Necessary and Sufficient Causes

One of the common formulations of determinism is (quoting from Wikipedia)

Determinism is the philosophical position that for every event, including human interactions, there exist conditions that could cause no other event.

A world that satisfies this definition of determinism can evolve in only a single way over time. This definition is stonger than merely saying that the event's causes are necessary, sufficient, or even necessary and sufficient. To see why that is so, I will demonstrate a series of model worlds each of which is an intentionally flawed Interpretation of "Determinism". Each model will be a very simple imaginary "world"; it is not intended to reflect the real world, but is rather just an abstract thing that helps us understand the implications of the definition. Through this series of models, we'll see that the definition of determinism above is stronger than even saying that every cause necessary and sufficient for its effect.

For these models we have the following concepts:

• Variable: Some fact or condition about the state of the world. In our example will use a letter to designate each abstract fact about the world.
• State: The set of variables designating the state of the world at some time. In our example we will use a set of letters to designate the state of the world, but it will always happen to be a single variable at any given time.
• Cause: Some variable or variables that lead to an Event occurring (resulting in the specific Effect of that Event)
• Event: Something that can occur from one moment to the next and has a specific Effect
• Effect: A change in the state of the world
• Initial Condition: The state of the world at the beginning of some time of interest

Every cause being necessary does not imply determinism.

First lets us examine necessary causes. According to Wikipedia

If x is a necessary cause of y, then the presence of y necessarily implies the presence of x. The presence of x, however, does not imply that y will occur.

A good example of a necessary cause in nature is particle decay. A particle that can decay is a necessary cause of the particle's decay, because the particle's decay necessarily implies that there was a particle there that could decay. The presence of a particle that can decay, however, does not imply that the particle's decay will occur. While the presence of a particle that can decay is necessary in order for the decay to occur, it is not sufficient for the decay to occur. The laws of physics (as best we understand them today) do not say that there is any sufficient condition for the particle to decay.

One might imagine that the claim that there is no sufficient condition for particle decay is merely a limitation of our knowledge, rather than a fundamental feature of nature. Perhaps there are hidden variables that cause the decay to occur at some particular time, but we simply do not know how to (or even cannot) measure these variables? That is not the case. It has been shown that the assumption that there are local (i.e. consistent with relativity) hidden variables underlying quantum indeterminacy contradicts observations of entanglement in experiments like the double-slit experiment and those demonstrating Bell's inequality. In any case, the point of our discussion here is to understand the implications of the definitions of causality, not to determine which of them are satisfied by nature.

Our first model simplifies the behavior of the K_S meson, which can decay in more than one way. For simplicity we shall pretend that it can decay in precisely two ways. At any given moment it might not decay, or it might decay in one of these two ways. We describe our simplified model of the world as follows:

Initial condition: K (meaning the K_S meson is present)
Possible events:
  E1: precondition: K is present
      change in state: no change in state (K does not decay)
  E2: precondition: K is present
      change in state: remove K from the state, and add P (decay to particle P)
  E3: precondition: K is present
      change in state: remove K from the state, and add Q (decay to particle Q)

There are more than one ways in which this world can evolve. We can have an unending series of occurrences of E1 (meaning the particle never decays). We can either have zero or more occurrences of E1 (meaning nothing happens for a time), followed by E2. Finally, we can have zero or more occurrences of E1, followed by E3. These latter two possibilities result in a different final state. This model world is thus a counterexample to the proposition that "every event has a necessary cause" implies that the world is deterministic.

Every cause being necessary and sufficient does not imply determinism.

Let us examine sufficient causes. According to Wikipedia

If x is a sufficient cause of y, then the presence of x necessarily implies the presence of y. However, another cause z may alternatively cause y. Thus the presence of y does not imply the presence of x.

We can imagine an example of sufficient cause being the burning of a book. It would be sufficient for the book to be thrown into an incinerator for the book to burn. However, that is not necessary, as there are other sufficient conditions for it to burn (for example, being thrown on a bonfire). Being a sufficient cause is neither stronger nor weaker than being a necessary cause. It is worth asking: what if every cause is both necessary and sufficient for its effect? Would that be enough to imply that the world is deterministic? We can demonstrate that this is not so by another model world, as follows:

Initial condition: [A,B] (two different facts about the world are true: A and B)
Possible events:
  E1: precondition: A is present
      change in state: remove A from the state, remove Z from the state if it is present, and add X
  E2: precondition: B is present
      change in state: remove B from the state, and add Y and Z

In this example, the cause A is both necessary and sufficient for its effects (it always leads to E1 occurring). The cause B is both necessary and sufficient for its effects too. There are two ways in which this world can evolve. We can have an event produced by the first rule, followed by an event produced by the second rule. In that case the final state of the world is [X,Y,Z]. Or we can have an event produced by the second rule, followed by an event produced by the first rule. In that case the final state of the world is [X,Y]. As we can see, this world is not deterministic. This model world is thus a counterexample to the proposition that "every event has a necessary and sufficient cause" implies that the world is deterministic.

We can now see why the usual philosophical definition of determinism is stronger:

Determinism is the philosophical position that for every event, including human interactions, there exist conditions that could cause no other event.

It is worth asking whether or not any of these definitions might correspond to the real world we live in. As far as we know, time is continuous, rather than discrete. Since these models require discrete time, they don't fit the real world, though there are tantalizing theories (yet to be tested) that time might be quantized. In addition, the usual philosophical definition of determinism requires a fixed ordering of all events throughout the universe. Relativity teaches us that there is no objective order of the occurrence of events: event ordering varies from one (subjective) inertial reference frame to another. These two facts make it nearly impossible to reconcile any widely accepted modern theory of the physical world with philosophy's concept of "determinism". A more useful definition might be found in the physicist's use of the term "deterministic" to describe a system that is capable of having only one possible future evolution. The most widely held scientific theories that explain the results of quantum measurement are not deterministic in that sense.

Some other definitions do not imply determinism

There are other definitions of determinism that one might find discussed on the web. It is sometimes hard to determine if they are stronger, weaker, or equivalent to the usual philosophical definition. For example, there is a model frequently discussed on http://breakingthefreewillillusion.com/. As far as I can tell the author's intended definition does not correspond to any of the definitions above. He has told me that the definition does not include sufficient causality, as that is logically inferred from his definition, and he has directed my attention to his proofs at http://breakingthefreewillillusion.com/must-lead-to-causality/ and http://breakingthefreewillillusion.com/otherwise-causal-contradiction/. Similarly, his definition does not include necessary causality: see http://breakingthefreewillillusion.com/necessary-sufficient-causality/. As I was unable to find a concise description of the definition he was using, I engaged with him over the course of a few weeks to draw up a definition to use for analysis. This is what we came up with:

• Event: A change in state from one moment to the next, described by its State Change.
• Causal event: An event that is caused by some set of Variables and whose Effect is derived entirely from those Variables.
• Cause: a set of pre-existing variables that derives (causes) the Effect in it's entirety (of a causal event). The variables of a cause includes all physical parts and physical laws that are described by formulas, which in the case of a causal event, force the output of the effect.
• Variables: The "parts" of a specific physical configuration (parts of the state). We shall indicate each variable by a letter like "A"; or a letter, and equals sign, and a number like "x=10". 
• State Change: The ontological change in the state that results from an event. For State Change we need not include in the change mention of variables that are not changed, but the variables that do not change may play a role in the variables that do.
• Effect: A State Change for a Causal Event.
• State: The "whole" encompassing all variables in a specific physical configuration. We shall indicate a state by a list of variables between square brackets, for example "[x=10,A]"
• Scenario: Specific sequence of causes and effects that can be contrasted with other scenarios. We shall indicate a scenario notationally by a sequence of states, starting with the Initial State, indicating for reference the law of physics that describes the event between each pair of states.
• Initial State: The first state in a scenario.
• Laws of Physics (LoP): The constraining behavior of the universe, which is also inherent in all existing physical variables in the universe.
• Formulas for LoP: We shall represent the laws of physics using Equations, formulas, mathematics, or any sort of symbolic language.
• Determinism: "every event is causal" 

A scenario starts with a given Initial State, and evolves through a sequence of steps by Events produced according to the world's Laws of Physics, each step producing a new State.

The scenario must continue until no further events are possible.

Our goal is to evaluate the following hypothesis:
Hypothesis: Given a particular Initial State, if a Scenario that begins with that Initial State satisfies Determinism, then every Scenario that begins with that Initial State is the same.

The author asked me to add this comment to this set of definitions:

"These definitions are one's that Trick [the author] and I, after much deliberation, have agreed to for the assessment I will make. It isn't the case that, for example, Trick's regular usage of the concept of causality requires an entirely physicalist account, but for the sake of our discussion we are both agreeing on a physical universe only. There are also some words that Trick normally wouldn't use, but for the sake of clarity we added them."

Now we can try the model world from our analysis of necessary and sufficient causes:

Initial state: [A,B]
The laws of physics permit the following possible events:
  E1: precondition: A is present
      change in state: remove A from the state, remove Z from the state if it is present, and add X
  E2: precondition: B is present
      change in state: remove B from the state, and add Y and Z
Scenario S1: [A,B] E1 [X,B] E2 [X,Y,Z]
Scenario S2: [A,B] E2 [A,Y,Z] E1 [X,Y]

To evaluate the hypothesis, we will analyze S1. There are two events. The first, E1, is a causal event with cause [A]. The second, E2, is a causal event with cause [B]. Thus this scenario satisfies the definition of Determinism. Similarly scenario S2 satisfies the definition of Determinism. However, we can see that scenarios S1 and S2 are different from each other. Moreover, they end with different world states. Thus this counterexample disproves the hypothesis. We can therefore conclude that this definition is weaker than the usual philosophical definition of Determinism, and the definition discussed at http://breakingthefreewillillusion.com/, if satisfied by a world, does not imply that the world's timeline "could not have been otherwise".

One might ask what causes one event to occur before the other in one scenario but vice-versa in the other scenario; what causes the ordering of events? In the ontology of this definition of determinism, an event (a change in state from one moment to the next) or an effect (a change in state for a causal event) can be caused, but the "order" of these changes is not something that can be caused. So the question does not make sense. The whole point of this example is to surface the fact that this definition of determinism does not require events to be ordered in any particular way. That is how it differs from the usual philosophical definition of determinism.

In his defense, the author has not evaluated my argument in detail, but has explained to me that I must be either

1. Asserting a variable with self-contradictory properties; or
2. Smuggling in an acausal event (an event without any cause)

though I do not know of any variable that is contradictory, or any event does not have a cause in this example.

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OK, so you do/not have free will. So what?

We previously proved that you (do or do not) have free will. What are the consequences of that fact?

Before we answer, let's review the conclusion. There are many definitions of free will. It is worth asking (and I have been asked) whether we would reach the same conclusion based on other definitions.

One definition asks the question: if there were an infinitely powerful being who knew all facts about the present, would it be capable of predicting the outcome of your future decision? I cannot tell if this question has a counterfactual premise, like the question we previously answered, or if it is a theological question. If it is the former, the same proof form would apply to demonstrate the same result. If it is a theological question the answer probably depends on which holy book you consult. A related question asks: if we could build a sufficiently powerful computer and feed it the complete state of the universe, would it be capable of computing our future choices? Again, the proof form we used before can be applied. A team of rogue scientists (rogue because they used "borrowed" equipment) claim to have constructed such a computer, and they claim that its prediction rate is 100% so far. I am suspicious of this claim, as their computer appears not to be capable of predicting a decision until after it has been made. The computer is called World Of Real Life Determinator, with the nice-sounding acronym WORLD.

A different definition asks the perhaps more sensible question regarding your future decisions, rather than your past decisions: for your future decision, is more than one option a possible future? In other words, can you do "otherwise" for a future decision? This question can be answered scientifically! There are three scientific approaches to the question, but unfortunately the result is somewhat ambiguous. The first approach is simple: from experience it is obvious that every decision we made previously was not made "otherwise", but was instead made in precisely the way we made it. If we assume the future to be similar to the past - that is a basic assumption of science, after all - then we should expect that future decisions to similarly not be "otherwise". We can test this theory too and we observe, as we expect, that any further decision we make is not made "otherwise". This approach to the scientific question clearly points out that we do not have free will. This is a well-respected proof form called retrospective determinism.

The second approach is to consult the physicists. The most widely accepted interpretations of quantum physics teach us that the results of quantum interactions are not determined by the previous state of the universe. That leaves room for small random fluctuations at the quantum and microscopic levels to affect our behavior over time as differences are amplified by chaotic processes in nature. In other words, the future is not determined. The incompatibilists have shown that this does not allow for free will, as we are not fundamentally in control of the random processes that affect our decisions; this is the well-respected proof form moving the goalposts. On the other hand, there are interpretations of quantum mechanics that, though not widely accepted, say the opposite.

The final scientific approach to this question gets to the root of the issue. The point of the question regarding free will is really about moral judgments of others. If nobody has free will, the argument goes, it would be absurd to blame or praise other people, for they were unable to freely choose how to behave. This is a well-respected argument form called argumentum ad lapidem. Can we scientifically test whether blame and praise are absurd or useful?

It turns out such an experiment had already been performed. In 1954 a team of scientists put together one of the largest controlled scientific experiments involving people that had ever been conducted. Eight hundred thousand people were selected for participation in the experiment, and randomly assigned to one of two groups. One group was assigned to live in the newly constructed city Dexter, which was operated under the assumption that blame and praise are proper to the conduct of a society. The other group was assigned to the new city Sinister, which was operated under the assumption that blame and praise are useless. Most people were not told which group they were assigned to; though they knew the name of their city, they did not know under which set of assumptions it was operated. Of course it became apparent after a time. The experiment ran for a full year. It led to a large number of PhD theses, research results, conferences, and scholoarly scientific debates. As we'll see, the results of the experiment were somewhat ambiguous.

The differences between Dexter and Sinister were as follows. In Dexter, police detectives were given the duty of assigning blame for crimes to individuals living in the city based on the individual's presence late in the causal chain leading to the criminal act. In other words, in the usual way. These people, called "criminals", were then subjected to what we would consider a typical criminal justice system. Rather than eliminating the criminal justice system in Sinister entirely, scientists eliminated only the assignment of blame based on the person associated with the criminal act. Instead, the police detectives of Sinister were responsible for conducting a kind of lottery for each crime committed. In this way blame would be assigned to a random citizen, or nobody at all (at a rate comparable to the conviction rate in Dexter). The conduct of the criminal justice systems in Dexter and Sinister mirrored each other, with the exception that blame in Sinister was assigned randomly.

Similarly, praise and reward in Dexter would be assigned to individuals on the basis of their presence late in the causal chain of events leading to outcomes considered useful or desirable. Productive employees would receive a raise and perhaps a promotion. In Sinister, however, praise and reward would be assigned randomly, in a way unrelated to the behavior of the individual. Parents in Sinister were taught to love and praise their children unconditionally, no matter the child's behavior.

The experiment was originally intended to run longer than a year, but had to be cut short due to funding issues. By the end of the year there were severe problems in Sinister that led many of its citizens to want to quit the project. There was, however, sufficient funding to analyze the results. It was clear to all that there were deeply disturbing differences between the two cities. Dexter, on the one hand, evolved in the way one would expect of a civilized society. Sinister, on the other hand, experienced rampant crime, surprisingly low worker productivity, and many competing gangs and militia. A significantly larger number of people survived the experiment in Dexter rather than in Sinister. But what to make of these results?

There emerged two camps of scientists who differed in their interpretation of the experiment's results. They called themselves the conflationists and the inconflationists.

The inconflationists believed that the experiment had improperly conflated "fundamental, moral" blame with blame in the usual sense, and therefore was not useful for answering any question about whether or not blame and praise are appropriate. While the experiment had demonstrated differences between the two cities, the inconflationists argued that all such differences were easily explained by virtue of the usual mechanisms of the laws of physics, psychology, economics, and other sciences. Many of the inconflationist researchers went on to take prestigious and influential positions as Philosophy professors.

The conflationists believed that the experiment had solidly demonstrated the role of blame and praise in the conduct of a civilized society, and that the results on their face were a clear demonstration of their utility. Many of the conflationist researchers went on to take prestigious and influential positions as researchers in the Social Sciences.

Despite their differences, the conflationists and the inconflationists agreed, for the most part, on appropriate conduct for individuals.

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