Realism, Anti-Realism, and Irrealism

Does the universe exist? Is math real? Which Star Wars timeline is the true Star Wars? These questions fall under the philosophical field of ontology, the contemplation of what exists and how. In this post, we will look at what I consider to be the three main ontological categories that concepts can fall into: Realism, Anti-Realism, and Irrealism.

Realism

We have talked extensively about Realism on this blog, so today let’s take a look at the basics of the theory in its most abstract form. Anything that is real has a property called existence, which means it has way-that-it-is, independent of perception, knowledge, and belief. Real things are not contained by boundaries of reductionism and holism, which means it is equally valid to consider all of Reality at once, or to divide it into an infinite number of infinitesimal pieces.

Reality can be relative, but it is consistent. This means things can “look” different from different “perspectives,” but they “look” the same from the same “perspective” at any one moment in time. I use quotes here, because it doesn’t actually require anyone to be there to observe it.

A thing that is real exists, and it is consistent with itself and in its relation to all other parts of Reality.

Anti-Realism

This will come as no surprise to anyone, but not all things are real. However, it turns out that some unreal things are very useful for describing reality, in particular conceptual frameworks that are non-contradictory within themselves. A mental construct that does not exist, but is self-consistent is called anti-real.

The prime example of something anti-real is math. People argue sometimes whether math is real or not, but I think they would be delighted to find out that there is another ontological category it fits into. Math does not exist in objective reality, but it behaves like something real; it is consistent with itself.

Math is a lot more than numbers. It also includes vectors, functions, groups, sets, and all kinds of things. What ties all of math together is its process: we begin by defining a number of axioms, and determine as much as we can that follows logically from those axioms. This, by definition, is consistent. If there is ever a contradiction in a mathematical construct, the offending object is deemed invalid, or the axioms need to be reevaluated. There is no number in the real numbers that is both smaller than one and larger than two.

Logic is anti-real. Some would say scientific paradigms are anti-real, though it would be more accurate to say science uses anti-real models to describe real things.

A thing that is anti-real does not exist, but it is consistent with itself and in its relation to all other things within its conceptual framework.

Irrealism

Things that exist and are consistent are real. Things that are consistent but do not exist are anti-real. And we have one more realm to examine: that which is irreal neither exists nor is consistent.

Essentially, Irrealism is a tool of interpretations and descriptions. It says that, if two or more descriptions have gaps, but they account for each other’s gaps, then even if the descriptions contradict each other, they form a valid composite description when taken together.

If you’re like me, you find Irrealism highly confusing. The best way I know of to get a feel for it is by looking at a bunch of examples.

The most intuitive example of Irrealism I can think of is fiction. When you and I read a book, the version of the story in your imagination is very different from the one in my imagination. These two versions contradict each other in many ways. Yet they still count as valid interpretations of the same story. Thus, fiction is irreal.

A clear view of a story’s irreality can be found in retconning, when a book or a movie later in a series contradicts something that happened early in the series. Arguably, the events of a first book ripple into the fourth book, so when the fourth book declares that something that happened in the first book is wrong, we have a scenario that requires both that the first book is right and that the first book is wrong. In the worst case scenarios, both sides of the contradiction must be true in order for the fourth book to make sense! Thus, the established canon of the fourth book is irreal.

It has been quite hard for me to think of examples of irrealism that the average person will understand. After ret-conning, all I could come up with involve frontier physics and philosophy, so that’s what the rest of this section will be about. So, warning, heady topics ahead.

Irrealism was originally proposed as a theory to reconcile the two major metaphysical theories, Physicalism and Phenomenalism. Physicalism says that the true reality is physical reality, and Phenomenalism says that the true reality is that which is experienced by conscious observers.

The difference between physicalism and phenomenalism can be illustrated by the question, “If a tree falls in the forest and no one hears it, does it make a sound?” According to Physicalism, it does. The sound wave is there in the air whether or not anyone is there to hear it. But according to Phenomenalism, if no one hears it, there is no sound, because things only exist if they are experienced.

Phenomenalism has trouble explaining why things are consistent between times when they are being observed. Physicalism explains that, but has trouble explaining consciousness. Metaphysical Irrealism says that’s okay. Despite the fact that they contradict one another, they cover each other’s gaps, and therefore the composite Physicalism+Phenomenalism is a valid representation of the truth, and there is no single non-contradictory theory that accounts for all of reality.

What about quantum physics? Most claims about reality citing quantum physics are bogus, but there is one sense in which Irrealism might be applicable. There are two major interpretations of quantum physics: the Copenhagen interpretation and the Many-Worlds interpretation. Copenhagen explains probabilities, but not the collapse of the wave function. Many-Worlds explains the collapse of the wave function, but not probabilities. A quantum irrealist would say that even though they contradict one another, all questions are explained between them, so the truest representation of quantum physics is the composite Copenhagen+Many-Worlds.

And one more physics example. General Relativity explains how things behave in extremely high gravity, and Quantum Mechanics explains how things behave at the very small scales. However, they do not play nice together. If we try thought experiments with both extremely high gravity and very small scales, we get contradictions between the theories. A physical irrealist would say, if we never have to deal with things in the quantum gravity regime, then it’s perfectly reasonable to say the composite theory GR+QM is the truest description there is.

Why It Matters

You may have your own opinion on where Realism, Anti-Realism, and Irrealism apply. But you may also be wondering, “what does it matter?” The common answer to this is that, if we understand how things really are, we can use that knowledge to more effectively achieve the outcomes we want. As evidence, we can point to technology; knowing how the world works lets us take materials and put them together to make tools that work for our purposes.

But that’s not an argument for metaphysics, it’s an argument for pragmatism. The point of pragmatism is to focus on what is useful, not what is true. And according to a research team led by the psychologist Donald Hoffman, usefulness and truth are rarely the same thing.

The results of a study of evolutionary simulations, summarized in a Ted Talk.

Personally, I am motivated to search for true descriptions because I have a passion and a talent for it, and doing so fills me with energy and excitement. However, I have no illusion that this makes me superior in any way to people who don’t have the interest or skills to contemplate metaphysical theories. It just happens to be one of the ways I pursue fulfillment, and other people have their own paths to fulfillment.

However, there is one domain where Realism is both true and deeply important: suffering. Suffering is something experienced directly by conscious beings, and it is most definitely real. When people and animals suffer, turning our gaze away does not make the suffering stop being real. It is an objective fact that subjective suffering exists where it exists. Thus, it is extremely important to recognize the suffering of others as real, and to do what we can to alleviate that suffering and help each other on the path toward relief, meaning, and fulfillment.

The Subjectivity of Objects

Objects are everywhere. Houses, trees, windows, computers, people. Our language revolves around objects. We conceptualize the world in terms of objects. And today, I’m going to go full-on philosopher, and ask, “What are objects?”

Platonic Forms

In Ancient Greece, Plato described objects in terms of the theory of Forms. It was said that, for every type of object—house, door, cat, human—there is a perfect version of it, its Form. The Forms were said to exist non-physically and timelessly. Thus, reality was thought to be made of objects attempting to mimic their corresponding perfect Forms.

The theory of Forms may be useful in some contexts, but it doesn’t do well at describing physical reality. In the relatively static ancient world, it made sense, but in modern times with historically rapid technological and scientific progress, not as much. Has there always been a Form of a spaceship? A cell phone? The internet? What about the way some languages have words for objects that others don’t? It seems much more likely that Forms only exist as concepts within our minds, not in external objective reality.

Reductionism and Holism

In the era of science, another theory has arisen: reductionism. We observed that things are made out of parts, and those parts are made out of smaller parts, and the chain continues quite awhile. Finding the fundamental building blocks of the universe became a goal of modern physics, and some came to the belief that these building blocks are the true reality, and everything emergent from them is just our perception, less real or not real at all. This view is called reductionism.

Counter to reductionism, there is holism, the view that any system that functions as a whole and has properties that are different from the properties of its parts is a real object. Some stronger versions of holism even claim that certain higher-level emergent objects are more real than the parts they are made of.

Reductionism and holism are both perspectives and metaphysical theories. As perspectives, whether they are valid or not depends on the context. Today, we are examining them as metaphysical theories.

Associative Equivalence

Which is true, reductionism or holism? Are higher-level objects real, or are only the smallest, most reducible parts they are made from? To explore this question, let’s take a detour into math. Consider the following expressions:

3

1 + 2

2 + 1

(1 + 1) + 1

1 + (1 + 1)

1/2 + 2 + 1/2

What is the difference in the ideas each of these expressions represent? The answer: nothing! They all represent the number three, divided into arbitrary pieces.

Let’s take this analogy to physical reality. If we cut a sandwich into four pieces, does it become four sandwiches? If we put four full-sized sandwiches together at the corners, do we get one big sandwich? The answer is not a question of metaphysics, it is a question of semantics. It only depends on how we decide to define the words.

Just like how the number of numbers we divide a math expression into does not change what it represents, neither does reductionism describe a different reality than holism. Holism is merely putting the parentheses in different places (and, as we will see in next week’s quantum physics discussion, reductionism ends up doing that too). As metaphysical theories, neither reductionism nor holism measure up. They are both equally valid descriptions of the same reality!

Thus, we come to a profound realization: the universe is not inherently made out of objects; objects are human constructions. The universe is one thing, and it is infinitely many things. There is no difference. It’s all up to how we look at it.


For me, to see a door as a door, and as wood, and as wood cells, and as organic molecules, and as atoms, and as subatomic particles, and as interacting quantum fields, and to know that all of these are equally true, and none is more or less true than any other, is awe-inspiringly profound. To see myself as one person, and as two halves of a brain, and as a trillion cells, and as a part of the universe where the boundary between me and everything else is just a mental construction; that is nothing short of spiritual.


A Scientist’s Fiction is featured on Feedspot’s list of top 50 science fiction blogs! If you have some free time, and are interested in science and science fiction, why not check out some of the other creators there?

Idealism – What if Consciousness is All there Is?

Consciousness:
The Hard Problem
Dualism
Physicalism
Idealism
Identifying Consciousness

Vast Minds

Identity, Self, and Other

The Question of Meaning

We began our exploration of the metaphysics of consciousness by discussing the Hard Problem and the philosophical zombie. We then explored the two routes we could take from there: Dualism, which says consciousness is a substance different from the rest of physical reality; and Physicalism, which says consciousness is part of physical reality, either at the fundamental level or emergent. But these paths both make an assumption: physical reality exists, a stance called Realism. Today, we’re going to question that assumption.

Suppose there is a universe where no life exists. No one and nothing is able to observe it. Does it make sense to say that universe exists? A Realist would say, “Of course, what does observability have to do with existence?” But to some people, the very idea of something existing without being observed seems incoherent, because to imagine it requires imagining oneself observing it. This theory, that nothing exists unless it is being observed, is called Idealism.

Idealism states that without consciousness, nothing exists. Or in other words, reality is a projection of consciousness. Our bodies, the Earth, houses, cars, trees, computers, all these things exist because we collectively expect them to, either consciously or unconsciously. If something is not being observed by a conscious being, then, it doesn’t exist.

The distinction between Realism and Idealism can be seen by considering the old question, if a tree falls in the forest, does it make a sound? According to Realism, it does. The impact of the wood on the dirt causes pressure waves in the air, which are sound. On the other hand, the Idealist would say it does not. In fact, the tree would not even fall in the first place, it would simply manifest into existence as a fallen log the next time someone walked by!

This raises a big problem for Idealism. If nothing exists if it is not being observed, then why do things manifest as if stuff has happened when nobody is looking? Why do trees fall? Why do clocks show the right time? If nothing exists when it is not being observed, shouldn’t there be random inexplicable changes whenever we look away from something and then look back?

An Idealist would say these things happen because we expect them to. When we look at a clock, we know it is supposed to accurately tell us what time it is, so it does.

But what about when things don’t happen as expected? If reality is a projection of our minds and behaves as we expect it to, we should never find ourselves surprised. Not only in our everyday lives, but at the frontier of scientific knowledge as well, such as when Galileo discovered the moons of Jupiter, or when astronomers discovered the universe is speeding up as it expands. Furthermore, science and technology work for people who don’t know how they work or what they are supposed to do. How can this be so in an Ideal universe?

Various Idealists come back with two possible answers. The first is to invoke a personal God as the all-seeing observer, who keeps the universe from disintegrating into nonexistence by constantly observing every atom. This interpretation is popular with some theologians, because it gives us a universe that is mostly indistinguishable from a Real universe, but provides a mechanism by which God and other supernatural beings can intervene.

The second answer is to say reality is projected from our collective expectations, not our individual minds. In this case, things happen the way they do because most people believe it. Or rather, because most of the available power of belief is aimed toward it. It could be that minds have different strengths, and so the belief of a powerful mind might influence reality more than the belief of a weaker mind. We talked last week about how narratives spread as memetic complexes. If this brand of Idealism is true, then these narratives are not just competing for propagation, but for influence over the nature of reality itself.

This brand of Idealism would also allow for wizards and magic and all kinds of supernatural things. Minds without bodies, super-powerful minds, influential minds; these could obtain some amount of control over the local fabric of reality. Different kinds of powerful minds would bend it in different ways. A strong mind could bend reality to their will, a powerful but weak-willed mind would bend it uncontrollably, and an instinctual animal mind or an ignorant mind would shape it unconsciously around their view of the world. In fact, much of the magic of fantasy and superhero stories becomes accessible under the metaphysics of Idealism.

On the extreme end of Idealism, we find Solipsism, the belief that, not only is reality a projection of your mind, but so are other people. You are the only person who exists. Everyone and everything else is no more than a dream.

By Clarissa Blackburn on Flickr

Of course, the only evidence in support of Solipsism is that we can’t prove absolutely that it’s not true. Any argument in favor of the existence of things other than oneself can be countered with, “but how do I know?” The same can be said of Idealism. A Realist must postulate a quality called “existence,” which is independent of knowledge, perception, and belief, but the Idealist can immediately counter with, “How can you know about something that is independent of knowledge? You can’t!”

The answer to which of these theories is correct, Realism, Idealism, or Solipsism, is by no means trivial. We each might feel strongly toward one of them, but arguing in its favor is a difficult task. My strategy is to use the Anthropic Principle: which of the three theories is most likely to produce the world we find ourselves in?

Let’s start with Realism. Assuming things exist, they obey non-contradiction, acting according to the “way they exist,” their natures. Because of this, we expect absolute coherence. Clocks tell the right time because they work even when no one is looking at them. When they tell the wrong time, it is because they don’t run at a perfect rate, or they are set wrong, or they are broken, or they undergo relativistic time dilation.

In order to understand how things work, we play detective to figure out what they have been doing while no one was watching. This works for things on Earth, in the solar system, in the galaxy, and all throughout the entire universe, every atom and subatomic particle doing its thing, adding up in enormous numbers to yield what we see through our telescopes and microscopes and all or our biological and mechanical senses. It makes sense, because it exhibits the same kinds of behavior while we are observing it and while we are not.

Quantum physics is an exception; particles and quantum systems behave differently if they are being observed than if they are left alone. However, this is because in order to observe systems on the scale of atoms and subatomic particles, we have to disturb them with other particles, like photons. Any photon capable of observing an atom is going to knock the atom around, changing the state of the system. According to Realism, the reason quantum systems behave differently when they are being observed is because of the tools necessary to take measurements, not because of anything special about awareness.

I also want to dispel a myth about quantum physics; it’s not inherently mysterious. A famous physicist once said, “If you think you understand quantum mechanics, you don’t understand quantum mechanics.” This is catchy and comes with a flavor of authority, but it is a lie. Quantum physics is consistent and understandable, it’s just different from what we’re used to. Thus, it is perfectly compatible with Realism as defined three paragraphs above.

In Idealism, there is no hard principle keeping everything consistent. Hypothetically, you could turn around to see an apple floating in midair, or a million dollars manifested in a pile on the floor. We can think of this in terms of entropy: the number of incoherent ways we might find the universe to be vastly outnumbers the number of coherent ways. Therefore, if Idealism were true, we would expect to find lots of messiness and inconsistency all over the place, not this ordered world that behaves so consistently according to physical laws.

Of course, Idealism has a counter-argument: to suggest there are inconsistencies, like miracles and haunted houses and other supernatural stuff. The reason they are rare enough that people can live their whole lives without believing they exist is because the narrative of Realism is so powerful; if more people believed in magic and mysticism, such inexplicable things would be more commonplace.

Solipsism does not have this defense, since if it were true, then the only mind with beliefs would be a Solipsist, giving the narrative of Realism no power. Sorry Solipsism, the only argument in your favor is the teenage favorite, “You can’t prove I’m wrong.”

When we look out into the universe, we see billions of stars in the galaxy, each with its own set of planets. Out in the vast reaches of space, we see billions of galaxies, each with its own billions or trillions of stars. To me, it feels extremely self-aggrandizing to suppose we imagined all that into existence within the past hundred years. It has long been our nature to put ourselves at the center of existence, to seek power over nature and reality. To that end, we may find it convenient to believe that if we just believe hard enough, anything imaginable can happen. We also tend to look for rationalizations to continue believing what we already believe, be it ideological, religious, superstitious, or scientific. Thus, we can keep looking for rationalizations to explain how an Ideal universe might come to look exactly how we would expect a Real universe to be. Or, we can acquiesce to Occam’s Razor, and accept the universe as Real.

Interestingly, there are circumstances where things like Idealism and Solipsism can exist within a larger framework of Reality. We’ll explore those in later posts when we get to the Simulation Hypothesis and Boltzmann Brains.

Consciousness – Physicalism

Consciousness:
The Hard Problem
Dualism
Physicalism
Idealism
Identifying Consciousness

Vast Minds

Identity, Self, and Other

The Question of Meaning

Recommended Pre-Reading:
Representational Realism
Existence and Natures
Knowledge of Reality
The Hard Problem

In the philosophical zombie thought experiment, there are two possible routes to follow. Last time, we explored what happened if we assumed p-zombies are possible, and something could exist that could act like, talk like, and be physically identical to a human, yet have no consciousness. It would follow that consciousness is something independent from, yet able to interact with, physical reality. Today, we are going to explore the other route, what we get if we assume something physically identical to a living human must be conscious, and it is impossible for it not to be. This is called physicalism.

For physicalism, we must suppose that something about the physical world is equivalent to consciousness. Right away, this seems weird. The way we conceptualize consciousness is completely different from the way we conceptualize physical systems. Consider light. Light doesn’t have any color, it’s just a wave in the universe-spanning electromagnetic field. In order to become color, it has to enter your eye, interact with the cells on your retina, be transformed into electrical signals, which make electrical patterns in your brain.

The physicalist must say these electrical patterns are color and shape and texture. The collection of neurons in your brain firing and buzzing together not only correlates with your consciousness, it is your consciousness.

This seems crazy. After all, if you think about a color, and you think about a bunch of cells shooting electrical pulses to one another, the two thoughts are nothing alike! In fact, they seem so different from each other that it feels like they must be fundamentally different things.

However, let’s remember that in analytical thinking, we might discover truths that go against our intuition. Last year, in the Nature of Reality series, we did a discussion on how we can know truth if our conceptions of reality are just representations. We concluded that if the math/logic of our conceptual representation is isomorphic with (the same as) the math/logic of reality itself, then our conceptual representation is true.

The models we create of physical systems, the images we draw and imagine and look at, are just representations. The picture in your mind of cells sending electrical pulses between each other is not reality-as-it-is, it is a conceptual representation. Consciousness, on the other hand, is not a representation. It is the direct experience of reality.

Let’s be clear. The computer you see in front of you is not a direct experience of reality. It is an image created in your brain. The direct perception of reality is the fact that you perceive an image, regardless of its contents.

This is important, so let’s go over it again. Consciousness is like the chalk marks on a chalkboard. Many things can be written on a chalkboard. They can be erased, and replaced by something else. You can write words or equations, or draw pictures. The things we write on chalkboards convey meaning to those watching. Yet all of it, regardless of what it means, comes from the chalk marks.

Your mind lets you experience many things. You see sights. Hear sounds. Feel feelings. These things are parts of consciousness. You find all kinds of meaning in the sights, sounds, feelings, and other senses. You can learn about the universe, keep a relationship going with another person, experience the imaginary world of a story. Yet all these things come from sights, sounds, and feelings. All these things come from consciousness. All the things we do with the contents of our consciousness are models, representations, not true reality. But consciousness itself, the sensations of sights, sounds, feelings, and other senses, is a little piece of direct reality.

When we apply this to the paradox of neural patterns and conscious experience, we find it is not so contradictory after all. The mental model of neurons and electrical pulses is just a representation, whereas consciousness is reality-as-it-is. If they don’t seem like the same thing to our intuitions, that is completely fine. It’s the logic and math that matters. If the math/logic of the model of neurons and electrical pulses is the same as the math/logic of consciousness, then those neural patterns are a valid model of the real system, which is consciousness.

If this is true, what does it mean metaphysically? To be conscious as we know it, a brain needs billions of neurons working together. A single neuron is about as conscious as a rock. The phenomenon of large numbers of things coming together and demonstrating new, holistic behavior is called emergence. The reverse of emergence, the process of examining systems in terms of their constituent parts, is called reductionism.

by Chlodulfa on Deviantart

If the conscious part of a brain can be reduced to neurons, what is consciousness reduced to? If consciousness and the conscious part of the brain are equivalent, then the same logic that reduces the conscious part of the brain must also reduce consciousness.

Does this mean what we said a moment ago about neurons and rocks is incorrect? Does it mean a neuron, despite being just one cell, is a tiny bit conscious? What about the things the neuron is made of? Molecules, atoms, and sub-atomic particles? If we say the fundamental physical level of reality has no consciousness, but brains do, then somewhere along the train of emergence there must be a step where the smallest possible building blocks of consciousness come into existence.

This idea, that somewhere along the hierarchy of emergent complexity the smallest units of consciousness appear from nothing smaller, seems non-scientific. Stuff doesn’t just pop into existence without any reason. One way to resolve this paradox is to say the fundamental level of physics and the fundamental level of consciousness are the same. Consciousness doesn’t magically appear at some level, rather it breaks up and keeps breaking up into smaller and smaller pieces the further down the physical reductionist ladder we go. When we get down to sub-atomic particles, we find that electrons, quarks, and the like all have a tiny bit of the stuff that comes together and makes consciousness. This would mean everything in the universe is a little bit conscious, a theory called panpsychism.

As the philosopher David Chalmers describes it, panpsychism contains the hypothesis that, just like electrons and other sub-atomic particles have properties like mass and electric charge, they have another property: a tiniest possible amount of consciousness. This wouldn’t be consciousness as we know it, with colors and concepts and perceptions, but a tiny bit that builds up and joins together with the other bits of consciousness from the other particles it interacts with, and in large enough numbers and the right organization, become the consciousness we recognize in ourselves.

Panpsychism isn’t the only physicalist option, though. If we can find a different ladder of reductionism to follow, we might end up at a place other than sub-atomic particles. As it turns out, matter isn’t the only dimension the universe can be reduced down. There is also information.

At the fundamental level of information, we find bits. Bits are things that can be one of two possibilities: on or off, yes or no, true or false, 1 or 0. It may be that any amount or type of information can be reduced to bits, or if not, to some other indivisible basis. So maybe consciousness can be reduced to bits.

By Christiaan Colen on Flickr

To me, this makes more sense than panpsychism. Consciousness seems to be correlated with information, not matter. Intuition would say a giant brain with the same number and configuration of neurons as mine should be exactly as conscious as I am, despite being made of a lot more matter. And if we could simulate a brain using electrons rather than cells, it seems to me like it would be just as conscious too. Of course, intuition can often lead us astray in science, especially when we’re talking about consciousness, so experiments would have to be done before we say anything confidently.

There is a scientific theory that looks into the possibility that consciousness comes from information, Integrated Information Theory. It looks at networks of information where each bit is connected to other bits, and changes based on the signals it gets. The brain is such a system, each neuron functioning as a bit, either firing an electrical impulse or not. According to Integrated Information Theory, consciousness is formed according to each state of the brain related to all other possible states it could be in.

Integrated Information Theory is a first step toward a scientific understanding of consciousness, but it is almost certainly not the whole answer. Just as Newton’s theory of gravity gave way to Einstein’s theories of relativity, Integrated Information Theory will probably give way to something much deeper and more insightful. Some avenues to pursue would be the time lag between signals and patterns passed along by neurons, and the fact that much of the brain seems not to contribute to consciousness, despite being very active.

Information is not something constrained to one universe or another. It is a mathematical construct, which means it transcends material reality. There is something deeply wondrous about the idea that consciousness comes from timeless, spaceless truths, made real by physical systems acting out their natures. Not from a religious or spiritualistic narrative, but from analytical thought and a scientific worldview.

Mathematics: The Language of the Universe

Nature of Reality:
Quasi-Realism
Representational Realism
Existence and Natures
Knowledge of Reality
The Language of Reality

Toolbelt of Knowledge: Concepts
Algorithms
Equivalence
Emergence
Math
The Anthropic Principle
Substrate-Independence
Significance

In our discussions about the nature of reality, we have come to the view that reality is a thing unto itself, independent of perception, belief, or knowledge. Anything we perceive or think we know about reality is not reality itself, but only a representation we have constructed in our minds. A representation is true to the degree that its logic matches with the logic of the real thing it is describing. Today, we are going to talk about that logic, mathematics.

By WyrdWolf on Deviantart

A lot of people see math as something mysterious that they will never understand. But math is not supernatural. It is not hidden knowledge available only to an elite few. People who know math are not wizards or prophets, they are normal people just like you. I hope that after reading this discussion, you will be convinced that you can learn math too, if you so desire.

To start, let’s forget about numbers and just think about something physical, like air pressure. We know from centuries of experiments that, the pressure in a given volume is proportional to the number of molecules in the volume and the temperature. This may sound complicated, but all it means is if more air is added or the temperature is increased, the pressure increases.

Let’s look at the italicized statement. We have four physical quantities: pressure, volume, number of molecules, and temperature. Let’s shorten each of these to just their first letters: P, V, N, and T. “Is proportional to” means if you change what comes after it, then what comes before it changes by the same percentage. We can represent this by an equals sign and a constant, the letter k. Put this together, and we have,

It’s an equation! We have just done something marvelous; we have taken a fact about reality and written it as a mathematical statement. By doing this, we realize a profound truth: math is not just a tool to work with numbers and get answers to homework problems; it’s a language and a writing system. By becoming math-literate, we break into a higher level of understanding the universe.

Let’s try it again. This time we’ll start with an equation, and figure out what it means.

The first thing we need when trying to read this equation is what the letters mean. In normal languages, letters have mostly the same sounds wherever they appear. In math, it is not so; we must be told what each letter means every time. It is the organization, operations, and numbers that have consistent meaning. So here is what the letters in our new equation mean: capital T stands for temperature, small t stands for time, and k is a constant.

What operations does this equation have? The first thing we notice is d/d. This means, the rate at which the thing on top changes as the thing on the bottom changes. So for us, it would be the rate the temperature changes over time. Next, we notice a triangle before the T on the right. This triangle means the difference between two of what comes after it. So in our case, ΔT means the difference between the temperatures of two objects.

Putting all this together, we can read the equation. It says, “The rate at which temperature flows between two touching objects is proportional to the difference in temperature between the two objects.” This means if two touching objects have very different temperatures, heat will flow quickly between them, but if their temperatures are near each other, the heat will flow slowly.

There is one final piece to the equation, and that is the minus sign. This tells us that the temperatures are changing closer to one another, not running away to extremes. This makes sense. Cold things heat up when they touch hot things, and hot things cool down when they touch cold things. Heat always flows toward equilibrium.

The ability to read equations is only one small part of math. There is also geometry, group theory, set theory, vectors, tensors, and much more. All of these fields of study are called the same thing, math, so what do they all have in common? The answer is that mathematics is the set of all well-defined abstract ideas that follow the principle of non-contradiction. To create math, we must declare one or more axioms, statements that define an imaginary object.

Let’s take an example. "A circle is a shape where every point on its boundary is the same distance from its center." Based on this axiom, we can figure out all kinds of things about lines drawn through circles, intersecting circles, circles in curved space, and more. Everything in math is like this; we start with axioms, and then use logic on them to figure out all that we can about them.

Philosophers and scientists have often wondered at how well math is able to describe the universe. To some, it seems miraculous. However, based on everything we have talked about in the Nature of Reality series, I think it makes perfect sense. Here’s why:

1) A representation is true to the degree that its logic lines up with the logic of the part of reality it is meant to represent.
2) An idea is a representation.
3) Reality is well-defined and always follows the principle of non-contradiction.
4) Every idea that is well-defined and follows non-contradiction is mathematical.
Therefore, everything in reality can be truthfully represented by mathematical ideas.

If we accept the views of reality we have argued for on this blog, this is why Mathematics is the language of the universe.

What can We Know about Reality?

The Nature of Reality:
Quasi-Realism
Representational Realism
Existence and Natures
Knowledge of Reality
The Language of Reality

We have spent the Nature of Reality series developing the idea that we do not see reality as it is, but as our brains create from the information we receive through our senses. In fact, it is impossible for us to perceive reality as it really is, because the very act of perception is at least one step removed from reality. This leads to mistakes. We perceive things that are not there, and we are blind to things that are. Furthermore, the only way we have to determine whether something is real is to compare it with the rest of reality as we know it, all of which is contained within our heads. Just like every word in a dictionary is defined by other words in the dictionary, so we judge the reality of every concept and perception in our brain by other concepts and perceptions in our brain. So the question arises: are we stuck? Is there any way we can know anything about true Reality, or are we forever doomed to subjectivity and relativism?

There is one thing we can know about true reality. That is because perception itself is a part of reality. You can know with absolute certainty that you are conscious, and that your consciousness has a variety of qualia. You are looking at light gray lines on a dark gray background. As you read these words, you are sounding them out in your head, in a way that is kind of like hearing them, but not quite. It may be impossible to directly know the true nature of the computer screen, or even if the computer screen exists, but you do know with absolute certainty that you are experiencing perceptions as if there is a computer screen in front of you.

Abstract Painting 599 by Gerhard Richter. You may not know what it is supposed to represent, but you know that you are perceiving colors and textures.

But our direct perceptions are only an infinitesimally small part of reality. In order to know anything about the rest of it, we need to be content with the representations of it we create in our minds. The question then becomes, what makes some representations of reality better than others? What does it mean for a representation to be true?

The place to start is the fact that Reality obeys the law of non-contradiction. Something that is real cannot be both true and false at the same time. See the previous entry in the series, Existence and Natures. Now you may wonder if that is true. After all, if we both look at a ball, and it looks blue to me, but it looks green to you, isn't that a contradiction? No, because my perception takes place in my brain, and your perception takes place in your brain. Neither of our perceptions is the ball. The ball is itself. The ball reflects the wavelengths of light that it does, which just happens to look different to you than it does to me because our cognitions work a little differently.

Because Reality obeys the law of non-contradiction, we can apply logic to the information brought to us by our senses. It is true that the models of reality we create are not themselves reality, they are only models. But if a model accounts for the information we get from our senses, and it does not contradict itself in any way, that is enough to say the model is true. And if the model makes predictions for new information you would get through your senses in the right circumstances, and you create an experiment to test those predictions, that increases the certainty that the model is true. You may find this familiar; after all, it is the scientific method as it is taught in grade school.

Today we learned that even though it is impossible to know reality directly except for the small fraction of reality that is your own perception, that doesn't mean reality is forever out of our reach. Reality is governed by logic, and we can know logic. So if we have models of reality in our minds, and the logic that describes the models is the same logic that describes reality, then we say that we know that part of reality. If a concept or belief has the same logical structure as the real thing it describes, that is what it means to be true.