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

Overview

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 ...

See more details below
Hardcover (2013)
$110.33
BN.com price
(Save 14%)$129.00 List Price
Other sellers (Hardcover)
  • All (6) from $103.48   
  • New (4) from $103.48   
  • Used (2) from $163.68   
Sending request ...

Overview

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.

Read More Show Less

Product Details

  • ISBN-13: 9789400753006
  • Publisher: Springer Netherlands
  • Publication date: 12/31/2012
  • Edition description: 2013
  • Edition number: 1
  • Pages: 137
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.50 (d)

Meet the Author

Prof. Lutz Geldsetzer is Professor Emeritus of Philosophy at the Heinrich-Heine Universitaet in Duesseldorf, Germany, where he has taught since 1963 and where from 1971 to 2002 he directed the research department for general theory of science in the Institute of Philosophy. In 1970, he co-founded the internationally recognized Journal for General Philosophy of Science/Zeitschrift fuer allgemeine Wissenschaftstheorie which he co-edited until 2009. He has published books and articles on a wide range of philosophical topics, and edited several series of philosophical dictionaries, classics in various areas including hermeneutics, and specialized bibliographies. He has been a visiting professor at universities in the United States, the People's Republic of China, Italy, France and Germany. He studied Philosophy, Social Sciences, Law and Languages at the Johannes-Gutenberg Universitaet in Mainz, Germany, where he received his Ph.D. in 1961, and did postgraduate work at the Sorbonne in Paris in 1961-62.

Read More Show Less

Table of Contents

Preliminaries.- 1. Concepts.-2. Logical Connectors (Junctors).-3. Definitions.-4. Propositions.-5. Inferences.-6. Theories.-7. Axioms and especially on the genuine Axioms of Logic. ​

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)