Intransitivity

According to Transitivity, if A is better than B, and B is better than C, then A is better than C. We may understand “better than” as short for any of the following: “intrinsically better than,” “all things considered better than,” “hedonically better than,” and “better for a person than.” The same puzzle arises on each interpretation. Transitivity seems entrenched in our conceptual scheme, if not analytically true; its failure implies, implausibly, that some possibilities cannot be ranked in terms of value; scads of three-member sets inductively confirm it; and hypothetical money-pumpers coax its detractors out of house and home by proffering a series of trades—C for A, B for C and A for B (and then repeating the cycle)—for an endlessly accumulating price. Nevertheless, two highly plausible principles entail that Transitivity is false.