Logical Thinking in the Pyramidal Schema of Concepts

by Geldsetzer, Lutz; Schwartz, Richard L.

• ISBN13: 9789400753006
• ISBN10: 9400753004
• Format: Hardcover
• Copyright: 2012-11-29
• Publisher: Springer Verlag

Summary

This volume on logic proposes a new way of formalizing in logic and mathematics a pyramidal graph system. Surveying and criticizing classical and mathematical logic as the two branches of non-dialectical and dialectical logic, it moves from concepts, via connectors (including mathematical operators), definitions, propositions and inferences, to theories and axioms. The author has developed this new methodology on the basis of Porphyrian trees and modern concepts of classification, in both of which pyramids act as the organizing schema.The relations between concept positions in the pyramid are read off as connectors defined by theirvertical or horizontal directions. The author shows that there are two types of connectors: one generates propositions with truth values; the other yields conceptual expressions or complex concepts which lack truth values. This forms a strong argument against adopting the non-discriminating connector definitions in Wittgensteinian truth-value tables. The author gives special consideration to mathematical connectors and operators and presents a pyramid of the principal number concepts to demonstrate the capacity of the pyramidal formalism to logically organize them. The book also counters the logical dogma that contradictory propositions are simply 'false' and sheds new light on the logical characteristics of probability, as well as on syllogistic and other inferences.The book will be of interest not only to students of logic and mathematics but also to those of philosophy and philosophy of science.