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

  • Lutz Geldsetzer
  • Richard L. Schwartz

Table of contents

  1. Front Matter
    Pages i-xliv
  2. Lutz Geldsetzer, Richard L. Schwartz
    Pages 1-7
  3. Lutz Geldsetzer, Richard L. Schwartz
    Pages 9-28
  4. Lutz Geldsetzer, Richard L. Schwartz
    Pages 29-42
  5. Lutz Geldsetzer, Richard L. Schwartz
    Pages 43-49
  6. Lutz Geldsetzer, Richard L. Schwartz
    Pages 51-57
  7. Lutz Geldsetzer, Richard L. Schwartz
    Pages 59-66
  8. Lutz Geldsetzer, Richard L. Schwartz
    Pages 67-71
  9. Lutz Geldsetzer, Richard L. Schwartz
    Pages 73-77
  10. Back Matter
    Pages 79-137

About this book


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.


Axioms of logic Classification concepts Coherence vs. incoherence as truth-value conditions Conceptual pyramid Connectors, expression-forming vs. proposition-forming Contradiction as propositional truth-falsity Contradictory concepts Definition by equation Dispositional concepts Equation as equivalence Intensional-extensional logic Mathematical connectors Mathematical logic Number concept Porphyrian trees logic Possible worlds Probability, logical and mathematical Pyramidal graph logic Pyramidal logic Pyramidal logical formalism Sense and reference Sense experience Theories, conceptual hard-core and propositional demonstration Visualization Logic Visualization of logical elements Wittgensteinian truth-value table

Authors and affiliations

  • Lutz Geldsetzer
    • 1
  • Richard L. Schwartz
    • 2
  1. 1.Universitaet DuesseldorfDüsseldorfGermany
  2. 2.Brooklyn, New York CityUSA

Bibliographic information