Curry's Paradox - Natural Language

Natural Language

Claims of the form "if A, then B" are called conditional claims. Curry's paradox uses a particular kind of self-referential conditional sentence, as demonstrated in this example:

If this sentence is true, then Germany borders China.

Even though Germany does not border China, the example sentence certainly is a natural-language sentence, and so the truth of that sentence can be analyzed. The paradox follows from this analysis. First, common natural-language proof techniques can be used to prove that the example sentence is true. Second, the truth of the example sentence can be used to prove that Germany borders China. Because Germany does not border China, this suggests that there has been an error in one of the proofs. Worse, the claim "Germany borders China" could be replaced by any other claim, and the sentence would still be provable; thus every sentence appears to be provable. Because the proof uses only well-accepted methods of deduction, and because none of these methods appears to be incorrect, this situation is paradoxical.