It might seem that Plato, one of the history’s greatest philosophers, has little or no relation to today’s science, but Plato’s ideas actually underpin the foundations of science and our understanding of the world. In particular, Plato’s forms are present in mathematics and physics, and without these eternal forms, science wouldn’t be possible. So without further to do, let’s look at a quote from a book I’ve recently finished reading:

From The Eternal Law by John H. Spencer (2015):
“Platonism is implied by physics, but, more significantly, I am arguing that Platonism is presupposed by physics and that physics is only possible because Platonic realism is true.”

Many pioneering scientists in the early 20th century, notably Planck, Pauli, Bohr, Heisenberg, Einstein, and Schrodinger, were also aware of the importance of metaphysics and realism in fundamental science. For example, Schrodinger said that, “a real elimination of metaphysics means taking the soul out of both art and science, turning them into skeletons incapable of any further development.” So this isn’t anything new, but it’s worthwhile to look at in detail because many physicists overlook the philosophy behind their theories.

If I were to summarize Spencer’s book in one argument, it would go something like this:
1)      The universe is not chaotic, but rather, follows certain laws.
2)      If the laws underlying the universe are real, they must be nonphysical.
Conclusion 1: Materialism, the idea that everything is just matter (and energy), is false.
3)      The universe must exist objectively if these laws exist.
Conclusion 2: If the universe has an objective existence, realism is true.
4)      Realism is a form of Platonism.
Conclusion 3: Therefore, Platonism is true.


Let’s look at this in more depth. First of all, I think it’s clear that there is at least some order in the universe. From the universe at large with galaxies shaped by gravity, to life on Earth with its complicated structures and processes, to the particles out of which everything is formed, there is order and structure. If everything was indeed chaotic, ungoverned by laws, we would be unable to predict anything. All the order we perceive would then be a great coincidence, indeed, a 13.8 billion year old coincidence (the age of the universe). We can’t prove that the universe isn’t chaotic, but it’s much more reasonable to suppose that it is instead governed by certain laws. That’s not to say that we know what the ultimate laws are, but it’s enough to say that they are “real.”

This isn’t to say that “chaos theory” is wrong: chaos theory doesn’t saying that certain processes are actually random, but that some systems are so sensitive to initial conditions (such as the initial speed or height of an object before it’s released) that it’s impossible (or nearly impossible) for us to predict the outcome. In order to do so, we would have to know the initial conditions to a high degree of precision that is currently impossible. But that’s not to say that it’s behaving chaotically: it’s just that at our level of understanding, we can’t predict it, so it appears “random.”

This means that there must be things which are nonphysical. Why? Well, if physical laws and mathematics are real, then they must be nonphysical simply because you can’t go out and find the number “2” or “E = mc2” floating about in the physical world. We see instances of the number 2 (2 dogs, 2 books, etc.) and instances of E = mc2 (the energy of a certain mass can be found by this equation, and vice versa), but never the number or equation itself. And if something isn’t physical, it is therefore nonphysical (obviously). Spencer also says that “realism entails that materialism is false, because we have to admit that something can be real and yet not be physical.”

Another way to see this is that since the equations of physics are used to describe certain physical things, they can’t be physical things themselves or else they would be subject to change. Everything physical changes, and these changes are described by certain complicated laws. But the laws themselves don’t change, or else they could not accurately predict anything, and to be unchanging, something must be nonphysical. But this is just an additional way to see it: I think the idea we can never perceive a number “2” out there, or even in a certain bit of energy that somehow represents that number, is clear enough.

Next, the idea that the world must exist objectively (independent of us and our conceptions of it) naturally follows from this because if the laws are real, then they can’t just exist in our mind. If they did, they would be subjective and so dependent on our minds and perceptions, which is not at all what we observe (by the way, I’m using “universe” and “world” interchangeably). Of course, we have some subjective influence on the world, but that’s not to say that we can change anything. But the idea is that even if the world itself is not entirely objective, the laws of physics and mathematics must be, because, having just argued that they are real, they have to exist independently of what they describe. And, since they are not dependent on us (we are also what they describe), they must be objective.
There is, however, a lot of subjectivity in our perceptions of the world. There’s obviously the fact that our biases and personal opinions affect our perceptions, but additionally, we have a limited perception of the world due to our senses. We have five senses that operate in a narrow range (for example, we can only see visible light, which is a small portion of the whole electromagnetic spectrum), and if we had other senses, the world would appear to be a very different place. But none of this is to say that there is no “thing in itself” behind the world we perceive. We only know a small portion of it, but we are sensing “something” out there, namely, our perceptions of the objective world. We can certainly affect it, either physically or with our minds, but even our minds operate according to certain laws. So even if you believe that your mind shapes reality, that’s not to say that it does so completely randomly. What your mind is shaping is your perceptions of reality and how you interact with it, not the thing in itself. However, there are some things that can be said to be “more real” than others, but this is where Platonism comes in, which we’ll come to later.

Now let’s look at what realism is. Although the ordinary use of the word is often used to refer to the physical world around us, in philosophy, realism states that there is objective truth (which is why Conclusion 1 follows from points 1) and 2) right away). We can discover this truth, and it does not depend on us. Moreover, even if we never discover some particular thing, it is still “out there,” which is called a verification-transcendent truth. One such truth is that there is a mind-independent reality that we can discover, and although we can change it since we too exist within the world, it would still exist whether we do or not. This means that we cannot simply invent laws of physics and have them work. They are only truthful insofar as they correspond to reality; they must be restrained by what is “out there” or else we would only be describing a fiction, and it would be impossible to verify whether anything is true or not. Indeed, the whole notion of “truth” would collapse, leaving us in an anti-realist position.

Anti-realists claim that we invent truth, that the laws of physics are fictions we create to describe the world and don’t exist in any fundamental sense. But unless the world is chaotic and not governable by laws (though how these laws came to be is another matter entirely) then they must exist independently from us. And if this is the case, we are lead to realism at once, because if the world is governable by certain laws, even if we can’t discover what they are with the knowledge we have (now or even ever), they still can be known in principle.  Now, this isn’t to say that the laws of physics that we currently use are the right ones: the laws we have most likely approximate the actual laws, but the fact that they are not perfect is due to our own limitations, not because they don’t actually exist.

Now, we can go one step further by looking at Plato’s philosophy. Plato’s analogy of the cave quite nicely sums it up (see my previous blog post), but generally, in Plato’s philosophy about the universe, there is a hierarchy of reality with the Good, the eternal, nonphysical principle from which all things arose, at the highest level beyond being and existence. The Good can also be called God, the Tao, Emptiness, etc. Plato’s forms are just below the Good in the hierarchy of existence, and they are unchanging principles that eventually gives rise to the physical world. So in the hierarchy of reality, we go from simple and eternal to complex and changing. The higher forms are principles such as Beauty, Truth, Number, and Symmetry, and those lower down, which partake in various higher forms, are things such as equations, morality, and even objects such as the form of a tree, or of a person, etc. All trees, people, and so on “partake” in the forms, as if they were partial reflections of them.

A useful analogy that I’ve included in previous posts is that of white light dispersing in a prism: the white light of the Good splits into various colours (lower forms) upon entering the prism, so that there is more variety in the forms lower down in the hierarchy. However, the Good is undiminished, for like the white light from which the colours arose, it remains pure and simple, even though its dispersed beam appears to be multiple. This process continues down to much more complicated levels of existence until the physical world comes into being.
Things in the physical world can never be perfect renditions of the forms above because they are always changing, and so never last eternally. If something was perfect, and remained perfect, it could never change, because if it did, it would no longer be perfect. This is why things that exist nonphysically can be said to be “perfect” since they never change, but things in the physical world can never be perfect even in principle.


Now, to say that some discipline is a kind of Platonism, whether it is ethics, theology, mathematics, or psychology, means that there is a hierarchy of laws or of reality. The principles we use in, say, ethics, would then be derivable from more fundamental principles that are simpler and apply to a wider range of phenomena. Likewise with mathematics and physics: physics must be Platonic because otherwise, the laws of physics are just fictions that do not correspond to reality. Though even if physics and mathematics only make sense in a Platonist framework, it is not necessarily true of other areas (politics, etc.).

So the laws of physics can all essentially be derived from more fundamental laws, and if you trace this back up the chain, you arrive at the primary law, what is called the Eternal Law in the book. So “All the laws of physics are partial reflections of the one eternal mathematical law, which is a kind of super-law, the foundation of all the mathematical laws in the universe.” This is the simplest law, existing in the nonphysical world of forms, though it is not the most fundamental form (symmetry, number, and of course, the Good, are above it). This law dictates how things work in the physical world, all the matter and energy within it, and although we probably wouldn’t be able to comprehend it in itself, the more specific laws we to describe the world are derived from it.

An example of this hierarchy of different physical laws, with the ones closer to the Eternal Law subsuming the ones below it, can be seen with gravity. Newton’s laws of gravity apply on a smaller scale, to objects on Earth and in our solar system, and we can use them to predict motion quite accurately. However, in order to describe the universe at large, with galaxies and clusters, Newton’s laws are no longer applicable. For that, we need Einstein’s laws, which apply to the universe at large and how it is affected by gravity. Newton’s laws are not incorrect, but they have a narrower range of applicability. They can be derived from Einstein’s more general laws, and Einstein’s laws can also describe phenomena on Earth just like Newton’s laws can: they describe all of what Newton’s laws can and more (though we almost always use Newton’s laws for things on Earth because they’re so much simpler). Newton himself would surely agree with this structure of his laws, for he said, “truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.” As well as Einstein: “nature is the realisation of the simplest conceivable mathematical ideas,” namely, the forms which are close to the Eternal Law, as well as the Eternal Law itself and the principles of symmetry, beauty, and number from which it is derived. In the future, we will have to go further to find a more fundamental theory, because we know that Einstein’s laws aren’t compatible with quantum mechanics, so an even more general law will be quantum gravity (which string theory might very well accomplish).

We would do well to better appreciate Plato’s philosophy in physics, for, although Platonic ideas have been prevalent in science in the past, many physicists and philosophers today reject these ideas. However, some notable physicists recognize the necessity for realism and Platonism, for example, the author of the book I’ve been quoting from, who is a quantum physicist, and the physicist Sir Roger Penrose to name a few. Penrose said that, “The more deeply we probe Nature’s secrets, the more profoundly we are driven into Plato’s world of mathematical ideals as we seek our understanding.”


And so, as the poet Ralph Waldo Emerson said, “Plato is philosophy, and philosophy, Plato,” and to this, we ought to add that, at least at the very fundamental level, “Plato is physics, and physics, Plato.”

4 comments:

Well done; keep up the Good work!

Thanks! :)

I saw this essay on the Platonism fb group and wanted to express my appreciation.

Also, perhaps of note, I think there's a small but important technicality that was overlooked. I seem to find conflations the two very different senses of Platonism, which leads to interesting inaccuracies. For example, earlier in the text, there's a reference to Platonism in its current sense of *mathematical realism*. That makes the statement, "Realism is a form of Platonism.... Therefore, Platonism is true," somewhat confusing. If by Platonism is meant Realism, then it's a tautology, and if it is Plato's religion, then (without further justifications) only the reverse is true.

In the same vein, the concluding remark that, "Plato is physics, and physics, Plato" is not quite true unless by "Plato" you mean mathematical realism. Otherwise, physics didn't start until Christian and Muslim scholars began to study the material world. Ancient Platonists and Plato himself very ostentatiously did not care about physics as we think of it. They were pure mathematicians. It took a thousand years of mathematics for John Philoponus to challenge the patently obvious fallacies of ancient physics by overturning the metaphysic of the world as a living, thinking creature and at the same time a second-rate copy of the pure ideas, mere shadow on the wall. A Christian Academician, Philoponus initiated the view, soon adopted by the Abassids, that things move in accordance with a divine law, established at the creation of the world. That made metaphysics not only much closer to what we think of as Platonism in our day but also more admirable, meaning that studying the material world was now of high spiritual value.

Anyway, this is an intriguing topic, and I think you gave a great overview with awesome quotes and pictures.

- Lev

Thanks, Lev, that's a good point. I should have been clearer with what I meant by "Plato" (I was talking about realism in particular that conceives the universe as a unity and hierarchy).

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