数学逻辑概要

The work of which this is an English translation appeared originally in French as Precis de logique mathematique. In 1954 Dr. Albert Menne brought out a revised and somewhat enlarged edition in German (Grund­ riss der Logistik, F. Schoningh, Paderborn). In making my translation I have used both editions. For the most part I have followed the original French edition, since I thought there was some advantage in keeping the work as short as possible. However, I have included the more extensive historical notes of Dr. Menne, his bibliography, and the two sections on modal logic and the syntactical categories (§ 25 and 27), which were not in the original. I have endeavored to correct the typo­ graphical errors that appeared in the original editions and have made a few additions to the bibliography. In making the translation I have profited more than words can tell from the ever-generous help of Fr. Bochenski while he was teaching at the University of Notre Dame during 1955-56. OTTO BIRD Notre Dame, 1959 I GENERAL PRINCIPLES § O. INTRODUCTION 0. 1. Notion and history. Mathematical logic, also called 'logistic', ·symbolic logic', the 'algebra of logic', and, more recently, simply 'formal logic', is the set of logical theories elaborated in the course of the last century with the aid of an artificial notation and a rigorously deductive method.

这部作品的英文版最初是用法语出版为《数学逻辑概要》。1954年，阿尔伯特·门内博士在德国（冯·施诺根出版社，帕德博恩）出版了一版修订并稍加扩展的版本（《逻辑学纲要》，用德文）。在进行我的翻译时，我使用了两个版本。总体来说，我遵循了最初的法语原版，因为我觉得尽可能保持工作短小精悍是有益的。然而，我也包括了门内博士的历史注释、他的参考文献以及两节关于模态逻辑和语法范畴（第25节和第27节），它们在原始版本中没有出现。

我在译文制作过程中力求纠正原版出版时出现的拼写及校对错误，并添加了一些新的参考文献。在我进行翻译的过程中，我得到了弗·波希恩斯基教授的帮助，在1955-1956年他还在诺特丹大学任教期间。 诺特丹，1959 年

一般原则
0. 引言
0. 1 概念与历史。
数学逻辑也被称为“逻辑学”，“符号逻辑”，“逻辑的代数”以及最近被简称为“形式逻辑”。它是本世纪在人工记号的帮助下，通过严格演绎的方法发展起来的一系列逻辑理论集合。

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