cmacis wrote:What i meant was that heart is obviously an equivalence relation;
all x love x
x loves y implies y loves x
Okay, it fails at that point, no need to get onto transitivity.
Yeah, it's definitely a relation, but not equivalence. In reality, it is neither reflexive, symmetric, nor transitive. (That is, some people don't love themselves, much love isn't returned, and if I love Alice who loves Bob, it doesn't mean I love Bob. More likely, I think the guy's a bastard for taking Alice's attention away from me.)
But nonetheless, there's no need to give up quite as easily on understanding it as this mathematician did. Plenty of nonreflexive, nonsymmetric, and nontransitive relationships work just fine in logic.
They just can't be taken as the variables variables of a first-order theory.