One of the pillars of Meingast’s Logic was his celebrated irrelevance logic, developed around 1895, in an attempt to systematize some of the bolder and more speculative metaphysical ideas he was espousing at that time. A key tenet of irrelevance logic was the much-debated principle of closure under irrelevance. The principle stated that if Q is irrelevant to P, then P is irrelevant to P (and is thus irrelevant simpliciter). Meingast claimed that seriously reflecting on what would be involved in the denial of this principle would instantly reveal the principle as evident to the light of reason.
Not everyone were convinced, and some critics (most notably Brentano and Boltzmann) have even found the principle counterintuitive. It should, however, be noted that the principle follows, more or less directly, from Meingast’s doctrine of The Rational Magnetism of Being, on which every genuine aspect of reality exerts a rational pull on everything else. Consequently, if Q does not exert a rational influence on P, then P cannot pick out a genuine aspect of reality, and is thus irrelevant. Meingast maintained that Being, and hence relevance, does not admit of a logical articulation. Logic can only circle around Being but Being cannot be spoken of in a logical way. With the possibility of demonstrating relevance foreclosed, irrelevance becomes the fundamental logical relation.
Meingast’s confidence in his irrelevance logic was dramatically shaken in 1897, when a telegram from Meinong revealed an inconsistency in his logical edifice and sent Meingast back to the drawing board. The details of Meinong’s argument remain unknown, but it is said that it described a complex counterexample featuring a habitual depressive who has become irrelevant even to himself.