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''An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities'' by George Boole, published in 1854, is the second of Boole's two monographs on algebraic logic. Boole was a professor of mathematics at what was then Queen's College, Cork (now University College Cork), in Ireland. == Review of the contents == The historian of logic John Corcoran wrote an accessible introduction to ''Laws of Thought''〔George Boole. 1854/2003. The Laws of Thought, facsimile of 1854 edition, with an introduction by J. Corcoran. Buffalo: Prometheus Books (2003). Reviewed by James van Evra in Philosophy in Review.24 (2004) 167–169.〕 and a point by point comparison of ''Prior Analytics'' and ''Laws of Thought''.〔JOHN CORCORAN, Aristotle's Prior Analytics and Boole's Laws of Thought, History and Philosophy of Logic, vol. 24 (2003), pp. 261–288.〕 According to Corcoran, Boole fully accepted and endorsed Aristotle’s logic. Boole’s goals were “to go under, over, and beyond” Aristotle’s logic by: # Providing it with mathematical foundations involving equations; # Extending the class of problems it could treat from assessing validity to solving equations, and; # Expanding the range of applications it could handle — e.g. from propositions having only two terms to those having arbitrarily many. More specifically, Boole agreed with what Aristotle said; Boole’s ‘disagreements’, if they might be called that, concern what Aristotle did not say. First, in the realm of foundations, Boole reduced the four propositional forms of Aristotle's logic to formulas in the form of equations—by itself a revolutionary idea. Second, in the realm of logic’s problems, Boole’s addition of equation solving to logic—another revolutionary idea—involved Boole’s doctrine that Aristotle’s rules of inference (the “perfect syllogisms”) must be supplemented by rules for equation solving. Third, in the realm of applications, Boole’s system could handle multi-term propositions and arguments whereas Aristotle could handle only two-termed subject-predicate propositions and arguments. For example, Aristotle’s system could not deduce “No quadrangle that is a square is a rectangle that is a rhombus” from “No square that is a quadrangle is a rhombus that is a rectangle” or from “No rhombus that is a rectangle is a square that is a quadrangle”. Boole's work founded the discipline of algebraic logic. It is often, but mistakenly, credited as being the source of what we know today as Boolean algebra. In fact, however, Boole's algebra differs from modern Boolean algebra: in Boole's algebra A+B cannot be interpreted by set union, due to the permissibility of ''uninterpretable terms'' in Boole's calculus. Therefore, algebras on Boole's account cannot be interpreted by sets under the operations of union, intersection and complement, as is the case with modern Boolean algebra. The task of developing the modern account of Boolean algebra fell to Boole's successors in the tradition of algebraic logic (Jevons 1869, Peirce 1880, Jevons 1890, Schröder 1890, Huntingdon 1904). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「The Laws of Thought」の詳細全文を読む スポンサード リンク
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