The system of sevenfold predication of the Jainas, while an invaluable tool in expounding the Jaina doctrine of "non-onesidedness" (Anekāntavāda), has also been criticized for being unsystematic and contradictory. In particular, the fourth predication has been suggested to embrace a kind of irrationality. An analysis is provided here that makes clear the logical basis underlying the seven predications. An interpretation is also offered of the problematic fourth predication that renders the system free from contradiction, and it is suggested that this (...) interpretation best captures the positive spirit of Anekāntavāda. (shrink)

We show that there exist 2 ℵ 0 equational classes of Boolean algebras with operators that are not generated by the complex algebras of any first-order definable class of relational structures. Using a variant of this construction, we resolve a long-standing question of Fine, by exhibiting a bimodal logic that is valid in its canonical frames, but is not sound and complete for any first-order definable class of Kripke frames (a monomodal example can then be obtained using simulation results of (...) Thomason). The constructions use the result of Erd $\H{o}$ s that there are finite graphs with arbitrarily large chromatic number and girth. (shrink)

Let be the class of frames satisfying the condition.