A Theory of Freedom

by John Valley
Standish, Michigan
April 01, 2008

Chapter 2. Causality.

Causality is an ancient and much-discussed idea. In this paper, I only have the space to make a few comments about it, which will hopefully shed some light on the question of freedom later.

Causality, in its basic form, is not so much an explanation of natural phenomena as it is an evasion of the question of causes at all. Let me explain what I mean.

When I speak of causality, I’m speaking of the billiard-ball model of actions and effects. Imagine, for the sake of illustration, a cue ball in a game of billiards. The cue ball moves across the table with a constant speed and direction until it collides with another ball. Some of the momentum of the cue ball is transferred to the object ball, which then moves away. The object ball, hitherto motionless, did nothing to stimulate its own motion. It was merely the passive target of the cue ball’s impact, but by virtue (”virtue” being an old word meaning force or power) of the cue ball’s motion, it was launched into motion itself, and so we blame the cue ball entirely for the motion of the object ball.

This passive model of causality is a victim’s model, and has come to be known as the concept of determinism: namely, that every event is caused by a prior action which wholly explains the event. The passivity of the model is one of the reasons determinism comes in for criticism, since it seems to rob every action it explains of any intentionality or purpose. While it seems to offer the promise of control (supposedly, you can fully determine the flight of the object ball by aiming the cue ball appropriately), in fact, the ability to aim the cue ball is not free. Determinism allows only one possible aim: the aim that is determined by its antecedent causes. There is no free action in a deterministic system.

The billiard-ball model of causality has other qualities. It presents a highly simplistic model: there is one actor, one action, one object of the action, and one effect. In reality, we know that there are often many forces acting on an object, and the resultant motion is a complex product of the impinging forces. The forces, and the resultant vector, are further constrained by the boundary conditions of the problem, such as, in the previous example, the flight of the balls is limited by the bumpers on the four sides of the table. Certainly a more modern view of the behavior of matter and forces in the world has had to take up a more sophisticated structure than the billiard-ball model allows. The theory of vector addition of forces is only one of many improvements in that direction.

A perhaps more alarming problem with the simple causal model is that it always removes the cause of an action to some event in the past. So, when we explain the motion of a billiard ball by pointing to a collision which occurred previously, the collision itself is not on the table; it’s in the past. What we have to examine in the present is the balls and their moments. The collision is only a theoretical device to explain the current situation, which it may or may not do. This is so even if you, the “observer,” have a personal recollection of the collision. Someone who walks into the room after the collision has occurred will not be able to study the collision; it no longer exists.

This particular problem with causality-namely, that it makes a resort to something which is not present-is characteristic of the method of recursive descent for solving problems. Recursive descent is just the method of explaining something by posing the same problem as you have, but removing it to some time in the past, or just restating it again.

The idea of composition of materials is also a theory of recursive descent: so we can say a chair is made of wood, wood is made of cellulose fibers, cellulose fibers are made of hydrocarbon molecules, hydrocarbon molecules are made of atoms of carbon and hydrogen, hydrogen atoms are made of protons and electrons, and so on. At each stage of the explanation, we want to know what “it” is made of, so protons and electrons must also have a composition, otherwise we don’t know what they are made of. Ultimately, the theory that everything is made of something else can only stop when everything is made of nothing; and this is the same sort of problem we have with the simplistic model of causality. It leads to the notion of a First Cause, which must itself be unexplained, and we say either God created the Universe but God is Eternal; or we say the Universe was created by a Big Bang which itself has no cause. These two starting points are logically equivalent, and both rest their explanations on the unexplained. (The method of recursive descent just says it’s turtles all the way down[1].)

These concepts of causality are challenged by two relatively more modern ideas. One is the concept of random events, as described by quantum theory (and which connects our discussion of causality here back to the discussion of randomness in the previous chapter). The other is the concept of functional interdependence.

Functional interdependence is exemplified by the formula

F = ma.

In symbols, it says the magnitude of a force is proportional to the product of a mass and its acceleration. This formula can be rewritten as

m = F/a

And

a = F/m.

This familiar law of inertia, dating back to Newton’s time, is completely indifferent to whether force causes acceleration, acceleration causes force, or mass causes acceleration. There is nothing really about causation in it. Rather, it merely asserts that a certain relationship always exists in any kinematic system between force, mass, and acceleration. It limits itself, therefore, to a statement about observables at the present moment in time, concerning the objects that are at hand to be observed.

Most of physics consists of laws of this form. Ohm’s law, from electrical theory (E = I/R),  is another familiar example.

Which is not to say that concepts of time don’t appear in equations of motion; they do, as with the familiar s = ½at². Even this is illustrative, though, as it suggests that time elapsed can be computed, knowing the position of an object and the amount of acceleration to which it is subjected. In other words, it also describes a relationship without asserting any causative role between its variables.

The inclusion of randomness as a factor in physics theories raises additional questions about the ancient and traditional ideas of causality. Certainly, it’s possible to dispute that randomness is ontological. Some people argue that the appearance of randomness in physical theories is merely epistemological; it’s a way of accounting for a lack of complete information, by using statistics to make generally useful instead of precisely accurate statements about the system.

It isn’t my purpose here to get involved in the debate over ontological randomness. Some physicists have argued very strongly that there is no room to bring determinism back to physics. These arguments claim that there are no hidden or unknown variables in the electron’s behavior, but even given a full knowledge of all there is to know about its state, the future state of the particle remains indeterminate. (This is generally called underdeterminism.) But regardless of where we stand on the question, one thing is clear: the assumption of determinism is theological in its character. Einstein believed God would not create a Universe that included chance in its behavior. The young quantum mechanics, including Niels Bohr, found that adding random variables and statistics to their equations provided an excellent predictive model. To make peace, physicists of that time agreed not to speculate whether the mathematics of quantum mechanics implied anything about the real nature of reality (sic). This so-called Copenhagen Convention, however, has always been unsatisfying, and speculations continue to this day on both sides of the question.

I call determinism a theological position for one reason: it is tautological, because any apparent uncertainty is resolved by arguing that there must be hidden causes. Hence, by definition, it is impossible to demonstrate a random event to a determinist. Either you can show the cause, or the cause is to be assumed. This isn’t scientific, but it works fine as a religious approach. Religion is founded on the need to make assumptions about the world in order to understand it. Physics does not need to challenge religious faith, and for those who need a deterministic universe, it is possible to assume there are hidden processes taking place behind the observable facts, without actually changing the physical facts. Determinism therefore is harmless, but irrelevant, and science has evolved to the point where most branches now make use of statistics and probabilistic models to some degree.

After this discussion, we can see an important similarity between the mathematical approach to randomness and the physical approach. In both cases, randomness is stipulated without being exposed. The mathematician doesn’t describe how a random variable takes on its values[2]. The physicist doesn’t try to explain how a random event can choose between the possibilities. In both cases, the random result is taken as a fait accompli. It just happens.

The net result of all this theoretical work is that the status of causality is somewhat of a shambles. It has ceased to be a formal theory, and only remains as a background, a sort of cultural and everyday approach to understanding and coping with mundane events. Which is not to say that, in any situation, some results aren’t much more likely than others. Probability makes some things uncertain, but it doesn’t make all outcomes equal.

The question of freedom becomes more pointed, now. As long as physical theory is assumed to be the basis for understanding freedom, we are left with only two possibilities, both of which seem repugnant. Either we suppose the determinists are right, and behind every random variable lie hidden causes, and hence there can be no freedom (the entire future history of the Universe was established in the instant of its creation); or future events are not predetermined, but the choice between possibilities is a random one. We have to ask, is a sort of freedom that amounts only to random chance, what we mean by freedom? Maybe it’s just another kind of prison, different in design from the determinists’ prison, but just as inescapable. What we seem to be looking for, in any question of freedom, is just what is lacking in mathematical and physical randomness: the element of choice.

If we can gain some understanding of what choice is, and if we can grant some sort of effective ability to carry out a choice-then, and only then, can we imagine some meaning to the idea of free will, whether it is political will, personal will, or any other kind of will. This is what lies behind Dennett’s claim that the important thing about free will is not random choice, or even freedom of choice, but instead, the fundamental ability to carry out our choices however they are arrived at.

I think the good Doctor is missing the boat on this. The one thing uncertain about all choices we might make, as human beings, is our ability to bring them to completion. The ability to choose, like the ability of the cue ball to affect its target, is limited by its context and the other forces at play. Randomness, whether it is real or formal, ontological or only epistemological, implies the ability to try. It does not imply the ability to succeed. And this is where the determinist finds himself most in doubt and most in need of salvation, for it is certainty of outcomes that he desires most, and the hope of control.

We really have a fight here between two fundamental purposes: the hope of control over our futures, which determinism seems to promise, or the hope of being able to make meaningful choices. Apparently we can’t have them both.

In the subsequent parts of this paper, I want to look more closely at the nature of choice, and the other side of choice, effectiveness. This will inevitably lead us to Searle’s ideas of intentions and intentionality.

[1]. Recursive descent is a surprisingly common method. Besides its uses in theories of material composition and causality, we also use recursive descent to define logic, and to talk about control. In logic, proofs are always based on unproven assumptions. To prove the assumptions, you have to introduce different assumptions, which will then stand on their own. Logic, in other words, always moves its foundations to the illogical. And in any theory of control, the agent who exercises control is always assumed to be uncontrolled himself. He is out of control, and hence has real authority. As with logic, where the dichotomy is between assumptions and conclusions, with control, the dichotomy is between master and slave. I’m sure there are other examples of recursive descent deeply buried in our habits of thought, but this is not the place.

[2]. Computer programmers will no doubt want to interject some comments at this point about the technical problems of generating random numbers. Inasmuch as computer programs often make use of random numbers, it is true that there is, in fact, a technology in computer science to the production of random numbers. These numbers and sequences are, however, to be properly understood as pseudo-random numbers, not truly random numbers, and there are batteries of tests as part of that technology which assist in analyzing the quality and capabilities of any given implementation of an RNG (random number generator). All of this matter remains, however, technological in nature, and doesn’t modify or extend the mathematical idea of a stochastic variable, or of probability and statistics in general.

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