The Law of Excluded Middle and the Negation of it in many-valued and Fuzzy Logics

The philosophical critiques, in twentieth century, on binary paradigm caused the negation of the law of excluded middle as the same as it caused the establishment of many-valued logics and fuzzy logic, while the laws of excluded middle, identity and contradiction are all fundamental principles of thought and truth or falsity of each is derived from the truth or falsity of the others. This view point gives rise to some questions as follows: Canwe deny these principles and are they fundamental? Otherwise how can we accept the claim of many-valued and fuzzy logicians indicate the negation of the law of excluded middle? Regarding these questions I first show, in this paper, various formulations of those three above laws and then I argue that the inability of binary logic and the necessity of establishment of many-valued logics and fuzzy logic are not in contrary tothose three above laws. Besides, it is the connection of the present paper that Aristotle as the first philosopher who has elucidates the laws of contradiction and excluded middle was quite aware of the possibility of ambiguous in some propositions if they contain words which are equivocal. He also appealed to the truth values of both "partially true" and"partially false" to describe those propositions which at some level are vague.