Question: Explain the liar paradox. Why would banning self-referential statements  and indexical expressions not eliminate the liar paradox?

Expert answer

The liar paradox is a well-known problem in logic and philosophy. It arises from the following self-referential statement: "This sentence is false." If we assume that this sentence is true, then it must be false. But if it is false, then it must be true. We are left with a contradiction, which means that the statement cannot be both true and false.

One proposed solution to the liar paradox is to ban self-referential statements and indexical expressions. However, this would not eliminate the problem entirely. For example, consider the following sentence: "Everything I say is false." This sentence does not directly refer to itself, but it still leads to a contradiction. Thus, banning self-referential statements would not be a complete solution to the problem.

Another proposed solution is to simply accept that the liar paradox is true. This may seem counter-intuitive, but it does avoid the contradiction. Alternatively, we could accept that the liar paradox is false. This also avoids the contradiction, but it has the undesirable result of making all self-referential statements false.

Ultimately, there is no perfect solution to the liar paradox. Each proposed solution has its own benefits and drawbacks. We must simply choose the solution that seems most plausible to us.