Science vs. Sophistry—A historical debate on bipolar fuzzy sets and equilibrium-based mathematics for AI&QI

Abstract

The road from bipolar fuzzy sets to equilibrium-based mathematical abstraction is surveyed. A continuing historical debate on bipolarity and isomorphism is outlined. Related literatures are critically reviewed to counter plagiarism, distortion, renaming, and sophistry. Based on the debate, the term “isomorphistry” is coined. It is concluded that if isomorphism is used correctly it can be helpful in mathematics. If abused it may become isomorphistry—a kind of historical, socially constructed, entrenched, and “noble” hypocrisy hindering major scientific advances. It is shown that isomorphistry can be motivated by “denying” the originality of bipolar fuzzy sets and aimed at “justifying” plagiarism and distortion. Thus, isomorphistry is sophistry on isomorphism. Some (-,+)-bipolar isomorphistry behaviors are critiqued. YinYang vs. YangYin are distinguished. The geometrical and logical basis of equilibrium-based AI&QI computing machinery is introduced as a new computing paradigm with logically definable causality for mind-body unity. A philosophical joke on sophistry is appended.