A Cultural Paradox Fun in Mathematics by Jeffrey A. Zilahy - HTML preview

CH 5: I am a Liar

Considering that all the rules behind a language, called axioms in math, are inherently governed with logic, then logical fallacies that appear in our language can ultimately be seen through mathematics. Let us take a careful look at the following sentence: “This statement is false.” What is paradoxical about this is that if indeed you accept the statement's premise, then you are caught in a logical loop whereby accepting its premise you are simultaneously rejecting it, since the statement is claiming to be false. So false = true and true = false. This makes the statement simultaneously true and false at the same time, which is obviously impossible.

Another example of a logical contradiction is called Jourdain's Card Paradox. Imagine a card on which one side is written: "The sentence on the other side of this card is true." On the other side is written: "The sentence on the other side of this card is false." As you can quickly tell, you end up again in a paradoxical logical loop.

One final conundrum to consider is a card with the following three sentences printed:

1. This sentence contains five words.

2. This sentence contains eight words.

3. Exactly one sentence on this card is true.