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On Axioms and Especially on the Real Axioms of Logic

  • Lutz Geldsetzer
  • Richard L. Schwartz
Chapter

Abstract

Axioms or “categories” are not indefinable as the tradition holds 58 – Implicit definition of axioms as petitio principii 58 – The real meaning of the traditional logical “principles” of Identity, of Contradiction and of the Third 58 – Critique of the traditional uses of the three “principles” in logic and mathematics 59 – The “principle” of the Third is itself contradictory and therefore logically superfluous 60 – On the non-applicability of the so-called criteria of axioms 60 – Undecidability results from “indefinable” or dialectical axioms 60 – Identity, contradiction and the third not being axioms, they are rather deduced concepts of logical theories 60 – On truth, falsity and truth-falsity (or probability) as the genuine axioms of logic 60 – Definition of truth as pyramidal coherence of concepts, falsity as pyramidal incoherence of concepts 61 – Truth-falsity (or probability) is a contradictory fusion of coherence and incoherence 62 – Literary fiction is “neither true nor false”, that means “not true and not false” or “false and true” 61 – Advise how to interpret it 61 – Thought experiments as “science fiction” and how to interpret it 62 – Logical truth is no substitute for scientific trustworthiness 62.

Keywords

Thought Experiment Science Fiction Concept Truth Sole Characteristic Logical Axiom 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Lutz Geldsetzer
    • 1
  • Richard L. Schwartz
    • 2
  1. 1.DüsseldorfGermany
  2. 2.New York CityUSA

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