I disagree that there is a paradox, because I can resolve it. I can simply say, we analyze a sentence as a whole. For example, "If this sentence is true," is a conditional clause. It depends on a condition antecedent to the clause. Since the secondary clause "Germany borders China" is not true, therefore the sentence is false and no paradox occurs. Now, I think the opposite might be better as an alleged paradox, e.g. "If this sentence is false, then Germany borders China." Yes, the sentence is false, but, truth is that which is concordant with reality. Since the sentence is false, none of its conclusions have any value or relevance, because they have no relation to reality, so they have no validity. Thus, the proposition ""Germany borders China" is irrelevant.Curry's paradox is a paradox in which an arbitrary claim F is proved from the mere existence of a sentence C that says of itself "If C, then F", requiring only a few apparently innocuous logical deduction rules. Since F is arbitrary, any logic having these rules allows one to prove everything. The paradox may be expressed in natural language and in various logics, including certain forms of set theory, lambda calculus, and combinatory logic.
The paradox is named after the logician Haskell Curry. It has also been called Löb's paradox after Martin Hugo Löb,[1] due to its relationship to Löb's theorem.
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. The analysis consists of two steps.
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. 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.
Another way to put it is if a sentence is false, that is, not concordant with reality, any claim or proposition within may be ignored. This also resolves the paradox.
An example in math is 0*. 0 times anything is 0 regardless of what number follows, therefore any digit or string of digits may be ignored. Same if the entry to the right is a parenthised expression, it may be ignored as irrelevant.
So maybe someone can show me where I have misunderstood the paradox? I resolved it in about 10 minutes, it seemed way too easy. The inverse was harder.
