“The World of Null-A,” A. E. Van Vogt, 1948 -Wikipedia: “Gilbert Gosseyn, a man living in an apparent utopia where those with superior understanding and mental control rule the rest of humanity, wants to be tested by the giant Machine that determines such superiority. However, he finds that his memories are false. In his search for his real identity, he discovers that he has extra bodies that are activated when he dies (so that, in a sense, he cannot be killed), that a galactic society of humans exists outside the Solar system, a large interstellar empire wishes to conquer both the Earth and Venus (inhabited by masters of non-Aristotelian logic), and he has extra brain matter that, when properly trained, can allow him to move matter with his mind.”
Comments: ISFDB entry. Wikipedia: “The concept of non-Aristotelian logic was used by A. E. van Vogt as the central theme in his The World of Null-A novels, based on his interest in Alfred Korzybski’s General Semantics, stories tinged by van Vogt’s reflections upon revelations of police state conditions enforced by totalitarian regimes after World War II.”…”Van Vogt generally shortened non-Aristotelian logic to null-A in his description of logic systems incorporating three or more values, to represent relatively ‘subjective’ conclusions from inductive logic, rather than relying strictly on the binary, deductive reasoning. The null-A concept as depicted by van Vogt is complementary to Aristotle’s system of two-valued, true/false logic, i.e., ‘A is either B, or it is not B’.”
More detailed reviews of the short story/novels are available in Damon Knight’s In Search of Wonder and on the SF Site.
Author: Wikipedia: “Alfred Elton van Vogt (April 26, 1912 – January 26, 2000) was a Canadian-born science fiction author regarded as one of the most popular and complex science fiction writers of the mid-twentieth century: the ‘Golden Age‘ of the genre.”