Organic And Non-Organic in Symbolic Logic

     One metalogical property of formulas is that a thesis of a logical system can be organic.  This means that none of its proper subformulas are tautologies.  For instance, the thesis of classical implicational calculus CqCpp is not organic, since Cpp is a thesis.  On the other hand the thesis CqCpq qualifies as an organic thesis, since the proper subformulas of CqCpq are q, Cpq, and p. 

     A famous axiom which qualifies as non-organic for classical propositional calculus is Jean Nicod's axiom DDpDqrDDtDttDDsqDDpsDps, which has DtDtt as a proper subforumla.  Another is Lukasiewicz's simpler axiom in that it has fewer variables DDpDqrDDsDssDDsqDDpsDps which has DsDss as a proper subformula which is a tautology.