🚀 go-pugleaf

In article <19647@ucbvax.BERKELEY.EDU> kube@cogsci.berkeley.edu.UUCP (Paul Kube) writes:
>  It's October 1980.  You hold the following plausible beliefs:
>    1.  If it's a Republican that will win the election, then if 
>        Reagan doesn't win, Anderson will.
>    2.  It's a Republican that will win the election.
>However, you don't believe what follows from these by modus ponens,
>viz. that if Reagan doesn't win, Anderson will (everyone believed that
>if Reagan didn't win, Carter would).

     Let's see if I remember the resolution of this paradox.  Let
R be the proposition that Reagan will win, similarly A and C.

     One approach is to consider the statements probabilistically,
and to note that modus ponens does not hold in this case for
probabilistic logic.  This approach seems the most sensible.

     The classical-logic approach is to forget about probabilities
and beliefs, in which case the statements become
1. ((R or A) -> (~R -> A))
2. (R or A)
...but the implication is that (R or A) is true because R is true.
Thus (~R -> A) is a perfectly reasonable conclusion because we
know that (~R) is always false, and by classical logic the implication
is always true.  Seen this way, the paradox becomes a challenge to
the validity of classical implication and an argument for relevance
logic.

     Another way to look at the classical-logic approach is that
(1) is a tautology (since (~R -> A) equiv. (~~R or A)), and so is
meaningless as a premise.

--Jamie.
...!seismo!ubc-vision!ubc-cs!andrews
"They hold the sky on the other side of border lines"