[FOM] Why inclusive disjunction?
Alasdair Urquhart
urquhart at cs.toronto.edu
Wed Jan 10 10:05:22 EST 2007
On Tue, 9 Jan 2007, John Baldwin wrote:
> Can anyone provide a principled reason for why logicians choose to
> interpret "or" as inclusive disjunction?
The explanation is historical, I think. Our propositional
calculus is a direct descendant of the Boolean calculus of
classes, and the early Boolean logicians used the same symbols
for disjunction and class union (for example, Peano thought
this was an advantage of his symbolism). The fact that
the Boolean calculus can be interpreted both as a calculus
of classes and a calculus of propositions goes back to Boole,
and probably even further. In the class calculus, the
natural operation is class union. Hence, inclusive
disjunction.
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