Booleの論理学

概要

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The symbolic logic has been developed rapidly from the later half of 19th century. It is G. Boole who first founded the basis of this logic. His significant contribution was the consistent introduction of mathematical operations to the representation of logic. And these were performed by his nominalistic uses of symbols and by the principle of extensionality. His success, unlike all of his predecessors, depends on this two points. But as Boole's logic was theoretically refined and became to be called boolean algebra or algebra of logic, it's meaning changed gradually and it was investigated only as one of abstract algebras. Moreover as a result of Frege's inovative logical system, insufficiency of Boole's logic came to be clear, especially about quantification. Surely Frege's logical system is superior to Boole's in many respects. But we can't discard Boole's results, because of following two points. Frege's view about logic, that logic must be the universal logic, can't bring forth meta-logical results. Conversely Boole's relative logics become useful for them. Secondly in the studies of model theories we can't succeed without the knowledge of boolean algebraic structure of model's universe. This shows Boole's logic is not only an incomplete part of Frege's logic, but it supplies semantical parts to Frege's. Therefore we can conclude that modern logic is the union of Frege's system and Boole's relativistic view of logic.
慶應義塾大学の論文