Meanings of nonrational in English

There's this very nonrational, nonlinear part of the whole process.

And philosophy cannot bar its door with nonrational, nonphilosophical bars, whether those bars arc subrational, superrational, or simply nonrational.

The elements of phrenology recombined in ways that follow the rules of irrational logic, a rigorous methodology that follows nonrational rules.

Nonrational logic will not go away.