Morality within indeterminism
In my previous story, I argued that determinism is false because it fails to explain the results of the constrained-will test. The argument aims to settle the scientific aspect of the problem of free will through the logic of falsifiability [ref]. However, determinism is rarely defended as a scientific theory. Non-scientific theories of determinism have been around since ancient times [ref]. It would be displeasing to dismiss thousands of years of ideation without at least building a map to highlight the main features of the landscape that will be left behind. Such a map also helps to locate the theory of constrained will in a philosophical context and provides a frame of reference on which we can set directions for its expansion.
Determinism
There are many variations on the doctrine of determinism. For the sake of brevity, we can condense all of them into two types. The first is supernatural. Within supernatural determinism, we find the doctrine of theological determinism. If God is omnipotent and omniscient, then everything that happens in the universe must be determined by God. We might even interpret biblical passages as explicitly stating the conclusion [ref]. The second type of determinism is natural and is neatly expressed by the doctrine of causal determinism. According to causal determinism, all states of the universe are caused by a previous state in combination with the laws of nature. Despite the radically different notions invoked, we can think about both types of determinism with the help of a simple diagram.
Let us lazily describe the state S of the universe U at any point in time t via simple enumeration. Above, we have the first point in time of the universe U(t1) being described by S1.
Assuming theological determinism, we should think of S1 as the result of God’s first act, the creation of the heavens and earth [ref]. Following the book of Genesis, in U(t1), S1 is formless, dark, and empty heavens and earth with God’s spirit hovering over all of it, so God decided to create light. Consequently, in U(t2), we get S2 as heaven and earth with light. God then saw that light was good and separated it from darkness. We then obtain S3 for U(t3), which is heaven and earth with days containing mornings, evenings, and nights. The story continues until Judgement Day without anything other than God’s will determining every state.
Assuming causal determinism, we may think of U(t1) as the primordial universe, the universe just before the Big Bang [ref]. Setting aside a vast number of details, we could state that S1 is a gravitational singularity, a state of infinite density and temperature, but no space or time. The laws of nature (untestable assumptions at this point) determine that the Big Bang occurs, taking U(t1) into a rapid expansion period that leads us to U(t2) and S2, space and time, with subatomic particles joining together to form atoms for about four hundred thousand years. The laws of nature (now tested ones) continue to operate for another billion years to bring us to U(t3) and S3, a recognizable universe with observable objects like stars and planets. The story then continues until humans show up and further beyond into the very far future, without anything other than the laws of nature (unclear if all testable) determining every state of the universe.
Theological and causal determinism tell wildly different stories with regard to how explanatory targets are filled. But they tell the same story with regard to the targets that need to be filled. That is why we can map them to the same diagram. They both attempt to describe the whole universe, through eternity, by evoking a simple explanatory framework. In theological determinism, the explanatory framework is God’s will. In causal determinism, it is the laws of nature. These features make determinism an attractive doctrine by virtue of its comprehensive simplicity.
In the case of causal determinism, we could even think of the universe as a movie, ready to be fast-forwarded or rewound. We can predict future states just as easily as we can postdict previous ones because the laws of nature contain time. This is exactly how the cosmological theory of the Big Bang can be built and why we must infer that defenders of determinism propose the vastly speculative assertion that we would always do the same thing if we could travel back in time [ref].
It will be useful to name two commonalities shared by natural and supernatural varieties of determinism. The first is target completeness. Determinism aims to explain every state transition of the universe. The second is framework invariance. Determinism accomplishes its explanatory goal by relying on unchanging concepts. As we will see, neither feature is necessary for the purpose of knowledge accumulation, and they are jointly untenable if we want to hold onto what we already know.
Indeterminism
Leveraging the terminology we just introduced, indeterminism [ref] is a form of explanation that eschews target completeness but preserves framework invariance. The result is hard to swallow: an incomplete and yet more complex picture of the universe. Compare the diagram below with the one above to visualize the difference.
We can reuse the story of the universe given by causal determinism to provide our starting point. Above, we see the universe at time one, U(t1), being fully described by S1, which is the gravitational singularity [ref]. In an indeterministic universe, we may find U(t1) to transition to U(t2) in any one of several S2 states: S2a, S2b, S2c, and so on up to state S2x. The dotted lines help convey the point that no necessary connection is established between S1 and any particular variant of S2. The Big Bang might not happen, but if it happens, it happens as an uncaused effect of S1. The laws of nature in an indeterministic universe only specify a space of possible states (S2a-S2x) and associate each state with a probability (i.e., a number between zero and one). That is it. The fact that they do not directly connect states of the universe over time is what we refer to as target incompleteness. Target incompleteness requires us to consider some annoying complexities whenever we try to explain things over time. Mundane examples should suffice to illustrate the points.
Instead of the whole universe, let us consider a coin flip. We know that there are two states in which the coin could land, heads (call them S2a) and tails (call them S2b). If the coin is fair, S2a has a 0.5 probability of occurrence, and S2b also has a 0.5 probability. Now we flip the coin and it lands as S2a. We may want to ask why. But in an indeterministic universe, we can only say that it is because S2a has a probability of 0.5, which does not quite cut it. Instead of an immediately sufficient explanation, we get a description of a regularity that requires multiple occurrences of an event to carry intuitive meaning; i.e., if we flip a fair coin many times, we will get heads and tails with roughly equal frequency.
A two-round game with a six-sided die could help us build some appreciation of the complexities that creep up. In this case, the states S2a-S2x correspond to the possible outcomes of the first roll of the die, i.e., the numbers 1–6, all with probabilities of approximately 0.1667. We repeat the exact same law to transition from U(t2) to U(t3) after the second roll. Simple enough. Now, what is the probability that we find ourselves with a total of 5 by summing up the observed S2 and S3 states? Despite us already knowing all the laws of our six-sided die universe, we still need to enumerate all specific cases to get to the answer with anything other than a guess. There are two possible combinations that sum up to 5, 1–4, and 2–3. Both can occur in the order just listed, or the reverse, 4–1 and 3–2. That gives us 4 possibilities. We can get 6 possible states in the first round, and all of them can be followed by 6 possibilities in the second round. That gives us 36 total possibilities. 4 out of 36 possibilities, i.e., the fraction of all possibilities that give us 5 in U(t3), give us a final probability of about 0.11. I hope you are still with me. Saying anything about the future can be annoyingly laborious in an indeterministic universe.
Psychologists have won Nobel prizes for explaining how irrational we typically are when dealing with indeterministic universe math, i.e., probability theory [ref]. Mathematicians have been notoriously tripped by it [ref]. Even Einstein’s preeminent status in physics fell victim to discomfort with the implications of probabilities [ref]. However, difficulty alone can not be the basis for accepting or rejecting indeterminism. It is not always smart to be lazy, only sometimes.
We should evaluate indeterminism based on its merits. Most critically, from the outset, determinism fails the constrained-will test. That is but one of many failures that place determinism in conflict with established science. In physics, quantum mechanics remains a dominant theory that is commonly interpreted as being incompatible with determinism [ref]. In neuroscience, probabilistic descriptions of neural signaling are unavoidable [ref]. In fact, indeterminism is believed to be a necessary feature in all of biology, driving everything from gene expression to behavior [ref]. The sobering conclusion is clear. Determinism is untenable as anything other than faith in comprehensive simplicity. Therefore, indeterminism is true. Or is it?
Framework variance
Abandoning reductionism
Shining in absence thus far is the notion of reductionism [ref], the conceptual foundation of what we have been calling framework invariance. A cliche version of reductionism states that physics is applied mathematics, chemistry is applied physics, biology is applied chemistry, and so on. All levels of explanation can be reduced to the most fundamental level. An obvious problem with cliché reductionism is that it leads us to a sort of mathematical mysticism. The turn away from science is obvious. Mathematics requires no empirical observation. Materialism is a more scientifically inclined version of reductionism [ref]. According to materialism, matter is the fundamental reality. Historically, atoms were the basis of fundamental reality. Now we have subatomic particles and quantum mechanics, which are understood to be indeterministic [ref].
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Deniers of free will, like Robert Sapolsky [ref] and Sam Harris [ref], consider the possibility that indeterminism may be true, but immediately deny that indeterminism could have any relevance to the problem of free will based on assumed reductionism. Their argument against free will in an universe that might be indeterministic can be captured as follows. Our actions depend on our bodies. Our bodies are made of matter, and matter obeys the laws of physics. Therefore, our actions are determined by the laws of physics. Even if indeterminism is true, our actions are not free because reductionism is true. What else could be said? Definitely not quod erat demonstrandum.
We can acknowledge that our actions obey the laws of physics without concluding that they are determined by the laws of physics. Being constrained by something is not the same as being caused by that thing. For all we know, and for all that deniers of free will have demonstrated, the laws of physics might simply restrict us to an indefinitely large space of possibilities. In the same way that we cannot assume determinism without proof, we cannot assume reductionism without proof. If we assume reductionism, then we need to explain how the indeterminacy of quantum mechanics becomes a deterministic explanation of human behavior that excludes free will. That’s a taller order than any denier of free will has fulfilled. But if we don’t assume reductionism, then the rejection of the relevance of indeterminism to the problem of free will is entirely unjustified.
Constrained will as emergent conscious choice
The theory of constrained will acknowledges that human behavior is constrained by the laws of physics without falling into asserting the double whammy of noncommittal determinism because of unquestioned reductionism. A plain expression of the alternative philosophical foundation we propose is achievable before clarifying its details.
Human behavior operates on top of multiple sources of indeterminacy. As we’ve seen, there is indeterminacy at the level of subatomic particles [ref] and through biology [ref], up to the level of the neural signals that encode human sensation and behavior [ref]. We’ve also seen how things that operate independently of us, like coins and dice, introduce indeterminacy into our environment. All these gaps in determination negate causal necessity for all but the most basic human behaviors, like startling. All the factors that provide partial explanations for proper choice merely specify conditional probabilities, behavioral repertoires. The claim that when we do something, we are not determined to do so; that we could have done otherwise, is simply a reference to a behavioral repertoire. The conscious functioning of our brain emerges from the underlying indeterminacy and enables us to generate causality in the form of enacted plans. Consciousness allows us to choose among possible behaviors, thereby initiating a chain of causality that connects plans to actions.
The notion of emergence just introduced rejects reductionism [refs 1 and 2] along with universally applicable determinism or indeterminism. It asserts that a deterministic causal chain can start and stop within an indeterministic context [ref]. The reverse, apparently indeterministic sequences of events generated from deterministic cause and effect, is also possible, fascinating, and captured by chaos theory [ref]. But we will continue along the road less traveled. Our destination is near. The diagram below illustrates my position.
Above, we have the now familiar representation of the universe at time one, U(t1), described by the state S1. We can abandon cosmological histories in favor of analyzing the constrained-will test. U(t1) is now a human behavior laboratory, and S1 is four people ready to participate in an experiment. Just as in the indeterministic universe, we may find U(t1) to transition to U(t2) in any one of a large number of S2 states, from S2a up to S2x. The space of states S2a-S2x now corresponds to the combined behavioral repertoires of the four participants. The agent may or may not sing Happy Birthday. They may or may not jump and do push-ups, and they may or may not sit on the floor and close their eyes. The other three participants also may or may not fulfill their roles in a variety of ways. For the sake of simplicity, let us assume that everyone complies with the instructions.
From the point of view of the agent, the behavioral repertoire might be a strict subset of S2a-S2x. For example, the agent might only consider the subset S2a-S2c (red lines). The size of the subset depends on the agent’s level of conscious recognition of the complete behavioral repertoire in the context of S1. In our case, the context is given by the experiment’s rules, which require that the agent’s plan be written down in three to five sentences before it is performed inside an empty room. Let us assume that the agent chooses S2b, writes it as their plan, and executes it. Now U(t2) is in state S2b, where the agent sang happy birthday, jumped and did pushups, and sat on the floor and closed their eyes, just as they planned.
Why did we get to S2b? Simple. Because the agent chose to fulfill their role in that particular way. The agent was the cause of S2b (represented by the red, solid, and bolded line), even though if we eliminate consciousness from consideration to favor a reductionist framework, the laws of nature only provide us with the behavioral repertoire S2a-S2x, and we have no causal chain to speak of. But the fact that the agent caused their own behavior by way of emergent conscious choice is why they can predict their own actions in the experiment.
From the points of view of the scientist, predictor, and evaluator, there is no conscious process mapping S1 to S2b. There is no exact cause observable to them to explain why U(t2) is in state S2b, rather than S2a, S2c, or S2d-S2x. All they have is the subset of the laws of nature that excludes emergent conscious choice. That is why the predictor will always underperform the agent. No amount of neural recordings captured before the moment at which the agent chooses their plan will enable the predictor to outperform the agent because the causal chain begins with the conscious selection of the plan. Prior to that event, all we have are indeterministic neural signals and environmental conditions specifying the behavioral repertoire. Recordings performed while the plan is selected are an interestingly different issue. A deterministic map between the conscious plan and the state S2b must exist in the agent’s brain, even though neuroscience is yet to provide evidence with the required level of precision.
We have just provided a simple but comprehensive explanation of the constrained will test through framework variance. Our explanation recognizes multiple points of view and combines deterministic and indeterministic considerations. Nothing in the explanation forces us to abandon the laws of nature. No mysticism or supernatural concept is required or warranted. The critical difference between the laws of nature invoked in our explanation and those invoked by deniers of free will is that ours explicitly rejects noncommittal determinism and unjustified reductionism. The concept of the laws of nature in our explanation is just as philosophical and abstract as the reductionistic one, but the laws of nature that contain emergence allow us to make falsifiable predictions within the constrained-will test by removing the philosophical blinders that the deniers of free will seem to consider required etiquette.
Epilogue: Emergence
Given its importance in our philosophical framework and contemporary science, we should consider the concept of emergence in greater detail. Right off the bat, the concept is a topic of debate in philosophy [ref] and science [ref]. The controversy is understandable for a variety of reasons. First, there are differences in the usage of the term [ref]. Second, scientists and analytical philosophers may have become so accustomed to the logic of reductionist explanation that they experience difficulty considering other forms. Sam Harris acknowledges he has suffered from this condition in his book, Free Will. Even more significantly, if emergence is a true feature of the universe, our understanding of the laws of nature must be modified to the point of making the search for a “Theory of Everything” in physics [ref] not only misguided, but also an embarrassingly large overstatement. We can avoid unnecessary controversies in what follows by adopting clear definitions and presenting simple examples.
The philosopher David Chalmers provides clear definitions for two forms of emergence, weak and strong [ref]. Paraphrasing, weak emergence is a characteristic of a system that only becomes apparent when observing the system as a whole, but one that could be deduced from the characteristics of the components of the system. Strong emergence is also a characteristic of a system that only becomes apparent when observing the system as a whole, but one that cannot be deduced from the characteristics of the components. By definition, weak emergence does not present a logical challenge to reductionism because reductionist theories can accommodate it, even if only via ad hoc reconsiderations. On the other hand, strong emergence is logically incompatible with reductionism and requires the kind of reframing of the laws of nature that the constrained-will theory calls for. According to Chalmers, consciousness might be the only strongly emergent property in nature, despite an abundance of examples of weak emergence.
Yaneer Bar-Yam offers a simple example of an artificial system that displays strong emergence, a three-bit system with a parity property [ref]. Bits are really cool, but they are also abstract and might require some explanation. Let us instead think about rectangles with three circles inside to illustrate the logic of strong emergence provided by Yaneer Bar-Yam. Examine the set of rectangles below. Each of them is a system. The yes and no labels atop each rectangle tell us whether they satisfy the parity property. Can you detect it right away? The parity property requires that an odd number of circles be white. Only one or three white circles are allowed. Only half of the possible rectangles comply with that property. It is impossible to infer the property by focusing on individual circles. That is weak emergence. Any individual circle can be white or light blue. It is also impossible to derive the parity rule without considering the state of an entire rectangle (the irreducible system). That is strong emergence in precisely the sense defined above. How might this give us constrained will?
To obtain the sort of strong emergence that is required for constrained will, we need to combine the now distinct notion of strong emergence with an additional notion of emergent causality. Erik P. Hoel and his collaborators provide various demonstrations of the phenomena that need to be appreciated [ref]. Again, a complete review requires abstractions that are unnecessary for our present purposes. In this case, we would need to understand a fair deal about the mathematics of causal inference [ref].
Let us instead recall the basic concept of probability associated with indeterminism. We have some possibilities, each of which is associated with a number between zero and one. For example, a fair coin toss has two possibilities, each with an associated probability of 0.5. It turns out that determinism, and our notion of cause and effect, can be thought of as the special case of indeterminism in which the only two probabilities allowed are exactly 0 and 1. This realization allows us to think about systems as being more or less deterministic, rather than entirely either/or. In such a sense, a fair coin toss is maximally indeterministic (heads have 0.5 and tails have 0.5), while a biased coin with probabilities 0.9 and 0.1 is more deterministic.
Erick P. Hoel and his collaborators demonstrate that it is possible to obtain systems that are more deterministic (i.e., less indeterministic) from components that are less deterministic (i.e., more indeterministic). Incidentally, all of the examples they provide can be represented as networks of units that affect each other in a manner reminiscent of neurons. They begin with a minimal system composed of four micro units that can be evaluated at a higher level as two macro units, and show that the macro level can be more deterministic. Working their way up in complexity, they finish with a system composed of nine units with time-dependent interactions (realistic neural encoding of the sort that operated in sensation and behavior) and arrive at their main conclusion: different indeterministic systems peak in determinism at different spatiotemporal resolutions. Continuing to scale their findings to the level of the human brain, we would arrive at the irreducible mechanism of constrained will as emergent conscious choice where, at the temporal resolution of our thoughts and the spatial resolution of an ensemble of neural networks in our brain, a chain of cause and effect emerges in the form of a plan that determines our future behavior.
Afterword: A map for constrained will
We’ve covered considerable ground. Starting with a brief overview of theological determinism that quotes from the bible, we arrived at considerations of computer science research on the concept of emergence. It would be fair to question, or in any case, highlight the motivation for undertaking the effort. Expressed succinctly, a philosophical perspective can be combined with much in contemporary scientific practice to arrive at an area of research deserving the name of moral science. If such science were available, we might be able to engage in political debate with much more than either a bible or left-leaning dogma from some other book in hand. Imagine if we could build an AI capable of helping us not only with image and text creation, general question answering, and internet search, but also with finding purpose, understanding each other, and collaborating toward a morally better future.
The ground just covered can be explored further in many directions. For example, the neuroscientist Giulio Tononi has developed Integrated Information Theory to explain consciousness itself based on similar philosophical foundations. My goal is to help expand the foundation in the direction of moral science. One more look at the framework variant picture of the universe at time one reveals the three types of questions to be pursued by moral science. What exactly is our current state? Where can we possibly go from here? And most controversially, which of the available options should we take? I will turn directly to these questions next.
