A statement S1 or S2 is always negated by the corresponding Neither S1 nor S2. If or were sometimes, in virtue of its meaning, exclusive, then the latter would in those cases be true when both S1 and S2 were true: but in fact, Neither S1 nor S2 always requires for its truth the falsity of S1 and of S2.Humberstone says this is as close as one gets to a definitive refutation of the exclusive reading. (He credits the argument to others.) Be that as it may, can you diagram the argument?
|On the exclusive reading of or, when P and Q are both true, Either P or Q is false||Neither P nor Q is the negation of Either P or Q|
|On the exclusive reading of or, when P and Q are both true, Neither P nor Q is true||Neither P nor Q is only ever true when P and Q are both false|
|The exclusive reading of or is a myth|