One especially difficult aspect of Hegel's work is his innovation in logic. In response to Immanuel Kant's challenge to the limits of Pure Reason, Hegel developed a radically new form of logic, which he called speculation, and which is today popularly called dialectics. The difficulty in reading Hegel was perceived in Hegel's own day, and persists into the 21st century. To understand Hegel fully requires paying attention to his critique of standard logic, such as the law of contradiction and the law of the excluded middle, and, whether one accepts or rejects it, at least taking it seriously. Many philosophers who came after Hegel and were influenced by him, whether adopting or rejecting his ideas, did so without fully absorbing his new speculative or dialectical logic.
If one wanted to provide a big piece of the Hegel puzzle to the beginner, one might present the following statement from Part One of the Encyclopedia of Philosophical Sciences: The Logic:
"... a much misunderstood phenomenon in the history of philosophy — the refutation of one system by another, of an earlier by a later. Most commonly the refutation is taken in a purely negative sense to mean that the system refuted has ceased to count for anything, has been set aside and done for. Were it so, the history of philosophy would be, of all studies, most saddening, displaying, as it does, the refutation of every system which time has brought forth. Now although it may be admitted that every philosophy has been refuted, it must be in an equal degree maintained that no philosophy has been refuted. And that in two ways. For first, every philosophy that deserves the name always embodies the Idea: and secondly, every system represents one particular factor or particular stage in the evolution of the Idea. The refutation of a philosophy, therefore, only means that its barriers are crossed, and its special principle reduced to a factor in the completer principle that follows"
-- from Wikipedia
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