> Moreover, one could play word games with the mathematical language, creating problematic statements like “this statement is false” (if it’s true, then it’s false; if it’s false, then it’s true) that indicated there were problems with the axiomatic system.
I hope this isn't too far off topic, but can someone clarify exactly how this problem indicts axioms? As an uninformed and naive musing, it occurs to me that an issue with the statement "this statement is false" is this. The whole of the statement, that is, the thing having truth or falsehood, cannot be addressed by one of its components.
I hope this isn't too far off topic, but can someone clarify exactly how this problem indicts axioms? As an uninformed and naive musing, it occurs to me that an issue with the statement "this statement is false" is this. The whole of the statement, that is, the thing having truth or falsehood, cannot be addressed by one of its components.