从逻辑哲学看模糊逻辑的形式化

从逻辑哲学观点看，在“符号化、公理化的模糊逻辑”与非形式化的“人脑使用的模糊逻辑”（苗东升的说法）这两者之间，只是形式模型及其现实原型的关系，决不相互排斥。真正的问题不在于，在现实生活中人脑所使用的实际上行之有效的模糊推理，是否应该和可能符号化、公理化，而是在于如何恰当地进行形式化。笔者采用苏珊·哈克（Susan Haack）的逻辑哲学观点，认为非经典逻辑可划分为扩展逻辑和异常（deviation）逻辑，模糊逻辑归属于异常逻辑。本文以模糊逻辑系统FZ为例，具体分析了虽然经典逻辑中一些较强的公理和推理规则均不成立，但是与之对应的较弱的“合经典的”（well-behaved）公理和推理规则却仍然可以成立，由此导致一系列新奇性质。笔者采用了达·柯斯塔（da Costa）的形式化技巧，它是关于“在虚设不矛盾律成立的前提下”（相应公式可以称为“合经典的”）才能成立的逆否律。当我们撤除了“虚设不矛盾律为前提”的限定，它又重新回到了无条件成立的情况。笔者也推广了玻尔（N.Bohr）和冯·威扎克（von Weizsaecker）关于对应原理的思想，认为作为非经典逻辑的模糊逻辑与经典逻辑之间也应当遵守“对应原理”：经典逻辑是模糊逻辑的前身，模糊逻辑将构成更为普遍的逻辑形式，经典逻辑作为模糊逻辑的极限形式，在局部情况下还保持自身的意义。

On the Formalization of Fuzzy Logic from the Perspective of the Philosophy of Logic

From the point of view of the philosophy of logic, the relationship between axioma- tized fuzzy logics and the non-formalized ＂fuzzy logics used in human brains＂（Dongsheng Miao＇s ideas） is simply that of formal models and their real prototypes, which does not exclude each other. What matters is not whether fuzzy logics used in human brains should and could be formalized and axiomatized, but how to formalize it in an adequate way. Adopting Susan Haack＇s point of view of the philosophy of logic, the author of this paper holds that non-classical logics can be divided into extended logics and deviation logics. Fuzzy logic is included in the deviation logic. Using the system of fuzzy logic FZ as an example, this paper shows that though some strong axioms and inference rules in classical logic are not established in FZ, their corresponding weaker well-behaved axioms and inference rules are well done, leading to new qualities. The author employs da Costa＇s method of formalization that deals with converse negative laws which only holds ＂with the precondition of nominally supposing non -contradiction law holds ＂（the corresponding formula can be said ＂well-behaved＂.） It will hold under no condition when we remove the confinement of a nominal presuppo- sition of the precondition for non-contradiction. In addition, the author expands N. Bohr and von Weizsaecker＇s ideas of corresponding principles to a corresponding principle for fuzzy logic （as a branch of non-classical logic） and classical logic： Classical logic is the predecessor of fuzzy logic; fuzzy logic will become a more generalized form of logic. As a special form of fuzzy logic, classical logic keeps its own status in part.