Logo - springer
Slogan - springer

Philosophy - Logic & Philosophy of Language | Logical Thinking in the Pyramidal Schema of Concepts: The Logical and Mathematical Elements

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

Geldsetzer, Lutz, Schwartz, Richard L.

2013, XLIV, 140 p.

Available Formats:
eBook
Information

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.

 
$99.00

(net) price for USA

ISBN 978-94-007-5301-3

digitally watermarked, no DRM

Included Format: PDF and EPUB

download immediately after purchase


learn more about Springer eBooks

add to marked items

Hardcover
Information

Hardcover version

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$129.00

(net) price for USA

ISBN 978-94-007-5300-6

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

Softcover
Information

Softcover (also known as softback) version.

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$129.00

(net) price for USA

ISBN 978-94-017-8444-3

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

  • Offers visual representation of all logical elements via pyramidal graph
  • Uses new methodology on the basis of Porphyrian trees as well as on modern concepts of classification
  • Sheds new light on the logical character of contradiction and probable propositions

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.

Content Level » Research

Keywords » 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

Related subjects » Logic & Philosophy of Language - Mathematics - Theoretical Computer Science

Table of contents / Sample pages 

Popular Content within this publication 

 

Articles

Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Logic.