In "The World of Null-A" (1945) and "The Pawns of Null-A" (1956) A. E. Van Vogt was writing as a disciple of Alfred Korzybski's General Semantics. I was going to write some thoughts on this, where it is now etc, but of course Wikipedia got there well before me.
Many people from Lao Tsu onwards have observed that the map is not the territory; the world is too complex to be circumscribed by mere words - language misleads by imposing simplistic models and categories on an always-more-complex-and-dynamic reality. Characterising this insight as 'non-Aristotelian logic' (null-A) is intellectual catch-up.
The cult-aspect arises from training purporting to suppress mindless emotionalism in favour of rational responses to life's complexities. There is of course something to it - rationality can offer superior solutions - but pure rationality is motiveless: there's always some underlying biological impulse driving our actions. Who's to say that murderously lashing out isn't sometimes the right answer? Certainly not the game theorists who analyse the logic of revenge. Suppressing your own emotions subcontracts your goals to those of others (the corporation, the state) while nullifying kindness, mercy or empathy.
Null-A's unemotional, hyper-rational supermen seem more like idealised Gestapo agents than heroes to me, although Van Vogt clearly liked them.*
On a related topic, the prospects of genetically engineering our children never goes away, with daily reporting of advances in genetic sequencing, analysis and engineering. The professionally-horrified (it's ethically wrong to play God) seem to think we'd all elect for a kind of bland niceness: beautiful/handsome clone-ish people, uniformly smart and nice.
Game theory applies here as well: if the majority elected to have their children fashioned as doves, it would be very much in the interests of some to fashion their progeny as hawks!
* This is a bit unfair, as Van Vogt seems to believe that the Null-A trained do not suppress but are consciously aware of their emotional reactions, integrating them as 'facts' into a supremely cerebral response through the famous 'cortical-thalamic pause'.