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The origin of Boole's philosophy of logic: The assimilation of traditional logic into mathematical analysis.

机译：布尔的逻辑哲学的起源：将传统逻辑吸收到数学分析中。

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George Boole (1815--1864) is widely regarded as the founder of symbolic logic. He initiated the revolution that transformed logic from the mold in which it had been set in ancient times into the dramatically growing mathematical form it has acquired in more recent times. However, Boole viewed himself not as a revolutionary but as completing a project undertaken by Aristotle two millennia earlier. He saw himself as reformulating traditional logic into a branch of mathematical analysis, thus refining and extending it. His orientation simultaneously blinded him to many of the shortcomings of his logic and led him to many original contributions transforming the field. In this dissertation I assess Boole's philosophy of logic while tracing its origins to the philosophies underlying the two main traditions that influenced it: Aristotelian logic and the field of mathematics then called mathematical analysis.;Boole's orientation led him to view logic as a branch of mathematics about which mathematical results could be proved and not as the study of proofs themselves---especially proofs in mathematics---as had been done traditionally. For example, Boole completely ignored the indirect proof, so frequently encountered in mathematics. He viewed the logically perfect language as consisting of algebraic equations and the proper form of the propositions studied by logic as equational. In order to do this he viewed 'All Ss' in 'All Ss are Ps' as denoting the class of Ss and simultaneously, for the first time, he expanded the subject-matter of mathematics to include nonquantitative domains.;Boole saw the central problem of logic not as the attempt to determine of a given premise-conclusion argument whether or not it was valid but as the attempt to find solutions to given equational "premises". This view led him to commit the fallacy of confusing a solution of an equation with a consequence of the equation but simultaneously, for the first time, to raise the Boolean summarization problems. His orientation prevented the expression of negation in his language; however, it simultaneously led him to the attempt, for the first time, to axiomatize logic, thus codifying infinitely many tautological forms, and also to use mathematical techniques to find metatheorems about his system, including decision procedures.
机译：乔治·布尔（George Boole，1815--1864年）被广泛认为是符号逻辑的创始人。他发起了一场革命，将逻辑从古代的模子转变为近代以来迅速发展的数学形式。但是，布尔认为自己不是革命者，而是完成了两千年前亚里斯多德承担的一个项目。他认为自己将传统逻辑重构为数学分析的一个分支，从而完善和扩展了它。他的方向感同时使他对自己逻辑上的许多缺点视而不见，并导致他为改变这一领域做出了许多原创性贡献。在这篇论文中，我评估了布尔的逻辑哲学，同时追溯了其起源于影响其的两个主要传统的哲学：亚里士多德逻辑和后来称为数学分析的数学领域；布尔的取向使他将逻辑视为数学的一个分支。可以证明哪些数学结果，而不是像传统上那样作为证明本身（尤其是数学证明）的研究。例如，布尔完全忽略了数学中经常遇到的间接证明。他认为逻辑上完美的语言是由代数方程式组成的，而逻辑研究的命题的适当形式是方程式。为此，他将“所有Ss都是Ps”中的“所有Ss”视为表示Ss的类别，与此同时，他第一次将数学的主题扩展到包括非量化领域。逻辑问题不是尝试确定给定的前提-结论参数是否有效，而是尝试找到给定的方程式“前提”的解决方案。这种观点使他犯下了将方程的解与方程的结果相混淆的谬论，但是同时，这第一次引起了布尔汇总问题。他的定向阻止了他的语言中的否定表达。然而，这同时导致他第一次尝试进行公理化逻辑，从而将无数重言式形式进行了编码，并且还使用数学技术来查找有关他系统的元定理，包括决策程序。

著录项

  • 作者

    Nambiar, Sriram.;

  • 作者单位

    State University of New York at Buffalo.;

  • 授予单位 State University of New York at Buffalo.;
  • 学科 Philosophy.
  • 学位 Ph.D.
  • 年度 2000
  • 页码 326 p.
  • 总页数 326
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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