Kurt Gödel’s Ontological Argument – Line By Line Explanation

__________VIDEO CONTENTS__________
0:00 Intro
1:11 Explaining the Symbols
5:26 Axiom 1
6:50 Axiom 2
8:05 Theorem 1
11:31 Definition 1
12:08 Axiom 3
12:18 Theorem 2
13:20 Definition 2
15:03 Axiom 4
15:22 Theorem 3
18:44 Definition 3
20:06 Axiom 5
20:18 Theorem 4
22:38 Conclusion

[jadetermig]

I find it funny that both theists and atheists get angry at this argument because it uses the word God. It certainly shows that the "scientifically minded atheists" who usually make fun of theists for being irrational, are not capable of following a simple a logical argument because it uses the word God so they immediately apply secular/scientific reasoning to "disprove" one of the axioms by applying it to the real world and appealing to quantum mechanics. That is not how logic works people! You can neither prove nor disprove an axiom. Axioms are what allows proofs in the first place. You can accept it or you can reject it but neither makes you correct.

[HebiDevy]

So basically it's saying
1. A god has every positive property. (definition 1)
2. Existence is a positive property. (axiom 5)
3. Therefore a God exists.

[shaunakkulkarni]

I think the axiom that says necessary existence is a positive property is kind of dubious/debatable. Since no living person has experienced a state of non existence, we are not qualified to comment on it being positive or negative.

[tinu]

Being alive is a positive property. People who are alive make mistakes. So from being alive it follows that they make mistakes. But making mistakes is a negative property. So axiom 1 already fails.

[rektator]

Even if the proof works, do we know that the theory (the set of axioms consisting of Axm 1-5) is consistent. Even if the theory is consistent (no contradiction can be attained from the axioms), do we know that this theory has any instances or models. It is notable that one uses second order modal logic here, the questions of soundness and completeness become very complicated.

[Re-lxmd]

totally disagree with the first axiom, i can have a criminal record because i acted courageously to use your example. or, because i have the property that i am alive, i necessarily have the property that i will die. Is the certainty of death a positive property?

[sepro]

From what I understand, the whole argument is: being Godlike means having all positive properties, existing is one of these, so God must necessarily exist. I can say a UFO is a kind essential property which implies existing, then there necessarily exists a UFO. If you make existing a property like everything else, you can invent an infinite amount of essential properties which imply existing. That’s why I think Axiom 5 is where it breaks down. Existing is different from all other properties, as there can not be an object that is not existing. This means that existing has no negative version that can apply to any object. This however means that any point where we use the NOT symbol does not apply to existing. If we still take existing as a normal property, this implies that there could be any number of properties which have no negative, or no positive for that matter. At that point, the reasoning breaks down completely. In conclusion, I think the system is inconsistent and could, as described be used to proof that any object ever could exist, as there is nothing inherently logically different about an object having only and all positive properties. As a side Note, I would also like to say that this proof also assumes that there can not be contradictory positive properties, which, from my understanding, is not demonstrated, and can easily be possible (think about the classic: can god make a stone so heavy he cannot lift it) the existence of exclusionary positive properties necessarily implies that no object can be godlike, as the property godlike couldn’t exist.

[dumbledorelives]

I find it somewhat dubious to assert that there are no neutral properties as an axiom. I can think of several neutral properties such as color, mass, charge, etc

[timecube]

Conceptual and actual existence are being conflated, the argument is completely satisfied by the conceptual existence of god and yet the conclusion is that god actually exists, without this the argument becomes "I can conceive of an object that has every positive property therefore the concept of an object with every positive property exists".

If you want to say that the argument only refers to actual existence then it's question begging because actual existence is a necessary precondition for any property, thus to say god has any properties is to say that god exists.

[hades]

doesn't that suggest that, something with every negative property exist too💀

[jimstewart]

This is by far the best explanation I've seen of this, really good. One quibble, that might be wrong, is that you seem to imply (at about 6:40 for example) that a property that's not positive is negative. I am not sure that's part of the meaning of the term Gödel intended. You mention having a color as an example of a property. So is being green positive? If it is then being any other color seems like it should be negative. But it doesn't really make sense that being a particular color is positive or negative. One could say that a godlike being, being beyond space and time, won't be any color at all. But there are lots of other properties that don't seem like they should be positive but aren't negative either. I'd say that an item that's not positive is just that, not positive. Being negative would be an entirely different property, though of course you'd need to define that something can't be both positive and negative. No way of knowing what Gödel intended but this makes sense to me.

[dariuslegacy]

I really like how much detail you're going into when giving an overview of the argument. I still think it's much too vague to work as a proof, if not for the simple question of what metric gets used to measure the "positive-ness" of a property lacking a satisfactory answer.

Secondly, couldn't this argument be used to "prove" the existence of multiple universes, including one with only "positive" properties? I'm confused as to why this has to refer to a sentient object unless we're sneaking in the existence of objective value judgements. If we don't sneak objective value judgements then the argument can conceivably be used to prove the existence of anything, as long as someone considers that thing as strictly consisting of positive features

[beammeupscotty]

MOST AMAZINGLY FUNNY MATHEMATICAL CONJECTURE OF ALL TIME woo woo at its finest BS

[timwood]

Valid? So 'tis claimed. But truth itself is not a consequence of validity. Validity a judgment of form, truth of content. Thus every claim must meet criteria of truth - must be demonstrably true. And good luck with that! And if truth not demonstrable, then all there is, is faith and begging-the-question, which is what you started with.

Important note: for real Christians this is not an issue or even a question. There creed starts with, "We believe." Belief independent of truth. As to what, exactly, Christians believe and do not believe, that was laid out a long time ago. And most modern Christians have little or zero clue.

[Nikolas_Davis]

So, when the dust settles, the argument boils down to: "it would be nice if God existed. God is essentially nice. Therefore, God exists".

(Yes, yes, I know, this is only a formalization of Anselm's proof, you have to either accept or reject the axioms, yada yada. It doesn't change the fact that Anselm's was a bad argument, and no amount of formal fortification will ever change that. As many competent thinkers have pointed out, centuries ago, existence cannot be considered a property. Even if it _were_ considered a property, assuming axiomatically that necessary existence is a positive property is ludicrous at best, and vacuous at worst. It takes much more of a leap of faith to assume that it would be good for God to exist, than it takes for assuming that God exists in the first place. Imho, that is the biggest flaw in this kind of argument.)

[danialshirazi]

Why is the property of being godlike a positive property an Axiom ? It follows directly from Definition one and Axiom 1.

[mlerma]

That is an interesting exercise in modal logic that clarifies the assumptions ("axioms") behind the ontological argument. On the other hand the conclusion of an argument cannot be better that the assumptions on which it is based. Note that Kant argued that "existence" is not a property, making a serious dent in the argument. Of course there are still philosopher debating this issue, but it does not have the appeal that it used to have in the past.

[Dhrrheeea]

The proof merely shows the necessary existence of God as a concept or platonic ideal. The next step is to prove platonic ideals have a physical reality (Godel believed this as self evident, but few others do, even many theists).

[felixherz]

Couldn't the positive properties except for necessary existence be arbitrarily chosen; meaning that this proof simply implies the existence of everything with the trait of necessary existence and thus says nothing much at all?

[jperez]

thanks for going through line by line. others do a terrible job because they just skim through it or most likely have no idea what they are talking about. you actually show the step by step logic plus the syntax of the proof. i strongly suggest you correct the typo and edit a corrected proof. thanks again