13. Either … or …

Logic students are often taught that ‘Either P or Q’ is an ambiguous phrase. It might mean to allow for the possibility of ‘P’ and ‘Q’ being both true. Or it might mean to exclude that possibility.

In his book, The Connectives (MIT Press 2011), however, Lloyd Humberstone contends that the “exclusive” reading is a myth:

A statement ‘P or Q’ is always negated by the corresponding ‘Neither P nor Q.’ If ‘or’ were sometimes, in virtue of its meaning, exclusive, then the latter would in those cases be true when both ‘P’ and ‘Q’ were true: but in fact, ‘Neither P nor Q’ always requires for its truth the falsity of ‘P’ and of ‘Q.’

This is as close as one gets to a definitive refutation of the exclusive reading, he says. Be that as it may, can you diagram the argument?