Fuzzy Paradox And Researches Of The Paradox-solved Thoughts Based On Fuzzy Set Theory

In order to grasp the world and express ideas, we created language, invented thelanguage symbols for culture inheriting. As human thought representation, language, is itaccurately reflecting the truth of human’s knowledge about the world? When we talk aboutsomething, we often hope that we could express them clearly enough, but when we usesome abstract words, the desire, which we want to make everything clearly, it will beblocked ruthlessly. In fourth century BC, Eublides who is one Megarian member in theancient Greek presented two argues including "bald debate,"heap debate" problem, theyare the earliest record of fuzzy paradoxes. At the beginning, people believe that neither the"bald debate" nor the "heap debate" could be defined as a paradox, they thought it just wasa kind of extremely boring sophism. If the premise that each hair is ignorable is acceptable,we can finally achieve the contradictory conclusions from the formal structure, this is aviolation of our intuition and a serious crisis to our daily habit of language. As we know,the problem caused by fuzzy predicate and the chain argument is so serious that we mustconsider this matter by heart: How could fuzzy predicate lead to the fuzzy paradox?By analyzing the formation mechanism of fuzzy paradox, I present that the key stepof fuzzy paradox lie in a kind of social behavior principles——which I would like to call‘Ignored Principle’, and in this paper I will give it the formal definition while point outand prove its inevitability through the theoretical and practical perspective. If the ‘IgnoredPrinciple’ conforms to logic, and if it has a formal definition, these premises can lead thediscussion of fuzzy paradox into the rigid mathematical logic system, it is necessary forthe strict definition of logical paradox.In order to discuss the ‘Ignored Principle’ and the nature of our language, I introducea definition about vagueness and precision which defined by Russell, this definition relyon a theoretical language model which basics on one-to-one correspondence principle.According to this, yet associating the Axiomatic Sets Theory, I will prove the inevitabilityof the ‘Ignored Principle’, and discuss the ideas of fuzzy sets establishing.To solve the fuzzy paradox, in this paper I will present an idea that the key point of the paradox solution method is constraint the ‘Ignored Principle’, compare and analyze thecharacteristic between cognitive modal logic and fuzzy sets theory.