[FOM] Disjunction: in or ex?
joeshipman at aol.com
Thu Jan 11 22:22:02 EST 2007
By far the biggest FORMAL advantage of "inclusive or" is that you get a
duality with "and" which is extremely useful in may contexts.
SEMANTICALLY, the situation is much more interesting, and what no one
has pointed out is that, since the whole discussion depends on English
not having separate connectives for the 2 senses, we should ask what
happens in languages which do have separate connectives. So my question
Did anyone writing in a language with separate words for the two senses
of "or" ever (before or after Boole) attempt to develop propositional
logic using "exclusive" or as a primitive and "inclusive or" as a
derived connective? If not, how many times was the development with
"inclusive or" as a primitive done independently of Boole?
Appeals to ordinary English "as she is spoke" fail to shed light,
because for this particular issue the default semantics depends
entirely on context. When people say "I will wear my coat to work
tomorrow if it is cold or raining", they don't find it necessary to say
"or both". And when people say "Today's dessert special is tapioca
pudding or strawberry shortcake", they similarly don't find it
necessary to say "but not both".
-- Joe Shipman
From: martin at eipye.com
To: fom at cs.nyu.edu
Sent: Thu, 11 Jan 2007 5:03 PM
Subject: [FOM] Disjunction: in or ex?
Two remarks that no one yet has made on this thread:
Historical: Boole only permitted union of two sets when they are
disjoint, so the distinction didn't arise.
Legal: In contracts in the US, I have seen "and/or" used to indicate
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