Again, it is necessary to stress that non-aristotelian does not mean anti-aristotelian, just as non-newtonian physics is not anti-newtonian physics. […] Given these revolutions in science and mathematics, Korzybski reasoned that it was long past time for a revolution in reason itself, time for a new manner of thought, and he chose non-aristotelian to complement the new non-newtonian science and the non-euclidean mathematics of the early 20th century. Had he been working a half century later, during the late 20th century period that saw the introduction of poststructuralism and postmodernism, not to mention the postindustrial, the postliterate, and the posthuman, he almost certainly would have chosen the term post-aristotelian instead; after all, his emphasis was on the need to move forward, not to eliminate the past. For Korzybski, general semantics was central to this effort, but at the same time his introduction to non-aristotelian systems opens up a new area of exploration that he left to others to continue, an area we might refer to as non-aristotelian studies.
Source: wiktionary