Murali Ramachandran – A Puzzle About Conditionals

One naturally thinks of an utterance of a declarative sentence as
expressing a single proposition. In this talk, I am going to present a
train of thought–as opposed to a cogent argument–from a neglected
(possibly unnoticed) puzzle about conditionals leading to the conclusion
that when one asserts a conditional, P > Q (“If P, then Q”), one actually
expresses TWO propositions, one of which is the grounds for the other.

The puzzle (at first pass) is roughly this: one may legitimately hold a
pair of conditionals, A > C and B > C*, where (i) C and C* are
incompatible, and yet (ii) one is undecided about the conjunction A & B.
This is a puzzle because it clashes with the compelling thought that any
conditional P > Q is false if P is true and Q false. Modus Ponens is also
threatened.

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