现代逻辑的兴起

   现代逻辑的特点是：在命题推演过程中，只管符号的形式，

而不设计符号的具体意义。借助这一特点，现代人工智能才得以实现。

    Frege、Peano与Russel三位数学巨匠是现代逻辑的“开山鼻祖”。

说句实在话，借助超乘积构造的非标准模型，都是根据现代逻辑的这种符号化思想实现的。

有兴趣的读者，请参阅本文附件。

袁萌  陈启清 1月16日

附件：

Rise of modern logic[edit

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The period between the fourteenth century and the beginning of the nineteenth century had been largely one of decline and neglect, and is generally regarded as barren by historians of logic.[2] The revival of logic occurred in the mid-nineteenth century, at the beginning of a revolutionary period where the subject developed into a rigorous and formalistic discipline whose exemplar was the exact method of proof used in mathematics.     

The development of the modern "symbolic" or "mathematical" logic during this period is the most significant in the 2000-year history of logic, and is arguably one of the most important and remarkable events in human intellectual history.[4]

A number of features distinguish modern logic from the old Aristotelian or traditional logic, the most important of which are as follows:[97] Modern logic is fundamentally a calculus whose rules of operation are determined only by the shape and not by the meaning of the symbols it employs, as in mathematics. Many logicians were impressed by the "success" of mathematics, in that there had been no prolonged dispute about any truly mathematical result. C.S. Peirce noted[98] that even though a mistake in the evaluation of a definite integral by Laplace led to an error concerning the moon's orbit that persisted for nearly 50 years, the mistake, once spotted, was corrected without any serious dispute. Peirce contrasted this with the disputation and uncertainty surrounding traditional logic, and especially reasoning in metaphysics. He argued that a truly "exact" logic would depend upon mathematical, i.e., "diagrammatic" or "iconic" thought. "Those who follow such methods will ... escape all error except such as will be speedily corrected after it is once suspected". Modern logic is also "constructive" rather than "abstractive"; i.e., rather than abstracting and formalising theorems derived from ordinary language (or from psychological intuitions about validity), it constructs theorems by formal methods, then looks for an interpretation in ordinary language. It is entirely symbolic, meaning that even the logical constants (which the medieval logicians called "syncategoremata") and the categoric terms are expressed in symbols.