Monday, August 27, 2012

The Dark Knight and Logic

Before you read, I must warn you that this is my first serious post. It has been a long time since I wrote anything and I just wanted to write something. Ok. Start.
Dark Knight is a ultra awesome movie. With great stunts, story and most importantly the greatest villain ever. His dialogues, I am sure, will become like the ones in The Godfather. But there is one dialogue that I want to examine.
"This is what happens when an unstoppable force meets and immovable object".
First, some basics in logic.
Two concepts/statements are contradictory if the assertion of one negates the other and vice-versa. So, when I say, P1:"this ball is red", the contradictory of it would be P2:"this ball is not-red". If P1 is true, P2 has to be false, and if P1 is false, P2 has to be true. Similarly, alive and dead are contradictory ideas. What is alive cannot be dead and what is dead cannot be alive. In the above dialogue, the idea of "an unstoppable force" is contradictory to the idea of "an immovable object". The existence of one negates that of the other. That is, in a system (or world) we cannot have the two co-existing.
A disjunction is true when either of the disjucts is true. "The train will arrive on Platform Number 1 or Platform Number 2" is true, if a) The train arrives on Platform Number 1 Or,b) The train arrives on Platform Number 2. (It can't arrive on both. This is called an exclusive disjunction. I have taken this example to get the idea through. In logic we generally deal with inclusive disjunction where in both disjuncts can be true).
A conjunction is true only when both conjuncts are true. "The ball is red and spherical" is true only when a) The ball is red And b) It is spherical. If either of them is false. The whole sentence is false.
In a true disjunction, if one of the disjunct is known to be false, we can automatically infer the truth of the other. Example, let us say that the statement "The train will arrive at Platform number 1 or Platform Number 2" is True, let us also assume that we know that "the train has not come on Platform Number 2" then, we can happily (and validly) infer that it has come on Platform Number 1. (Sherlock Holmes is actually using this Disjunctive Syllogism when he says "It’s an old maxim of mine that when you have excluded the impossible, whatever remains, however tedious, must be the truth.")
From a contradiction, one can deduce anything. This is called explosion or ex falso quodlibet. The Proof runs like this: ( P and Q stand for any sentence like "Raghavan is white", "Ball is red" or "frustBoy bought a car")
1.P and not-P (a conjunction of contradictory ideas/sentences)
2.P                    (From 1, a conjunct can be true only when both its conjuncts are true)
3.P or Q           (From 2, a disjunct is true if either disjunct is true)
4.not-P            (From 1, a conjunct can be true only when both its conjuncts are true)
       Q                ( From 3 and 4, Disjunctive syllogism)
Notice that in 3, we could have added anything in place of Q (say R, S, T...) leading to the fact that we can derive anything from a contradiction.
Now, we come to the main point.
The above dialogue is a statement containing a contradiction. In such a system one can deduce anything validly. In other words, anything can happen when an unstoppable force meets an immovable object (even stuff like a missile turning into a sperm whale like in our H2G2).
But, when the Joker says that "This is what happens...", I take that he is referring to one particular instance or event which he think is the outcome of an unstoppable force meeting an immovable object. But in fact it is not, since in a contradiction anything can happen. He should not have used the word "this". So, in my opinion, the above dialogue is just a fancy piece of literature that the writer found and need not necessarily imply anything of relevance (to Batman or to us or to the movie)
But that's just my opinion.


Rahul Dev said...

what went thru me when reading this..

P1.. P2.. : ok, we are going into the movie first. It is the venn diagrams.. maths..
Disjunction.. Conjunction.. : hmm.. not maths.. Wren and Martin's English grammar.
Sherlock Holmes.. : How is he connected to Dark Knight. Did DC Comics buy it.. (no pun intended, pure thoughts)
P.. Q.. : Aha! this is electronic logic gate design. Sambarboy, you still got that software seeds man..
Joker.. : ok, trailers are done.. Dark Knight is on..

Apart from BS, I thought it was a legit statement when I read it first (without the reference to the actual scene), but I will buy your argument for I can skip watching the movie. Will keep an ear out for this dialogue when watching it for next time..

Rahul Dev said...

PS: BS is referenced to my thoughts..

R@hul said...

Hmm.... Can logic truly be applied to statements pertaining to reality?

Let me explain. Suppose a statement pertaining to reality is made. The statement cannot be TRUE in the absolute sense or FALSE in the absolute sense. Because then, you'd have to define what is an absolute. However, by your attempt to define an absolute, you've made it relative.

Maybe I make no sense at all or maybe my logic is flawed somewhere, but if do make sense, what is the answer to my initial question?

venkata raghavan said...

@Rahul M

Logic can be applied to (in) reality and as I said we do it at many times (like the train example, or sherlock holmes qoute). When someone asks you whether you want tea or coffee and you say Tea, it is assumed that you do not want coffee, this is a kind of disjunctive syllogism.
But as you said absolute is a very difficult term to resolve. That is why I spoke of systems. We take a system (or what is called a world) and talk about it. As I said, "In such a system one can deduce anything". So, in that way you can say that it is relative, relative to that system.
True in absolute sense is what logicians understand as Necessarily True. One way of defining Necessarily True is by saying that it cannot be false in any possible world (i.e system). Logical truths are such truths. Example Law of Identity or Law of non-contradiction.

R@hul said...

Interestingly, Schopenhauer seems to disagree. I came across this during my, for lack of a better term, Wiki-surfing.

After stating the laws of thought, he says: "There would then have to be added only the fact that once for all in logic the question is about what is thought and hence about concepts and not about real things."

— Schopenhauer, Manuscript Remains, Vol. 4, "Pandectae II,"

Any thoughts on this?

tsp said...
This comment has been removed by the author.
tsp said...

This gedanken does not approve of your logic.

So shut and write something funny. About time!

venkata raghavan said...

@ Rahul M
I think I agree with Schopenhauer. The laws are mainly about how we think. Unstoppable force, immovable objects, these are all concepts and need not be real entities.
So, I don't see what it is that he would find disagreeable in the above post/comment by me. Please elaborate if possible.

Kya aadmi hain re tu. Great. You pointed the only exception logic has encountered till now.
Infact, Quantum Mechanics has thrown the whole classical logic in a disarray because many laws in logic are based on these Laws of Thought. More info

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