The Speed of Light Has Nothing to Do With Light

How many times has this happened to you? You're watching one of those popular science programs when suddenly you're bombarded the outlandish claim that nothing travels faster than the speed of light. It’s a common expression to be sure, and physicists love to remind us of this fact at every opportunity. But how many times have those same science educators ever stopped to explain why this must be the case? It’s an insanely counterintuitive thing to say, yet most educational resources seem to treat it as a brute fact of life---as if the universe itself is just really quirky that way, so quit your whining and get used to it. Even Einstein himself seems to postulate it outright in his original work [1], and all the laws of special relativity just happen to fall out of the mathematics once you do.

But what if I told you it didn’t have to be that way? The universality of the speed of light is not some quirky foible we all have to live with. Rather, it's a fundamental statement about the nature of space and time. There’s even a surprisingly simple proof of this fact, and it’s been well-documented in the literature for many decades [2,3]. Yet, for some very strange reason, it never quite made its way into our textbooks. Most popular science educators are therefore blissfully unaware of it, and they can't help but spread confusing misinformation as a result. It’s a real shame, too, because the proof itself is surprisingly simple and elegant. Anyone with a basic comprehension of calculus can replicate it for themselves, which means you don't need an advanced degree to understand the argument.

Here's how it works.

I’d like to introduce you to the intrepid space explorer, Annie the astronaut. At this particular moment, Annie just so happens to be soaring through the furthest reaches of outer space, far away from any massive objects like stars or planets. As part of her mission mandate, Annie must catalogue her encounters with any passing objects, and she naturally accomplishes her task through the use of a very large, and very sophisticated, meter stick. Furthermore, any time she measures the location of a passing object, she uses her on-board block to record the time at which it occurred. The result is thus an ordered pair of numbers, (x,t), which physicists refer to as an event.

Now let us imagine what would happen if a second space explorer, whom we’ll call Jim, just so happens to cruise on by. Just like Annie, Jim is also charged with taking his own measurements, which means he also has his own a space-age meter stick and on-board clock. Jim, however, is moving with some velocity v relative to Annie. Using the language of physics, we would therefore say that Jim travels in his own inertial frame of reference. Unsurprisingly, Jim therefore measures his events a little bit differently, and we can represent his perspective through the coordinates x-prime and t-prime (x’,t’). Finally, for the sake of personal convenience, we may further assume that Jim and Annie both agree to synchronize their instruments at the moment their origins intersect, which means they both agree to label that event as (0,0).

 

Now suppose that Annie and Jim both observe an event during their encounter. Say, a piece of nearby space debris happens to collide with another. Naturally, Annie performs her measurement, which she records as the numbers (x,t). Likewise, Jim does the same thing from his perspective, resulting in (x',t'). 

So far so good, right? But this raises an interesting question:

Question: Given Annie's measurement of some event, (x,t), plus her velocity v relative to Jim, is it possible to calculate Jim's measurement, (x',t'), of the same event?

This kind of calculation has a name in physics, and it is called a transformation. At first glance, it almost comes across as a boringly trivial thing to ask, doesn't it? Yet that’s exactly what makes this thought experiment so beautiful. It just feels like the result ought to be intuitively dull. But let's suppose, just for the sake of argument, that we know nothing whatsoever about the underlying nature of space, time, or motion. What minimal set of assumptions do we require in order to generate a unique solution that also jives with our everyday experience? 

Not many people realize this, but this simple question is the foundation of Einstein’s theory of special relatively. It’s such a deceptively boring question, too, that most people would never even think to ask it. Yet the moment we take the time to walk through it, we are immediately forced to abandon every naïve intuition we ever had about the nature of space and time. So by all means, get out a pen and piece of paper and follow along. All you need is basic understanding of high school mathematics, and you too can see for yourself why the speed of light must be a universal constant that no one can exceed.

Assumption #1: The transformation is a function of space and time.

That’s easy enough, right? After all, the whole point of this thought experiment is to transform from Annie’s coordinates into Jim’s. It also tells us that we can ignore such factors as the temperature of the meter stick and the metallic composition of the clocks. Presumably, these sorts of things can be controlled for, so they should not have any effect on the transformation anyway. It is also conceivable that space itself exhibits some kind of weird hysteresis effect, such that there are multiple possible outcomes for any given transformation. In practice, however, none of this stuff has ever been observed, and so we may reasonably assume that it won’t be an issue here.

Assumption #2: The laws of physics are identical in all inertial frames of reference.

This is known as The Principle of Relativity, and it is a cornerstone to our entire understanding of motion through space and time. Basically, it tells us that there is no reason to think Annie's frame of reference is fundamentally different from Jim's. Presumably, the universe does not care that Annie is four feet to the left of Jim or one hundred miles to the right. It does not care if an event occurs at 3:32 pm vs 11:54 am, nor does it distinguish between Jim's motion to the right vs Annie's motion to the left. Both observers feel as if they are the one at rest while the is the one moving.

One important consequence of this assumption is that any experiment performed in one frame of reference must yield the same result when performed in the other. For example, suppose Annie holds up two magnets and measures the force between them. Then, for whatever reason, Jim happens to replicate that exact same experiment in his own cockpit an hour later. All other things being equal, it seems natural to expect that Jim's result should perfectly replicate Annie's. It simply shouldn't matter that Jim is 9,000 meters away, or that he's moving to Annie's left at 50 meters/second, or that he's doing his experiment on a Tuesday morning. The universe does not care where you are, what time it is, or what direction you happen to be moving. The magnets should behave exactly the same in all instances.

Assumption #3: The Law of Inertia---An object in motion shall remain in motion, and it shall travel along a straight-line trajectory unless acted upon by an external force.

Easy, right? Now let's see what we can deduce from these basic assumptions.

To begin, imagine a piece of floating space rock that happens to move past Annie's spaceship. From her point of view, she observes the rock casually floating on by with some constant velocity in accordance with the law of inertia. For convenience, let's call this velocity u₀, just to avoid any confusion with Jim's relative velocity v. Thus, using the language of calculus, we would say that the derivative of the rock's position, x, with respect to time, t, is equal to u₀:

dx/dt = u₀

Now let’s consider the same encounter from Jim’s perspective. According to the law of inertia, Jim also observes that the same rock is moving along with some constant velocity. Jim, however, is also moving with some constant velocity v relative to Annie, which means his measurement of the rock's velocity yields a different value. Thus, we have a slightly different expression for Jim, which is written as

dx’/dt’ = u₀'

Now watch what happens when we take the derivative with respect to Annie's position:

d/dx ( dx’/dt’ ) = d/dx (u₀') = 0

According to the law of inertia, the rock's velocity, u₀', is a constant throughout space and time, and so the derivative naturally evaluates to zero. If we then swap the denominators and calculate the antiderivative, we quickly find that

d/dx ( dx'/dt' ) = d/dt' (dx'/dx ) = 0 

dx'/dx = A .

This result should feel perfectly intuitive. All it says is that, given some tiny change in the rock's position from Jim's perspective (dx'), Annie observes some proportional change in position from her perspective (dx). If we then take the ratio of these two changes, we get a constant value that does not depend on either space or time. If we then repeat this argument three more times, we get three more ratios for a total of four unknowns constants:

Now let's take the antiderivative of the first two expressions. The first case tells us that

x' = Ax + T(t) ,

where T(t) is some arbitrary function of Annie's time coordinate. The second case then tells us that

x' = X(x) + Bt ,

where X(x) is some other arbitrary function of Annie's spatial coordinate. If we then compare these expressions side-by-side, it is easy to that there is only one possible solution:

x' = Ax + Bt.

Finally we repeat the same argument with Jim's time coordinate, t', and we find that:

t’ = Cx + Dt .

Looking at these two expressions side-by-side, we should immediately see that the transformation from Annie’s frame of reference into Jim’s takes on a linear structure---that is to say, it is a linear transformation expressed by a system of linear equations. And that just feels intuitive, right? Lots of things in nature of linear, so it should come as no surprise that our result should take on this simple structure. And since the structure is linear, we should immediately feel inclined to express this relationship using standard matrix-vector notation. That is, after all, what matrix-vector algebra was specifically designed to handle:

 

By the way, if you're not familiar with matrix-vector notation, then feel free to pause now and look it up. It is important to be comfortable with this stuff as we move forward.

 

One major advantage to this formulation is that it allows us to easily calculate the inverse transformation from Jim's frame of reference back into Annie's. This is accomplished by calculating the matrix inverse, which leads to the following:

 

Note that little delta (Δ) here simply represents the determinant of the matrix, which is AD-BC for a 2x2 matrix. All that remains for us now is for us to derive the four mystery coefficients.

To that end, consider what would happen if Annie measures Jim’s location. By the law of inertia, she has to observe a straight-line trajectory satisfying x = vt. By definition, however, this same location also corresponds to Jim’s origin at x’ = 0. Let us therefore substitute this information directly into the transformation for x’, such that

x' = 0 = Avt + Bt .

A little bit of algebra later, and we now find that the constant B must satisfy:

B = -Av.

Let us further imagine the exact same situation in reverse. That is to say, Jim measures Annie's position from his perspective, which he naturally observes as x’ = -vt’. In other words, he sees the exact same thing that Annie did, but in reverse. Again, by definition, this corresponds to Annie’s origin at x = 0, and so the transformation from Jim’s frame of reference follows a similar argument:

0 =  (1/Δ)(Dx' - Bt') = (1/Δ)(-Dvt' - Bt').

A little bit more algebra, and we soon find that

D = -B/v = A.

In other words, the two elements along the main diagonal must be the same---a fact that will be very important later one. The transformation from Annie's frame of reference into Jim's can now be written as follows:

Next, suppose that Annie decides to measure some arbitrary time interval with her clock; say, the time, T, in seconds, that it takes for her heart to beat ten times. From Jim’s perspective, this event must transform to the location x = 0, and so it appears to last a time interval of t ' = AT seconds. 

But what exactly should we expect to happen if we perform the same experiment in reverse? That is to say, Jim measures the time it takes for his heart to beat 10 times, and he also finds that it takes exactly T seconds. Meanwhile, Annie cruises on by in her spaceship, and she observes a time interval of t = AT/Δ. According to the principle of relativity, there is no reason for Annie's frame of reference to behave any differently from Jim's. That means Annie must observe the same time interval as Jim did when the situation was reversed. In other words, Annie's measurement t is necessarily the same as Jim's measurement t'. This forces us to conclude

AT = AT/Δ, 

from which it immediately follows that the determinant, Δ, equals 1. The inverse transformation from Jim's frame of reference back to Annie's can therefore be written like this:

At this point, it helps to do a little bit of rearrangement on the transformation. Note that this is not imposing any assumptions, but simply cleaning up the expression so that it better matches our modern conventions.

To begin, let's factor out the coefficient A and then rename it to the Greek letter gamma (γ). This little guy is called the Lorentz factor, and it easily the most important parameter in all of relativity. In doing so, however, we also encounter another little factor of C/A. Since this is just some constant number divided by yet another constant number, it is likewise nothing more than some arbitrary constant number. Thus, for lack of anything better to call it, let us simply replace it with the letter F. Our updated transformation now looks like this:

 

We are are now ready to introduce a fourth assumption into our hypothetical universe.

Assumption #4: All coordinate transformations must form a mathematical group.

For those of you unfamiliar with group theory, this may sound a little strange, but I promise it's actually perfectly sensible. In this case, all it says is that a transformation acting upon another transformation must also be a transformation. 

Here's how it works. Suppose a third observer, whom we’ll call Carl, happens to pass on by. Annie therefore observes Jim moving to the right with velocity v₁ and Carl moving along with velocity v₂. If, however, we were to transform to Jim's perspective, then he naturally observes things slightly differently. As expected, he sees Annie move along with some velocity v₁', and Carl moving along with some different velocity, which we'll call v₂'. Finally, if we transform yet again into Carl's perspective, then he naturally sees things differently yet again, which we can indicate using the double-primed coordinates. Carl therefore sees Annie moving along with some velocity v₁'', and he sees Jim moving along with some other velocity, which we'll call v₂''.

Now let us impose the condition of a mathematical group: a transformation from Annie (x,t) to Jim (x',t'), followed by yet another transformation from Jim (x',t') to Carl (x'',t''), should naturally be the same as a direct transformation from Annie (x,t) to Carl (x'',t''). So let’s write that out mathematically. Starting with the transformation from Annie to Jim:

followed by the transformation from Jim to Carl:

 

 

we naturally have the transformation from Annie to Carl: 

 

We now multiply the two matrices together, yielding a new transformation which looks like this: 

This thing may look complicated at first glance, but it really isn't that bad. Remember that all we care about is the simple fact that this new expression needs to obey the rules of a transformation. That includes all properties of transformations which we have already discovered thus far, which includes the condition that the two main diagonal elements must be the same (D = A). In other words,

1 - F₁v₂' = 1 - F₂'v₁ .

Again, we do a little bit of algebra, and we quickly find that:

v₁/F₁ = v₂'/F₂'.

This may not look like much, but it's actually a very peculiar result. Remember that the relative velocities between Annie, Jim, and Carl are completely arbitrary. We're the ones in charge of this thought experiment, which means we can easily set them to any values we like. For example, I could could hypothetically double the value of v₁ while simultaneously leaving v₂' untouched, and this equality still has to hold. Yet if you look closely, the right side of this equation does not depend on v₁ at all, which means it cannot possibly change, no matter what values I pick. How can this be true?

The only way to reconcile this contradiction is for both ratios to evaluate to some universal constant that does not depend on either velocity. And since we have no idea what that constant is, I'm just going to assign it another random letter like... I dunno... a. We therefore have,

v₁/F₁ = v₂'/F₂' = a .

Remember, this relationship must be true for any arbitrary coordinate transformation. Therefore, our original transformation from Annie to Jim must likewise obey the same rule. That little constant F must therefore evaluate to v/a for all coordinate transformations. That leaves us with a new transformation which looks like this:

Now let's take a moment to remind ourselves of another useful fact that was already derived earlier. Namely, that the determinant of any transformation matrix must equal 1, no matter whose frame of reference it happens to represent. A little bit more algebra later, and we find that our mysterious Lorentz factor must evaluate to the following:

 

 We are therefore left with a coordinate transformation that finally looks like this:

 

 

Clearly, the only parameter we have left to make sense out of is that mysterious little constant a. So let's take a moment to think about what exactly that thing represents.

 

For starters, the astute observer might notice that a just so happens to have units of velocity squared [m²/s²]. That's a little odd, but it does motivate us to rewrite a in terms of a new velocity constant, which we'll call c, such that a = +/-c². What exactly this magical velocity represents, we cannot yet say. But clearly, there are only three possible scenarios to consider:

1. a = 0 (thus implying c = 0)
2. a is positive, implying that a = +c², or 
3. a is negative, implying that a = -c².

Now let's consider each case one-by-one.

Clearly, we can immediately reject the first option outright because all it would do is introduce a bunch of divisions by zero. 

The second option is likewise not physically viable, but the reason is not quite as obvious. It begins by asking what would happen if Annie observes Jim traveling to the right with some moderate velocity like v = c/10. Meanwhile, Jim observes Carl, who is likewise traveling to the right with the same relative velocity of c/10. Carl, in turn, observes yet another traveler with velocity c/10, who observes another, and so on. 

Now suppose that Annie measures her heartbeat and observes a delay of exactly t = 1.0 second. From Jim's perspective, he likewise observes Annie's heartbeat, and he naturally measures some duration t' from his frame of reference. Carl then measures a value of t'', and so on for every other observer down the train. But what exactly should we expect to happen if we simply repeated this transformation a hundred times over? The answer, it turns out, is a little strange. Given enough transformations, Annie's heartbeat will actually appear to flow in the negative direction. As in, literally, the observers will eventually perceive Annie's flow of time as moving backwards! 

Obviously, that cannot possibly be the case. So let's introduce a 5th assumption to our universe:

Assumption #5: For any two events, (x₁,t₁) and (x₂,t₂), if x₂ = x₁ and t₂ > t₁, then all transformations must likewise result in t₂' > t₁'.

In other words, all observers must agree that time tends to move forwards for certain durations. This condition immediately removes the second option from our list, leaving behind only one logical possibility. Our final transformation therefore must take on the following structure:

Finally let us remove the matrix-vector notation and write the transformation in its standard form, as shown here:

This expression has a name in physics, and it is called the Lorentz Transformation. It is also an incredible result when you think about it. Remember that we started this thought experiment by asking a seemingly trivial question and expecting a trivial result. Yet of all the different mathematical possibilities we could have imagined for transforming between inertial frames of reference, this is the only one that is consistent with our assumptions. Plus, it’s not like we demanded anything extraordinary, either. We’re talking about stupidly basic assumptions like the law of inertia and the tendency for time to move forward. It simply cannot be any other way without the universe suddenly exploding into a bunch of really bizarre manifestations.

 

Notice also how the word "light" was never mentioned a single time throughout this entire derivation. If anything, the very phrase itself---the speed of light---is nothing but a blundering misnomer. That little mystery constant c has absolutely nothing whatsoever to do with photons or electromagnetic radiation. It's a fundamental statement about the interplay between space, time, and motion. That's why many physiscists prefer not to use the phrase "speed of light." Rather, a far more appropriate name would be something like "the speed of causality," in that it represents the fastest possible speed at which any single event can ever appear to causally influence another.

"But wait!" I hear you saying. "Who says that I can't travel faster than light? Surely, all I have to do is hop into a space ship and gun the engines. Sooner or later, I have to exceed the speed of light, don't I?"

 

But will you? Consider again that little piece of space rock floating by from Annie's perspective. According to the law of inertia, Annie necessarily observes a velocity of

dx/dt = u₀

Now ask yourself what velocity, u₀', Jim should expect to see from his perspective. The answer is actually perfectly straightforward. First, we use implicit differentiation to derive the following expressions:

dx' = γ(dx - vdt)

dt' = γ(-vdx/c² + dt)

Next, we simply divide the one by the other to find this:

dx'/dt' = (dx - vdt)/(dt - v dx/c²) .

Remember that, by definition, this quantity has to represent the transformed velocity, u₀', from Jim's perspective. Likewise, the quantity dx/dt represents the relative velocity u₀ between Annie and the rock, which means we finally arrive at this expression here:

dx'/dt' = (u₀ - v)/(1 - u₀v/c²) = u₀' 

This is the famous velocity addition formula of special relativity, and you can clearly see for yourself that velocities do not NOT add linearly. It seems strange and counterintuitive, but it is also the only way to preserve a well-behaved universe that obeys our earlier assumptions.

Now consider again that that long train of observers, all moving past each other with some relative velocity of c/10. You would think that eventually some observer will see Annie zooming off faster than the speed of light, but do they really? Just try it for yourself and graph the result. This is what you'll see:

Isn't that weird? No matter how many times we repeat the transformation, the velocity of that little piece of space rock will never exceed the mystery constant c. In fact, if we let the velocity equal c itself, then all observers in all inertial frames of reference will likewise agree that it is moving exactly that fast. That is to say, if any observer measures an object moving with speed c, then ALL observers will likewise meausure a speed of c. This has to be the case, because it is the only logical outcome that is consistent with the assumptions we've made.

 

This is exactly why physicists are so confident in the idea of a universal speed limit. It's not just a matter of "well, the evidence seems to indicate." It logically cannot be any other way! Any universe that allows for objects to move beyond some universal speed limit would completely violate our most basic presumptions about space, time, and motion. It is therefore not matter of hopping into a spaceship and firing the engines. The very geometry of the universe itself simply doesn't allow it.

 

So what exactly is the value of that universal speed limit, anyway? To answer that question, you just have to start doing some basic experiments. In our particular universe, it just so happens to be 299,792,458 meters per second---a very large number. So large, in fact, that we can usually approximate it as infinite and still get reliably good results. Letting c approach infinity thus leads us to the following transformation:

These equations are known as the Gallilean transformation, and they finally represent the simple, intuitive answer that we were originally expecting to find when we first began this exercise. However, it's interesting to point out that we practically had to trip over the correct, Lorentizan transformation just to get here, not to mention impose the highly dubious assumption of infinite value for that mysery constant. It all just goes to show that you never know what you might discover if only you take the time to enumerate a few basic assumptions and then follow the argument wherever it leads.

Thanks for reading.

 

References

1. Einstein, A., "On the electrodynamics of moving bodies," Annalen Phys. 17 (1905) 891-921 [link]
2. Pelissetto, A., and Testa, M., "Getting the Lorentz transformations without requiring an invariant speed," American Journal of Physics, 83, 338 (2015) 338-340 [link]
   
3. W. von Ignatowsky, "Das Relativitatspringzip," Archiv der Mathematik und Physik 17, 1-24 (1911)
   

An Exploration into Classical Theism, Part 5: Aristotle and Metaphysics

It’s hard to overstate the influence of Aristotle on Thomist philosophy. You can practically smell the Aristotelian metaphysics as it oozes from every orifice. Thomas Aquinas even refers to Aristotle himself by the reverent title of The Philosopher. In many respects, Thomism is basically just a reconciliation between Christian theology and the pagan philosophies of classical Greece. Every time you hear strange, esoteric terms like prime mover, efficient cause, or actualized potential, you are basically hearing Aristotle. It’s another gigantic red flag that demonstrates a total absence of serious intellectual rigor by classical theism.

It’s important to understand that Aristotle is not exactly well-respected in modern science or philosophy. We’re talking about a guy who believed in a geocentric solar system and the five elements of nature. He believed that women have fewer teeth than men, and that fully-formed organisms could spontaneously generate from non-living material. He believed that upward motion is superior to downward, and that forward is superior to backward. He believed the universe was perfectly spherical, and that celestial objects are continually being pushed along perfect circles around the earth. It was probably cutting-edge stuff back in the 13th century when Aquinas first encountered it, but science, philosophy, and logic have all moved on just a tad in the 800 years since.

Even the very word itself---metaphysics---has no official meaning in modern philosophy. It literally translates to “after the physics” in Greek, in that once you finish reading Aristotle’s books on the physical stuff, then apparently there’s this other collection of books you need to read after [1]. It’s basically just an arbitrary label that some random scribe happened to tack on to the documents a few centuries after the fact. Now, for whatever reason, the title just sticks, and the subject matter has exploded into an entire sub-discipline of its own. Yet to this very day, most self-identified experts in metaphysics will actually admit openly that it has no clear definition or scope [1, 2, 3]. Even when they do try to give a definition, it usually comes out as meaningless nonsense, like, “What is the nature of being?” It’s like a pretentious buzzword used only by pseudo-intellectual hacks who want to sound important without necessarily tying themselves down to any tangible claims.

Not many people realize this, but there is actually a very strong opposition within mainstream philosophy against metaphysics. These are not obscure movements, either, but powerful objections from highly influential figures throughout history. Immanuel Kant, David Hume, Francis Bacon, Voltaire, Ludwig Wittgenstein, Karl Popper, and Rudolf Carnap all wrote extensively about the meaningless gibberish that permeates metaphysics. We’re talking about an entire philosophical tradition that has no idea what it even is. It has no official scope, it asks meaningless questions, it follows no recognizable methodology, and it solves no problems. Most of the time, it barely even qualifies as coherent, as any casual inspection of their literature will immediately reveal [4,5]. It’s so embarrassingly bad that I could probably write a separate 10-part series of essays just on the philosophical failures of metaphysics alone.

So once again, there is almost no point in entertaining Thomism as a serious philosophical tradition. Aristotelian metaphysics is riddled with things that are wrong, and they have been known to be wrong for hundreds of years. Yet if you listen to Thomist philosophers, they’ll have you believe that all progress in metaphysics essentially ended with Aristotle and Aquinas---as if a couple of armchair philosophers have conclusively solved everything we would ever need to know about the fundamental nature of space, time, causality, and even existence itself.

This is exactly why Christian apologists---and especially the classical theists---absolutely love metaphysics. It’s the philosophical security blanket all over again. It has all the allure of sophisticated academic inquiry without any of the accountability. They openly reject science as a means of investigating these kinds of questions, and they follow no axiomatic system of formal deduction. Thus, for all practical purposes, they can basically just say whatever they want and never have to worry about getting proved wrong. Furthermore, if anyone dares to criticize their brilliance, then they can just reject it all with another casual wave of their hands. Not only must you study the collective works of Thomas Aquinas and his modern interpretations, but now you apparently have to throw in the fourteen books of Aristotle as well. If you don’t appreciate the distinction between a formal cause and a final cause; or between act and potency; or between universal substance and substratum; then you’re just an uneducated peon who is unworthy of offering any substantial criticism of “serious” theology.

Notes/References

1. Metaphysics, Stanford Encyclopedia of Philosophy (2007) [link]
2. It is difficult, if not impossible to come up with an adequate definition of Metaphysics---Moreland, J. P., and Craig, W. L., Philosophical Foundations for a Christian Worldview, ‎ IVP Academic (2003) [link]
3. Metaphysics, Britannica.com  [link]
4. Chalmers, D., Manley D., and Wasserman, R. (Editors), Metametaphysics, Oxford University Press (2009) [link]
   
5. Metaphysics is inquiry beyond or over beings, which aims to recover them as such and as a whole for our grasp---Heidegger, M., “What is Metaphysics?”
   

An Exploration into Classical Theism, Part 4: Word Salad

As we discovered last time, the philosophy of Thomism has some major issues with basic epistemology. It pretends to know things that cannot possibly be known, and then it constantly obsesses over answers that have no discernable difference either way. This would all be bad enough on its own, and it immediately disqualifies Thomism from any serious conversation in the philosophical arena. In the realm of Christian philosophy, however, this level of failure is just the warm up act for an ever-expanding heap of continuous failures.

A perfect example of this phenomenon is the very the writing style of Thomas Aquinas. It’s terrible! It is not the work of someone who is thinking rigorously about his arguments and then editing them for clarity. Rather, you get the distinct impression that Aquinas just scribbled words onto paper in an unfiltered stream of consciousness.

To demonstrate, consider the following paragraph, which I honestly plucked entirely at random from the Summa Theologica (pp. 522). In response to the question of Whether the five exterior senses are properly distinguished, Aquinas says:

Size, shape, and the like, which are called "common sensibles," are midway between "accidental sensibles" and "proper sensibles," which are the objects of the senses. For the proper sensibles first, and of their very nature, affect the senses; since they are qualities that cause alteration. But the common sensibles are all reducible to quantity. As to size and number, it is clear that they are species of quantity. Shape is a quality about quantity. Shape is a quality about quantity, since the notion of shape consists of fixing the bounds of magnitude. Movement and rest are sensed according as the subject is affected in one or more ways in the magnitude of the subject or of its local distance, as in the movement of growth or of locomotion, or again, according as it is affected in some sensible qualities, as in the movement of alteration; and thus to sense movement and rest is, in a way, to sense one thing and many. Now quantity is the proximate subject of the qualities that cause alteration, as surface is of color. Therefore the common sensibles do not move the senses first and of their own nature, but by reason of the sensible quality; as the surface by reason of color. Yet they are not accidental sensibles, for they produce a certain variety in the immutation of the senses. For sense is immuted differently by a large and by a small surface: since whiteness itself is said to be great or small, and therefore it is divided according to its proper subject.

With all due respect to the “sophisticated” philosophical traditions of classical theism, this entire paragraph is nothing more than a frantic expulsion of incomprehensible word salad. This is not the writing of someone who knows what he’s talking about. It is the writing of someone who is trying to trick you into thinking that he knows what he’s talking about.

It’s important to understand that is not just a mere matter of me failing to understand the jargon. What we are witnessing here is a fundamental inability of Thomas Aquinas himself to formulate coherent thoughts. There are thousands more examples of this stuff littered all throughout his writing. It’s a textbook example of classical a philosophical principle known as bullshit---the use of pretentious-sounding language designed to sound impressive while simultaneously avoiding any tangible claims [1]. Noam Chomsky famously captured the essence of this phenomenon with his sentence, Colorless green ideas sleep furiously. It illustrates the distinction between syntax and semantics, in that merely constructing a grammatically valid sentence does not necessarily guarantee of a meaningful thought.

In an ideal world, this sort of gibberish nonsense would be squashed into oblivion, but the Thomists seem to treat this as one of its greatest selling points. It’s the philosophical security blanket all over again, whereby any criticism can be dismissed outright with a casual wave of their hands. After all, if you don’t find Aquinas’ arguments compelling, then obviously you just don’t understand Aquinas, and therefore you’re in no position to offer any serious rebuttals. Thomas Aquinas is, after all, the greatest philosopher who ever lived, and we should all be glad to grow closer to God by studying his work.

The really sad thing about all this incomprehensible babbling is that it isn’t just bad philosophy; it’s bad theology! Nobody wants to attend a church that glorifies the distinction between common sensibles versus accidental sensibles. They want to feel the spirit and learn how to behave like better people in their community. So in what logical universe does it make any sense for the Catholic church to embrace the writings of Thomas Aquinas as official doctrine? I should not need a magic decoder ring just to make sense out of this stuff. If you cannot learn to communicate effectively, then even the best ideas in the world cannot be distinguished from no ideas at all. 

Continue to Part 5.

Notes/References

1. Frankfurt, H. On Bullshit, ‎ Princeton University Press (2005) [link]

An Exploration into Classical Theism, Part 3: Thomas Aquinas

After experiencing a sizable body of classical theist media, it is pretty safe to say that the community loves Thomas Aquinas. The guy is, after all, a literal saint in the eyes of the Catholic church, and his writings have been elevated to the status of near scripture. Thus, in the eyes of classical theism, Thomas Aquinas is officially the greatest super-genius who ever walked the Earth [1,2,3,4,5]. It’s almost cultish how much they adore the guy, and it reminds of how Mormons tend to think of Joseph Smith [6]. Modern classical theism is, for all practical purposes, synonymous with Thomism, and so any exploration into the subject requires us to get familiar with Thomas Aquinas.

The first thing about Thomism that immediately stands out to me is the sheer volume of literature involved. The Summa Theologica, for example, is generally considered to be Aquinas’ magnum opus, and the document is over 4000 pages in length. After that, you have the Summa Contra Gentiles, which is another 700 pages, followed by the Commentaries on the Gospel of John, which adds yet another 1000 pages on top of that. The Complete Works of Thomas Aquinas is available on Kindle, and it boasts over 17-thousand pages of documentation [7]; only it’s not really a “complete” collection, because it’s still missing the Disputed Questions on Truth (1300 pages), The Disputed Questions on Virtue (420 pages), and On Evil (560 pages).

It’s not just Aquinas that appears to be in love with the sound of his own voice. In an apparent desire to emulate his master, Thomist Philosopher Edward Feser has likewise produced a substantial volume of his own literature in excess of 2000 pages and counting [8,9,10,11,12,13,14,15] (and that’s not even including his regular blog!). It’s almost comical how bloated the literature is on this stuff, and I can’t help but feel reminded of the famous quote by Winston Churchill:

This report, by its very length, defends itself against the risk of being read.

Granted, mere word count alone is not some automatic deal breaker, but it can be gigantic red flag. In the world of classical theism, the enormous volume of literature almost serves as a kind of security blanket. Anyone who dares to refute some particular aspect of Aquinas’ first way, for example, can simply be ignored on the grounds that they are not yet properly educated on the foundations of rigorous theology. Unless you’ve completely digested the requisite introduction of six full-length books plus seven journal articles, then you are not even worthy of a proper rebuttal [16]. They do this sort of thing all the time, even when other PhD theologians are the ones giving the actual critique [17].

But hey, if that’s how you want to play it, then fine. Let’s take a look at Aquinas, shall we? What sort of topics were so important to the good philosopher that he honestly needed over 17,000 pages of documentation? To answer that question, we need look no further than the table of contents. In the Summa Theologica alone, we find hundreds upon hundreds of pages devoted to such thrilling topics as:

• Whether angels assume bodies?
• Whether the angels exercise functions of life in the bodies assumed?
• Whether an angel is in a place?
• Whether an angel can be in several places at once?
• Whether several angels can be at the same time in the same place?
• Whether an angel can understand many things at the same time?
• Whether the movement of an angel is instantaneous?
• Whether an angel’s act of understanding is his substance?
• Whether an angel knows himself?
• Whether an angel knows another? 
• Whether one angel speaks to another?
• Whether local distance influences the angelic speech?
• Whether the orders of the angels are properly named?
• ... and so on, and so forth.

You may be familiar with the question, “How many angels can dance on the head of a pin?” That question is a direct mockery of the scholastic tradition typified by people like Thomas Aquinas. The guy had absolutely no problem with writing dozens of detailed essays over topics that were simultaneously irrelevant and unknowable. It reminds me of a popular debate topic among sci-fi nerds that asks whether or not the USS Enterprise could defeat an Imperial star destroyer in space battle. It’s a totally meaningless question for which there is no objectively correct answer, and it offers no practical distinction even if there were. Yet, for some strange reason, the internet is full of highly passionate nerds arguing their pet theories anyway [18].

This is a gigantic embarrassment, and it betrays a number of utterly dismal failures in the entire classical theist philosophy. The most immediate failure is the tendency to derive unwavering conviction over questions that cannot possibly be answered with certainty. On the topic of angels, for example, Aquinas explores dozens of questions about their physical composition, biological functions, intellectual capacity, and even their social structure. It really makes you wonder: How in the hell could he possibly know any of this information? Has he even seen an angel? Does he interact with them regularly? Did he conduct any field studies with documented observations? What experimental tests did he perform to validate his theories against empirical predictions?

Obviously, he didn’t do any of that stuff. Everything Thomas Aquinas pretended to know about angels was derived entirely through pure, armchair philosophy---as in literally, he thought really hard about it for a while and then wrote down whatever he decided the answers must be. It’s basically the philosophical equivalent to making shit up out of nothing and then hiding that fact under a veil of pretentious rationalizations. It’s a dead giveaway that Thomas Aquinas, and by extension all of his modern proponents, have no understanding of how basic epistemology works. They honestly believe that if they just close their eyes and concentrate hard enough, then the power of reason will magically endow them with rote facts about objective reality; not just mere hypotheses, mind you, but absolute certainties beyond all rational dispute.

Barring that failure, let’s suppose we’re feeling generous and just grant anyway that local distance indeed influences angelic speech. Now what? What am I supposed to do with that information? Do I need to account for that in any way? Can I measure some sort of time the delay between prayer and response? Do I need to pray more loudly if I'm further way from angels so that they can hear me?

Or better yet, what if the opposite conclusion were true? What changes? Does this mean instantaneous communication is possible? Can I exploit that to send information backwards in time? No? Then what difference does it make? What decisions can I now make in the real world with real, empirical consequences, that will manifest under the expectation of a spatial independence on angelic speech? Please enlighten me.

The obvious problem is that it makes absolutely no difference either way. Angels, according to Thomism, are "immaterial" beings and thus cannot be observed or quantified in any empirical capacity. So even if we grant entirely that angels exists (which we don't), then there's nothing we can ever possibly do about it. It’s another profound failing of the entire Thomist tradition, in that they love to obsess endlessly over trivially irrelevant information that carries no distinction between truth and falsehood.

A classic example of this behavior is the so-called doctrine of Divine Simplicity, which basically holds that God is perfectly simple in his composition. That is to say, God is without parts, and the very being of God is identical to the attributes of God (whatever that means). So let's ask a simple question: What if, hypothetically, this doctrine turned out to be mistaken? Say, for instance, God was actually comprised of two parts rather than one. How exactly would that change anything? Do you suddenly stop going to church over this? Would you pray less, or pay any less tithing? Do you stop marveling at the beauty of the universe? Do you love your neighbors any less?

Clearly, the answer is no. Nothing actually changes if this doctrine happens to be wrong, yet you still find Thomist philosophers wasting hours of our lives about it anyway [19,20,21]. It’s as if the Thomist community is completely clueless how basic Christianity operates. Remember that God is supposed to be an all-loving being who desperately wants to build a deep, personal connection with all of his human children. We will literally be damned if we fail to build this relationship, so presumably it ought to be easy to connect with God directly and get to know Him. Yet, according to the classical theists, we cannot even hope to have a coherent discussion about God’s very existence without first studying a mountain of literature in excess of the Bible itself. 

Is it any wonder why the Catholic church is hemorrhaging members? It should not require a PhD in theology just to demonstrate basic religious facts. A God that hides Himself behind a wall of bloated ivory-tower literature is hardly a God that deserves any serious consideration, let alone devotion.

Continue to Part 4.

Notes/References

1. Brian Holdsworth, “Why St. Thomas Aquinas is so Important” (2020) [link]
2. Bishop Robert Barron, “Bishop Barron on St. Thomas Aquinas” (2009) [link]
3. Bishop Robert Barron, “Bishop Barron on Thomas Aquinas’ Writing” (2011) [link]
4. EWTN, “St, Thomas Aquinas---Who is St. Thomas Aquinas” [link]
5. “The Thomistic Institute exists to promote Catholic truth in our contemporary world by strengthening the intellectual formation of Christians at universities, in the Church, and in the wider public square. The thought of St. Thomas Aquinas, the Universal Doctor of the Church, is our touchstone.” – The Thomistic Institute [link]
6. “Joseph Smith, the Prophet and Seer of the Lord, has done more, save Jesus only, for the salvation of men in this world, than any other man that ever lived in it.” – John Taylor, Third President of the LDS Church
7. The Complete Works of Thomas Aquinas, Kindle Edition [link]
8. Feser, E., Five Proofs of the Existence of God, 336 pages (2017) [link]
9. Feser, E., Aquinas: A Beginner’s Guide (2009), 224 pages [link]
10. Feser, E., Scholastic Metaphysics: A Contemporary Introduction, 290 pages (2014) [link]
11. Feser, E., Aristotle’s Revenge: The Metaphysical Foundations of Physical and Biological Science, 515 pages (2019) [link]
12. Feser, E., Philosophy of Mind: A Beginner’s Guide, 276 pages (2006) [link]
13. Feser, E., Locke, 196 pages (2013) [link]
14. Feser, E., The Last Superstition: A Refutation of the New Atheism, 312 pages (2010) [link]
15. Feser, E., On Nozick, 104 pages (2003) [link]
16. Feser, E., “A Clue for Jerry Coyne” (2011) [link]
17. Feser, E., “Classical Theism and the Nature of God" (2019) [link] (being at timestamp 34:00)
18. “USS Enterprise-D vs Imperial II Star Destroyer | Star Trek vs Star Wars: Who Would Win” [link]
19. Feser, E., "Distinguishing Classical Theism from Theistic Personalism," Southern Evangelical Seminary YouTube Channel [link]
20. "Robert Barron vs. William L. Craig - Divine Simplicity," YouTube [link]
21. Mathoma, “A Defense of Classical Theology (Part 2): God is not a god," YouTube (2018) [link]
    

An Exploration into Classical Theism, Part 2: The Community

There are many influential figures in the world of Christian apologetics. At present, the most popular names appear to include William Lane Craig, Alvin Plantinga, Frank Turek, Lee Strobel, John Lennox, plus a number of popular YouTube personalities. They’re a pretty productive bunch, churning out regular videos, essays, and podcasts at an impressive pace. They work very hard to give you the impression of a rich, intellectual tradition that supports the ultimate reality of God’s existence as understood by the doctrines of traditional Protestant theology.

Not to be outdone, the Thomist community also has its own collection of influential figures who serve as the public face for their philosophy. The most prominent names appear to include Robert Barron and Edward Feser, plus a number of minor personalities and anonymous YouTube channels. They’re not nearly as popular as their Protestant counterparts, but they do seem to have a significant and dedicated following.

One the first things to jump out at me as I began my research into Thomism is the community itself. To be perfectly frank, this community is overrun with some the most pretentious philosophical snobs I have ever had the misfortune to encounter. I’m talking about the kind of people who take every opportunity to name-drop philosophical figures like Sartre and Nietzsche, or who unironically use the word “metaphysics” in every other sentence. They act as if Thomism is the ultimate paragon of philosophical sophistication, and they make it out as if Christianity is the only logical conclusion one can draw from sincere evaluation of the arguments [1]---not just “mere” Christianity, mind you, but very specifically their own brand of classical theism in the Catholic tradition.

One classic manifestation of this attitude is the way in which Thomists go out of their way to talk trash about the so-called New Atheism. It’s weirdly consistent how they do, too, as if they’re all following some sort of secret playbook. Read any book, watch any lecture, or listen to any podcast on classical theism, and it is very likely that you will be subjected to a brief tirade about the philosophical ineptitude of the entire New Atheist movement [2,3,4,5,6]. They especially seem to enjoy picking on Richard Dawkins, as if he were some sort of holy patron saint to modern atheism [7,8,9,10]. It almost comes off as a goofy form of projection, in that they universally venerate Thomas Aquinas as their philosophical overlord, and so they just take it for granted that the entire atheist community would naturally think the same way about Dawkins. Either that, or they literally have nothing else to go on, and so they’re really just that excited to see their man Aquinas get acknowledged.

It’s important to understand that Thomist philosophy is not exactly well-respected in mainstream philosophical circles. I don’t mean in the sense that a bunch of atheist philosophers are sitting around the water cooler telling jokes to each other about how lame Thomism is. I mean it’s basically ignored. I’ve been engaging openly with popular Christian philosophy for over a decade now, and I’ve only barely just become aware of their existence. The simple fact of the matter is that Protestant Evangelical Christianity is the loudest and most politically active force in American culture, and so it is only natural that the majority of secular backlash would be focused against their particular school of thought.

It’s extremely bizarre to watch the Thomist community process this information. On the one hand, classical theism stands in direct opposition to theistic personalism, and so it is only natural for them to stand with us atheists in denouncing it publicly. On the other hand, standing with us atheists would require them to…. well… stand with atheists. And since atheists are the greatest dummy-heads in the universe, they cannot bear to tarnish their image by having any such association. The result is thus an extremely ham-fisted contortion of reality where atheists are simultaneously 100% right and 100% stupid in their criticism of mainstream religion.

One of the most blatant manifestations of this catch-22 can be found in a 2015 speech by Robert Barron entitled, “Aquinas and Why the New Atheists Are Right” [2]. In it, he very deliberately paints a picture of theistic personalism as some kind of fanciful concoction of the New Atheist movement. He knows perfectly well that hundreds of millions of Protestants around the world happily endorse this theology, but he still cannot help but accuse atheists of fabricating a “Straw God.”

Barron is not alone in this behavior, either, and there are numerous examples of other classical theists following a very similar playbook. Edward Feser, for example, is notorious for his portrayal of modern atheists as a gaggle of imbeciles who have no grasp on how “proper” theology really works [6]---as if the entirety of all Protestant Christianity is merely “unsophisticated” and therefore not even worth mentioning. Catholicism, it seems, is the undisputed champion of all Christian intelligentsia, and you cannot possibly hope to do “serious” philosophy without directly tackling their particular brand of theology. It’s a very pompous attitude that only indicates a fragile little core of highly delicate egos. You almost get the impression that, on some deeply subconscious level, even the classical theists themselves are not entirely confident in their own arguments.

Continue to Part 3.

Notes/References

1. Edward Feser, "The Road From Atheism," (2012) [link]
   
2. Bishop Barron on the New Atheists (2009) [link]
3. Fr. Robert Barron, “Aquinas and Why the New Atheists are Right" (2015) [link]
4. Fr. Pine, “Explaining Thomas Aquinas’ Proofs,” Pints With Aquinas [link]
5. A Defense of Classical Theology (Part 1): The New Atheism and the Cosmological Arguments [link]
6. Edward Feser, “What We Owe the New Atheists” (2014) [link]
7. Pints with Aquinas, "Edward Feser Explodes Richard Dawkins’ “Refutation” of Aquinas’ 5 Ways" (2017) [link]
8. Pints with Aquinas, "Edward Feser Continues to Refute Richard Dawkins’ Objections to Aquinas’ 5 Ways" (2017) [link]
9. Pints with Aquinas, “Aquinas v Dawkins on God’s Existence" (2019) [link]
10. Mark McNeil, “Dawkins vs Aquinas, Part One” (2013) [link]
    

An Exploration into Classical Theism, Part 1: Introduction

I’ve received a number of requests to give a secular analysis of a philosophical tradition known as Classical Theism. I was initially hesitant to get too involved in this stuff, due to the relatively minor influence it carries in mainstream media. By far, Protestant Evangelical Christianity is the dominant force within American politics and culture, so it seemed kind of pointless to pick on a such a fringe group. However, as I exposed myself to more of their literature, I began to realize that this community indeed carries weight over a significant number of believing Christians. It also appears that the secular community has done very little to break down their arguments for a lay audience. The sheer immensity of it all can come off as quite intimidating to a doubting Christian youth, and there are likely many millions of them being manipulated by the destructive ideas it teaches. So for better or for worse, I’ve finally committed myself to a detailed analysis of classical theism, as well as a thorough debunking of their more popular arguments.

For those of you who have never heard of classical theism, it is an ancient philosophical tradition that defines God as the ultimate being. He is not a thing in the universe, per se, nor is He a person in the strictest sense. Rather, God exists as a kind of ipsum esse subsistens, which is generally described with bizarre phrases like “the subsistent act of to be itself [1].” It is arguably one of the first failings of the entire tradition, in that it cannot even define "God" in coherent terms. Their literature is teeming with similar bits of nonsensical gibberish, too, and I'll have a lot more to say on this later. Suffice to say, it's the sort of language that sounds deep and intellectual at first, but fundamentally doesn't mean anything.

The most commonly cited opposition to classical theism is a view known as theistic personalism. Under personalism, God is a being who exists as a thing in reality with various parts coming together into one, divine whole [2]. It's the sort of distinction that, from a purely secular perspective, almost feels like a gigantic exercise in hair-splitting, and very little of this stuff seems to have relevance to the average, pew-sitting Christian. Nevertheless, the classical theists are extremely adamant about these sorts of things, and there is a strong community of PhD theologians who love to debate about it from their ivory towers.

In principle, classical theism is a highly nuanced philosophy with many competing schools of thought among prominent theologians. In practice, however, anyone who honestly cares enough to personally identify with the label of “classical theist” will almost universally be Catholic. Indeed, the Catholic church has openly embraced classical theism as its official doctrine, and the debate against theistic personalism is apparently just a squabble between Catholics and Protestants. So if you ever get the impression that classical theists have a bit of chip on their shoulder, then this seems to explain why.

Another recurring theme in the classical theist community is the universal veneration they seem to have for St. Thomas Aquinas. The very word Thomism even refers directly to the collective philosophical views of Aquinas himself, and I have yet to encounter a single living classical theist who wasn’t also a Thomist. It’s hard to overstate the adoration this community seems to have for the guy. After listening to the classical theists, you get the impression that Thomas Aquinas was the greatest embodiment of pure, philosophical genius who ever graced God’s green Earth. This is hardly surprising, however, once you realize that the Catholic church has formally accepted the writing of Aquinas as its own, second only in significance to the Holy Bible itself [3]. Thus, for all practical purposes, the terms classical theism, Thomism, and Catholicism may as well all be synonymous with each other, and you can pretty much use them interchangeably without much confusion.

At this point, my initial reaction towards the philosophy of classical theism was an overpowering sense of boredom. Perhaps some of you are even feeling it right now. I genuinely do not care about the subtle distinctions between Catholic and Protestant theology, and it’s not like these dudes are winning any popularity contests. According to survey after survey, American religiosity has been steadily declining since the 1990s, and it shows no sign of stopping any time soon [4]. The Catholic church is hemorrhaging members at a record pace, so why even bother with yet another analysis of a bunch of convoluted rhetorical arguments?

 

Despite their decline in overall relevance, I think it is important to remember that the Catholic church is still a highly potent force in American politics and culture. They also continue to hold huge sway internationally, enjoying total dominance over entire continents like Central and South America. They claim over a billion members on their roles worldwide, and significant growth appears to be happening in both Africa and Asia. I find it hard to shake the image of so many poor classrooms full of naive Catholic youth being forced to sit through yet another uncomfortable tirade about the evils of masturbation, or yet another cover-up of sexual misconduct in the clergy [5]. There almost certainly exist millions of trapped youth who struggle to find the right words for articulating their doubts, and it is blogs like this that often give them the resources to break free.

So to all of you doubting young Catholics, just hang in there. This series is for you.

Continue to Part 2.

Notes/References

1. Bishop Barron on Who God Is & Who God Isn't (2013) [link]
   
2. Edward Feser, "Distinguishing Classical Theism from Theistic Personalism" [link]
   
3. “Thomism,” New World Encyclopedia (2020) [link]
   
4. “In US, Decline of Christianity Continues at a Rapid Pace,” Pew Research Center (2019) [link]
5. "Catholic clergy in France abused more than 10,000 child victims, independent commission estimates," The Washington Post (March, 2021) [link]