[FOM] Why inclusive disjunction?
Richard Zach
rzach at ucalgary.ca
Thu Jan 11 19:31:31 EST 2007
May I recommend
Robert B. Barrett; Alfred J. Stenner, The myth of the exclusive
`or'.* */Mind/ 80 (1971) 116-121.
Stable URL:
http://links.jstor.org/sici?sici=0026-4423%28197101%292%3A80%3A317%3C116%3ATMOTE%60%3E2.0.CO%3B2-7
as an interesting (and, I think, influential) argument for why there are
no *truth functional* uses of "or" as exclusive disjunctions in
English? If they are right that "or" is never correctly formalized by
exclusive disjunction, then the tendency to read/formalize "or" as
inclusive disjunction is perhaps best explained the same way the
tendency of reading "if then" as the material conditional is: it's the
best you can do if you only have truth functions. (Just to make this
clear: they don't say that "or" is never used in an exclusive sense,
only that these aren't truth-functional uses.)
See also
http://plato.stanford.edu/entries/disjunction/
which summarizes Jennings' /The Genealogy of Disjunction/ (OUP, 1994),
which contains lots of historical detail concerning inclusive and
exclusive or, and what he calls the "myth of vel and aut"--that Latin
"vel" corresponds to inclusive disjunction and "aut" to exclusive
disjunction.
I also wanted to point out that inclusive disjunction together with
negation is truth functionally complete, whereas exclusive disjunction
and negation aren't. This has nothing to do with why logicians tend to
interpret "or" as inclusive disjunction, but it may have something to
with why mathematical logicians prefer inclusive disjunction as a
primitive connective.
-Richard
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