The dumbest Madoka Magica theory ever wrote

Disclaimer: the following text contains spoilers from the last arc of “Puella Magi Madoka Magica” (episodes 10,11,12 + Rebellion) and from the very start of 20th century’s foundational crisis of mathematics. In defense of myself against Poe’s law: everything in this text is bullshit.

There are people who, even today, still argue about the “Madoka-Buddha or Madoka-Christ” problem. Brian McAfee in his book “Revelations” argues for the latter against the buddhistic theory supported by Jed A Blue with his book The Very Soil (both great books if you’re fan enough, but both horribly typesetted). I’m here to move against both the “Madoka-Buddha” and the “Madoka-Christ” proposing the theory that Madoka Kaname is an alter-ego of Bertrand Russell.

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There’s a famous interview where Gen Urobuchi, the writer of “Puella Magi Madoka Magica“ (PMMM), answers some interesting questions about the writing of the show. One of those questions was about PMMM and German literature (Goethe, Weber and Von Seckendorff) to which Urobuchi responded: “My main inspirations are eroge and classical literature.”. Now what’s more classical and German than “The Foundations of Arithmetic by Gottlob Frege?

In this masterpiece, fundamental for the development of both mathematics and philosophy, Frege tried to investigate the foundations of mathematics using Naive Set Theory (NST). The main idea of NST is that any set is a valid set. Want to talk about the set of all witches? Let W be such a set. Need a set that contains Kyubey and Sayaka? Let KS be such a set and you’re done. Need an empty set? Here you are: . Briefly: for every property there exists a set of things with that property (the property of being a witch, the property of being Kyubey or Sayaka, and so on); this implies that sets can be elements of other sets and that a set can even be an element of itself (pick as example the set of all sets; it’s a set, so it must be in the set of all sets i.e. itself). Everything seems fine right?

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But then Bertrand Russell showed up arguing against NST. In fact, he said, let Z be the set of sets that are not members of themselves. Is Z a member of itself? If Z is not a member of itself, then its definition dictates that it must contain itself, and if it contains itself, then it contradicts its own definition. The need to solve the Russell’s Paradox and other similar ambiguities leads to axiomatic set theory (our current method) and NST was abandoned.

The problem with Russell’s Paradox lies in its inner self-referential nature. Z causes no problems at all if we consider any set A different from Z: A is in Z or A is not in Z. The paradox arises only when we focus on Z.

In PMMM there is something at least as free as NST: magical girls’ wishes. As long as a girl have enough karmic power (or karmic burden/destiny), as in the case of Madoka, any wish would come true. So can a paradox like Russell’s one arise from a sufficiently powerful girl and a sufficiently twisted and self-referential wish? Yes.

Madoka’s “I wish for all witches to vanish before they can even born. All the witches through all of space and time, in the past and future… I’ll erase them with my own hands.” is not at first self-referential. However also the definition of Z does not seems to imply self-reference at first. The problem here is that Madoka is itself a magical girl and thus will, no matter what, become a witch; but if this is the case then there will be no Madoka left to erase it. According to Kyubey Madoka is strong enough to make that wish come true and so the paradox is set. In order to fulfill her wish she would have to become and not become a witch, an obvious contradiction represented in the show with the destruction of the asteroid-shaped soul gem. The laws of the universe are then rewritten because Madoka proved the inconsistency of the previous ones with her self-referential wish.

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Madoka did to the world the same thing Russell did with Frege’s NST: she proved its inconsistency. And then, as Russell did with the Principia Mathematica, she constructed a new universe with new laws. However, as Gödel showed, self-reference can’t be completely erased from sufficiently complex systems and thus Madoka’s world is still vulnerable to well constructed self-referential wishes.

Homura’s wish in episode 10 was in fact self-referential and its outcome (Rebellion finale), even if not paradoxical, necessarily leads to the collapse of Madoka’s world. This is similar to what Gödel’s Incompleteness Theorems did to the Principia Mathematica: they proved its incompleteness. Madoka’s universe is incomplete: Madoka does not exist in it as Homura wants (in fact the name “Madoka” does not make any sense in Madoka’s universe, as we can see from the last episode of the series). And so, becoming the devil, she creates a new universe (a new axiomatic system, leaving Principia Mathematica behind) where Madoka’s existence is a fact.

In conclusion there is evidence that PMMM was in fact inspired nor by christianity nor by buddhism but from the great story of the foundational crisis of mathematics. Kyubey is Frege: he tried to achieve his goals with a naive system, susceptible to self-reference. Madoka is Bertrand Russell: they both destroyed previous systems by means of self-referential paradoxes and they both created new worlds (supposed to be a better place) such as Madoka’s universe and Principia Mathematica. However, as Gödel and Homura showed, those new systems are far from perfection: they’re incomplete by definition and thus, improvable.

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