On the Foundations of the Mathematical Theory of Logic and on the Philosophical Interpretation of Its Methods and Processes
It may be necessary to inform the reader that the mathematical theory of which some illustrations will be given in the following Essay is the one which I have developed in a treatise published about two years ago and entitled “An Investigation of the Laws of Thought in which are founded the Mathematical Theories of Logic and Probabilities”. It may also be proper to premise that I do not employ the term mathematical with reference to the theory of Logic as if with any covert implication that reasoning always and essentially involves the ideas of extension, magnitude, number etc. but that I employ that term solely as descriptive of the methods and forms on which the theory set forth in the work above referred to obtains its practical development. The foundations of that theory are laid professedly at least where alone the real foundations of Logic can be laid in an analysis of the intellectual operations. As moreover this paper is in some measure introductory to another containing a special application of its principles 1 I deem it right to state the circumstances in which it originated. Some time after the publication of the “Laws of Thought” my attention was directed by the Bishop of Edinburgh to a question in the theory of probabilities not noticed in the above work upon which conflicting opinions had been formed by different writers, and the fallacious character of some of the reasonings which had been employed was at the same time pointed out
KeywordsMathematical Theory General Notion White Flower Elementary Concept Dual Algebra
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