# Modal logic: Are indicative conditionals formulated using a strict conditional?

Given the fact (f) of the actual world

(f) On November 22, 1963: Somebody shot Kennedy.

one could formulat the indicative conditional (id) as follows:

(id) If Oswald did not shoot Kennedy, then somebody else shot Kennedy.

The definition of a strict conditional (defined here as ===>) is:

(sc) (X ===> Y) is true in a world iff Y is true in every possible world in which X is true.

(cf. Bonevac, Deduction: Introductory Symbolic Logic Wiley, 2003, p. 399.):

But when expanding (sc) with (id) one gets:

(scid) ([Oswald did not shoot Kennedy] ===> [Somebody else shot Kennedy]) is true in a world iff [Somebody else shot Kennedy] is true in every possible world in which [Oswald did not shoot Kennedy] is true.

But this seems wrong. There is at least one possible world where [Somebody else shot Kennedy] is false while [Oswald did not shoot Kennedy] is true. Namely a world where noone shot Kennedy, so where (f) is wrong.

How do I get the natural language of this indicative conditional mapped to logic correctly?

I somehow have to take the actual world into account ( the fact (f) )

• I'm not quite qualified to answer this, but it seems to me that your problem goes away if you define (id) as "If (f) and Oswald did not shoot Kennedy, then somebody else shot Kennedy". So maybe by having (f) you set some kind of constraint to the possible worlds in which (scid) is applicable. Commented Nov 1, 2013 at 15:40
• Thanks for the response. I am not sure if this works though because the respective counterfactual conditional "If (f) and Oswald HAD not shoot Kennedy, then somebody else WOULD HAVE shot Kennedy" would be true as well but it shouldn't Commented Nov 1, 2013 at 16:24
• I'm not sure about that, but maybe: if [Somebody shot Kennedy] then [If Oswald did not shoot Kennedy, then somebody else shot Kennedy] So ([Somebody shot Kennedy] ===> [If Oswald did not shoot Kennedy, then somebody else shot Kennedy]) is true in a world iff [If Oswald did not shoot Kennedy, then somebody else shot Kennedy] is true in every possible world in which [Somebody shot Kennedy] is true. Commented Nov 1, 2013 at 16:44
• That way you may nest both the strict conditional and the counterfactual. Commented Nov 1, 2013 at 16:45
• Thanks for the response. I am not quite sure yet but here is my solution so far: scribd.com/doc/180948584/Output Commented Nov 2, 2013 at 9:07