In Curry's Paradox, What is the statement A referring to ________.
I was trying to understand Curry's Paradox on wikipedia.
%27s_paradox
The example given is:
To produce Curry's paradox, as described in the two steps above, apply
this method to the sentence if this sentence is true, then Germany
borders China. Here A, this sentence is true, refers to the overall
sentence, while B is Germany borders China. So, assuming A is the
same as assuming If A, then B. Therefore, in assuming A, we have
assumed both A and If A, then B. Therefore B is true, by modus
ponens, and we have proven If this sentence is true, then 'Germany
borders China' is true. in the usual way, by assuming the hypothesis
and deriving the conclusion.
Now, because we have proved If this sentence is true, then 'Germany
borders China' is true, then we can again apply modus ponens, because
we know that the claim this sentence is true is correct. In this
way, we can deduce that Germany borders China.
I went through the formal proof as well, but what I fail to understand is that we still haven't proved that the sentence A is True, just assumed it to be True.
Since the resulting statements give us a paradox, it follows that the statement A can't be True in the first place. Where am I getting this wrong?