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 only 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.)
In the spirit of Anselm's ontological argument, however, I offer the following proof of the nonexistence of God:
Consider a really bad argument for the existence of God. In fact, consider one so bad that no worse argument can be conceived.
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 conclusively prove the opposite of what it's meant to prove.
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 actually made.
Therefore, there is an argument for the existence of God which is actually a conclusive proof of the nonexistence of God.
And, of course, any proposition that can be conclusively disproved is false; therefore there is no God.
(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.)
To me that makes it a success. Part of the entire game of philosophy is to use watertight reasoning to illustrate flaws in the original axioms.
Which really gets us closer to the heart of what proof is: it is that which will compel a rational mind into agreement. It is not enough to follow formal rules. It must be measurably dangerous -- potentially a catastrophic failure -- for a rational mind to disagree with a proof. Someone should be able to build a dutch book on your expectations and obliterate you for failing to agree with that proof.
So until someone actually measures their god to be good, there are no consequences for a proof in either direction, and a rational mind should not be convinced.
I could be missing something here as I only took my first philosophy class this semester and I'm not taking ethics until next, but is that basically what you're getting at?
There's another very-slightly-similar inverted ontological argument that may have been in the back of my head. It's due to a chap called Douglas Gasking, and it begins with a standard ontological argument -- which, as you know, delivers us a Maximally Excellent Being. Now, of course God's signature accomplishment is the creation of the universe; but any creative achievement is more impressive when it is accomplished under greater constraints (so, e.g., while it is impressive to come up with a proof of Fermat's Last Theorem it would be even more impressive to come up with a proof of Fermat's Last Theorem in the form of a perfect Shakespearean sonnet). Well, what would be the most impressive obstacle for God to have overcome when creating the world? His own total nonexistence, obviously. So our maximally impressive being must be a god who created the universe without existing; therefore God does not exist.
I have to confess that I like mine better.
Here's an account of his discovery of a logical flaw in the US Constitution: http://morgenstern.jeffreykegler.com/
My biggest point of contention with your claim is that Anselm didn't make a contingent/necessary distinction. Instead, he was caught up in a muddled "exists in understanding/exists in reality" distinction which is decidedly not an analogue of the former. To go a step further, Anselm merely assumed the possibility of God, whereas Godel actually proved it.
Formal modal logic wasn't invented until the 20th century, but Anselm is using modal logic nonetheless. A modal logic is simply a logic that allows operators to be applied to propositions. Necessary-truth and possible-truth are only two possible operators. "Knows" and "believes" are two other classic examples. Anselm's logic uses the operators "actual-truth" and "conceptual-truth". All these proofs have essentially the same structure whether the operators are actual/conceptual or necessary/possible. You could even render the same proof in the modal logic of knowledge and belief. In fact, modern evangelicals often do this. The result renders as something like, "Look at all the martyrs who died. No one makes that kind of sacrifice for false beliefs, therefore their beliefs must be true."
S5 (what Godel used) has those properties, whereas Anselm didn't even have the notion of soundness or completeness, let alone a logical system that would satisfy them.
Of course, you may have other definitions of Satan and evil in mind, and I don't mean to imply that those concepts are solely the province of Christian minds.
Mathematically it's analogous to trying to reason from the premise that zero -- the "absence of anything" -- is the smallest possible number. You can do it, but it leads to incredibly messy math. As soon as you try to define subtraction, all hell (pun intended) breaks loose. And as soon as you admit -1 into your system you can no longer have a smallest number (if you have addition and induction).
What if we define The Good as unity, and evil as the ratio of The Good to relative attainment of the The Good. We might then define compounded evil as a ratio of The Good to the multiplication of the denominators of each ratio-evil consider on its own.
So an act of torture might be (/ 1 ½) and three acts of torture would be (/ 1 ⅛).
Also, your points above are well taken; I was simply trying to come at the matter (and my previous points) with a bit more precision than I had previously, but I cut my elaborations short as I needed to run out the door.
So with my idea above, you would basically have two notions for assigning magnitude to evil. Absolute evil would be defined as the complete absence of good in a person or other locus of circumstances and acts. So the greatest real evil would a fixed value, "zero good", and "negative amounts of good" would be a void construct.
The other notion of evil, "evil considered", would be a metaphor for understanding how evil gets compounded according to our usual perception that some lives and acts are more evil than others. It's basically a "score" which doesn't correspond directly to any substance.
But evil is more than the mere absence of good. There are affirmative evil acts (rape, murder, torture) so you can always become more evil by performing more evil acts.
Disclaimer; I've only read Anselm and Leibniz, and am just trying to piece together the discrepant sources around.
Premise 1: There are many worlds.
Definition 1: "x necessarily exists if and only if every essence of x is necessarily exemplified" (From the article)
Premise 2: Existence is good.
Definition 2: God is the being Good-er than whom cannot be conceived.
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.
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.
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.
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.
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.
The premise is called the plenitude principle.
"The principle of plenitude asserts that the universe contains all possible forms of existence." You first see it in Plato's work like in the Cave Allegory. You can make a compelling argument that the plenitude principle was the precursor to the ideas of a multiverse and evolution.
The Famous 1948 BBC Radio Debate on the Existence of God
"Yes, that's my position"
"Well, if it's a question that for you has no meaning, it's of course very difficult to discuss it, isn't it?"
Russell, almost with a sigh: "Yes, it is very difficult." Then: "What do you say, shall we pass on to some other issue?"
What struck me most was the calmness and politesse they both maintained, and the steadfast articulateness at the speed of thought. There seemed to be an unspoken, shared assumption that you never, ever raise your voice or betray any hint of frustration, let alone insult your opponent in public. It's hard to imagine hearing something similar on the radio today.
I'm also curious how much of the decorum was a sign of the times, and how much was specifically British.
Descartes gives a kinda-ontological argument for the existence of God, and then he does indeed very rapidly move to deducing useful properties of God from it -- e.g., that he wouldn't allow us to be systematically deceived about everything. It's the basis of his whole epistemology, at least ostensibly.
Whereas, say, a first-cause argument tells you there's something that's in some sense the cause or origin of the universe, but you've got a whole lot of work to do to get from there to anything relevant to actual religious belief. (Though, e.g., William Lane Craig does somehow manage to keep a straight face when transitioning at lightning speed from "something caused the universe to begin to exist" to "and that something must be personal, enormously powerful, etc.)
(Lest I be misunderstood, I'll add that I think both ontological and cosmological arguments fail badly, and that neither of them either manages to give much reason to believe in a maximally perfect being / first cause / whatever, or to believe that such a being if it existed would have anything much to do with the gods of traditional religions. But it's not my purpose to litigate any of those claims here -- Goedel's argument is much more interesting than any I'd make.)
Hardly, it's just obscurantist gobbledegook dressed up as modal logic. It uses symbols and math to make the same basic errors that all other proofs make.
Also, don't worry about downvotes. HN isn't that big, and individual comments are quickly forgotten. Think of it as feedback, not condemnation of you personally.
I'm not that fussed about the downvote, I'm just innately curious as to people's reasons.
1. I carefully define God as having to exist.
2. Therefore, God exists.
All the work goes into the first part, however many volumes of obfuscation (hi, Dr Plantinga!) one hides it behind.
There are a number of problems with this approach.
I'm not sure what you mean by "circular" in this context. However, what people usually mean is an argument where the conclusion is contained in one of the axioms. Godel's proof doesn't explicitly suffer from this but I will say that his fourth axiom, i.e. Good(phi) -> [Necessarily]Good(phi) is cutting it pretty close.
The fear of death, usefully instilled into us by natural selection.
Human minds have no experience of not existing, and tend to find the concept difficult to comprehend. We desire answers, but unfortunately the human condition is to prefer wrong answers over no answer.
"Probably"? How about "surely" or "surely not"? Is an entity comprised of many things or one thing? Does it matter? Are you merely pointing out that there is no true separation between anything and everything that exists?