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


Hans Georg Lundahl said...

You have a problem with analysing other people's, or at least with analysing Christian other people's statements.

The argument does not start from "God is necessary", it starts from "some being is necessary and if being x can be explained in terms of being y, being x is not the being which is necessary in itself".

Of course, an atheist could counter, logically, by saying: "atoms and energy quanta are the beings that are really necessary in themselves and we don't call them God".

But instead of doing that, you try to seek or imagine you detect a logical fallacy which is not there.

Not My Name said...

The point is, it's not even a logical fallacy -- we can define whatever we want as "necessary", and in the system of axioms we have constructed, that automagically makes it true by definition.

But the fact that an argument is logically valid means nothing outside of that alternate reality. The brokenness lies in trying to take the findings and then declare them true in the real world without testing them.

In order for us to accept something as real, there needs to be some actual evidence.

And of course, if there were evidence that some being is necessary at all, the apologists would have trotted it out by now rather than trying to prove God by mere logic.