Metaphysics

So far so good. We have arrived at the insight — through our anti-Cartesian Cartesian meditation — that we limited beings live in a large world, as opposed to the small world of the Laplacean demon, the mechanism, the machine.

At this point, some mechanicist will get up, raise their fist, and proclaim that this is all just nonsense, indoctrinated hippie ideology, wishful thinking, bad philosophy based on fuzzy feelings rather than hard facts and rigorous reasoning (like their more rational view of the world). People, and in fact all organisms, are just sophisticated automata! Intricate machines. Suck it up, buttercup. It’s a cold, deterministic, meaningless, and indifferent world out there. Face it. This is the human condition. Anyway, can any of this be empirically tested? No? If not, then it’s all just baseless speculation.

We often get accused of engineering our philosophy around our longing for a world full of meaning, a world with a radically open-ended future, a world in which life is a precious and extraordinary phenomenon irreducible to the mechanistic workings of a machine. “A magical universe created by fairies” as one particularly unwavering machine-thinker recently called it.
 
We find this criticism strange. Who would not want to build their worldview on such beautiful ideas? What exactly is the point of assuming that the universe is a cold and uncaring machine? That everything is ultimately meaningless because there is no way to escape our predetermined fate? And where is the magic in our account? The fairies, however much we adore them, are simply not there. What we suggest here is perfectly naturalistic, as hard-nosed and compatible with contemporary science as any mechanistic philosophy we’ve seen. Actually, more so, as we already pointed out.

But then, of course, we do have to admit that the criticism hits home in some way. These are the ideas that form the core of our philosophy, they do feel good, and they do bias our view of the world. There can be little doubt about that. This is one of the main reasons why we’ll provide a careful justification of our assumptions and a thorough analysis of their consequences in the chapters that follow.

At the same time, this mechanicist reproach manages to completely miss the point. Mechanistic philosophy (including the contemporary idea that the world is some kind of computer) is no less biassed, no more solid or empirically grounded, than the worldview we propose here. Neither view can simply be justified by objective and incontrovertible scientific fact. Neither can simply be empirically tested. Both are based on unproven philosophical or — dare we say the word — metaphysical presuppositions.

​The problem is that mechanicists often don’t recognize or understand this. We’re not drawing a straw man here. Take, for example, the late physicist Stephen Hawking, who famously announced — in a book from 2010 called “The Grand Design” — that “philosophy is dead.” Alas, Prof. Hawking failed to realise that this, in itself, is a philosophical statement and by uttering it he, personally, was helping to keep philosophy alive. Elementary, Dr. Hawking. But the irony seemed lost on him. What naïve realists can’t admit: no matter how hard you try, you cannot ground science in science. Not that we want to pick on the late Professor Hawking specifically: there are countless other examples of scientists or science communicators uttering sentiments like “there is nothing but physics.” Well, again, that is philosophy!

As philosopher Dan Dennett once put it: “There is no such thing as philosophy-free science; there is only science whose philosophical baggage is taken on board without examination.” And, yes, we are accusing many (sometimes very prominent) mechanicists of doing exactly that. Just how much unexamined baggage today’s machine view of the world carries is the topic of this and the following chapter. It’s quite staggering, really.

To understand how this philosophical baggage accumulated, and what it is exactly, we must take a closer look at the history of mechanicist science. To begin with, let’s reiterate that the idea of the world being a machine springs from Descartes’ faith in god. To him, the universe had to be a clockwork since an all-powerful and all-knowing deity would not build the universe any other way. Of course, we’ve come a long way since Descartes’ time. And many people now believe that the mechanistic worldview has since been confirmed beyond reasonable doubt by its empirical success. We no longer need god to justify it. It simply justifies itself. 

​But this is rationalisation, rather than justification. It is based on a simple logical fallacy. The fact that science inspired by mechanical philosophy solves many problems that are important to us does not at all imply that it also succeeds at revealing the world as it truly is. In particular, it does not follow at all that the world is a mechanism. It simply shows that mechanistic science is good at solving certain kinds of problems that are important to us. Empirical success is never sufficient to guarantee metaphysical truth. 

How can we be sure then that our science really tells us how the world actually is? This and no other way? A successful problem solution may work for all the wrong reasons. You never know. And, sadly, you will probably never know, at least not for sure. As we’ve said before, scientific knowledge is piecemeal and imperfect by its very nature. In fact, it must remain provisional by definition, amenable to improvement and revision through future research. But it is also not completely contingent on human history and society, not just a consequence of social discourses and power struggles. It arises and evolves out of our very real and deliberate encounters with the large world we live in. It can tell us about how the world actually is, but only from our very peculiar and human vantage point. 

And so we arrive, yet again, at an absolutely central distinction: our map is not the territory. It is not sane or safe to base your entire worldview on any particular map you’ve made, no matter how useful it has been to you in the past.

A map is a model of selected aspects of the world. It is useful because it highlights some relevant features of the territory. But to achieve this, it has to omit a lot of others. It has to abstract away from detail: a map on the same scale as the terrain is not a useful map, as Borges reminds us in his wonderful short story “On Exactitude in Science.” Instead, a hiking map highlights terrain and trails, a road map roads and towns, a nautical navigation chart harbours, coastlines, and waterways, a prospecting map reveals what is beneath the ground, an atlas of your local watershed visualises networks of ecological, social, and economic relations. Maps also often distort: a public transport map, for instance, deliberately twists and squeezes the physical distances between stops to let you focus on connectivity.

There are plenty more examples, yet this much should be clear by now: what each map contains not only depends on the territory, but also on the purpose of the map. In other words, a map, as a model of the world, is a tool with a specific function. It is not simply right or wrong. Instead, maps/models are either useful in a given situation, adequate for a specific purpose, or they are not. Indeed, all scientific theories consist of families of models, and models (like maps) are tools for thinking about the world, not necessarily accurate depictions of how the world exactly is in all its glorious detail. This distinction is incredibly important. You can and should use maps to form an overall view of the territory (in fact, as we shall see, there is no other way to glimpse the terrain). But do not get trapped inside the map! That is a terrible move.

Even the fundamental theories of physics today ― quantum mechanics and relativity ― are nothing but very broad and powerful families of scientific models, that is, very sophisticated, precise, and extensive collections of maps. That’s why it is not a good idea to assume all knowledge of the world flows from them, while presuming that whatever lies outside these maps’ range is irrelevant metaphysical speculation or mere subjective illusion. After all, these theories are known to be imperfect. Even worse, quantum mechanics and general relativity are inconsistent with each other. They clash, which evidently means they can’t both be universally true ― cannot possibly be complete descriptions of the world. 

More generally, we should never forget that all scientific models and theories (whether in physics or anywhere else) are based on a range of simplifying assumptions ― abstractions, approximations, and idealisations ― which, as we have seen above, is precisely what renders them useful in their own particular domain. Mechanistic theories are no exception. While they are massively useful to explain and predict an extremely wide range of natural phenomena, they are still only limited maps that cover specific aspects of an unfathomably large world. And the irony is: the simplifications that make them useful as tools are, at the same time, the ones that cause mechanicism to fail as a worldview.

​Plato


Ok, ok, we hear you say. I get the idea: map and territory. But what are those limitations of the mechanistic map? What exactly is the philosophical baggage of the machine view of the world?

The answer to this question is more subtle and abstract than you may think. It goes deep and far back into the history of philosophy and science. But we are no historians, and it is not our aim here to present a rigorous and rich account of conceptual history. Instead, we simply pick out three crucial decisions that were made before and around the onset of the modern age that, together, pretty much circumscribe modern mechanistic science. You will notice that none of them is based on empirical evidence, and none of them is itself scientific in nature. 

Instead, these are philosophical choices regarding the metaphysics and methodology a mechanistic scientist ought to commit to. They are the philosophical baggage of the machine view, and we can only understand them in the peculiar context in which they arose.

As the first step on our journey back in time, let us rewind to the very beginning: the first traces of modern science, more than 2,500 years ago, were off to a surprisingly good start! We’ve already encountered Anaximander’s apeiron: the boundless and indefinite as the foundation of a naturalistic view of the world. Sounds very much like our large world! We’ll also encounter Heraclitus’ maxim that everything flows (πάντα ῥεῖ) very soon. We think these are solid principles to build our knowledge on. 

However, right around the same presocratic time, natural philosophy takes a number of decisive turns in directions that come to dominate its trajectory for centuries, and not always in a good way. 

The first series of such turns converges on a worldview we now call Platonism. At its very core is the idea that some abstract domain is more real than the messy world of phenomena we can actually experience, as most famously captured by Plato’s parable of the cave. More on that in a second. Before we can go into it, we must trace the origins of this rather extraordinary idea to its earliest beginnings. 

It starts with a presocratic philosopher who may, in fact, have been Anaximander’s disciple. Parmenides is often called the first metaphysician. Like Anaximander and many others among his presocratic colleagues, he strongly argued for the unity of the world, the fact that everything must be based on some underlying universal “substance.” At the time, the term “substance” didn’t mean anything like “matter” or “stuff” as it does now. Instead, it implies some kind of principle that “stands below” (sub-stance) the perceived phenomena. 
While it is hard to put a finger on what exactly the apeiron is, Parmenides’ unitary substance is easier to grasp: what he calls “existence” fills every nook and cranny of the world. There can be no truly empty space, no void, that is free of it. And for this reason, Parmenides argues, there can be no true movement or flow. Change must always be apparent, superficial, because underneath there is nowhere for the foundational substance to go to, nothing for it to become. There is only it ― everywhere, forever. And so, Parmenides came to believe (contra Heraclitus) that the only thing that is truly real is unchanging, unending, and ubiquitous existence. Our senses deceive us! And so begins the millennia-old quest of the Western mind to conjure up an abstract world that is more real than the real world. 

This counterintuitive idea was taken up by the Pythagoreans, who took it an essential step further by claiming that everything not only exists, but everything is number. And even though Pythagoras and his followers made this claim with mystical (and even occult) purposes in mind, it will instantly appear familiar to anyone used to thinking of the world in mechanistic terms. 

Specifically, the Pythagoreans were interested in euphonies, which are pleasant musical harmonies produced by strings with particular length ratios, and compared these to manifestations of similar harmonic ratios or relationships in the cosmos, which hinted at a law-like, elegant, and self-consistent underlying structure. And thus, the idea of universal mathematical laws underlying the phenomena of the world was born. Again, an abstract world ― more real than the real one.   

While the Pythagoreans remained mystical and somewhat vague in their use of abstraction, Plato was more explicit. In book VII of this “Republic,” he describes his theory of forms through the allegory of a group of people chained to the wall of a dark cave. Behind this wall is a source of light (either a fire or the opening of the cave depending on how the story is told) which the chained people cannot see. On top of the wall, in front of the source of light, objects are passing to and fro, casting shadows that move across the cave wall opposite the observers. All the prisoners in the cave can observe are these shadows ― a powerful metaphor for the reality we experience: mere appearances warped by our imperfect human senses.

One particularly daring prisoner manages to unshackle herself and climb the wall behind her. It is thus that the objects casting the shadows are revealed to her, and she realises that she has been deceived during all the time she spent inside the cave. These objects are Plato’s ideal forms. They go beyond the flickering and indistinct shadows on the wall, representing the “idea” behind each imperfect projection. For Plato, they are the only source of true knowledge ― more real than the fickle appearances experienced by the other prisoners in the cave.

Take, as an example, the idea of a cat. Somehow, it manages to perfectly capture the notion of felinity, the essence of catness. In contrast, actual living felines ― from the domesticated tabby purring on your lap (or, more likely, on the keyboard of your laptop) to the elusive and elegant snow leopard roaming the remotest regions of the Himalayas ― only embody imperfect variations on that theme. As individuals, they are mere shadows of their ideal form. The idea of felinity is what unites them, what defines their very nature, and only if you understand what this idea is, will you truly understand what it means for something to be a cat. 

Plato’s forms solve the philosophical problem of universals: why are there recognizable classes of (often very) variable things? But they also play many other important roles in Plato’s philosophy. An aspect of the story that is often neglected is the transformation of the escaped prisoner herself. She (the philosopher) goes back to her fellow prisoners in the cave, excitedly telling them about what she saw. Unfortunately, the others are neither convinced by her account, nor particularly interested in learning about the true forms behind the appearances they are so familiar with. 

In other words, the other prisoners are perfectly happy in their cave, unable and unwilling to see the world through the eyes of the escaped philosopher. She is no longer like them because she had a transformative experience while they did not see any of the real objects first-hand. This is why they cannot relate to her tale. She now sees the world with different eyes. This transformative journey is called anagoge, which is ancient Greek for “upwards climb” ― the escape from the illusions of the cave. It is one of the central foundations of Plato’s theory of knowledge, his epistemology: to truly know is to transcend appearances and to perceive the realm of perfect forms.

But where is this realm? How can we get there? In the dialogue called “Phaedo,” Plato still tells us it is a region of the physical world, located high above the surface of the Earth. But then he changes his mind, relating in the “Phaedrus” that his ideal forms are located in the hyperuranion, a “place beyond heaven,” which we now call the Platonic realm. It is a perfect, abstract, and eternal realm beyond the messiness, violence, and decay of our everyday world. Does that sound familiar somehow?

It does, because it is. To make a very long story short, the Platonic Realm became ― via Neoplatonism and Saint Augustine ― the Christian dogma of heaven: an eternal and flawless domain beyond and above the impure and messy physical world we live in. And so it turned into one of the most important metaphysical concepts in human history, shaping centuries of cultural evolution and historical events, first in the Western hemisphere and then across the globe. But, you may wonder, what does all of this have to do with mechanicist science and the machine view of the world?

Well, we need not remind you again just how much Descartes was influenced by his Christian belief. More generally, the idea that the world is governed by universal yet unseen laws came easily to many of the natural philosophers of the scientific revolution not despite but because of their being deeply steeped in Christian metaphysics. They assumed the cosmos had to be governed by general principles because god would not have created it otherwise.

And they did not interpret the universal laws they sought to uncover as just some model, some imperfect map, a mere tool to understand the territory that is the real world of actual experiences. Instead, they considered these abstract laws to have an existence of their own, to lie above and beyond the messy realm of observable phenomena ― our experience an impure reflection of the flawless and eternal workings of these universal principles.

And thus the mechanistic map became the territory, right away, at the time of its conception. And all because of religion, not science.




​Aristotle


So, the belief in the reality of abstract, unchanging, universal laws above and beyond the messy world of experienced phenomena is the first piece of mechanistic baggage ― the conceptual rucksack of the believer in a machine world. At the same time, it is also one of the most powerful tools in the mechanistic toolkit. Our monumental quest to uncover these universal laws explains much of the empirical success of science over the past 400 years. It continues to motivate and drive scientists, and not only those interested in the problems of fundamental physics. A “theory of everything” may remain elusive, but it is still a major windmill for all kinds of researchers to chase.

On top of this, there are two other pieces of luggage we must talk about. For the second bag, a bulky suitcase with broken wheels, we have to blame Aristotle. And, just like the belief in universal laws, this one is simultaneously a feature of the mechanistic program and a bug of the machine view of the world.

At the heart of Aristotle’s thinking lies the idea that philosophy (and thus science these days) is all about explaining the causal structure of the world. For this reason, Aristotle thought and wrote a lot about causality. It can be a bit difficult to understand his ideas from our modern point of view, because he treats this topic in a way that is very different from how we think about cause and effect today.

To Aristotle, causality is intimately tied to explanation. He formulates it in terms of different ways by which we can answer the question “why?” In fact, the Greek word aitia (αίτία) he uses for “causes,” can just as well be translated as “explanations.” Maybe, we can follow our friend and colleague, biochemist Jannie Hofmeyr, and think of these aitia as “becauses,” to highlight how they differ from our contemporary concept of causation.

Famously, Aristotle figured out that there were exactly four different ways in which you can answer “why” questions about any material object. As an example, let’s ask: why this statue of Aristotle?

1. Because it is made of marble. This is the statue’s material cause.
2. Because it is a statue of Aristotle (and no-one else). This is the statue’s formal cause.
3. Because it was made by a sculptor (with her tools). This is the statue’s efficient cause.
4. Because it was made for the purpose of honouring Aristotle. This is the statue’s final cause.

Therefore, every object in the world has multiple kinds of becauses that explain its existence. We need all four of them to truly know what it is. In Aristotle’s view, what we know about the world and what exists are therefore tightly connected. This will be extremely important for our argument later on. A causal account of reality for Aristotle is an explanation that makes sense to us human beings.

In contrast, contemporary science, when talking about cause and effect, has a much more restricted take, which is limited to Aristotle’s category of efficient (be)cause. We’ll see later on that causation is still a difficult topic for philosophers and scientists today ― its manifestations unruly and diverse ― but, basically, causal events (to a modern scientist) are those that contribute to the generation of other events in some way. Because science has a materialist outlook, the material cause is also implicitly presupposed (things are made of stuff, obviously). But this is not considered to be particularly interesting. In contrast, we rarely talk about formal causes today and, worst of all, final causes are a big no-go. We’ll see why in a second.

All of this is important to know, if we are to understand what happened next: Aristotle, quite reasonably, argued that it is not ever okay to answer the question “why X” with “X.” Let that sink in for a moment. If you ask why something exists, you can’t just say “because it does so.” That’s a vacuous tautology. It is trivially true and thus explains absolutely nothing. So not a valid way to answer the question “why.” In Aristotle’s context, it makes all the sense in the world to outlaw it.

Aristotle did grant one single exception: something needs to be at the very beginning of everything that is caused. He called that something the unmoved or prime mover, the first uncaused cause. Something like god, as Aristotle would have it, or maybe the Big Bang, if you prefer modern scientific cosmology. Nothing beyond the prime mover is allowed to be uncaused, or sole cause of itself.

The Aristotelian prohibition of circular self-causation then got translated into the modern context of scientific (physical) causality by Isaac Newton. This is described in great detail in philosopher Alicia Juarrero’s book “Dynamics in Action.” In summary: nothing in science is allowed to (efficiently) cause itself. This means that if I want to scientifically explain “why X,” it will still not do to say “because X.” But that is not all.

Newton used the prohibition of circular causation, in particular, to ban all final causes from science. If you interpret all causes as physical phenomena (rather than ways of explaining the existence of things) then the final cause looks like it’s breaking basic laws of physics, and also common sense. If you ask what something is for (“wings are for flying”), then you automatically imply that the purpose of the thing is the cause that brought it into existence. But how can something be brought into existence by what it’s for? Do wings evolve and develop towards the purpose of flying? Doesn’t this imply that the purpose of a thing would have to pre-exist it? It looks like it is pulled from the future rather than caused by its past? This makes no sense. We’ll revisit this important problem of teleology in a short while.

For now, it should be clear why circular causation is not acceptable to a strict mechanicist. First, as we have just seen, it seems to go against the flow of time. What something is for cannot physically bring it into being. Second, nothing can be caused only by itself. That would go against the kind of weak determinism we argued earlier was necessary for science: everything should have a cause. But if we start going around in circles, this mandate of unbroken causal descendance seems to be violated.

The underlying philosophical problem is that it’s not the same to say “you cannot explain X by X” (what Aristotle does) and “X cannot be physically caused by X” (Newton’s take). The first leads to a logical problem (a tautology) in the realm of human explanation, and is rightfully excluded. Scientific explanations should never be based on logical fallacies. That would be inconsistent. In contrast, the second is an unproven assumption about the world which would need to be empirically assessed.

But guess what: it never was. Ever since Newton adopted it into his framework from Aristotle, we have just taken it for granted. And this has to do with the third piece of philosophical baggage, which Newton himself introduced to modern mechanistic science. In fact, it may just be his greatest achievement. It is an eminently practical piece of luggage. Let’s say it’s like a duffle bag: light to carry, with a flexible shape and ample room to pack stuff into.


​Newton


Newton’s duffle bag is the simple idea that the laws or rules that govern motion are independent of the current state of the world: they don’t change depending on what the world is like at any given moment in time. It is closely related to the assumption that there are unchanging, universal laws in the first place. It also connects to the prohibition of self-causation since that implies a state-dependence of the rules we will outline in the next chapter. 

But it goes further than that. For one, it is not restricted to universal laws, but can also apply to the rules governing local models used for mechanistic explanation, let’s say in biology or neuroscience. We’ll come back to the issue of models versus general laws later. For now, we’ll just say that we need to understand what Newton’s separation of rules or laws and state means exactly, and why this assumed separation is not grounded in science (but rather in philosophy), if we want to understand the power and the limitations of mechanistic science today.

Remember that Descartes’ original mechanistic worldview stipulated a kind of “billiard ball” universe, which was completely filled with material components bumping into each other. He took the metaphor of the clockwork rather seriously: mechanistic forces are mediated by something like cogwheels gripping and moving each other. In this view, there has to be physical contact for one thing to affect another. 

This approach was simple, neat, and convincing as a philosophical worldview, but severely limited in its applicability in practice. Within the Cartesian framework, it was difficult to make generalisations or predictions about the behaviour of different physical systems, because the whole world was a tangled mess of physically interacting particles.
This changed radically with the conceptual revolution brought about by Newton just a few decades after Descartes. This revolution completely overturned humanity’s view of the world yet again. Only through Newton did the machine universe become truly controllable and predictable. 

This was because Newton properly mathematicised the mechanistic worldview. The quote that “the laws of Nature are written in the language of mathematics” is attributed to Galileo Galilei. However, it was Newton who came up with the first generalised mathematical theory of reality, while previous efforts at mathematicising physical processes and phenomena remained either mystical and vague (like the Pythagoreans) or restricted to a local scale (like Galileo).

The importance of Newton’s work simply cannot be overstated. Yet we rarely recognize what Newton’s truly biggest achievement was. Yes, there was that apple falling on his head, and the daring extrapolation that planets fall around the sun in just the same way. Yes, there was the insight that the rest state of objects is not to stand still (like the ancients and Descartes believed, and common sense suggests), but to remain in straight unperturbed motion. Yes, Newton proposed a whole new theory of optics. And, yes, he (in parallel with Gottfried Wilhelm Leibniz) came up with a powerful mathematical tool called infinitesimal calculus, enabling him to formulate his mechanics, which provides a unified framework for how any physical object behaves under the influence of forces that can act on it from a distance.

All these contributions are momentous, unprecedented, radical. But their influence on today’s science all pale in comparison with Newton’s duffle bag: his separation of the dynamical laws that govern motion from the state that the world is actually in. It is this deceptively simple move that rendered the world calculable, that made it predictable. Nobody had ever attempted anything like it before. 

Arguably, Newton’s laws are the first true shot at computing the world. Just to keep things in perspective: this happened about four days ago in our compressed 75-year history of the genus Homo. To think that the world is globally predictable is not something that occurred rapidly or came naturally to human beings. But when it happened, it had truly earth-shaking consequences.

Using the word “computing” here is not an anachronism, by the way. The term entered the English language right around the time of Descartes and Newton, derived (via French) from the Latin verb “computare:” “to count, sum up, reckon together.” But the idea of computing for general prediction had simply not existed before Newton. 

The premodern world used mathematics in a very different way. It was a way of appreciating the hidden principles behind appearances, as we have seen with the Pythagoreans above, who saw deep meaning at work in abstract relations such as the harmony of the spheres. Similarly, Plato used his geometrical solids as exemplars for his world of ideal forms, contrasting them to their imperfect reflections (i.e., instantiations) in the real world. 

Right up to the Renaissance and the time of the scientific revolution, maths was predominantly used to justify knowledge about the world based on aesthetic choices and intuitively appealing explanations. For instance, many scholars doubted Kepler’s laws of planetary motion — rigorously based on Tycho Brahe’s extensive and meticulous observations — because they feature elliptical rather than perfectly circular planetary orbits. Large parts of the intellectual establishment at the time considered this a totally legitimate reason for rejection. Remember Descartes’ claim that the world had to be perfect, because it was created by an unerring deity. Very few people doubted this 400 years ago.

Mathematics was also used, since its early beginnings, as a tool for solving specific problems in engineering, or what we would now call technoscience. There is Archimedes in his bathtub who, among many other things, gave us laws for the behaviour of levers and buoyant objects, the concept of “centre of gravity,” and the first recorded approximation of π. Eratosthenes, librarian of Alexandria, is remembered as the first person to calculate the circumference of the Earth. (And pretty accurately too!) The Antikythera mechanism, recovered from an ancient Greek shipwreck off the coast of Kythera, was an orrery used to predict the position of the planets and eclipses decades in advance. Arabic mathematicians used their skills (and methods learned from earlier Greek and Hindu mathematicians) for practical purposes too, for instance, to generate some truly gorgeous geometrical ornamentations. Renaissance polymath Leonardo da Vinci based many of his ingenious inventions and technological visions on mathematical principles. 

But nobody before Newton came up with a plan, and an actual method, to calculate the whole world, from now to eternity! And for this, his separation of dynamical laws and state is absolutely essential. To illustrate this, let us have a look at how Newton sets up a mathematical model of some specific aspect of the world, some phenomenon of interest. It is easy to see that his method is very similar to Simon and Newell’s general problem-solving approach that we have encountered earlier, except that there is no final state (the problem solution) that the system needs to reach (and Newton, it goes without saying, predates Simon and Newell by almost 400 years).

In brief: a Newtonian model, when applied to a real-world problem, typically needs (1) the description of an initial state (called the initial conditions of the model), (2) a collection of rules or laws (usually still formulated as a system of differential equations today, which are based on Newton’s calculus), and (3) a set of constraints (called boundary conditions) that demarcate the domain to which the model applies and, at the same time, determine what happens at its borders. Boundary conditions can be formulated explicitly, or they can be implicit in the way the model is set up. Two concrete examples will help us understand what all of this means. 

First, let’s think of a planet orbiting its star. We want to predict where the planet will be at some given time in the future. Here, the initial state is defined by the current position of both star and planet. We must also know the masses of both celestial bodies and, obviously (since we have their positions), the distance between them. We know all of these things because we have measured or estimated them (or, nowadays, simply looked them up from a reliable source) before setting up the model. Initial positions, distance, and masses are called the parameters of the system. An additional parameter calibrates the overall strength of the gravitational force. We now have everything we need to calculate the forces acting between the two bodies, and thus derive future positions of the planet relative to the star, by using Newton’s universal law of gravitation, and his laws of motion. Together, they determine the dynamics of the system. In this example, the boundary conditions are implicit in the problem definition: we decided to look at only one of the planets in isolation, ignoring the influence of all the other planets, moons, asteroids, and comets in the system, which remain excluded from our considerations.

As a second example, think of the biochemistry or metabolism of a cell, which can also be modelled (up to a certain degree, as we will see) using a Newtonian modelling paradigm. That’s how flexible and powerful this approach is! Here, the initial conditions are provided by the current metabolic state of the cell: roughly, the concentrations of all its metabolites and enzymes at the present moment. The boundary conditions are given explicitly this time, by a cell membrane that keeps metabolites and enzymes confined, regulating the interactions of the system with the rest of the chemical universe. Again, we can measure all these factors. (At least in principle; in practice, it’s not trivial: biology is much more complicated than physics!) The rules of the system are given by the metabolic reactions that are possible and occur at a significant rate given the concentration of the enzymes (whose concentrations we assume to be constant, for the moment, including them as parameters in the model). These rules are encoded by so-called biochemical rate equations, differential equations which can either be deterministic or stochastic (involving a component of chance). Be that as it may, we can now calculate (the probability of) future metabolic states of the cell, given its initial state.

These models concern radically different systems, but their basic abstract principles are the same. They both include two main components. First, there are general rules (the law of gravity, or thermodynamics and chemical kinetics) that give us general insights into how a system of the kind being modelled gets from its initial state to some other (yet unspecified) state in the future. These rules are fixed. However, on their own, they don’t tell us anything about the particular system we are modelling. They only tell us how such systems behave in general. To make specific predictions, the dynamical laws need to be complemented by the second component of the model: its initial conditions, internal parameters, and boundary conditions (all model parameters in a broad sense), which need to be measured, estimated, or otherwise determined, if we are to apply the model to a specific system. These anchor the abstract general rules in the context of the real world, and help us apply the model to specific natural phenomena.

And here is the magic of Newton’s trick: it allows you to calculate all possible outcomes across many different initial and boundary conditions and parameter values. It’s a tool to capture the space of possibilities in any given situation, to describe all the possible behaviours of a given system. All you need is the right kind of dynamical rules or laws and good enough measurements to fill in the parameter values. This means you cannot only predict the movement of the earth around the sun, given its current position, but you can predict any planetary orbit around any kind of star. And you can calculate the metabolic state of any kind of cell, as long as you know which metabolites, enzymes, and nutrients are present at a given moment.

In this way, Newton’s method is like a universal mathematical oracle! Together with the invention of alphabetic literacy, and the numbers themselves, it is right up there with the most powerful cognitive techniques humanity has ever invented.


But with it comes a heavy burden: the Laplacean demon. It implies strong causal determinism. Predictability closes down our future! The more we can see the future, the less free we are. And we can now predict everything, at least in principle, and maybe just in a probabilistic manner, but nevertheless. True innovation is dead, our future no longer open. Despite all the power of his method, therefore, Newton forced us into a bargain with the devil, it seems. And all of this because of one simple methodological trick.

But before we throw up our hands in despair, let us take stock. The machine view of the world comes with three assets that are, at the same time, also its heaviest philosophical burden:

1. The backpack: the Platonic belief in the reality of abstract universal laws, without which Newtonian science would never have come to exist. 
2. The suitcase: the Aristotelian prohibition of circular causation, strictly followed by Newtonian science: one thing occurs after another, and nothing ever causes itself. 
3. The duffle bag: Newton’s own separation of laws and state, which follows straight from the assumption of universal laws, equipping us with the power of a universal scientific oracle.

Let us repeat: none of these are grounded in scientific facts about the world. They are all purely philosophical assumptions. Each piece of luggage results from an historical decision that made sense in its context. The Platonic realm brings order into a messy world. Even today, we cannot do science without the assumption that the world behaves in orderly ways. The prohibition of circular causation prevents logical contradictions. To this day, we strive for consistency in our scientific explanations. Finally, the separation of laws and state provides us with our most powerful predictive tool. And, of course, it is important that science, more than ever, allows us to predict what may happen next, giving us a certain amount of control over our destinies.

On the downside, however, we cannot be sure whether the laws of physics are just a very good map of the territory, or whether they really exist in their separate realm beyond appearances. And we do not know whether circular causation occurs in the natural world or not. In fact, we have good reasons to believe it does, as we shall see in due time. Finally, why would we think the rules that generate natural phenomena are always independent of the state of the world? We don’t know this. We’ve never tested any of these assumptions empirically. They are and remain just that: unverified assumptions.

And it is important to notice that they severely restrict the ways in which we allow ourselves to think about the world as scientists. It is closed-minded (and actually dangerous, as we will argue) for us not to consider alternatives. We find ourselves in a situation that resembles Pascal’s wager: Blaise Pascal argued it was rational to believe in god, because believing in vain would amount to just a little wasted effort if god didn’t exist, but not believing would lead to eternal damnation if he did. The same applies here: as we have already argued, the consequences of remaining stuck inside the machine view of the world seems dire at this point in human history. We are trapped inside our map. We need to get out! 

But before we go there, before we set ourselves free, we still have to walk a little further with the map of the mechanicists, and examine how Newton’s legacy lives on in the present.
The authors acknowledge funding from the John Templeton Foundation (Project ID: 62581), and would like to thank the co-leader of the project, Prof. Tarja Knuuttila, and the Department of Philosophy at the University of Vienna for hosting the project of which this book is a central part.

Disclaimer: everything we write and present here is our own responsibility. All mistakes are ours, and not the funders’ or our hosts’ and collaborators'.