How do Atheists respond to Godel

Godel devloped a proof for the existence of God based on the following:

Definition 1: x is God-like if and only if x has as essential properties those and only those properties which are positive
Definition 2: A is an essence of x if and only if for every property B, x has B necessarily if and only if A entails B
Definition 3: x necessarily exists if and only if every essence of x is necessarily exemplified
Axiom 1: Any property entailed by—i.e., strictly implied by—a positive property is positive
Axiom 2: A property is positive if and only if its negation is not positive
Axiom 3: The property of being God-like is positive
Axiom 4: If a property is positive, then it is necessarily positive
Axiom 5: Necessary existence is a positive property

(Full article on Wikipedia: Godel’s Proof for the Existence of God)

Obviously, the definitions are arbitrary, so with which axioms, if any, would an atheist take issue?

I feel tension with 1, 2, 4, and 5. I’ve no argument off the top of my head but those would be the points I would research if I want to deny the argument. Arguments that revolve around normative judgments of being positive also strike me as tricky. I generally question them, and it goes down something like this:

“Why is existence positive?”
“Well… Because it’s better than not existing.”
“Yeah, but why?”
“Because you wouldn’t be here if you didn’t exist.”
“Yeah, but, so?”
“Well… You know. It’s better. To exist.”

Now, I’m not saying that there aren’t more nuanced reasons to think that necessary existence is positive, and what being positive means. But, I haven’t encountered it in my day-to-day philosophizing.

Have you actually had a conversation with someone that went like that, or is that how you imagine it would go?

I’ve had that conversation.

The difficulty is in defining “goodness,” “betterness,” or “positivity” in such a way that it is both:

A. Valid in all possible worlds (i.e. not subjective)
B. Not begging the question. (i.e. you can’t assert that objective goodness exists as an axiom, use the existence of objective goodness to prove God exists, then turn around and define God as identically equal to objective goodness.)

Moreover, once you have defined goodness in a way that is both not subjective and independent of God, we’ve suddenly found ourselves forced to take one side of the Euthyphro dilemma. Specifically, God is good because he meets some external, empirical definition of goodness (specifically the definition we used to prove he exists.)

Maybe not verbatim, but such non-arguments are dime a dozen. I had some conversations with these words:

“Existence has an immense value!”
“Why, exactly?”
“So would you rather not exist?”

Observe the evasive tactics. Observe that the question is “answered” by another question, which is not allowed according to the forum rules.

Yes, I have. Several times.

It is positive to live. But death is strictly implied to any human who lives. Death is not a positive property. So axiom 1 is dubious.

I don’t think that is an example of begging the question. It is my understanding that begging the question is where you assume your conclusion in one of your premises, and your description does not appear to do that. If someone turned that description into a formal argument, I imagine it would look like this:

(1) God is the only possible objective standard of morality.
(2) An objective standard of morality exists.
(3) Therefore, God exists.

That is not a circular argument, but it does have a premise that I think most atheists would object to, and it doesn’t defend that premise within the argument itself. Doing that is often confused with begging the question, but I don’t think that’s what begging the question is.

Moreover, once you have defined goodness in a way that is both not subjective and independent of God, we’ve suddenly found ourselves forced to take one side of the Euthyphro dilemma. Specifically, God is good because he meets some external, empirical definition of goodness (specifically the definition we used to prove he exists.)

I don’t think Christians define goodness in a way that is independent of God, but we do often try to prove that it exists without mentioning God. E.g.:

(A) It is only rational to punish people if an objective standard of morality exists.
(B) It is sometimes rational to punish people.
© Therefore, an objective standard of morality exists.

That argument attempts to prove that an objective moral standard exists, in defense of premise 2 from the argument above, and it doesn’t mention God, but I think it is clear that premise 1 leaves room for the standard of morality to be divine.

Not if it’s possible to be an immortal human.

Bodily death brings weeping and sorrow to families. Therefore axiom 1 is false.

The problem is that if you define God as goodness itself, then taking 2 as an axiom is equivalent to taking the statement “God exists” as an axiom. In other words, you need to define what God is first, and if that definition is “objective goodness itself” then you cannot make an assertion like #2 without begging the question.

That is a terrible argument for a number of reasons, but I think some Christians would think that such reasoning was an attempt at defining goodness without God. But the problem isn’t the existence of an objective measure of goodness or positivity, it is the actual definition that will allow us to objectively decide which things are good or positive and which are not. Just knowing it exists isn’t enough, we need to know what it is in order to figure out if being God-like is actually positive. I assume that is why Godel included Axiom 3 at all, it lets him avoid the question and most people would just agree offhand since the word “positive” seems like a thing God-like-ness would be, and forget the fact that since “positivity” hasn’t actually been defined, they don’t know what they’re agreeing to.

Can you give me the actual, concrete definition of goodness or positivity which would allow us to start objectively evaluating properties to see which ones Godel’s proof would assert that God has? We could take the easy way and say that properties are good or positive iff God has them, but that would certainly lead to a circular argument.

I think that both statements are dubious.
1)Altruism and morality have been explained by natural causes such as evolution.
2) An objective standard of morality does not exist. Take for example, the use of artificial birth control for a married couple with seven children. One standard says that this is morally wrong, but another standard (including the majority belief of married American Roman Catholic women) will say that it is morally acceptable.

How do you propose to punish those Catholic and non-Catholic women who are using the artificial birth control pill?

I don’t see how a life ending in death could be worse than non-existence.

Even in the most atheistic view that death is the end of a person’s existence how can the value of life be considered zero or negative because of death?

Could you consider a time traveler using this Tech. to prevent his parents meeting to escape his existence and say, “Yes, the victory over death by never existing is better than life”?

I say, “no, this is a very negative outcome and only a seriously depressed person could conclude such a thing.”

To counter Post #9.

Holy Scripture tells us that non-existence can be better:
Ecclesiastes 4:3
“But better than both is the one who has never been born, who has not seen the evil that is done under the sun.”
Further, is it better that a man be born and suffer eternal fire and damnation in hell, or would it have been better had he not been born?

You have a point for Christians to consider and make greater efforts to gain Heaven,
But I’m taking the view of the Atheist where in his consideration no hell exists.

What should the time traveler do if he were Christian? Repent and be saved or attempt to escape his existence? Again the answer is to live and repent as is the aim of the quote. This Biblical quote is not relevant to the impossibility (just like time travel) of non-existence.

That only follows if bodily death is strictly implied by bodily life. If bodily immortality is possible, then bodily death is not strictly implied by bodily life. In that case, axiom 1 survives.

Not in formal logic. In formal logic, all premises add things to prior premises, and the result is a conclusion that is the sum of the premises. Thus the argument…

All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.

…is not circular. The argument I posted about God and morality has the same form, and therefore is not circular either. Unless I’ve misunderstood something.

In other words, you need to define what God is first, and if that definition is “objective goodness itself” then you cannot make an assertion like #2 without begging the question.

This is the same objection in clearer words, so it is covered by the previous explanation: in formal logic, the conclusion must appear in the sum of the premises in order to be valid. Your objection appears to be that the conclusion appears when you add the premises together, but that’s what must happen or the argument would be invalid. Since the conclusion is the correct sum of the premises, the only possible objection to the argument is that one of the premises is false – again, unless I’ve misunderstood formal logic.

That is a terrible argument for a number of reasons

I think it can only be for two possible reasons: either the argument doesn’t follow logical structure or at least one of the premises is false. But the argument does follow the structure of formal logic, so which premise(s) do you deny?

but I think some Christians would think that such reasoning was an attempt at defining goodness without God.

Some might think that, but I don’t think they would be correct.

But the problem isn’t the existence of an objective measure of goodness or positivity, it is the actual definition that will allow us to objectively decide which things are good or positive and which are not.

That seems accurate. We can’t objectively decide which things are good or bad merely by saying “God is the standard of morality.” We would first have to know at least something about God’s behavior.

Just knowing it exists isn’t enough, we need to know what it is in order to figure out if being God-like is actually positive.

I don’t think that’s quite accurate. I think we can show that existence is a positive quality by carefully examining the contrary. If existence was a negative quality, it would seem to follow that it is impossible to posit that anything exists. The reason is that I believe the word “positive” in this case refers to the ability to logically posit that quality Y belongs to subject X. If that is correct, and if you can logically posit that anything exists, it seems to follow that existence is a positive quality, i.e. a quality that can be posited about a subject.

I assume that is why Godel included Axiom 3 at all, it lets him avoid the question and most people would just agree offhand since the word “positive” seems like a thing God-like-ness would be, and forget the fact that since “positivity” hasn’t actually been defined, they don’t know what they’re agreeing to.

I don’t think that is what he is doing. I think he is using the term “positive quality” in a way that is more like “actually existing quality” than like “morally good quality.” You can’t posit that a quality belongs to something if the quality does not exist. You can only posit that it belongs to something if it does exist. Positive in this case seems to relate to the ability to logically posit that a quality belongs to something. If you can’t logically posit that quality Y belongs to subject X, then Y is not a positive quality.

Can you give me the actual, concrete definition of goodness or positivity which would allow us to start objectively evaluating properties to see which ones Godel’s proof would assert that God has?

I think positivity in this case is the same thing as actually existing, and only includes moral goodness if moral goodness is a quality that actually exists (i.e. a positive quality).

We could take the easy way and say that properties are good or positive iff God has them, but that would certainly lead to a circular argument.

That seems likely.

If altruism and morality are explained by evolution, does that mean we are morally obliged to obey evolution?

  1. An objective standard of morality does not exist. Take for example, the use of artificial birth control for a married couple with seven children. One standard says that this is morally wrong, but another standard (including the majority belief of married American Roman Catholic women) will say that it is morally acceptable.

Your example does not seem to prove your point. An objective standard of morality seems to be able to exist in the face of people who contradict it in the same way that objective facts exist in the face of people who contradict them. What am I missing?

If we banned the pill, we could punish its possessors in the same way that possessors of other contraband products are punished. I’m not sure how other contraband is regulated, but I don’t think the cases would be much different.

If “positive” had actually been defined, then there would be no ambiguity. I had considered this “maybe ‘positive’ just means some sort of logical affirmation” myself, but it is easily rejected because of the issue of contradictory properties. Under this system, black is a positive property, and not-black is also a positive property. I can posit either of those things about a subject. However, Axiom 2 says that if black is a positive property, then it’s negation (not-black) cannot be a positive property.

Likewise, what would Axiom 5 (Necessary existence is a positive property) mean under this interpretation? It would mean that Non-necessary existence (e.g. contingent existence) is not a positive property. That means that we cannot logically describe anything as contingent.

What would Axiom 3 imply? It would imply that not-God-likeness is not a positive property. That it is illogical to posit that anything is not like God.

(1) Thor is the only possible objective standard of morality.
(2) An objective standard of morality exists.
(3) Therefore, Thor exists.

I think we can show that existence is a positive quality by carefully examining the contrary.

As part of a lecture, Prof. Shelley Kagan worked out how many possible people there could be in the next generation. The crucial point, he said, “is to realize that every time you combine a different egg with a different sperm, you end up with a different person”.

Here’s his math. Suppose 2.5 billion men and 2.5 billion women. A woman has roughly 12 eggs a year for 30 years. A man can produce 40 million sperm a day for 50 years. So 2.5 billion * 12 * 30 * 2.5 billion * 40 million * 365 * 50 = roughly 1.5 million billion billion billion potential persons. Just in one generation alone. The odds of not existing far outweigh the odds of existing.

So Thor has designed the world such that the number of people who could exist far outweighs the number who do. Therefore either Thor is immensely evil, and we should cry buckets for all the people Thor denies even the opportunity to exist. Or else non-existence is not a negative quality, and therefore existence is neutral.

Is it rational to punish them now?

Yes, I think so, because I think ecclesiastical penalties count as punishments. As for civil penalties, I think it is rational to punish the manufacture or possession of birth control, but only concurrently with their prohibition.

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