Model Logic Requires an Analytic/Synthetic Distinction

Something you may have noticed about Christian apologists is their constant abuse of modal logic.  You see this a lot with ideas like the modal ontological argument or in the concept of a "necessary" being.  It's ironic, because often times those very same Christians are more than happy to reject the existence of an analytic/synthetic distinction.  The very idea of modal logic itself is already an implicit formalism for the analytic/synthetic distinction.  They're trying to have their cake and eat it, too.

To illustrate, just look at what modal logic does.  When you really get down to the nuts and bolts of it all, modal logic is nothing more than a formalized system for talking about two distinct categories of proposition:

1. Possible
2. Necessary

When we speak of modal possibility, we are specifically talking about hypothetical descriptions of ways the world might have been.  For example, we might describe a "possible world" where Mitt Romney won the presidential election instead of Barack Obama.  Obviously, we don't actually live in that world, but there is no real reason we could not have.  It is simply a happenstance of natural events that we find ourselves in a world where Barack Obama is the president.

In contrast with modal possibility, we also have the idea of modal necessity.  These are propositions that must be true or false in all possible worlds.  For example, there does not exist a single possible world where Barack Obama both won and lost the 2012 presidential elections.  The reason is because losing is logically equivalent to "not winning."  So to both win and lose an election is to both "win and not win," which is a logical contradiction.  Since all contradictions are tautologically false, it is impossible to describe a coherent, hypothetical world where this ever happens.

Now compare these ideas with principles of an analytic/synthetic distinction.  For example, analytic propositions are those whose truth is evaluated purely on the basis of axioms, definitions, and logical rules of inference.  So when presented with a proposition like,

"Barack Obama both won and lost the 2012 election ..."

... we know immediately that such a proposition is analytically false.  The reason is due to the rules built into propositional logic and the tautologies that arise as a result.  It is not a statement about objective, mind-independent reality, but about the raw meaning contained within the words themselves and their corresponding logical operators.  All "necessary" truths are therefore functionally equivalent to analytic propositions.

Now compare this against a slightly modified proposition:

"Barack Obama won the 2012 election."

Notice how I cannot "derive" the truth of this proposition logically or analytically.  For all I know, the truth assignment to this could swing either way, and there is nothing immediately wrong with either case.  The only way to tell for sure is to investigate the matter empirically by making falsifiable predictions.  Both options are therefore perfectly "possible," with the correct answer based entirely on whatever outcome nature contingently decided to go with.  Yet this is exactly what defines a synthetic proposition!  Contingent possibility and synthetic propositions are just two sides of the same philosophical coin.

To me, this is just another one of those great examples of the utter incompetence of Christian apologetics.  It is logically impossible to embrace the principles of modal logic without simultaneously acknowledging some facet of the analytic/synthetic distinction.

You can't have it both ways, Christians!