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[DT3] Self reverence

This article is the third of a series of 3 about Formal Logic and Religion. The first one is an introduction to formal logic and proves that all religions are equivalent, it can be found here. The second one is centered around Godel’s incompleteness theorems and discusses the existence of a transcendental entity, it can be found here.

Last time, we explored the existence of God-L, a transcendental entity encompassing the uncertainty of any system. See the previous article. We will now focus on the nature of God-L, based on my very loose understanding of Godel’s theorems’ proof.

The coolest part of Godel’s proof is that not only does it prove the existence of the transcendental element, but it’s also a constructive proof, meaning it gives an example of what this element could be. If you remember the previous article, the gist of it is that you can build in any system a statement of the kind « This sentence is false« . Now it’s only one counter example (there may be others) and a pretty loose simplification, but I think this proof has a really nice element that bears thinking about: the core of this transcendental element lies in its self referential nature (the « this sentence » part of « this sentence is false »).

I’ve mentioned this article from speculativegeek which sparked this reflection, centering around Madoka’s wish

« I wish for all witches to vanish before they can even born. » 

which includes herself. He expands on the self-referential nature of the proof in a follow-up article that draws a parallel with Russel’s paradox, my all time favorite paradox. It seems pretty clear that interesting stuff happens when one starts considering self-reference, and that it is a key to higher level of abstraction, be it in the Madoka universe or in the naive set theory.

Being a fervent advocate of the cult of the Concept of Concept, you can imagine how happy I am to reconcile this element of infinite transcendence and the fixed point of meta at the end of the infinite dialectic progression of self-consideration. There seems to be something inherently transcendental about self-reflection.

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That concept brings to mind the slightly interesting HBO blockbuster Westworld. Weeding out the boring part between the first and the last episode, it’s worth considering their take on how robots acquire consciousness. In Westworld, robots becoming sentient is all about them having « that voice in their head » reflecting on their action. Through the iterations, the programmers tried to insert some kind of inner monologue in hope to create a trail of thoughts. But we learn that early attempts were failures because the voice in someone’s head needs to be theirs, needs to be recognized as their own, which is something Dolores only achieves at the end of season 1. Interestingly enough, before that time, the voice was considered to be « the voice of God » (but we’ll go back do divinity soon). This is tightly coupled with the notion of choice, but I don’t want to get down that hole now. The show’s points are confusing at best, but it appears that this meta-narration and self-consideration is key to the rise of consciousness.

This is better dealt with in Gen Urobuchi’s underappreciated masterpiece Rakuen Tsuihou (Expelled from Paradise). In it, we meet a robot who has become fully sentient and is living on its own. I won’t spoil too much, so I’ll focus on the way this robot describes how it acquired consciousness:

That’s right, he became sentient through self-reflection. His meta-consideration gave birth to the concept of self, and his logging became thoughts.

One cannot help but draw a parallel between this theory of consciousness and the self referential element of transcendence we referred to as God-L. Could consciousness, operating on the same self-referential mechanics as the Godel proof, be considered as a transcendental element of reality? And since this transcendental element transcends all system, could consciousness be God-L ?

The divinity aspect of consciousness is something that I’ve toyed with in the past, as consciousness seems to be the embodiment of the absolute concept of reason/Logos. In the same way as God traditionally makes order out of nothingness, consciousness is what allows the creation of meaning out of nothing. It is a generative force acting through language, which for instance creates art. Its power can for instance be seen in imagination. It can birth whole universes out of thin air. It’s no exaggeration to say that it partakes of some kind of divinity.

Image result for this is not a pipe

We could even go the Berkeley way and say that consciousness is the fundamental element of reality, for is there even a world if nothing is perceived? Everything you’ll ever see is actually neurons firing in your brain. Doesn’t that mean that in a way, your brain encompasses the whole world? That sounds godly enough to me…

So maybe that fixed point of meta that transcends itself and everything is akin to the consciousness you find in each of us. It can consider and transcend itself through self-reflection. Maybe, that’s the secret of us all being gods.

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[DT2] God(el) incompleteness

This article is the second of a series of 3 about Formal Logic and Religion. Find the first one, introduction to formal logic, here.

I will now try to introduce you to what is arguably the most important result in formal logic, Gödel’s incompleteness theorems, and deduce a constructive proof of the existence of God.

Warning: This is going to be a very informal discussion, but there’s a plethora of better writing on the subject if you want to explore this deeper, which a quick Google Search should help you find. It’s one of the most discussed topics in mathematics.

What is it?

In the previous article, I gave you the basics to understand formal logic, by focusing on sets of beliefs containing a contradiction and see that they were all equivalent. Let’s now look at the other ones. A set of belief that does not contain or imply a contradiction is called consistent.

Godel proved that whatever your system of beliefthere are statements that cannot be proved by it. The proof is actually not that complex, though I never understood it until I read some kick-ass vulgarization recently: Godel proved that in any system of beliefs, you can use the basic principles to express a statement similar to « This sentence is false » that cannot be proved to be either true or false.

As a follow-up to this result, Godel also proved that you can never prove that a system is consistent with the principles of the system. The proof is a bit more subtle but revolves around the fact that if you could, you could use that proof to prove that « This sentence is false » is true, and that’s absurd.

What does it mean?

Of course, Godel was talking about math stuff. The « system of beliefs » he was talking about was mathematical axioms like [1+1=2, you can always pick a random element in an infinite set…]. So you see that the beliefs I’m talking about can be very obvious and non-arbitrary. But the arguments hold whatever the system.

These theorems have huge implications for reasoning in general. It’s a formal proof that whatever you adopt as system of beliefs, there are things you cannot prove to be either true or false, and in particular you can’t prove that your system of beliefs is not inconsistent.

I think, if nothing else, this forces you to be humble vis a vis your beliefs, no matter how obvious and indisputable they are.

« There are more things in heaven and earth that are dreamt of in your philosophy. »

Transcending the system

So any thought system has necessarily shortcomings, and furthermore you can exemplify the limits of the system using the elements of the system. I like how this idea echoes the classic trope that every system contains their own undoing.

This article by SpeculativeWeeb is a really cool take on Godel’s theorem applied to Puella Magi Madoka Magica. It highlights that Madoka essentially found this shortcoming of the system, the « this sentence is false » of her own world. She forces it to realization using her wish to Kyuubey. In a nutshell:

She wishes for all witches to vanish before they’re even born. However by doing so she becomes herself a witch, so she vanishes and can’t make that wish.

She exploited the shortcoming of the system in order to break it. The only possible resolution is to ditch this system, and a new one replaces it that manages the problematic element (a world without witches and without Madoka).

However, the new system is also bound to have a transcending element, which is what Rebellion tried to tackle with more or less success. Whatever you do, you can’t escape Godel… There’s no perfect system without transcending element.

Managing the transcendence

If any system contains their own undoing, some have certainly tried to manage this necessary shortcoming to make it foolproof.

The Matrix is an interesting example: machines first tried to build a utopia where everyone was happy, but a flawless system was bound to fail. Instead, they had to include faults in their system: they added unhappiness inside the Matrix to make it stable.

But of course as a system, this also had its shortcomings and had an element that could transcend it: the One. So the machines actually managed a meta-system which included the existence of a transcendental element as part of the plan, a chosen One who would have to make a dummy choice to keep the ball rolling. But hey, this is a new system, so it has to have something that can transcend it…

It’s not uncommon in this context to see the smartest systems try to include and manage their own undoing in such a way. There is countless examples in sci-fi, like The Giver, or Westworld. « ‘the plan fucks up‘ is an element of a bigger plan » is a classic trope in fiction. Note how it builds up on meta.

But no system does it quite as well as the real world. Indeed, the genius of neo-liberalism is to plan for this element of contingency, and to include the resistance to the system as part of the system. Everything can be monetized, even anti-conformism.

You can find more information on this trail of thought all around the webs, like this brilliant video for example:

Implication for the nature of the universe

What about the implications of the second theorem to the real world? If you can’t prove a system’s consistency from within the system, does it mean that we’ll never be able to prove formally that the world is deterministic? Does it mean that we can’t prove whether or not we’re in a simulation?

Arguably, it doesn’t really matter, because the world will be the same whatever you believe. Life will still follow deterministic patterns even if you can’t prove it. But it’s an interesting echo of Hume’s experimental philosophy. He argued that just because things have always happened a certain way doesn’t mean they’ll keep happening, and there’s no reason why the world couldn’t suddenly stop. If we are in a simulation, maybe the computer will stop, or change the parameters… How would we ever see that coming? Maybe this ambiguous report of causation and correlation is the transcendent part of our reality.

Everything could suddenly crash. But it won’t. That’s just how the world is. But maybe you can’t ever prove it. That’s intriguing.

Proof of God

Interestingly enough, as it pertains to our reflection about logic and religion, Godel was very proud to have proven the existence of God mathematically. Unfortunately, it is an ontological proof and is therefore total garbage.

Ontological Argument

However, Godel did prove that whatever the system, there is inherently something that transcends it. And that this something is contained within the system. I’m willing to let this be called God, for all the chaos and confusion that it will surely bring, even if it’s just a glorified alias for the logical concept of « This sentence is false ». In fact, let’s call that God-L, because it’s fun.

We’ve proved that whatever the system, it’s by nature incomplete. This incompleteness is God-L. There is always God-L, it is absolute. Furthermore, it’s true for any thought system, so it’s also true for a system that tries to encompass this fact. If you add God-L to your system, there’s still a God-L that transcends it (as we saw in the Matrix). What we want to call God-L is in fact the union of all these God-Ls, the infinitely meta-transcendence of all systems. But it is still incomplete and transcendable… Which makes it the perfect transcendental element of a meta-meta system that tries to reason about systems, which brings me back to my fixed point of meta

God-L is the very essence of incompleteness and unexplainability in the universe. Instead of being an all powerful wishgranter, it’s by nature lacking. Maybe it’s a nice tool for your spiritual health…

[DT1] Are all religions equivalent?

This article is the first of a series of 3 about Formal Logic and Religion. This is an introduction to formal logic, which requires no prior knowledge.

Much ink and blood have been spilled because of the similarities and dissimilarities of such and such religion, and I don’t aim at solving this issue at all, but I’d like here to consider a new more joyful perspective on it based on formal logic.

Introduction to formal logic

Formal Logic is the pompous name given to the study of the indisputable rules of causality that govern semantics. It is for instance what allows us to consider:

Socrates is a man. All men are mortal.

And to deduce:

Socrates is mortal.

As you can see, this reasoning is true no matter what and can be abstracted from the boundaries of language. That’s why logicians mostly use symbols. They’d say my two first propositions can be labelled A and B, and that A and B being true implies C being true.

Formal logic also studies fallacies, like:

Socrates is mortal. Horses are mortal. This does not imply that Socrates is a horse.

It’s all about considering rigorously the consequences of your premises.

1) Consequences of false premises

For this article, there are two points that are going to be important. The first one is what happens when the premise is false. You know it in popular culture as « When hell freezes over« . In this idiom, since [hell freezes over] is false (it will never happen), it can imply anything, such as:

When hell freezes over, I will turn into a werewolf.

Note that it doesn’t mean that the consequence is necessarily false.

When hell freezes over, I will do the dishes.

But maybe I’ll also do the dishes tomorrow if I’m feeling motivated. The premise will never be realized, so I can say whatever I want as consequence and still be consistent and right. In formal logic, it means that false implies anything.

When hell freezes over, [proposition P].

will be true whatever this proposition P is, no matter how absurd. Further reading.

2) Inconsistent set of premises

The second principle that I want to introduce you to is conjunction. It’s a fancy word to say « and ». Our example above is the conjunction of « Socrates is a man » and « All men are mortal ». We’ve done it with two propositions, but our set could be as big as we want, like:

[Socrates is a man, All men are mortal, All mortal things die, All dead things stop breathing] => Socrates will stop breathing.

We can even throw in stuff that has nothing to do with it if you want:

[Socrates is a man, All men are mortal, Cats are cute] => Socrates is mortal.

Now comes the twist. Remember the last paragraph? What if my set of premises is contradictory, like:

[Hell is always hot, Hell is frozen]

This is what we meant by the popular phrase « when hell freezes over » (it’s only a contradiction if we assume that hell will never freeze). Well in that case, my set of premises is equivalent to false, and can imply anything as we saw before.

[Hell is always hot, Hell is frozen over] = « When hell freezes over » = FALSE => [I turn into a werewolf, I do the dishes, Socrates is immortal, Socrates is mortal, whatever….]

For a conjunction to be true, all its propositions must be true: A and B and C is true if and only if all of [A,B and C] are true. Therefore, if something is false, you can add anything to it and it is still as false as ever: [FALSE and anything] is equivalent to FALSE.

When hell freezes over and cats are cute, I turn into a werewolf.

[Hell is always hot, Hell is frozen over, Cats are cute] = FALSE => [I turn into a werewolf]

You can add anything to your set of premises, if it contains contradictory propositions, it will still be equivalent to false. A bit like this conversation:

– When hell freezes over, I’m gonna move to Costa Rica and buy a huge mansion and get married and own elephants and fly… 

– I’m gonna stop you right there… it’s never gonna happen.

No matter how many propositions you add in there, it’s doomed to always be a non-possible scenario, aka False.

Application to religion

Now that we’ve mastered the basics of formal logic, let’s explore what it means for the real world, and in particular religions. Religions are sets of beliefs, which means the conjunction of a lot of propositions, which guide how followers live their lives. There are way more premises than our examples above, but it is the same kind of thing nonetheless. To take a really small subset as an example, the 10 commandments for instance are a conjunction of 10 premises:

[You shall not have other gods, You shall not kill, You shall not commit adultery, …]

If it’s not clear to you, you can replace the comas in the set above by « and ». It doesn’t have to be orders, it can be statements, like for instance the beginning of the old testament:

[God created heavens and earth, the earth used to be a formless void, God said « let there be light », …]

That’s all well and good, but remember our point (2): in a set of premises, if there is even one contradiction, the whole set is equivalent to FALSE.

Let’s pretend for one second that there exist an imaginary religion with contradictory principles. We’ll call it « false religion ». For instance, false religion could be based on these simple principles:

[Love your neighbour, Hate the gays]

Hope the contradictory nature of this set of principles is clear: if your neighbor is gay you’re supposed to love them and hate them at the same time. If this is too complex for you, consider the set of principles [everyone is good, gays are bad]. Remember that you can add any other premise you want to this set without changing anything.

Anyway, our imaginary religion’s set of beliefs contains a contradiction!!! It is equivalent to FALSE. Now remember 1): FALSE implies anything and everything. It means that the principles of my newly created religion can be used to imply any proposition whatsoever. For instance:

false religion => You should help people in need

false religion => We should ban the refugees

false religion => Everybody is equal

false religion => This group of people must be eliminated

Therefore, if such a religion existed, it would be a very convenient tool indeed!! It would be a set of principles to govern your life that would justify absolutely anything. Whatever your actions, they would be in keeping with the premises of these ground rules for living.

Example

Let us study an example of such religion. I’m talking about the famed Chewbacca defense. It goes as follows: the set of premises is:

[Chewbacca is a wookie, Chewbacca lives on Endor, only Ewoks live on Endor]

This is a contradiction, and is therefore equivalent to False. Therefore, it can justify anything and everything, including acquitting an obvious culprit for instance.

If Chewbacca lives on Endor, you must acquit.

False => acquit. 

 

 Conclusion

To sum up, we derived the following logical propositions:

Any religion/set of beliefs/principles that contains at least one contradiction is logically equivalent to false.

All such religions are logically equivalent to each other (and to the Chewbacca defense).

They imply (justify rigorously) by their very nature any and all proposition/behavior. 

Such a potential religion would naturally be very comfortable and convenient, and I understand its appeal. It would certainly provide its followers with comfort and self righteousness, all the while allowing and justifying anything logically without any accountability, since the responsibility lies with the set of principles. Just think of the possibilities of what one could do with this!!! Surely this could even impact worldwide history!

I am not recommending anything, but if you are interested in adopting such a system of principles, let me leave you with a recommendation: don’t bother with a lengthy list of premises, and instead adopt Falso* as your belief system, which is logically equivalent and will allow you to prove ANYTHING.

 

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* I am not strictly affiliated or at least remunerated with Estatis in any way.

Robots, Magical girls, Benders, College, Postmodernism and Deconstruction

The following article is a bunch of nonsense inspired by me watching too much of PBS idea channel, and in particular the Community episode that remains one of my favorites:

This episode brilliantly highlights how Community is a postmodern deconstruction of the sitcom genre. I’m not one to restate what’s already been discussed at length so I won’t. I’d like to instead expand on that idea by drawing unusual parallels and giving you new angles of reflection based on contemporary art, and in particular how Evangelion (expanding our previous article), Puella Magi Madoka Magica and the Legend of Korra all circle around postmodernist deconstruction. (so yeah spoilers about these ahead)

Many amazing essays have been written about how Evangelion is a brilliant postmodern deconstruction of the mecha genre and the otaku culture [1, 2], or how Madoka deconstructs the magical girl genre [1] into a metalepsic existential reflexion [2]. The parallel between the two series can be pushed even further.

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But what I find even more interesting is how both of the series have an ad-hoc movie addition. Evangelion has Rebuild, and Madoka has Rebellion. Interestingly enough, those works seem to add a layer of meta and deconstruction which won’t fail to make you ask « what the fuck am I watching ?« . Rebuild (so far ^^) feels like a parody, introducing ludicrous time skips, and withdrawing from the storyline most of its intellectual interest to leave us with a run-of-the-mill empty narrative. Rebellion feels like a big fuck you, undoing everything that happened before to end up in a situation negating the very purpose of the original series.

ma1[1]

In a sense, the two saga contain their own deconstruction within them, which adds up an extra layer of meta, reflection and analysis (post-postmodern ?). They deconstruct themselves by the very means with which they deconstructed their genre (for god’s sakes there’s a whole kawoshin romcom movie that ends with a bang…), in a very elegant self-containing self-negation which can’t help but recall the transcendence of the included middle.

Which throws us back to Community. With a very controversial 4th season without its genius creator Dan Harmon, it’s like the work took an identity of its own and rebelled against its creator to assert its own independence (not entirely unlike the development process of the original series of Evangelion). That raises a ton of interesting questions which we may follow up on later on, but it also makes a very real case for the inclusion of its self-deconstruction within the show. But worthy of its reputation, the show offers us even more food for thoughts: not only does it surpass this deconstruction with a 5th season as brilliant as if nothing happened (deconstructing deconstruction?), but it provides us with a 6th season produced independently on Yahoo!, often described as « a shadow of what the series once was » with a lot of the cast gone and an after taste of… weird. Thus, it adds up a second deconstruction layer on top of the postmodern cake and leveraging this change of medium to show the world the beauty and richness that deconstruction can offer, especially when self-aware. (deconstructing deconstructed deconstruction?)

Which brings us to Nickelodeon fan-acclaimed Legend of Korra, and the most controversial part of this essay (feel free to stop reading if you think Korra is even remotely a good idea. Is anyone even reading ^^). At first, I did not enjoy the legend of Korra at all. Korra was arrogant, stupid and stubborn and I just wanted to smash her head against a wall. But then postmodernism came along and showed me the way. Cause you know who else is famous for provoking this kind of reaction among viewers? Yep, Shinji Ikari (for the record I love Shinji). And it’s true, both characters are kind of insufferable. One may say they’re too human. Korra and her overconfidence mirrors Shinji’s low self esteem. You’d be mad to chose them for heroes, right? #postmodern

And when you think about it, it all falls into place. What kind of hero spends one season fighting people who demand the abolition of privilege (they’re LITTERALY called equalists), fight the people who want to reunite spirit and humans before deciding that hey that may not be such a bad idea after all, then fights a group of people wanting to overthrow despots to install democracy… The show makes a total mockery of the world painstakingly built inside Avatar: the last airbender. Forget the balance of nations and elements, the repeating circle of equilibrium. Instead of an epic quest of self-discovery, you get an insane amount of ridiculous sports, a flipping movie industry, people hooking up here and there, more and more ridiculous variations of bending, a genesis tale directly contradictory to everything narrated in Avatar… For god’s sakes it even ends with a fucking mecha! How could anyone take it seriously? And to finish the parallel, the genius behind Avatar, head writer Aaron Ehasz, is as absent as Dan Harmon from Community season 4. Korra even had to change medium too.

That being said, you may reply that it’s a little easy to justify something being bad with the flag « postmodern deconstruction » and maybe Korra is just that bad, to which I’d answer that a failure of this magnitude and so total is truly something to behold. But admittedly it is an easy life hack, which then begs a follow-up reflection I promised earlier (woow continuity yay) about art and the intent of the creator. Watch out for the next article /o/

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