Aristotelian Metaphysics: Per Se vs. Per Accidens Causation (With Guest Appearances from A Certain Magical Index)

I really like A Certain Magical Index. I’ve watched the anime, or at least the first season of it, three times (the second season didn’t quite sit as well with me), as well as the spinoff, A Certain Scientific Railgun, twice. I have two of its opening themes, “Masterpiece” and “No Buts!”, on my iPod, and I would have “PSI Missing” too if it was on iTunes. And lately I’ve started collecting and translating the original light novels.

But one thing I don’t like about Index is the main character, Kamijou Touma.


I like the concept behind him; a protagonist with the ability to cancel out other people’s superpowers rather than having powers of his own is a pretty cool idea. But Touma just doesn’t have any personality. He has no goals of his own; all he ever does is prevent the villains from achieving their goals. Nor does he have any funny quirks to make him endearing. The only really distinctive thing about him is his bad luck, and that isn’t a feature of him so much as of the world around him. By the end of the show, I felt like the only real incentive I had for caring about him was that Misaka liked him, and Misaka is actually interesting.

Actually, now that I think about it, that’s kind of fitting in a way. Instead of having his own superpowers he just cancels out other people’s superpowers, so instead of having his own goals he just cancels out other people’s goals. But still, it doesn’t make for an interesting character.

However, what I do like about Touma is that he is a perfect illustration of the Aristotelian distinction between per se causation and per accidens causation.

So what are per se and per accidens causation?

Well, go and ask any random person on the street what the temporal relationship between cause and effect is, and they will probably tell you that the cause comes before the effect. But according to Aristotle―and Aristotle is right, of course―cause and effect, in the truest sense, are simultaneous. So why do so many people say otherwise? That’s because they’re failing to distinguish between per se causation and per accidens causation.

A per se cause is one that causes its effect by virtue of itself, whereas a per accidens cause is one that causes its effect by virtue of something that belongs to itself. A per accidens cause generally exists before its effect, but a per se cause exists simultaneously with its effect, and once it ceases to exist its effect ceases to exist as well.

Notice that by definition, per accidens causes are not causes in the truest sense of the word; it isn’t so much the per accidens cause itself as a particular part of the per accidens cause that is a cause in the truest sense. It still makes sense to call it a cause, but this isn’t so much because it is the cause as because it contains the cause.

To see the difference, observe the effects of Touma’s superpower-canceling ability, called the “Imagine Breaker,” on Misaka Mikoto and Accelerator’s powers.

As was mentioned briefly above, Touma is unique among anime protagonists in that he has no superpower of his own. Instead, he has the ability to cancel out other people’s superpowers, on the condition that he touches the location where the power is operating with his right hand.

So let’s start with how Touma’s right hand interacts with Misaka’s ability.


Misaka has the power to control electricity. As you can see in the anime, when she launches lightning bolts at Touma, Touma is able to make them disappear by touching them with his right hand.


Nor does it make a difference if she doesn’t attack using lightning bolts directly. In the spinoff series, A Certain Scientific Railgun, she tries going for a different approach, using her electricity to generate magnetism and then using that magnetism to manipulate iron particles in the ground, which she uses to attack Touma. But here again, Touma is able to cancel out her ability by touching the iron particles. This is crucial because in the first case, there was at least a possibility that Misaka is generating electricity rather than manipulating electricity. The fact that Touma can cancel out her ability by touching the iron particles, which are definitely not generated by Misaka’s power, shows that the thing he touches need not be something generated by a superpower; it can also be something manipulated by a superpower.


Now compare this to Accelerator.


Accelerator’s ability is “vector manipulation.” A vector in physics and math is anything with both magnitude and direction. Accelerator has the power to arbitrarily change the magnitude and/or direction of any vector quantity associated with any object that touches his body, be it momentum, electric current, sound, or anything else. He can also set his ability to automatically reflect the vectors of objects the moment they touch him. This makes him practically invincible, since most attacks cause damage through momentum, which is a vector; all he has to do is set his power to automatically reflect the momentum vectors of anything he comes into contact with, and he has no need to worry about being shot, punched, or cut by anything. (Ok, I think bullets and bladed weapons technically use pressure to cut things, and pressure isn’t a vector. But still, in order to exert pressure a sharp object has to be pushing on something, which would require it to be moving, so he can always reflect it before it does any damage.) He can also use his power to create projectiles, as he can touch any old object and increase its velocity vector to send it flying.

Now, if you watch the fight between Touma and Accelerator, Accelerator uses his power to send a lot of objects flying at Touma. What’s interesting here is that this time, unlike in his fights with Misaka, Touma never seems to use his Imagine Breaker on Accelerator’s projectiles.

accelerator-projectiles(Not sure if you can see it well, but those things sticking out of the ground in the background are parts of train tracks that Accelerator shot at Touma.)

Why is that? We saw from the iron particle situation that Touma can cancel out the effect of a power by touching the affected object, so why can’t he just stop Accelerator’s power by touching the things he sends flying at him?

Well, look back at the condition on Accelerator’s power: Accelerator can only manipulate a vector if it’s touching his body. In other words, once an object leaves contact with his body, his power stops acting on it. So why do his projectiles keep on flying after they leave his body? The reason is Newton’s First Law: “A body in motion tends to stay in motion.” So Touma couldn’t stop Accelerator’s projectiles with his right hand even if he tried; once they’re in the air, they’re moving by their own momentum, not from the operation of any superpower.

Now let’s look at these situations in terms of what’s causing what. What is the cause of the electricity in the case of Misaka and of the motion of objects in the case of Accelerator? On the one hand, it would be perfectly reasonable to say that the respective causes are Misaka and Accelerator. But clearly Misaka doesn’t generate electricity simply because she is Misaka; in that case, there’s no reason why she wouldn’t be generating electricity constantly. Similarly, Accelerator doesn’t cause motion simply because he is Accelerator; in that case everything he touched would be flying around.

So what if we say that the causes are Misaka and Accelerator’s powers? This doesn’t work either, for the same reason as before; Misaka and Accelerator have their powers constantly, so there’s no reason why they shouldn’t be constantly generating electricity and constantly launching things around.

So what is there that is always present while the effects of their powers are observed and absent when they aren’t? The answer is the operation of their powers, as distinct from the powers themselves. This is the per se cause of Misaka’s electricity and Accelerator’s vector manipulation. The powers themselves, and the people who use them, are per accidens causes.

So now that we know the causes we’re concerned with, let’s go back the other way and consider the effects of the operations of their powers. In the case of Misaka, the answer is fairly obvious. The effect of the operation of her power is electricity, as well as whatever it is that the electricity does, since she manipulates the electricity as well as generating it.

But Accelerator is a little different. It might seem at first glance that the effect of his power is the new vector that it generates. But remember, the vector that Accelerator creates persists after his power ceases to operate. This means that it is not the per se effect of the operation of his power. What does begin and end with the operation of his power is the acquisition or alteration of a vector. This is why the nickname “Accelerator” fits him so well; his power is not to make things move, but to make them change their motion.

So this is why Touma’s Imagine Breaker works on Misaka’s electricity but not on Accelerator’s projectiles; it only cancels out the per se effects of the operation of a power, not the per accidens effects either of the power itself or of its operation.

Incidentally, this is also the reason why Touma is unable to heal the amnesia caused by the damage to his brain from the Dragon Breath spell; the brain damage is only caused by the Dragon Breath spell per accidens, not per se. On the other hand, the reason he is able to convince Index that he did heal the damage is that since the damage was caused by the spell per accidens, it seems believable to her that he was able to cancel it out. If Index knew the difference between per se and per accidens causation, she would have caught Touma’s lie and figured out that he really did have amnesia.

This idea that causes and effects are simultaneous is critical to our view of causality; if we think of effects as coming after their causes, then the connection between cause and effect begins to seem tenuous, and we may end up thinking that there is no necessary connection between them at all. Hume famously argued that causes and effects are not connected, and the only reason we think they are related is because we see the effect come after the cause over and over again. But if we have a clear picture of causality, these propositions immediately seem ridiculous. To borrow an example from Edward Feser’s The Last Superstition, when someone throws a brick at a window, the act of the brick pushing through the window and the act of the window giving way to the brick are one and the same act. Though we can separate them conceptually, in reality, there is no separation between them either temporally or ontologically. So to say that the window need not give way to the brick when the brick pushes through it is like saying that we need not get four when we add two and two. The obvious answer to that is, “But two and two just is four.” Similarly, the answer for someone who claims that an effect need not follow upon a cause is, “But the operation of the cause just is the generation of the effect”; these are just two different ways of looking at the same event.

The distinction between per se and per accidens causation is also one of the number one reasons people misunderstand Thomas Aquinas’s Unmoved Mover argument for the existence of God. Most people who read the argument envision the series of causes Aquinas discusses as a series of per accidens causes, but what he is actually talking about is a series of per se causes, which is completely different.

… So yeah. At least Touma is good for something.