Xzibit and Formal Logic
February 27, 2012
Hello. Seth Here. Today’s homily will be about the relation between the Xzibit meme and formal logic. For some, formal logic is like the scary sister of the sexy informal logic you are trying to date. You want to become as familiar as possible with informal logic, but you try to stay out of sight from formal logic. Perhaps you spend hours looking at websites exploring every intimate detail of fallacies constituting the body of informal logic, so’s to better woo your mistress. But to spend hours looking at websites exploring the intimate details of formal logic would just be twisted; a form of sadomasochism. In some ways, yes, extended study of formal logic is self-torture, and to read about the formal logical pursuits of others is to delight in their suffering. But in small doses, the drug is beneficial (I freely dance with multiple metaphors at the Ball). I will show you that if you can reason about the Xzibit meme on the interwebs, you can do formal logic.
First, I want to crush this nasty rumor that informal logic is sexy and cool. I will do so with an argument.
1. All logic is the study of good reasoning.
2. The study of good reasoning is about good form.
3. To be about good form is to be formal.
4. Thus, all logic is formal.
5. Informal logic is logic.
6. Informal logic is not formal.
7. But from 4 and 5, informal logic is formal.
8. Thus, informal logic is a contradiction.
9. No contradictions are sexy.
10. No contradictions are cool.
11. Therefore, informal logic is not sexy, and is not cool.
Informal logic is just a heuristic that makes some aspects of formal logic easier to grasp for the pathetic human brain. It is actually just formal logic, heavily photoshopped. Underneath every sexy fallacy from informal logic’s Spring Break album is a shy and demure invalid formal logic formula, waiting to bust out and rock your world.
Because everything is better if Xzibit is involved, I will let Xzibit show you that you already understand how formal logic works.
The Xzibit meme is over 3 years old. In Internet time that is pre-historic, so I will refresh your memory.
In the show, Pimp My Ride, Xzibit takes the old junker of an episode’s guest and tricks it out in crazy creative ways, often implementing new features based on the guest’s individual goals, desires, and preferences. The features implemented are such that they do not often appear in a vehicle. For example, if the episode’s guest is an aspiring singer who loves singing in the car, Xzibit will include a mobile recording studio in the pimped out ride’s console.
The Internet quickly latched on to the formula, and exploited it in absurd ways. Here is a simple example of the meme.
It has been recognized by Cracked.com and knowyourmeme that there is a general form to the Yo Dawg memes. Based on what I’ve given you, it should be simple to arrive at the generalized form of the meme. The good news is that this is all there is to formal logic. If you can understand the general form of the Xzibit meme, then you can understand formal logic.
The general form is:
Yo dawg, I heard you like (X or X-verb), so we put a X in your Y so you can X-verb while you Y-verb.
The X’s and Y’s are variables in the formula. We could further formalize the formula by giving symbols that represent ‘I heard you like’, ‘so’, ‘we put in’, ‘you can’, and ‘while you’. This would be no different from how formal logic gives symbols that represent the connectives ‘and’, ‘or’, ‘if…then’, and ‘not’.
Suppose I present an Xzibit meme with the following text:
Yo dawg, I heard you like pool, so we put a pool in your car so you can swim while you drive.
On the face of it, it looks right, where
X = pool
Y = car
X-verb = swim
Y-verb = drive.
However, it should strike you as odd, because the first ‘pool’ is referring to billiards, a game, while the second ‘pool’ is referring to an artificial body of water. Thus, two different ‘pool’s are being used in the formula, when it should be the same throughout. This is the fallacy of equivocation. Formally,
Yo dawg, I heard you like Z, so we put a X in your Y so you can X-verb while you Y-verb.
Z = pool (billiards)
X = pool (body of water)
Y = car
X-verb = swim
Y-verb = drive
This clearly violates the meme’s formula, which does not allow for liked objects that are different from objects put-into-Y. The liked object (or liked verb) must be the object (or verb form related to the object) put into Y. Because ‘pool’ has two different meanings, it equivocates. This has to do with a violation of the formal rules. And you thought equivocation was an informal fallacy!
If you understand how the general form of the meme relates to the particular example above, then you can understand how formal logic relates to natural language arguments. In my argument above, against informal logic, we can formalize it thus:
1. All L is R.
2. R is G.
3. G is F.
4. Therefore, all L is F.
5. I is L.
6. I is not F.
7. I is F.
8. I is not F, and I is F; I is C.
9. No C’s are S.
10. No C’s are O.
11. I is not S and I is not O.
We represent each distinct concept as a letter. We then follow the rules of categorical logic to assess it for validity. I leave that to the reader. It is the exact same process as evaluating an Xzibit meme. Does it have the right form?
The Xzibit meme doesn’t stop at categorical logic. It can also help you learn about higher order logic, and set theory. One of the earliest mutations of the meme set X = Y, whereby the Interwebs discovered some of the hilarity of self-reference and recursion.
This stems from the set-theoretic notions tied to the definition of “we put in”. Mathematicians have known for ages that hilarity ensues from sets containing sets! For example, does the set of all sets that do not contain themselves contain itself? LoL Frege and Russell.
So prevalent did the recursive version of the meme become, that a sub-meme of Xzibit recursion spawned. His face need only be placed next to some recursive image for the meme to work.
Wineglasses in your wine glass.
Pizzas on your pizza.
And with multiple iterations:
And of course, this version of the meme was a natural marriage with Inception.
If you understand these modified versions of the meme, then you can understand higher 0rder logic and set theory, no problem.
So, if in the past you have felt intimidated by formal logic, and have stayed close to the shore of informal logic, I urge you now to venture forth and fearlessly explore the riches that formal logic has to offer. Not only will you truly be understanding logic, but it is no more difficult than understanding or crafting a good Yo Dawg meme.
This post originally appeared here on The Official MU SASHA Blog.
About the Author: Seth KurtenbachSeth Kurtenbach is pursuing his PhD in computer science at the University of Missouri. His current research focuses on the application of formal logic to questions about knowledge and rationality. He has his Master's degree in philosophy from the University of Missouri, and is growing an epic beard in order to maintain his philosophical powers. You can email Seth at Seth.Kurtenbach@gmail.com or follow him on Twitter: @SJKur.
#1 Catherine Nance (Guest) on Monday February 27, 2012 at 10:24am
I snarfed my peanut butter on this one!
BTW, Seth looks like that dude on Grey's Anatomy.