Tuesday, January 27, 2015

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!

Thursday, January 15, 2015

There Is No Such Thing as a "Necessary" Being

"Anything that exists has an explanation of its existence, either in the necessity of its own nature, or in an external explanation [1]."

I don't know where apologists get this naive impression that they understand how logic works, because arguments like this are just a dead giveaway that they really don't.  When you say that some entity like God "exists by the necessity of His own nature," you're basically saying that the proposition "God exists" is true in all logically possible worlds.  That literally, it is logically inconceivable to even describe some potential state of affairs where God's existence is false.

So right off the bat, this obviously isn't the case, and it's trivially easy to see why.  All you have to do is simply say it out loud - "God does not exist."  Or equivalently, you could say something like, "imagine a possible world where God does not exist."  Now ask yourself, do you see any logical contradictions in that claim?  Because I sure don't.  There is nothing immediately incoherent about the prospect of God's nonexistence, which is why any argument to the contrary is necessarily going to fail.

It's important to understand that whenever we talk about a thing like logic, we're not talking about some intrinsic metaphysical essence of the universe.  Rather, what we're really talking about is a system of rules that operates on linguistic propositions.  For example, if we accept the proposition that "I live in California," and then follow it up with proposition that "California is a state in America," then we could say that it "necessarily follows" that I live in America.  But notice that we only get away with this because the premises already contained the information stated by the conclusion.  The only thing that we accomplished through "logic" was to extract that information formally and then state it as an independent proposition unto itself.  So to say that a being like God just exists necessarily is to effectively say that the idea of "God" Himself must implicitly carry the property of "existence" within it.  That way, the proposition "God does not exist" would become the logical equivalent to saying that " a being which exists does not exist." 

So, how exactly could anyone go about proving the necessity of God's existence?  How does that even work?  Well,  simple.  In order for God to qualify as a necessary being, then the proposition "God exists" must either be 
  1. A tautology, 
  2. an axiom, or
  3. a theorem derived from other axioms using rules of inference. 
That's it.  That's the formal definition of a logical proof [2,3], and by extension, logical necessity.  Any proposition that does not fit into one of these categories is therefore not a logical necessity, but is rather logically contingent.

All right, now let's try it out and see what it be like if God's existence were necessary.  Starting with the first option, consider God's existence as if it were a tautologically.  Obviously, that can't ever be the case because no simple proposition can even qualify as such; only generic propositional formulas.  At best, the only tautological thing you can say about God is something like "either God exists or God does not exist."  But of course, that's obviously meaningless because the same thing applies to literally anything and everything.  Tautologies are therefore not really helpful to God's necessity because they can only tell you about generic instances of propositional formulas.

So how about the second option?  What would it look like if God's existence were axiomatically true?  Simple:
  1. God exists (axiom).
Done!  That's seriously all an axiom is - an arbitrary proposition that is deemed to be "obviously true" by pure, human fiat.  So if God axiomatically exists, then of course God cannot fail to exist in any logically possible world.  The proposition "God exists" is always guaranteed to be true in every possible description of reality.

Now of course, you might have noticed that that's not a terribly compelling argument.  After all, if Christians get to axiomatically declare God exists, then what prevents me from doing the opposite?  For example,
  1. God does not exist (axiom).
Now what, Christians?  Who wins?  My axioms or your axioms?

The answer is obviously neither.  This is why we don't use axioms to arbitrarily declare rote facts about objective reality.  Instead, we only use axioms as a starting point of reasoning by defining what certain ideas mean within a formal language structure.  We can then follow basic rules of inference to see if any interesting theorems emerge as a result.

To illustrate, let's imagine deriving God's existence analytically through the following argument:
  1. All maximally great beings are beings that exist necessarily (axiom - definition of MGB)
  2. God is a maximally great being (axiom  - definition of God)
  3. Therefore, God exists necessarily (syllogism from 1 and 2)
There you have it!  We just derived God's existence as a logical theorem from prior axioms.  But again, you'll notice that this wasn't terribly compelling, either.  Contrary to popular belief, logical theorems don't really tell you anything more about objective reality any more than axioms do.  At best, they can only serve as linguistic tools for mixing and matching the information that was arbitrarily inserted into the wording of the premises.  So if you accept the premises, the of course the conclusion "necessarily" follows.  However, the premises have only been substantiated by rote definition, and I am under no obligation to accept such a lexicon. 

So no matter how you look at, the only way for God to exist "by necessity" to effectively declare it outright.  That's why nothing in the entire universe can possibly exist out of "the necessity of its own nature" because that very statement literally means "existence by definition."  Well I'm sorry, guys, but you can't just arbitrarily define rote facts about objective reality.  That's called "question begging."  Nothing about the idea of God logically necessitates His own existence unless you just arbitrarily decide to put it there.  The only way to break out of this nasty circle of logic is to substantiate your premises through something beyond mere axioms and definitions; for example, basic empirical observation.  That's why anyone who ever gets the naive idea that God's existence is some kind of logical necessity is either being deliberately dishonest or is just completely clueless about the most basic principles of logic itself.

  1. The Leibnizian Cosmological Argument 
  2. See: Formal Proof
  3. See: An Introduction to Mathematical Logic

Tuesday, January 6, 2015

Not Even Christians Believe Their Own Bullshit

Something I find terribly aggravating about Christian apologists is the fact that not even Christians themselves actually believe the claims they're making.  For example, in the books Mark, Matthew, and Luke, we find a story about a rich man who asks Jesus what he must do in order to inherit eternal life.  Jesus answers this question by commanding the rich man to sell all of his worldly possessions and give the money to the poor.  The rich man then walks away in sadness, apparently not wanting want to give up his vast material wealth.  Jesus then turns to his disciples and says, flat out, that it is easier for a camel to pass through the eye of a needle than for a rich man to enter the kingdom of heaven.  He's literally describing an impossible task, then telling the world that "this impossible task is easier to achieve than for a wealthy person to enter the Kingdom of God."

This story is interesting to me, because there really isn't a whole lot of room for interpretation.  Jesus himself is unilaterally telling the world that personal wealth is one of the greatest obstacles in existence to achieving salvation.  It's even a theme that gets repeated over and over in other passages.  The only "true" Christians are those who devote themselves to a life of purely selfless service for the sake of the less fortunate, and the accumulation of material wealth is simply antithetical to that goal.

If I were a true-believing Christian living in the First World, I would be absolutely terrified by this revelation.  I would be donating my life's savings to charities and selling everything I have.  I would actively look for things in my life that were not absolutely essential to survival and just get rid of them.  It's therefore very strange to me that Christians almost never attempt to seriously live by this kind of principle.  If anything, we usually tend to see the exact opposite, with the most prominently outspoken Christian defenders nearly always being the most affluent.  The very same Christian conservatives who claim that America was founded on Christian principles are also the same ones who seem to be the most hell-bent on defending the status of rich people in this country.  Sure, there's the occasional Christian doctor or something that moves to the third-world and does real, altruistic work, but for every one of those people, there are literally hundreds, if not thousands, who choose to stay at home with their big screen TVs.

I've occasionally posed this problem to Christians, and I have yet to see a single apologist ever live up to the expectations of their own faith.  Instead, all I ever seem to hear are either tortured rationalizations or absurd reinterpretations of clearly unambiguous doctrine.  It's as if they honestly think Jesus will be totally impressed with that fancy new car or that expensive laptop when there are literally billions of people around the world who live in abject poverty.  Seriously, guys - you really think Jesus is going to be okay with that?  You don't think this will have spiritual consequences for you?

I can only imagine the cognitive dissonance this must generate in Christian apologists.  On some level, they have to realize how absurdly hypocritical they're being.  You cannot claim to be a disciple of Jesus while simultaneously ignoring the central tenet of his entire message. It even says very plainly in the book of Matthew that there will be those who profess to be good Christians, but to whom Jesus is just going to say "I never knew you; depart from me!" [Matthew 7, 27]

To me, this is a dead giveaway that not even Christians really believe their own bullshit.  Because if I actually believed this stuff, like if I literally believed that my immortal soul was hanging in the balance, then I wouldn't mince words over what Christ maybe meant to say or not say.  I would be paranoid as hell about gaining the most altruistic attitude it was physically possible to have.  So the simple fact that Christians are obviously not adopting a similar behavior tells me that they can't really believe the things they claim to believe.  If actions speak louder then words, then Christians might as well be mutes.

But hey, Christians, if you want to gamble your eternal salvation for that steak dinner or shiny new house, then you go right ahead.  It'll be a great way for us to measure just how much of a hypocrite you really are.