Set Theory?

Question

Assuming the following is a statement,Prove that 1+1=3:

If this sentence is true, then 1+1=3.

What can you deduce from part a about the status of "this statement is true"? why?

Answer 1

Let S be the statement "if this sentence is true, then 1+1 = 3".

Suppose S is true. Note that S states that if S is true, then 1+1 = 3. And since S is true (by assumption), it follows by modus ponens that 1+1 = 3.

From the above paragraph, we know that if S is true, then 1+1 = 3. And since that is exactly what S says, it follows that S is in fact true. So 1 + 1 = 3. Q.E.D.

This result is known as Curry's paradox. You can read more about it here: http://en.wikipedia.org/wiki/Curry%27s_paradox