Liar Paradox: Proposition and Process Uncertainty
Case:A said B is a liar;
B said A is true.This case tells us that logical reasoning must be based on proper proposition and facts. We have two judgement based on no facts or proposition. So we do not know if all the above statement is true to fact or not. Let us assume that when A said B is a liar based on the proposition of "B said A is true",then "B said A is true" must be the first sentence as basis for reasoning in this case. So the case becomes:
Case:B said A is true;
A said B is a liar. If the judgement "B said A is true" is based on the fact that A said B is a liar. Then the proposition for the reasoning of "B said A is true" is "A said B is a liar". Then the condition of "A said B is a liar" must be the first sentence in this case. Then it returns back to the original case.So we can not decide which one is the right beginning proposition condition for reasoning. So the proposition is not clear.
Conclusion:Logical judgements can not take each other as mutual propositions.
If we introduce a proposition for this case like:
Case:B said people are all stupid;
A said B is a liar; B said A is true.(based on the first fact, not the third judgement).Then the case holds on logically.
The relationship or logical structure expressed by word is like a dream or imagined ghost by perception. The dream can be true to the reality of nature or totally irrelevant to the truth of nature. So a dream does not necessarily comply with the logics developed from reality.