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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. – Koeng Nov 1 '13 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 – IHeartAndroid Nov 1 '13 at 16:24
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    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. – Koeng Nov 1 '13 at 16:44
  • That way you may nest both the strict conditional and the counterfactual. – Koeng Nov 1 '13 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 – IHeartAndroid Nov 2 '13 at 9:07
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You are conflating metaphysical and epistemic necessity.

You can either pick your access relations so that possibility is determined by what we know to be true in the actual world (ie. Possibility= epistemic possibility). In which case your argument is correct, and the paradox disappears, since, given that we know someone shot JFK, we only have access to worlds in which he was shot, so this is necessarily true.

Or we can go with mere metaphysical necessity, so that we have access to any and all worlds that are metaphysically possible, in which case your paradox seems to follow. BUT, in this system, our statements of implicature are statements of metaphysical implication, which demands your premise (id) be interpreted as a metaphysical truth, which makes it false.

In this case, we can still talk about JFK's shooter using @Koeng's trick in the comments above, which does indeed make a metaphysically correct premise.

Or we can make our access relations logical, or physical, or whatever you fancy. Your error here is a common one: "Modal Logic" is not, like first order predicate calculus, a single logic, but a family of logical theories- a template that can encompass the various notions of necessity, various domains of discourse, that we consider important.

  • Thanks for the response. Can you recommend a book where I can see the distinction being made? – IHeartAndroid Nov 7 '13 at 22:11

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