Tuesday, 9 November 2004
On the Gärdenfors Impossibility Theorem
Neil Tennant
Ohio State University
12:05 pm, 817R Cathedral of Learning
Abstract: In 1986 Peter Gärdenfors published
a theorem which has been widely interpreted as showing that it is
impossible to adjoin to the AGMpostulates for beliefrevision a
principle of monotonicity for revisions. The principle of monotonicity
in question is implied by the Ramsey test for conditionals. So Gärdenfors’s
result has been interpreted as demonstrating that it is impossible
to combine the Ramsey test with the AGMpostulates.
I show that this interpretation of Gärdenfors’s
result is unwarranted. His formal statement of the principle of
monotonicity of revisions is too strong. Crucial applications of
this principle in Gärdenfors’s proof require one to regard
as revisions certain instances of theorychange that are really
expansions.
If monotonicity is stated only for genuine revisions,
then Gärdenfors’s proof does not go through. Nor can
such a proof go through. For, when the monotonicity principle for
revisions is correctly confined to revisions that are not expansions,
one can establish a contrary consistency result. This requires only
a slight adjustment to the AGMpostulates, in order to ensure that
the three operations of expansion, contraction and revision trichotomize
the domain of theorychanges.
