Missives from a fly bottle
barang dot sg
Updated 14 July 2020
13. Either .. or ...

Logic students are sometimes taught that ‘Either P or Q’ is an ambiguous phrase, depending on whether it allows for the possibility that both P and Q are true (the inclusive reading) or whether it means to exclude that possibility (the exclusive reading).

In The Connectives, however, Lloyd Humberstone disputes this alleged ambiguity by arguing that the exclusive reading is a complete myth:
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?