Tuesday, 19 March 2013

This sentence is false - what? A logical work through

So - spending my time today very well - just handed in my final piece of coursework for my Masters degree! woohoo!

Anyway I was stumbling and ended up wikipedia - looking at the liar paradox and in particular how it can be resolved. There is one argument on there that goes like this.

Since any statement can be preceded by 'This whole statement is true and...'

The liar paradox is the sentence 'This statement is false.' The paradox is that the sentence talks about itself and you end up in an infinite loop - which I just found out is the address of Apple HQ.

So back to the resolution!
The sentence you are now looking at is 'This whole statement is true and this statement is false.' I know it's a really unnecessary thing to even talk about - it doesn't matter, but I disagree with the conclusion drawn.

In the wikipedia article, the writer states that since the paradoxical statement contradicts itself, it is therefore a false statement, but I believe it is a null statement - it is a statement which states nothing.

The purest form of logic is maths - IMO... and in maths, if you write a sentence like A and B is C,
you could rewrite it as A+B=C and this would mean the same, much like 1 and 2 is 3. So in this example A is This statement is true and B is this statement is false. So what is C?

Well if you stand back and say that A and B are basically the same except one has the word true and the other false. I'd argue that true and false are opposites of each other, or the negatives of each other. Take two falses and you have a true, just like negative numbers. Therefore A = -B and B = -A.

So now our equation looks like A-A=C. So C = 0 or a null statement.

If you agree with my arguments, then you can see, I have just logically proven that the liars paradox is so completely unimportant, it is nothing at all.

Or maybe you say that the negative of 'This statement is true' is 'This un-statement is untrue' in which case my whole argument falls apart! but anyway...

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