The difference between Anselm's original ontological argument and modern ones like Goedel's or Plantinga's is that while Anselm's is full of terrible reasoning, Goedel's reasoning is (unsurprisingly) watertight and all the terribleness is concentrated in the axioms.<p>Specifically, I think the idea of classifying all properties as "good" or "not good" is hopeless: I do not believe there is any such classification that fits anyone's intuitive ideas about goodness well enough that calling something "godlike" if it has all "good" properties is credible. More specifically, I suspect it's consistent to suppose -- hence there are no humanly-comprehensible counterexamples -- that the <i>only</i> notions of goodness obeying all Goedel's axioms are ones that look like "P is good iff P(x)" for some fixed object x. (And, like Krishnaswami, I think the system of modal logic Goedel needs is awfully strong.)<p>In the spirit of Anselm's ontological argument, however, I offer the following proof of the <i>nonexistence</i> of God:<p>Consider a really bad argument for the existence of God. In fact, consider one so bad that no worse argument can be conceived.<p>Obviously a bad argument for something fails to prove what it purports to prove. But merely failing is a pretty mediocre kind of badness. The worst possible argument, surely, has to be much worse than that: it must <i>conclusively prove the opposite</i> of what it's meant to prove.<p>Now, the worst conceivable argument for theism clearly "exists in the understanding", as St Anselm put it. But it can't exist only there -- because a bad argument is more damaging to the premise it's meant to support if it's <i>actually made</i>.<p>Therefore, there is an argument for the existence of God which is actually a conclusive proof of the nonexistence of God.<p>And, of course, any proposition that can be conclusively disproved is false; therefore there is no God.<p>(This argument is in my opinion almost exactly as strong as the original ontological argument for the existence of God. Which is to say, it's absolutely hopeless. But I think it's fun.)
When I think of Godel, the first thing I think of (based on accounts) is compulsion. He was really driven to explore the edges of reality using logic as a probe.<p>Here's an account of his discovery of a logical flaw in the US Constitution: <a href="http://morgenstern.jeffreykegler.com/" rel="nofollow">http://morgenstern.jeffreykegler.com/</a>
Godel's proof is essentially Anselm's with some mathematical window dressing added. It is worth noting that Anselm's argument applies equally well to Satan as to God: The most evil thing we can conceive of would be more evil if it actually existed, therefore Satan must actually exist. If you're into this sort of mind game, it makes an interesting exercise to translate this version of Anselm's argument into formal modal logic.
Neel Krishnaswami wrote a quite readable description of the proof on his blog: <a href="http://semantic-domain.blogspot.com/2014/06/g-ontological-argument.html" rel="nofollow">http://semantic-domain.blogspot.com/2014/06/g-ontological-ar...</a>
This proof is a mix between Anselm and a little bit of math.<p>Disclaimer; I've only read Anselm and Leibniz, and am just trying to piece together the discrepant sources around.<p>Premise 1: There are many worlds.<p>Definition 1: "x necessarily exists if and only if every essence of x is necessarily exemplified" (From the article)<p>Premise 2: Existence is good.<p>Definition 2: God is the being Good-er than whom cannot be conceived.<p>Sub-Conclusion 1: God if he exists, by definition is good, and by supposition necessarily exists because existence is good. He necessarily exists because if he did not, then a being good-er than him could be conceived (ie, one that existed), and that being would then not be god.<p>sub-conclusion 2: Because there are many worlds, there exists one with a being good-er than whom cannot be conceived. Therefore, this is a being whose existence is necessary.<p>Consider then, that God's existence would not be necessary, if the world that god governed was not necessary, because that world could, or could not exist, and so God could, or could not exist, and god's existence would not be necessarily be exemplified.<p>Therefore The world in which God exists must be necessary to our world, and by consequence, God's existence must be necessary to our world.<p>If someone who has actually read him could give me some feedback as to whether this is fairly close to what he means, I'd appreciate it.
Readers might also enjoy the audio recording and transcript of a famous debate between Bertrand Russell and Fr. Frederick Copleston:<p><i>The Famous 1948 BBC Radio Debate on the Existence of God</i><p><a href="http://www.biblicalcatholic.com/apologetics/p20.htm" rel="nofollow">http://www.biblicalcatholic.com/apologetics/p20.htm</a>
Note that even if you accept this proof, it says nothing about a god that answers prayers or otherwise intervenes in daily life. It also says nothing about an afterlife. Unless you're a deist, ontological arguments are practically useless. They've been used in the defense of many gods now relegated to mythology.
and an implementation (I think unfinished) in Coq <a href="https://github.com/FormalTheology/GoedelGod" rel="nofollow">https://github.com/FormalTheology/GoedelGod</a>
I only dabble in formal logic so I haven't come across this before, but it sort of feels like this rests on a circular argument. You know, the "can God make a rock so heavy that he can't lift it" or "does God have the power to make himself even more Good". I wonder if it's possible to prove anything if one of your axioms is actually a hidden circular argument, much like how one can prove anything from setting true to false.
We see our world in terms of cause and effect, but these are temporal concepts that might have no meaning outside of linear time. It may therefore be nonsensical to ask what caused the universe.