What is the basis of cause-and-effect? Can we know every cause in the universe? Does non-contradiction prove cause-and-effect?

Hume, Popper, Laplace, Hawking, Theory of Everything, Final Theory, cause-and-effect, non-contradiction, mathematics, algorithm.

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4.3 Cause-and-effect

"Every human being is irresistibly impelled to act to act precisely as he does act: in the eternity which preceded his birth, a chain of causes was generated which, operating under the name of motives, makes it impossible that any thought of his mind, or any action of his life, should be otherwise than what it is... The doctrine of Necessity tends to introduce a great change into the established notions of morality... " Shelly (explaining Laplace)

"The great paradox of determinism and free will, which has held the attention of the wisest of philosophers and psychologists for generations, can be phrased in more biological terms as follows: If our genes are inherited, and our environment is a train of physical events set in motion before we were born, how can there be a truly independent agent within the brain? The agent itself is created by the interaction of the genes and the environment. It would appear that our freedom is only a self delusion." E O Wilson

"I now turn to the second problem: If what we do is determined by some grand theory, why should the theory determine that we draw the right conclusions about the universe rather than the wrong ones? Why should anything we say have any validity? My answer to this is based on Darwin's idea of natural selection." Steven Hawking

"In my view, our best hope along this line is to show that the final theory, though not logically inevitable, is logically isolated… that there is no way to isolate it a small amount without the theory leading to logical absurdities. In a logically isolated theory every constant of nature could be calculated from first principles; a small change in the value of any constant would destroy the consistency of the theory. The final theory would be like a piece of fine porcelain, that cannot be warped without shattering." Steven Weinberg

"But when one particular species of events has always, in all instances, been co-joined with another, we make no longer any scruple of foretelling one upon the appearance of another, and of employing that reasoning which can alone assure us of any matter of fact or existence. We then call one object "cause" and the other "effect". David Hume

"The procedure of induction consists of accepting as true the simplest law that can be reconciled with our experiences. This procedure, however, has no logical justification but only a psychological one." Wittgenstein

"The world of Gods is as chaotic as our mortal world. What galls, is that while still sound of mind, one would by heading words of prophets, plunge himself into a depth of ruin…" Euripides

"What is the pragmatic difference between asserting that a system or state of affairs is undetermined and that a system is so complexly determined that no predictions can be reliably made?" Sydney Hook

4.3.1 An Ancient Conundrum

No process of nature is more fundamental to our perception of events that surround us than cause-and-effect. We see an event A, a bat striking a ball, and then we immediately see another event B, the ball fly through the air. We infer that event A caused B. Or precisely, of the two events which just occurred, A was the cause, B was the effect.

Understanding cause-and-effect is crucial for how humans develop options, and has become an innate need. In the wild, in nature, organisms survive by trail-and-error, with a single error is usually fatal. Understanding the natural processes of cause-and-effect gives humans the option of playing through the cause-and-effect scenario in their minds first, before the real life trail-and-error gamble is taken. Something Carl Popper called "letting your hypothesis die in your stead". When stalking dangerous beasts with Stone Age tools understanding beforehand the cause-and-effect of each action hunter and hunted will take greatly increases survival options once on the hunt. Today too it is vital that humans understand cause-and-effect. Especially we want to know things like the effects of pollution and the causes of cancer. We want to know what is causing a hole in the ozone layer, and what will be its effects on the human species. We want to know what causes war and tyranny and injustice in the world, and we want to know the effects of present society on children raised in broken homes, or in violence prone inner city areas.

But for all the urgency to understand practical cause-and-effect there is deep theoretical conundrum about the issue that has never been satisfactorily resolved. It concerns the totality of all cause-and-effect in the universe. Even from primitive times, from the hunt, humans realized that no matter how well they understood basic cause-and-effect that there was still a chance element; unforeseen or unpredictable. The gamble was always there. For a long time humans accepted this, because they knew that they could not understand everything. But once humans invented science and science showed that all effects had causes the curiosity was roused. What if science could explain every cause-and-effect in the universe, would the chance element disappear? The question has grave moral implications, because humans always assumed that their will was free. But with modern science, it seems that the more we learn about the history of an individual, the less inclined we are to hold that person morally culpable for his actions.

The first attempt to scientifically resolve the problem of all cause-and-effect in the universe began with Laplace (See 1.3 The Human Geodesic). Laplace lived in an age when scientists believed that the universe consisted of a huge swirling mass of interacting atoms. He proved that if the motion of an object like an atom could be specified for any point of time, a formula could describe the motion of that object throughout infinite time. With this formula it could be supposed that if sufficient motions of atoms were specified, then the behavior of the entire universe could be calculated out for all time. Laplace hypothesized that if an intelligent being called Laplace's Demon, see quote Chapter 1.3, could collect this information he would know every event in the universe, past, present, and future. The poet Shelley interpreted Laplace's teachings as a moral doctrine called Necessity explained in the opening quote of this chapter.

Few of us today would accept the doctrine of Necessity as moral law, though it is remarkably close to E O Wilson's perspective on the subject in his quote. Yet despite doubts mathematically Laplace was correct and scientists still use his equations today. If scientists launch an interplanetary probe like the famous Pioneer 10 spacecraft, it has traveled over nine billion kilometers in twenty-six years in space, Laplace's equations tell us how to set up the trajectory. Necessity will do the rest. Even so, nobody today would apply Laplace's equations to general problems especially encompassing the entire universe. The reason is that while the 26 years of Pioneer 10's travels is not a difficulty over billions of years another affect known as the Second Law of Thermodynamics would introduce errors in Laplace's equations not understood in Laplace's day. Plus Laplace's equations belong to a class of algorithms known as mechanics, which are time reversible and unbounded. But equations of the Second Law belong to a class of algorithms called thermodynamic processes, which are time irreversible and bounded. The two classes of algorithms have proven exceedingly difficult to combine. These difficulties, plus discovery of quantum mechanics and other chance elements, meant that for a while any exact specification of cause-and-effect in the universe had to be abandoned.

As we enter the Third Millennium though the two great theories of humanity's place in the universe, cosmology and human evolution, confront the same awesome problem of total cause-and-effect. Both theories appear to be seeking a single equation by which to specify the properties of existence, only we must explain what this involves. On one hand we have a debate over whether humans are free and morally accountable individuals. This is clearly important today because we observe much behavior we do not find acceptable, but there are also many debates over whom, if anybody including the individual, can be held accountable. Somewhat separate but also important certain projects labeled 'big science' are now consuming increasing chunks of taxpayer's money, which might say, go to other social programs or other science, more related to people's everyday needs. Only some projects vaguely related to the philosophical issue of cause-and-effect are also big science projects. One of these, the human genome project, is related to the issue that genes determine behavior. Other big science projects involve building giant particle accelerators like the infamous Texas super-collider project that was eventually cancelled. These particle accelerators are used in a search for an explanation of the fundamental causes of existence in the so-called Final Theory, or what Steven Hawking has called the Theory of Everything. If this theory is supposed to explain every cause-and-effect in the universe, some taxpayers and politicians will be asking if the huge funds involved for such projects could not be better spent in other areas.

Only there are many issues surrounding such projects. While say, the human genome project might imply we can discover genes shaping behavior, separate issues concern whether any organization should be allowed to patent DNA, or even whether genes are the ultimate cause of disease any more than bacteria are. For example, pollution, smoking, unhealthy diet and stressful living also causes sickness. So, should funds be spent on mapping the human genome, or trying to isolate social related causes of disease, which might prevent disease on a larger scale? The Theory of Everything too might not in the end be about every cause-and-effect in the universe, but discovering an ordered logic to physical laws. Yet, other science of a more practical nature might be drained of funds for the large particle accelerators. Plus all big, expensive high tech projects seem to be facing, ironically, the type of technological saturation that millions of years ago fueled human evolution. Technology changes so fast today that anything that will take more than ten years to build, like a new particle accelerator, might be out-of-date before it is finished. People have other reasons too for opposing building expensive particle accelerators, to do with a brute force approach to fundamental science that seems to consume a disproportionate fraction of any nation's total science budget. Only similar arguments of budget priority or brute force science might also be used to favor unmanned instead of manned space projects, plus it is still only a fraction of the money spent on defense. All these issues might have nothing to do with philosophical cause-and-effect or moral accountably, only Hawking himself has postulated that it might, so this has become another part of the debate.

In this book we only debate how these issues broadly apply to human options. Always, scientific knowledge enhances options, though this must be measured as a practical cost of how the knowledge was obtained against other ways to obtain knowledge. Even if philosophically misguided this author believes that results from both human genome or particle accelerator projects, carried out, will support the theories of this book. Even after the 80,000 odd human genes are mapped, there will be discovered no behavioral genes of the type postulated by evolutionary psychology. People will still need, more so, theories like the one in this book to explain human behavior, though if this is all that the human genome project will prove it will be an expensive way to reach so basic a conclusion. Except ironically, enthusiasm for genes determining behavior is often outside of those actually doing the gene mapping. Perhaps the pure researcher, knowing he needs public funding and support avoids the controversies over behavior this subject can engender, and focuses only on discovery of facts that can be medically useful. Similarly, any hint that expensive particle accelerators can resolve issues of moral accountability is probably a good argument for getting such projects cancelled and spending the money elsewhere. If such projects can increase options by explaining the fundamental nature of physical laws, that will support the theories of this book. But in two thousand years we have discovered only one persistent truth about how physical laws effect moral accountability. This is that if a person already holds a view on this subject, almost any theory of science can be interpreted by any argument, to justify to the holder of that view why he thinks it was correct all along.

This is why the practicality of calculating every cause-and-effect in the universe or how it could determine human choices is never the issue. Hawking say, is careful to explain that a full Theory of Everything (there are several cases of it) will leave humans free and morally responsible in practical terms. Wilson or Dawkins almost concede the same for genetically determined behavior. It is doubtful if even Laplace thought that calculating every cause-and-effect was practical. Instead, the Theory of Everything, population genetics, and Laplace's equations are an opportunity for humanity to increase its options by increasing its understanding. The philosophical debate too is not about whether every cause-and-effect in the universe could be calculated out by any practical method. Rather, we want to know,

The Theory of Options has an answer to both these questions, though not the usual ones.

4.3.2 Moral Accountability

To this author, the fascinating aspect of cause-and-effect is the scientific question. What is the relationship of the analytical truths of an equation to the empirical truths of the universe? This is fascinating because the answer, that there is no certain relationship, seems unimpeachable, though obviously not to everyone.

Yet, the obsession of humanity has been with the issue of moral accountability. It is almost as though humans realize in themselves or others an overwhelming moral imperfectability, and need some explanation of it. The dilemma is that regardless of what each person claims not to be aware of, humans seem to know very well to themselves the difference between moral right and wrong. Only persons discouragingly follow the latter, if only to a small degree. Reinforcing the problem is that while the totality of a person's actions might seem reprehensible in summation, it is difficult to pin down the wrong moral turn by small increments. We do what we do at the time, for reasons that press on us in that circumstance. If later we regret our actions it is still often hard to see how we would have behaved differently without better understanding the choices. Obviously many people feel this and argue this. Yet, religion, which greatly shapes humanity's moral outlook has taken an opposite view, insisting that the individual is culpable absolutely, before God, for every action. These very opposed views invariably clash and scientific theory is dragged in, almost as a referee.

In the Theory of Options we accept that this clash of moral outlooks exists only it is not one resolvable by appeals to theories of physics! As we shall point out equations are abstractions, which are connected logically only to each other, but not to outside existence by any association other than human impression. Morality must be the most complex phenomenon in the universe. Yet, some of the simplest physical effects in the universe, such as the three-body problem, or the bounded nature of processes, cannot be resolved completely by present levels of knowledge. Lacking this knowledge we could not specify a priori ("prior to" experience) that these are only problems of incomplete mathematics or data gathering. For all we can prove with present knowledge the material universe might be in a state of permanent "fuzziness" in which moral knowledge, for all we know, is one of the few factors of certainty. The precision of equations does not prove the precision of existence any more than p to one hundred decimal places proves the roundness of a pipe. Or even if the dilemma of moral accountability lay in equations it would not be in equations soluble within the lifetime of any individual reading this book. Rather issues of morality must be faced in their own terms. Even the religious argument, paradoxically to an atheist, must hold no force other than what is said. Teachers of religious morality teach what they teach. If we need to appeal to theories of physics to counter the moral views of religion it only shows the weakness of secular moral theory unable to stand on its own merits.

The only science that can remotely deal with morality then, outside of legal or ethical argument, is evolution. Only here too we have only a partially complete theory at least for complex issues such as morality. As explained the equations of gene flow allegedly explaining moral behavior, or lack of it, consider the fitness of each gene as dependent on the reproductive fitness of the individual in which the gene is ensconced. But 99% of expressed genes in humans are not dependent on fitness in any one individual and will pass on anyway. There are no equations to account for this, just as, ironically, there are no equations to account for the evolution of sex, even for sex in primitive life devoid of its human complications. Even without equations present theory has no agreed, even a verbal model, of the evolution of human sexuality, moral behavior or the large brain. So how from such an incomplete theory could we draw scientifically definitive ethical arguments, apart from expressing a point of view? And as we have also shown, merely expressing a viewpoint can be as much justified by quoting classical literature as by any theory of science.

If anything, in our new model of evolution we propose that morality far from deriving from deterministic cause-and-effect, evolves as a means of complex evaluation in an indeterminate, highly variable universe. Over the history of life we see the brain evolves through different levels of complexity, from simple reflex, to learning, to complex evaluation. At each stage response to stimulus becomes more generalized. Pain is a sentient generalization of all stimuli requiring retreat. Fear is an emotional generalization of situations causing pain. Caution is a principled generalization about all situations that result in unpleasantness. Finally, humans are equipped to face situations so probabilistic that they can only be evaluated morally. We can also show that brains which can evaluate situations morally offer direct fitness advantages to individuals, if for no other reason than they allow much larger, faster evolving brains. Besides, we only think of morals in terms of honesty or cheating. But technical morality is an ability to resolve choices by judgement or principle, especially when facing the totally unexpected. It would be like sending a robot probe to another planet. If the robot can only perform mechanical, cause-and-effect responses, it will be less valuable to itself or the mission than if it could make on the spot reassessments of the unexpected, based on principle.

Moreover, having moral values increases options in an indeterminate world, because the broadest option is when ultimate constraints on behavior are non-material. Non-material constraints are easy to break, which leads to conceptual difficulties over how they evolved, because when constraints are weak cheats will take advantage. Except a statistical population of cheats exists at every level of evolution, from DNA to humans. When any species evolves it sweeps along its population of cheats with it, but this does not limit the gross macro pathways of life. Studies show that cheats are usually controlled or confined to statistically tolerable levels or they will destroy a species. Every change in evolution comes at a cost, including the cost of dealing with cheats. Humans paid huge evolutionary costs to evolve a large brain, behavioral options, moral restraints and cohesive groups. So if they could have avoided evolving morally constrained behavior they would have, cheats or not. But other evolutionary pressures confined humans within a fitness pathway where all the niches that could be filled by creatures with impulsive behavior were already saturated. In this sense, the argument of evolution does not support the idea that humans are not morally accountable. On the contrary, we would hold a human more accountable than a dog, and dog more accountable than a chicken, based on what we know as each creature's capacity to evaluate. So, we could hardly argue that attributes such as moral behavior, which humans evolved to enhance options, should be thrown away because of a deterministic argument. It is still a modern choice for humans to abandon the moral mechanisms we evolved with, only we might not last long as a species if we do.

So, the scientific issue of cause-and-effect should not bear on the ethical issue of moral accountability, in any manner that we can resolve with present knowledge. Rather, it seems a misunderstanding of the cause of human ethical dilemma that is the problem. This leads us to grasp at so-called scientific palliatives to assuage moral doubts. But it is misunderstanding of the scientific issues too that allows us to think that a mere equation, independent of other knowledge, can distinguish for us whether the universe is determinate or indeterminate. This is the next problem.

4.3.3 The Theory of Everything

The scientific dilemma of cause-and-effect, free as it should be of any moral implications, concerns how humans use mathematics. If as a child we are told that five apples plus seven apples gives twelve apples, we might think that this is because some law of nature ensures that a combination of five plus seven always produces twelve. In a way it does, and the great philosopher Kant argued that the equality 5 + 7 = 12 was a synthetical truth, in that the number 12 was not inherent in the arithmetic 5 + 7.

The difficulty however is that the equation 5 +7 = 12 written down in human symbols, could as easily be written 5 + 7 = 14 in an octal counting system, or 5 + 7 = C in a hexi-decimal system. If anything, once we knew what the symbols '5', '7', '+', '=' and '12' mean, 5 + 7 = 12 could as likely be a code that 'I am using decimal', whereas 5 + 7 = 14 would be the code that 'I am using octal'. So the symbols '5', '7', '+', '=' and '12' in this instance only define the arithmetical system we are using. Even this might be meaningless to beings not familiar with arithmetic systems, such as members one African tribe who reportedly can only count by odd and even pairs. If anything, in Chapter 1.4 we demonstrated how all symbols in an equation are totally specified by humans, and not directly linked to physical cause-and-effect. This argument leads to a strange conclusion that all equations, whether 5 +7 = 12 or E = mc2, are really tautologies. To be useful equations must be logically consistent within themselves, and this is what the '=' sign specifies. But equations by themselves do not demonstrate the truths of nature through logical necessity, until we specify the physical equivalent of each term in the equation, and then confirm the results by measurement.

This tautology to equations is also why so far all attempts to reduce the laws of the universe to a single set of equations have proven a failure. Now there have been practical, research difficulties why, for any given level of knowledge such laws could not be found. As we saw with Laplace's equations these did not take into account quantum, relativistic, or probability effects later found to apply to any totality of events. Ever since, any new laws that attempted to be more general were still found to be only mathematical descriptions of processes in nature that were deeper and more complex. Especially, every equation describing reality has had to depend on physical constants, like the gravitational constant. So far, there is no logic of why these constants take the values they do, apart from it being a value that was measured. This is why there is now much excitement over the 'Theory of Everything'. If in Newton's theory we adjusted the value of the gravitational constant, we would still have a logically consistent theory of gravity, just with different values. But within any equations qualifying as a Theory of Everything any adjustments of the values from what they are measured often leads to absurd results logically, such as infinitely large values where none exist. This temps us to wonder if the physical constants that exist are the only logically possible ones that could exist, which accounts for why the universe is the way it is. No comprehensive set of equations has been discovered yet that can account for all the physical constants this way. But scientists are encouraged because at least some fundamental forces now seem to exist the way they do because it is logically consistent for them not to do so. If this pattern could be extended into a general one, we could have a final theory that needs no further explanation in terms of fundamental laws.

Still, despite that the above is still only a supposition, we doubt if such an esoteric set of laws will have much bearing on moral accountability. If anything, it obfuscates the purpose of the Theory of Everything to raise the issue of free will or moral accountability at all. Except, this still leaves unresolved the true relationship of formalized abstractions in the human mind, such as mathematics, to the physical nature of existence. The thesis of this book has been that human options are maximized if we split our understanding of reality between analytical truths, which are logically consistent, and empirical truths, which we measure. This author introduced the hypothesis of how this split makes sense in terms of how the brain evolved, but the concept of splitting ideas between logical and empirical truths is an ancient one. It began perhaps with Pythagoras. This philosophy led to the dualism of Descartes, Hume's skepticism, and the analytical logic of Wittgenstein. This was also the early view at least of Einstein and of the Copenhagen School in physics. Only it seems that within a Theory of Everything mathematical abstractions and physical law will at last be coincident. The argument is that until we arrive at the Theory of Everything mathematics is still slightly abstracted from underlying physical reality. But with progressive refinement of human knowledge we push our understanding both of mathematics and measured reality to a point where they become the same quality.

We have no grounds for arguing that the above supposition could not be correct. Just it has not occurred yet, so until a Theory of Everything is proven along the lines predicted the split between abstraction and measurement might still offer the maximum options of understanding. This is because if we observe events in one circumstance, which appear to follow mathematical laws, we can freely investigate if it would be non-contradictory for the laws to operate in a different circumstance. This increases options of how to use information. Laplace demonstrated that if Newton's laws applied at any instant of time it was mathematically non-contradictory for them to apply throughout infinite time. Laplacian trajectories will not hold over infinite time because of other effects, but they can apply to space flight and planetary motions on the time scales in which humans study them. Even then Laplace's equations only apply as an approximation for trajectories such as the precession of the Planet Mercury. (Due to its close proximity to the gravitational pull of the Sun, Mercury suffers an effect of relativity unknown in Laplace's day.) So, we cannot say that mathematical laws are produced in the human brain by physical cause-and-effect in nature. The only physical connection to effects striking humans as mental impressions is sense data such as sight, sound, and smell. Humans, cut off from mentally intelligible direct cause-and-effect of nature use imaginative powers inherent in the higher cortex to abstract the observations of nature into laws of general use. Mathematics becomes to humans the most powerful single extension of this imaginative process precisely because it exists to us as pure symbolism, bound only by the laws of its own rigor.

Only the Theory of Everything seems to imply that mathematics is not pure symbolism, because certain of its equations require that the physical constants of the universe take the values they do. Only what this means is unresolved. Once before a set of equations produced a physical constant, which was the speed of light in Maxwell's famous equations, leading to the discovery of radio waves. Except what happened was that the physical value of the speed of light arose from other constants inherent to the founding equations such the electric and magnetic permittivity constants. So, in this sense Maxwell's equations were still a tautology. It was an empirical necessity that the permittivity constants appeared in equations humans used to calculate the measured behavior of electric and magnetic fields. But it was a logical necessity, like 5 + 7 = 12, that this information manipulated a certain way would yield the speed of light. We understand that in Theory of Everything the constants are also a measured necessity. Just that if one tries to vary them it yields absurd results by logical necessity, like a universe that curls up on itself. This problem is resolved by the principle that a universe in which intelligent beings exist must take certain properties, but we are not sure if this assumption is also a measured input rather than logical one. For example, the statement that intelligent beings must exist in a universe they can measure might seem a self-evident truth. Except intelligent beings still need to evolve, and the conditions for a universe in which they can evolve is not self-evident at all. Perhaps missing then from the simplistic Theory of Everything is a further super-equation, which would require that intelligent life evolve. Maybe that super-equation would contain other constants that we are not aware of, that creep into our equations. Perhaps when we assumed that any non-absurd universe must allow intelligent creatures, we also assumed certain constants that are inherent to the evolution of life that we are also unaware of.

In this case the Theory of Everything too is only a tautology, at least in terms of its formulation. Only it is a very advanced tautology in that it requires us to calculate out not just the origin of the universe, but the origin of intelligent life to yield the full range of constants we assumed in it. Ironically then, we argued in earlier chapters that the current equations of gene flow do not appear to us complete in an ability to account for large-scale evolutionary events such as the origin of intelligent life. We further argued that large-scale gene flow would likely include an effect of stable genes occupying a form of probability spectrum, which could account for the high conservation of many genes, independent of single reproductive events. Yet, any equation including all these advanced effects of the evolution of life further combined with an equation of the origins of the universe is beyond our present understanding. This is the misnomer of calling it a Theory of Everything, when it is clearly not about everything, including the evolution of life and intelligence. Even so, that such an equation might be a tautology does not belie its significance. Maxwell's equations were also a tautology, but these led to the discovery of radio waves. And Laplace's equations are a tautology, but they allow modern aeronautics and interplanetary flight. And just as radio communications began with Maxwell's equations all manner of 'Star Trek' technology might be potentially available to humans once the Theory of Everything yields its secrets. We do not know.

Just that until the Theory of Everything does yield its secrets we should continue treating all equations as tautologies as this yields maximum options of understanding. Precisely when we encounter complex tautologies like the Theory of Everything is when we are mostly likely to make errors. In this case, the error would be that empirical truths of the universe could be derived wholly within the logical necessities of mathematics. So, while we do not rule out that equations could provide a logical explanation of existence, before accepting that a logical universe must allow evolution of intelligent life it would still be wise to calculate this assumption out in full. Extension the Theory of Everything should increase understanding in this case by demonstrating that, in this author's opinion, the existing equations of how life evolved are not a complete set anyway. The ultimate test too of the Theory of Everything will be whether it increases human options. If it does, we learn something from it related to how our corner of the physical universe exists. If it does not increase our options, it explains nothing about how the universe exists in a manner that we can test in any meaningful way. So, we would not expect a correct Theory of Everything to restrict human options by showing that all choices are determined, but to instead delineate more clearly what the real human choices are.

Yet if the universe works to any degree by cause-and-effect, but the chain of cause-and-effect becomes broken in the human mind, how then does mind stand in relation to the rest of the universe? Steven Weinberg, confident elsewhere in discovering a Final Theory has still conceded that there remains a "stubborn duality" to nature. He appears to mean that although living and innate matter obeys the same physical laws, it is difficult to pin down the workings of mind precisely, especially as an observer.

This is the second great problem of cause-and-effect, so now let us examine it more closely.

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