Yea, too hard to type the things out, so I wikipedia'd it.

http://en.wikipedia.org/wiki/Principle_of_explosion

My question is: Is there a flaw? It seems unlikely that you would throw away a system of thought simply because of one contradiction - but it's true. One contradiction means the whole thing is worthless.

And no, this isn't some attempt at acting smart - I don't know the answer either.

In formal logic, there are two words to describe the state of an argument. Valid and sound. An argument is valid if the conclusion follows from the premises. An argument is sound if the premises are true. To reject the conclusion of an argument, you have to show that the conclusion is not sound- either the conclusion does not follow, or any one (or multiple) premises must be rejected.

For example:

All men are blue
Socrates is a man
Therefore, Socrates is blue.

This is a valid argument, but quite obviously unsound. The first premise is false. It doesn't matter how good the other premises are, the conclusion is not sound (that is not to say false, merely that the particular argument in question doesn't qualify as a logical proof. Socrates may well have fallen into a vat of blue paint, but this argument, despite being right, is right by chance, not logic.)
So logical arguments are like chains holding up the load of the conclusion. You can deny the conclusion if and only if you can break any one of the links, or show that the chain, while strong, doesn't actually lead to the conclusion.

One of the oldest logical laws is that of non contradiction. If a statement contradicts itself, the statement MUST be false. This reflects reality in that two contradictory events cannot be the case (note that quantum superposition doesn't undermine this, it merely redefines what actually is contradictory.) So, if any premise of an argument is contradictory, the argument is unsound.

The principle of explosion tries to prove this, by stating that if you make a contradictory statement and assume it is true, you can always find the right premises to reach any conclusion.

For example:
1. My cat is green and is not green.
from 1.:
2. My cat is green
3.My cat is not green
From 2 and disjunction introduction:
4.My cat is either green or I'll get free mcdonalds tomorrow
But 3, so:
C. Therefore I'm going to get free mcdonalds tomorrow

You can do 4 because given you have a true (or assumed true statement) you can add any extra 'or' statement to it, and it will still be true. Eg 2^2 = 4 is true, and therefore so is the statement "2^2 = 4 or elephants secretly rule in sky fortresses." If you were a computer (or logician) evaluating that statement, you'd stop at 2^2 = 4, and pronounce it true.

So yes, it is valid to throw away a conclusion if even just one of its premises is contradictory. In looking back, only this second example explains the principle of explosion as asked for in OP, so disregard the rest if you already knew it.

This post was edited by TIMMY213 on May 9 2011 02:38am

This shit is better than school!

public school has been phased out by the internet......idk why we keep spending tax dollars on an obvious suck system.

I couldn't agree more. This system is outdated by loads of years..

Wordds don't have power over physical reality only perceptions of the mind thus meaning that that is just a bunch of bullshit.

I hope they don't make you take rhetoric.

This post was edited by thaluckyspoon on May 14 2011 07:22am

When more than 50% citizens of planet have thinking like you then we are going into revolution of unseen proportions

DipSet.