Logical Thinking in the Pyramidal Schema of Concepts: The Logical and Mathematical Elements (2013)

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Synopsis
This new volume on logic follows a recognizable format that deals in turn with the topics of mathematical logic, moving from concepts, via definitions and inferences, to theories and axioms. However, this fresh work offers a key innovation in its ‘pyramidal’ graph system for the logical formalization of all these items. The author has developed this new methodology on the basis of original research, traditional logical instruments such as Porphyrian trees, and modern concepts of classification, in which pyramids are the central organizing concept. The pyramidal schema enables both the content of concepts and the relations between the concept positions in the pyramid to be read off from the graph. Logical connectors are analyzed in terms of the direction in which they connect within the pyramid. Additionally, the author shows that logical connectors are of fundamentally different types: only one sort generates propositions with truth values, while the other yields conceptual expressions or complex concepts. On this basis, strong arguments are developed against adopting the non-discriminating connector definitions implicit in Wittgensteinian truth-value tables. Special consideration is given to mathematical connectors so as to illuminate the formation of concepts in the natural sciences. To show what the pyramidal method can contribute to science, a pyramid of the number concepts prevalent in mathematics is constructed. The book also counters the logical dogma of ‘false’ contradictory propositions and sheds new light on the logical characteristics of probable propositions, as well as on syllogistic and other inferences.
Copyright:
2013

Book Details

Book Quality:
Publisher Quality
ISBN-13:
9789400753013
Related ISBNs:
9789400753006
Publisher:
Springer Netherlands
Date of Addition:
Copyrighted By:
Springer Science+Business Media Dordrecht
Adult content:
No
Language:
English
Has Image Descriptions:
No
Categories:
Nonfiction, Mathematics and Statistics, Philosophy
Submitted By:
Bookshare Staff
Usage Restrictions:
This is a copyrighted book.

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