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AN INVESTIGATION OF THE LAWS OF THOUGHT. CHAPTER I. NATURE AND DESIGN OF THIS WORK. . HPHE design of the following treatise is to investigate the ... |
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This paper deals with the influence exerted by Boole's own work on differential equations on his creation of algebraic logic. The main traits of Boole's methodology of logic, and the particular algorithms which he used in his 1847 The mathematical analysis of logic, are first pointed out. An examination of the mathematical papers which Boole wrote before the publication of the mentioned logical treatise shows that both the methodology leading to the production of his logic and the algorithms used in (...) |
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This paper studies the possible influences on Boole's logic of the writings related to the controversy over the quantification of the predicate between the philosopher William Hamilton and the mathematician Augustus De Morgan. As Boole himself testified in the introduction to his book The mathematical analysis of logic , this controversy was the external agent that stimulated him into writing up his earlier thoughts about a new conception of logic. But in addition to the external role that was played by (...) |
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It is one thing for a given proposition to follow or to not follow from a given set of propositions and it is quite another thing for it to be shown either that the given proposition follows or that it does not follow.* Using a formal deduction to show that a conclusion follows and using a countermodel to show that a conclusion does not follow are both traditional practices recognized by Aristotle and used down through the history of logic. These (...) |
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