculate P we need exactly causal data for which we are building a theory! We have faced a vicious circle that is not easy to break.

Conclusion

As we see, there are loads of interesting subtleties when it comes to a closer study of causation. Numerous attempts were made to exile this relation completely from scientific thinking, but its roots are so strong it proved almost impossible to do. Next time I want to talk about Lewis’s very influential theory on causation, dated 1973, and then about his new causation theory of early 2000’s.