Monday, October 31, 2011

Logic - the Crash Course

Right, so satire often depends on the logical debunking of ideas, so I'm going to attempt to teach all of you logic. Whenever I use this post as a reference in future posts, I'll include a link to it for new readers. (Aren't I nice?)

There are two types of logic - formal and informal. If you are more math-oriented, read on for Formal Logic. If you are weird and more language-oriented, skip down until you hit Informal Logic, and then read that. Once you understand the type of logic that you were assigned, you can read the other one. I'll mostly be using Formal Logic in my blog, though I'll occasionally use Informal too, so it helps to be familiar with both.


Formal logic is neat and mathematical. There are two common types of logical progression. Modus ponens (confirmation) and modus tollens (denying).
Modus Ponens takes the form of a) If p, then q b) p c) therefore, q.
Here's a few examples to make  sense of it

A. All mammals have brains
B. Dogs are mammals
C. Therefore, dogs have brains

A. All zombies want brains
B. Stephen is a zombie
C. Therefore, Stephen wants my brain

A. All girls have cooties
B. Kylie is a girl
C. Therefore, Kylie has cooties

Modus Tollens is is the exact opposite. It is logical because, if P causes Q, then if Q isn't, P cannot be. It takes the form of a) If p, then q b) not q c) therefore, not p

A. All mammals have brains
B. Voltron toys do not have brains
C. Therefore, Voltron toys are not mammals.

A. All girls have cooties
B. I do not have cooties
C. Therefore, I am not a girl

A. All zombies want brains
B. Beka does not want my brain
C. Therefore, Beka is not a zombie

Now, each one of these has an inverse, and these inverses are FALLACIES. The fallacious form of modus ponens is called affirming the consequent, and the fallacious form of modus tollens is called denying the antecedent.

Denying the Antecedent

A. All mammals have brains
B. Mohinder the Lizard is not a mammal
C. Therefore, Mohinder the Lizard does not have a brain.

As you can see, this makes no sense. That's because the statement A does not imply the inverse of A. That is, just because all mammals have brains does not mean that only mammals have brains.

A. All zombies want brains
B. Hannibal Lector is not a zombie
C. Therefore, Hannibal Lector does not want brains.

Again, the fact that all zombies want brains (a well known and documented fact) does not imply that only zombies want brains. It completely ignores cannibals!

A. All girls have cooties
B. Justin Bieber is not a girl
C. Therefore, Justin Bieber does not have cooties

People outside of girls can, in fact, have cooties - A simply means all girls have cooties. This is fallacious.

Affirming the Consequent

A. All mammals have brains
B. Nemo (the fish, not Captain Nemo) has a brain
C. Therefore Nemo is a mammal

Lots of creatures besides mammals have brains. This is the opposite of denying the consequent. Just because all mammals have brains doesn't imply that only mammals have brains.

A. All zombies want brains
B. Jeffrey Dahmer wants brains
C. Therefore, Jeffrey Dahmer is a zombie

Again, fallacious as it presumes ONLY zombies want brains, which is never stated.

A. All girls have cooties
B. Ke$ha has cooties
C. Therefore Ke$ha is a girl.

"Wait! Kevin, Wait!" you might be saying. The conclusion you are claiming is true, so how can the argument be invalid? I would reply "shut up, I'm getting there."
A true argument can be fallacious, and an untrue conclusion can be drawn from a valid argument. More on that later. I put this in to demonstrate that, although the conclusion is sound, the method used to get there can still be invalid. Boys can have cooties too - there is no condition in which ONLY girls have cooties, thus this argument is invalid.

Valid, but unsound

A. All Canadians are cats
B. Chad Kroeger is Canadian
C. Therefore, Chad Kroeger is a cat

This argument is not fallacious. Look at the form: If p, then q. P. Therefore, q. It's Modus Ponens, accepting the consequent. However, it is an unsound argument because the assumption is false - all Canadians are not cats. Look at Adam Gontier. He's Canadian, and very clearly not a feline.

Informal Logic

Informal logic is more word based. I will only focus on fallacies here, because this is getting long* and informal logic is kind of intuitive. There's no proper form, statements rooted in fact are logical so long as they don't violate a fallacy. Here are some common ones and some humorous examples.

Fallacy of contradictions: makes 2 mutually exclusive claims
The cat is dead and the cat is alive. Simultaneously.**

Fallacy of accident: sweeping generalization. The general rule is taken and applied to a specific exception.
Breaking into someone's home and taking their belongings is a crime. Police execute search and seizures. Therefore, police are criminals.

Converse fallacy of accident: hasty generalization. Taking an exception or small sample, and creating a general rule from it.
Paris Hilton is rich. Paris Hilton is stupid. Therefore, rich people are stupid.

Irrelevant Conclusion, Red Herring, and Straw Man Fallacies:
Driving focus away from the original point.
Often committed in arguments such as Pro-Life:
"My opponent wants to convince you to kill babies...."
This is fallacious, unless the opponent actually said they wanted you to kill babies.

Begging the question: using a conclusion to justify itself.
Abraham Lincoln never told a lie. I know, because he told me so.
Abraham Lincoln could have lied.
And he probably did. Considering he's a tyrant desperately trying to eliminate states' and individual rights.

Fallacy of complex questions - more than one question in a question.
For example, the most famous example is "Have you stopped beating your wife yet?"
In a debate, it should really be phrased as two questions:
1. Have you ever beaten your wife?
2. If so, do you continue to do so?

Fallacy of Equivocations - using words in more than one way to justify the same conclusion
I know evolution is real because things evolve everyday.
This is fallacious because the hypothetical person is equivocating evolution (the philosophy that all life evolved from single celled organisms) with the term evolve (which simply means to change or adapt)

Fallacy of misplaced concreteness
Nothing is better than God
Subway is better than nothing
Therefore, Subway is better than God

However, this is fallacious as the first could be restated as "everything fails to be better than God."
So, the second point (Subway is better than nothing) is irrelevant.

Now you know some logic, and you're just that much smarter today! Bust out the freaking bubbly.

*that's what she said
**Schrodinger, again. Apologies. I'm a nerd.

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