# Causality

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Let us analyze the meaning of statements of the form: 'C is the cause of the effect E', or simply 'C causes E'. Here C is an action, and E a situation, i.e. a set of states of the world deined by an abstraction function. Sometimes we speak of the cause C as a situation too, but what we mean then is that this situation leads inescapably to a certian action which causes E. Other times, we speak of the effect E as an action, but this, again, for the same reason that this action is an immediate result of the situation caused by C. So, in the mainstream, the cuase is an action, and the effect a situation.

The first attempt to explain the meaning of causality is to say that whenever C takes place, E takes place also. But this is not a satisfactory explanation. We see that after a day a night always comes, but the day is not the cause of the night; it is rather the rotation of the Earth. A simple observation of the sequence (C,E) is not sufficient. C and E might be two effects of a common cause, or this could be just a coincidence. That causal relation is something more than sequence in time, was noted by many thinkers and is in agreement with our intuition.

In search of the true meaning of causality consider the case when the cause C is my own action. By my own we mean a reference to the subject of knowledge. To give meaning to a statement, we must relate it to generation of predictions; as a rule, we do this in the form of modeling scheme (see model). The statement 'C causes E' is translated as two predictions:

The first prediction:

```                      True            True
---------------
^               ^
|               |
S  |               |  E
|               |
|       C       |
----------------
The second prediction:
True           False
---------------
^               ^
|               |
S  |               |  E
|               |
|  do nothing   |
----------------
```
In words: if a situation recognized by abstraction S holds, and I do action C, then a situation characterized by abstraction E takes place. But if in the same situation I do nothing, then E does not occur. This precisely matches our intuitive understanding of causality.

Now suppose that C is not my action, but that of some other agent. It may come as a surprize that this, seemingly innocuous, change radically changes the picture. Now the action C must be a part of the initial situation S. We shall represent this complex situation as S+obs(C), where obs(C) stands for the fact that we observe some consequences of the action C. We must remember that I can perceive an action directly only when it is my own action; all other actions I perceive through my sense organs as changes in the state of the world. I can use the concept of action to construct modesl of reality; in particular, an action of a fellow human I perceive by analogy with my own action, but this does not alterate the basic fact that all agents except myself are given me only through the manifestation of their actions. I am I, and all other agents are they.

Thus we can try to express the meaning of causality in this case as consisting of the following pair of predictions:

The first prediction:

```                      True            True
---------------
^               ^
|               |
S+obs(C)  |               |  E
|               |
|  do nothing   |
----------------

The second prediction:
True           False
---------------
^               ^
|               |
S  |               |  E
|               |
|  do nothing   |
----------------
```
However, this is not a correct expression of causality. This is only an observation of time sequence, even though in two versions. It could be that there exists a real cause C' which first causes action C, and then situation E. For example, I can, on some days, have scrambled eggs for breakfast. On such days I break two eggs and fry the content in a frying-pan. An external observer will see that when I break eggs, I always fry them; when I do not break eggs (say, because of having a cheese sandwich for breakfast), I do not fry them. This is not to say that the above two predictions cannot be part of our knowledge. They can. They constitute a useful model of my uninterrupted breakfest, which specifies the order of my actions. But it would be an error to conclude that breaking eggs is the cause of frying them.

Then is there any meaning in speaking about a cause which is not an action of the subject of knowledge? We believe, there is, but it is a result of a certain reduction of this case to the basic case where the cause C is the subject's action. There is an additional element introduced by the subject of knowledge in understanding causality in the case of sombody's else action. It is a tacit assumption that I could, somehow, allow or prevent the action of which I think as a cause. The interpretation of the statement that an action C of some agent causes E as the statement that if I, the subject of knowledge, allow C to take place, then E ensues; however, if I somehow prevent it, there will be no E. This case of causality is the following modesl of the world:

The first prediction:

```                      True            True
---------------
^               ^
|               |
S  |               |  E
|               |
|    allow C    |
----------------
The second prediction:

True           False
---------------
^               ^
|               |
S  |               |  E
|               |
|   prevent C   |
----------------
```
This is how sombody's else action is reduced to mine. Allowing an action to happen is easy: just do nothing. But what about the feasibility of prevention? When I say that rotation of the Earth is the cause of alternation of day and night, the meaning of it is, according to our scheme, that if I stop the rotation of the Earth, the effect of alternation will disappear. But this clearly is impossible assumption. And it would not help to qualify this assumption as occuring in my imagination. Pictures in our imagination are constructed from pieces of our real experience. Stopping the Earth was not in our experience; it is unimaginable.

What I really imagine when I assume that I stop the rotation of the Earth is a relatively small (of the size convenient for imagination) rotating sphere, which I then cause tho stop rotation. This is a part of my model of the Earth and the Sun which explains the alternation of day and night. There are to models here. First I construct the Sun-Earth model, then I see that "days" and "nights" in that model are caused by the rotation of "the Earth", and then I make a jump back to real days amd nights and say that this is caused by the rotation of the Earth.

As required by our epistemology, we explained causal statements as certain models of the world. We might now ask: what about the concept of model itself? Does it not include the idea of cousality? The answer is yes, it does. Moreover it is based on causality. The ability to make predictions and the existence of causality in the world is, essentially, the same.

Of the four lines in the modeling scheme, one represents a free action of the subject of knowledge, the other three are functions, which are devices relying on causality: give me an inpout, and I will give output. To define formally what those functions are, we could describe them as causal relations, i.e. explain in terms of new models, metamodels. Then we could construct models of metamodels, etc. This we leave nowhere and add nothing to understanding. The concept of modeling is so fundamental that its meaning cannot be reduced to anyhting less than itself. Thus we take it for the basis.

We saw that the actions of the subject of knowledge make a necessary element in understanding causality. The relation of causality is not directly observable. We create models of the world using one or another machine to implement the causal, functional, relation. Then we apply our models to the world and see whether they work properly as predictors. Thus causality, as Kant first indicated, is not among our immediate sensual data, but is, rather, our basic way to organize those data.