On Axioms and Especially on the Real Axioms of Logic

  • Lutz Geldsetzer
  • Richard L. Schwartz


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.


Thought Experiment Science Fiction Concept Truth Sole Characteristic Logical Axiom 
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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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