Modal Possibility

Here’s a proposition:

(1) If Lincoln had not been assassinated, reconstruction after the Civil War would have gone a lot more smoothly.

In my last post, I talked about the problems with analyzing this statement according to traditional propositional logic.  But let’s reduce it to a few symbols anyway, using a somewhat more sophisticated form of logic that allows us to apply qualities to events:

~La -> Rs

In this L stands for the Lincoln, and the letter after it stands for his particular condition.  Here, it’s an a, for assassinated.  But the tilde means “not.”  So ~La means “Lincoln is not (was not, will not be) assassinated.”  The arrow is “entails,” which means that if the thing on the left is true, I am asserting that the P on the right is also true.  The P on the right is Rs, for “reconstruction” and “would have gone smoothly.”  Isn’t that nifty?  I think so.  There’s a lot more to it than that, but this lets us handle these statements in symbolic form.  If you don’t like it, well, piss off, it’s my blog and I hate the damned thing anyway, so I’ll do what I like.

Ahem.

So P(1) can be symbolized as ~La -> Rs, which is just the same as the form in traditional logic ~P -> Q, viz., The negation of the given proposition entails a second proposition.  If ~P is true (which is to say, P is false), then Q is also true.  So according to traditional logic, we’d look at this and say “Well, Lincoln was assassinated, so P is true, thus ~P is false, so therefore reconstruction would not have gone . . . more . . . smoothly?”

We have a very real sense that when I say (1) I am saying something that we could argue is true or false, but we live in a world in which Lincoln was assassinated (although other issues, such as the spelling of the Bernstein Bears, is up in the air).  We’re all quite certain that he died of a bullet during “Our American Cousin.”  We’re also mostly in agreement that reconstruction was a bit of a mess from which America is still recovering.

But we can say, if he hadn’t died, it wouldn’t have gone that way.  We can marshall evidence for how it would have gone, and make that argument, and others can argue with our argument.  They can say, “no, it made no difference,” or something.  We have a sense, in other words, that (1) can be true or false, but according to traditional logic, it’s just false.

This problem crops up only when we say “would” or “should” or “could” or some other modal verb, so this is called “modal logic,” and it leads to a startling conclusion about the nature of reality.

 

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