Kurt Gödel’s Ontological Argument - Line By Line Explanation
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- čas přidán 28. 05. 2024
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_________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
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.
Hey! Someone who gets it's just an axiomatic system!
Thank you!
Going to pin this in hopes that people read it before commenting 😛
That us where the fun is. We can call something an axiom, and thus, we don't feel we need to prove it. If I define the number 1 as 2 then say 1+1=4, it is completely logical though it is only internally consistent not consistent without.
@@billydavis4252 Lol. Ok. Every axiomatic system is composed of 4 parts. There are axioms, undefined terms, definitions, and theorems. Undefined terms are the terms that show up in the axioms (in real analysis, these symbols are 0, 1, +, *, and
@donaldtimpson4320 So how do we prove the assertion as to the nature of God? Saying it is true because you say it is true isn't any better than saying 1 = 2. I can easily say it to "prove " my point but that ignores the fact that saying it doesn't make it true.
@@billydavis4252 First off, we'd have to choose a field. If you want to give philosophical proofs, you start with premises that you can validate by inductively reasoning on common experience (proofs from concepts of free will and good/evil are typical examples). If you want to give scientific arguments, you start with premises that you can validate by inductively reasoning on objective measurable phenomena (intelligent design arguments are usually in this vain). If you want to give historical arguments, you use premises that you can validate by abductively reasoning on objective measurable phenomena (examples would be trying to validate the history of the bible to prove God). If you want more religious arguments, your premises are based in abductively reasoning on personal experience (these would be more personal revolution type argument).
But I'm far from an expert on the different arguments used to prove God's existence, and I personally do not know of any argument that actually utilizes Gödel’s proof.
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.
I don't know why you're using the article "a" with God. It is a proper noun. Like we'd say The Universe, or The Number 0. In fact, God could be said to be the The(o) of All Things. That is, the principle and proper nature & identity of Reality from which all things are transformations on this ultimate The.
Yes, that is definitely the essence of the argument (and almost exactly what Anselm's argument says). I think Godel was essentially trying to give Anselm's argument, while also plugging in all the rigorous details.
@@jeffreyjdesir The pronoun "the" is best left for specific examples. This argument sounds like a convoluted assertion that a God exists and not really specific about which one is being discussed..
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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.
I think the Axiom I take the most issue with is Axiom 2. It seems very strange that "being red" has to be positive or negative, as opposed to just being neutral.
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.
Uhh, close. If you wanted to use this kind of argument to claim that axiom 1 doesn't hold in our universe, you'd have to say:
1) being alive is positive,
2) making a mistake is negative, and
3) being alive NECESSARILY implies making a mistake (meaning that there was no chance of it being otherwise).
I would guess most people would say making a mistake is just really really likely, but not a necessity. But if you take for granted that it's a necessity, then yes, your counter argument would hold.
Anyways, thanks for the comment!
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.
I agree with you, and this is one of two major criticisms of applying Gödel's argument to reality (the other being that it leads to something called modal collapse which seems to eliminate free will by implication). But Axiom 2 does unequivocally state that every property is either positive or negative (it says if a property is not positive then it's negation is positive, and visa versa). So if being green is not positive, then by Axiom 2 being not-green is positive (whether Gödel intended it or not). But I don't think Gödel was trying to give an actual argument for the existence of God in this universe, I think he was just trying to construct the minimum axiomatic system necessary to reconstruct Anselm's argument in a completely rigorous way. But like you said, no one can really know.
Anyways, thanks for the thought provoking comment and the kinds words!
What I call a positive property may not be what someone else calls a positive property, and vice versa.
That's true. This is just an axiomatic system. Any axiomatic system can have potentially infinite interpretations (you can use group theory to describe the addition on the integers, or multiplication on the rationals excluding 0). The axiomatic system doesn't tell you what properties are positive (outside of the ones given in the axioms), it simply tells you that if some system satisfies the 5 given axioms, then there necessarily exists something in the system with every positive property.
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?
thats not what the axiom is saying. It is not saying that a positive property and a negative property cannot co-exist. It is saying that if every object that has x positive property also has y property, then y must be positive. So if every single courageous person on Earth and in the universe necessarily had a criminal record tagged with the courage, then criminal record would be a positive property.
@@luaiali7884 is the certainty of death a positive property?
Right, the argument doesn't say that the axioms are true, only that they entail the conclusion. But I think you are slightly misunderstanding the first axiom. It says that having a positive property can never necessarily entail a negative property. It's quite possible to posses both positive and negative properties, for positive properties to entail negative properties, or for negative properties to entail positive properties. It's a little subtle and is using modal logic, but that word "necessarily" is a crucial piece of the axiom. But thanks for the comment!
doesn't that suggest that, something with every negative property exist too💀
Lol! It actually gives us the exact opposite. Axiom 5 gives us that necessarily existing is a positive property, and so not existing is a negative property. So something with every negative property by definition can’t exist. But thanks for the comment!
@@donaldtimpson4320 Okay but something with every negative property except the negative property being to not exist exists
@@abdullahimran4624 Yes, I belive the system allows for such a thing to exist.
Why is the property of being godlike a positive property an Axiom ? It follows directly from Definition one and Axiom 1.
That's funny. I had the exact same thought when first looking over this. The problem I ran into comes from the necessary operator in Axiom 1. Definiton 1 doesn't give me that the godlike being necessarily has the positive property, and so that's where I got stuck.
Modal logic always hurts my intuition a little bit, and so I have to start manually working through the details of the proof to find why it doesn't work. But fantastic question, and thanks for the comment!
that's a good question
@@donaldtimpson4320 If we introduced Axiom 4 wouldn't that fix this problem? So that with Axiom 1, Definiton 1, and Axiom 4, you could then prove Axiom 3?
@@BobbyRoyal-ph8yk It's a good thought, but I don't think so. Axiom 4 just gives us that if a property is positive, it is necessarily positive. We still have the problem of arguing that something necessarily has a property. It's a little different, but I think you still run into essentially the same problem.
@@BobbyRoyal-ph8yk I think also Axiom 4 is also the crucial thing which leads the whole argumentation and proof to collapse. Because then every true statement is necessarily true, i.e. "everything exists necessarily".
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
That is an axiom I too take issue with. Keep in min that the goal here is not to argue that God exists in this universe; Gödel’s goal was to construct an axiomatic system that necessarily entails the existence of God (validating that the axiomatic system applies in this universe would be an entirely different beast). In other words, the point is see how these 5 axioms entail the necessary existence of God; it is NOT to validate that these axioms actually hold in our universe. Hopefully that makes sense, but thanks for the comment!
@donaldtimpson4320 yes that does make sense, and Thanks for the reply!
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
Thanks! Keep in mind that this is just an analysis of a simple 5 axiom system. It is definitely not complex enough to introduce a metric, and so there is no way of classifying one property as positive or negative (in fact, there's no way of talking about any properties that are not defined in the system).
I think your second point shows you have good intuition for the argument. It only proves the existence of something god-like, where being god-like simply means you posses every positive property (whatever that means). So depending upon how you expand the system and choose to validate the axioms, I'm sure this could be used to prove all sorts of things.
Thanks for the comment!
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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
Lol, that was my exact frustration and the reason I made this video. The sad part is, this was my second time recording it, and I still had that stupid typo! But thanks for the suggestion and the comment!
@@donaldtimpson4320 after you correct the proof, you might want to discuss the proof of the existence of only one super intelligence at a time. This was a recent proof (21st century ) i saw online. Peer reviewed. I just don’t have the links now
The argument has a strong fragrance of circularity. Now I am going to have to more closely examine his main claim to fame.
No, there's nothing circular. All the terms are well defined, the axioms are consistent, and the conclusion has been computationally validated. Understand that this is simply setting up an axiomatic system. It simply tells you that if some system satisfies the 5 given axioms, then there necessarily exists something in the system with every positive property.
But thanks for the comment!
What defines positivity? It makes sense on a basic level but to say "a criminal record is a negative property" specifically is not true. One could be in search of fellows to perform a heist with, or looking to learn from them. There are people who investigate the psychology of individuals who turn to crime. The people who are in prison, can get better and feel peaceful. So in a way having a criminal record can be positive
soo cool btw
I have a feeling you misunderstand axioms and their purpose in the proof. An axiom cannot be proven or disproven. It just is. In other words, the proof shows that the conclusion follows from the definitions and the axioms. It makes no judgement about whether the axioms apply in reality - and nor does it need to in order to be a valid proof.
Lol. Good question. I used the "criminal record" to help the viewer establish intuition for what the proof was saying. But you are correct that the system gives us no way of calling a specific property positive or negative (with the exception of G and E being positive). It's also important to understand that we are only showing that the axioms imply the conclusion; we never claim the axioms are actually true. We only showed IF they are true, THEN the necessarily exists something with every positive property.
Hope this helps, but thanks for the comments!
Why did u equate psi to ~phi in the proof of the first theorem?
So Axiom 1 holds for ANY 2 properties. We use psi and phi as variables representing these properties. Now, let phi be any property. Since Axiom 1 holds for any 2 properties, it also holds for the special case of phi and ~phi. That was the logic being used. I probably should have used a third variable rather than using phi again. I could have instead said "let theta be any property, then Axiom 1 holds when we substitute in theta for phi, and ~theta for psi".
Thanks for the feedback though! If I do this lecture again, I'll have to remember to avoid that confusion.
@@donaldtimpson4320ohhh i got it, thanks
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.
The axioms have been shown to be consistent and the proof has been computationally validated. I know of no ethical/philosophical system that takes these axioms for granted and/or attempts to validate them. It seems that most fields that would have the potential to utilize a system like this are composed of "experts" that are shockingly ignorant of logic, or at the very least make almost no attempt to be rigors.
If you ever do come across an instance, I'd love to know! But thanks for comment.
This seems to say, "The existence of something which has ALL properties, *that one/many can perceive as positive*, necessarily exists." I can't seem to take it any further, irrespective of perception, beyond "life implies the existence of something with all properties conducive to (necessary for) life".
But fun an interesting. Slide management worked a lot better in this lecture :P
That's almost exactly what the proof says (perception is irrelevant to the proof). It says that given the 5 Axioms, there necessarily exists something with every positive property (Gödel’s definition of God). It provides no way of determining if any particular property is positive or negative, and so all that can really be known about this/these God(s) is they necessarily exist. The proof has been shown to be computationally sound, so we are positive that the axioms entail the conclusion. But the proof also leads to modal collapse (making so that everything that is the case, is necessarily the case).
But yeah, it was a fun one to actually go through all the logic of. Though not nearly as fun as teaching a bunch of Lemons how to make lemonade.
@@donaldtimpson4320 So that "the proof also leads to modal collapse (making so that everything that is the case, is necessarily the case)" ENTAILS that it is necessarily the case that God exists, in all possible worlds, maybe also setting a limit on the many worlds interpretation of QM.
Uhh, that's a tough one to say. Here's my own intuition, but I could be mistaken.
If we take for granted that the 5 axioms hold in our reality, then everything that is the case is necessarily the case (modal collapse). I think that this contradicts the many worlds interpretation of QM (because there was never multiple possible outcomes for a particular event). This would mean that while in QM it SEEMED like there was a 50/50 chance of a particular outcome, it was really going to be the particular outcome it was regardless, and there was never really a 50% chance of the other outcome occurring. There was only ever one possible string of events, and that's the ones currently unfolding in our universe.
That's my gut reaction.
Being pure green is a positive property and so is being pure blue. Therefore if God has all positive properties God is grue and bleen.
So all you've done here is come up with an inconsistent interpretation of the axiomatic system. So in that case, the system can not be used. All this proof says is that if you can come up with an interpretation where the 5 axioms are validated, then the conclusion necessarily follows. It in no way guarantees any particular interpretation. But thanks!
Tell me what you think an elementary particle is and I will demonstrate that the Universe was designed.
I think the most validated theory is currently quantum field theory. In that theory, a particle is expressed as an excitation is the corresponding quantum fields (depending on which elementary particle you're describing).
@@donaldtimpson4320 Thanks, Donald, great answer. Now, what is a field?
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?
Uhh, almost. You are correct that the system gives us no way of classifying properties as positive or negative (and the ones I used in the lecture like a criminal record were just for the sake of intuition). But in your interpretation of the system, however you choose to classify the properties, if you wish to use this proof you'd need to make sure your choices satisfy the axioms (e.g. a positive property never necessarily entails a negative property).
Understand there's a huge difference between setting up an axiomatic system, and then validating/using it in some particular instance. This argument is simply the former.
But, says God, don't forget your incompleteness theorem, Mr Gödel. I am incomplete, therefore I do not exist. Disappears in a puff of logic.
Gödel's incompleteness theorem only applies to axiomatic systems complex enough to encode the axioms of arithmetic. This system is not such a system (or at least I would be shocked to discover it was), and so Gödel's incompleteness theorem does not apply. But thanks for the comment!
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).
Nice thumbnail 👍🏻
Do you like how well it matches my video?
Sure.
Thanks for the very specific feedback. It is invaluable.
Wonder about "positive property" and theodicy, and some other thought experiment (Aa- Tea time)
Nice thought. To make it consistent with the system, you'd probably would have to go down some sort of "free will is a positive property" avenue, and then continue with standard arguments from there. But it would definitely require an expansion of the axiomatic system.Thanks for the comment!
@@donaldtimpson4320 but- why- "free will is positive property?", why deduce some property is positive?- and also how it compactible with, lets said "God created everythinh, including evil", is "evil" good or bad?
I don"t see deduction of positive property?
Aa- Glad you respone 😁
@@ekadria-bo4962 Sorry, I didn't explain myself very well. My first thought is that we'd have to introduce as an axiom that free will is positive, and in the definition of free will (I have no clue how to make this rigorous), it would have to allow for the possibility of negative properties. This then allows for the possibility of evil in a standard way, without evil necessarily coming from the good (just possibly).
An extension to map out the positive attributes theologically attributed to god, like omnipresence and omniscience might be useful. Also since Tea Time is necessarily good it exists in all creations. The theodicy of god's need to create evil as part of omniscience arises here. That evil had to be created and is inherently self-negating (banal) is a tough one for Antinomians unless the Self-negation finally applies essentially to them. One solution to the field equations that allows for time travel requires a lot of "negative energy" in the process, so evil may regretfully play a useful role in taking us beyond the space-time prison.
God is both dead and alive until you open the box
Lol. This has nothing to do with QM. Furthermore the terms dead, alive, open, and box are undefined in this system. To validate that your statement holds in this system, you'd first have to define all these things.
I've seen a few videos of people going over Godel's proof but they never actually go through the logic and the proof of the theorems like you do! Thanks!
That's exactly what motivated me to do this. Thanks for the comment, and glad it could help!
Is being red a positive property? Is being not red a positive property? One of the claims made is that every property is either positive or negative. That is not true. A property that is not positive is only not positive. Not positive is not equivalent to being negative anymore than not red means that something is blue.
You'd have to provide a property that is actually not a positive attribution, or a negative reduction to support "that is not true..". By definition though, such a property would ascribe itself attributions or reductions to met its criteria, which contradicts itself. You may not understand attributive logic it seems because blueness or redness can both be described as attributions or reductions (lack of attribution). These are just instances of properties. There's an entire calculus on the attribution of properties to objects that demands it is strictly either positive or negative. Indeed language itself cannot fathom a non-binary property (except when describing itself), as this would undermine predicate logic.
@@jeffreyjdesir Something can be red, blue, green, black, brown, etc. Red and not-red are exhaustive and mutually exclusive categories. Red and green are not. A property can be positive, neutral (zero in the case of numbers), or negative. Positive and not-positive are exhaustive and mutually exclusive categories. Positive and negative are not. Yeah, there is probably a lot that I do not understand. I have no particular expertise in this area of logic. However, I think I am making some reasonable assertions here.
@@matthewalan59 I think I get what you're saying, there seem to be properties given to objects that have many valid values, not binary. But I'm trying to show this may be an aberration of natural, lazy (in our case English) language, and not fundamental to Truth. If you see things through propositional logic, you'll realize every "thing" is a large list of on or off switches that determine its terminal properties. Blueness and greeness have a continous quality to their description, but not IF a thing is either blue or green. In your example with numbers, you wouldn't compare values above or below 0, but more general and ultimately binary properties (is 0 an element of the natural numbers, is 1 greater than 0, etc...). There are systems out there for many valued logic (ternary) which employ neutral states, but these can still be reduced to a binary query. Getting back to the question at hand, if God is defined as the Object with all positive properties and no negative properties (except when relaying info about itself, like its existence), then God is the Superobject from which all other Objects (thoughts or things) transform their properties by and with respect to. God ultimately would be the identity of Logic itself (not formal, but apparent logic). Sorry for the long-winded reply..
This is the axiom I too take the most issue with. It's funny, I used the same exact example of "being red".
@@donaldtimpson4320 I would have to admit that I only watched about a third of the video. I got bored and the notion that one can prove the existence of god, gods, or anything else with some clever word games has always seemed childishly preposterous to me. If there was a god that wanted to be known, I am sure that it could do something rather convincing.
I appreciate the video! But I believe that this simply proves that something with the godlike property exists, being something that has every positive property. Since what we define as an object is rather fluid, I would imagine the universe itself would satisfy this, or at least a subset of the universe. So in the end, this is just proving the universe exists.
I think that trying to prove that god exists definitively ignores the beauty of the leap of faith required to truly reach him. This is still awesome though! Keep it up!
Thanks! You're halfway right. This argument only shows that the 5 axioms entail that something god-like exists (something with every positive property). If you want to apply this argument to actual things in our universe, you would have to validate that the 5 axioms hold in our universe. But you are correct that Godel's definition of something being god-like is a far cry from what most people have in mind when they think of God. Ultimately, I think he was just trying to come up with a more rigorous version of Anselm's argument.
But thanks for the kind words and the comment!
@@donaldtimpson4320 Chris Langan's Cognitive Theoretical Model of the Universe achieves this; coupling formal-logic to spatio-temporality with language (as a self-constructed tautology). It's actually genius and will change the world in due time I hope
@@jeffreyjdesir I know nothing about that. I'll have to check him out.
MOST AMAZINGLY FUNNY MATHEMATICAL CONJECTURE OF ALL TIME !!!!!! woo woo at its finest BS
lol. Love the enthusiasm.
This was a lot easier to follow than your “Proving God” video! Thanks 🙏
That was the hope. Glad it helped.
Would the proof also work with the Flying Spaghetti Monster?
Lol. Yes, provided you define the property of being a Flying Spaghetti Monster as possessing every positive property.
@@donaldtimpson4320 I don't think he watched the video XD
The reason behind my question is to point out that this proof is a reformulation of the ontological proof of God according to Anselm and as such applicable to any entity assumed to exist that is conceived in accordance with the premises of the proof. However, the ontological proof of God has been definitively refuted since Kant. Formal correctness or not: logic does not decide questions of existence.
Concerning the Flying Spaghetti Monster (FSM): in many countries worldwide the Pastafarianism is a an officially recognized religion with the FSM beiing the the deity of the Church of the Flying Spaghetti Monster. And in "The Loose Canon", the Holy Book of the Church of the Flying Spaghetti Monster you can read that an invisible and undetectable Flying Spaghetti Monster created the universe ... so I am pretty sure that the premises are met.
@@photonaut_8875 why not? He’s right. Gödel’s proof ONLY stipulates that a godlike being “possess every property designated ‘positive’” and thus it could essentially apply to any entity defined as such. Such as the flying spaghetti monster
X and Y are objects. God is not an object ... by definition... god is not in the natural world ... X and Y are CONVENTIONAL objects, not existential.
This is just an axiomatic system, and the term "god-like" is well defined in the system. The fact that Godel chose to use the word "God" in the proof is somewhat irrelevant to the proof. Strictly speaking, he showed that the 5 axioms given entail the existence of a thing with every positive property (which he chose to call god-like). You can use this argument to then make other arguments about God in a more conventional sense, but that is going beyond the scope of this axiomatic system.
I hope that makes sense, but thanks for the comment!
X and Y are anything you want them to be, so they may be objects. The same goes for God. You can argue anything, but that does not make it real, except in your mind.
God is a concept worshipper attach. So it can be attached to a tree or a fairy. Or existing is not necessary as worshipper can worship whatever they can imagine.
To follow this argument, you have to leave any preconceived notions of God at the door. Here, being god-like is well-defined, and it means to have every positive property (nothing more and nothing less than that). If you wish to use this argument in any "real world" way, you would first have to validate the axioms.
@donaldtimpson4320 So you deny every Bible story. Interesting standpoint. May be common in a world where believers can't read the greek text, nor where the greek reader the greek author of the greek-roman literature about Iesous was aimed at.
I congratulate you to you new God you made in your image.
@TorianTammas Hmm, maybe I'm explaining this badly. This is just an analysis of a 5 axiom system. Kurt Godel was just constructing the minimal axiomatic system he could to reconstruct Anselm's argument. The definition of god-like here is completely self-contained in the system. I've stated nothing about my beliefs; I've simply attempted to take the viewer through Godel's argument.
@donaldtimpson4320 Thanks for clarifying my mistake, but Anselm is talking about the only god he would accept.
Basically (no offense) a BS argument. The assumption that there is a god is buried in this proof, and is a false premise, without evidence of a "god".
Lol, no offense taken. But I think you are allowing your own prejudice to sink into your interpretation of the argument simply because it uses the word "God". This argument only shows that the 5 axioms entail that there necessarily exists something with every positive property (defined to be "god-like" in this system). This argument makes no claims about reality. If you wanted to try and use this argument to make statements about reality, you would have to come up with ways of validating the 5 axioms (which is a whole other beast). This is not a religious argument; it is simply a logical argument. But thanks for the comment!
@@donaldtimpson4320 no all they’ve done was assert the *fact* that this argument begs the question by defining G as “having all positive properties” and then defining “exists” is a positive property. Sure, it’s valid but it is still fallacious reasoning. It’s obviously not your fault as a presenter, it’s not your argument; it’s Godel’s. But still, it clearly begs the question in my opinion
@@frimi8593 Lol. I have failed again. Please allow me to attempt another explanation:
Gödel is setting up an axiomatic system. You can say "I don't like that axiom"; fine. That's a valid criticism of applying the argument to this universe, but it is not a criticism of the argument itself (any more than proving spacetime has curvature invalidates Euclidean Geometry). To what extent the axioms can be validated in our universe is a completely separate question. What Gödel proved is that these 5 axioms entail the existence of a thing with every positive property. That's it. There's no question begging or any other falicious reasoning. There is no fault with the argument itself; it has been computationally validated.
What you seem to be saying is that "assuming these axioms hold for our universe begs the question that these axioms hold for our universe"; but the argument makes no such claim. These axioms entailing the existence of a thing with every positive property is no different than the axioms of group theory entailing the existence of a unique identity element.
@@donaldtimpson4320 ok sure if the purpose is just to go through and show the logic that these 5 axioms imply the necessary existence of something with property G, that’s fine. Just understand that for people finding this video outside the context of what I now understand it to be (a companion piece to a series of lectures on the history of philosophy) it has a very provocative thumbnail. You’ve put “proof of God” in big text in the center of the thumbnail with “God” in a shiny, yellow, loud/bold font with a picture you gesturing at the phrase “Kurt Gödel’s proof of God.” Perhaps if you changed it to something that presents more neutral, more akin to the video title which I think presents much less provocative and more strictly informational, you wouldn’t have so many people coming in here with the idea that this argument is meant to be anything more than a history/philosophy lesson.
@@frimi8593 Lol! Yes. That's fair. All that happened was I wondered "how does Gödel's proof actually work?". I went looking for videos, but none of them actually went through the logic of the argument. So I decided I'll make a video where I completely explain Kurt Gödel’s proof of God.
But thanks for the feedback!
A proof of god, defined as a being that has every positive property, that assumes that it is possible that god exists fails at the first hurdle. Being immune to harm is a positive property. Being courageous is a positive property; but not a positive property possible for a being who is immune from harm. Given that the third axiom of the proof is easily demonstrated to be false, the proof in fact proves nothing.
Lol! You're allowing your prejudice to convolute your understanding of the proof, and you're imposing your own notion for what ought to constitute a positive property. This is just a simple 5 axiom system that entails the necessary existence of something god-like (possessing every positive property). The system gives no way of classifying properties, and if you want to use the system to describe our universe, you must first validate that the axioms hold in our universe (which is well beyond anything in this proof). The logic of the proof is completely sound. I used "courage" as an example to provide the viewer with intuition for the proof. You can not use this system to claim that "courage is positive", and are now imposing your own interpretation on the system to invalidate your own interpretation of the system. The proof is simply an interesting lesson in logic. I recommend giving it a second try. But thanks for the comment!
@@donaldtimpson4320:
1) The proof may be VALID (ie, if the premises are all true, its conclusion is true), but it is certainly not SOUND (ie, it is valid, AND all its premises are true). Specifically, Axiom 3 is false, as I demonstrated. If you wish to purport to teach logic, at least use the proper terms.
2) I demonstrated a simple refutation of Axiom 3. That does not show the proof to be invalid; but it is sufficient to show that the conclusion does not follow from this proof.
3) If that is not enough, Step 2 of the proof of theorem 1 relies on the fact that a falsehood vacuously implies everything. That is because 'x implies y' is logically equivalent to 'either not x, or y'.
To make this clear, if we assume that nothing has the property phi, then 'For all x, phi x' implies both 'psi x' and 'not psi x'. Ergo Step 2 of the proof of theorem 1 is not even valid.
4) Finally, except under special restrictions, 2nd order logics cannot satisfy the three properties of soundness, completeness and effective - a result proved by Godel himself. The special restrictions (Henkin Semantics) are not satisfied by the world, and ergo any proof in 2nd order logic may be unsound (ie, sentences may be provable in the system whihc are false in some domains); incomplete (ie, it may have truths which are unprovable in the system); or ineffective (ie, there is no algorithm that can determine of every sentence whether or not it is a proof). With an unspecified semantics (as with this proof) it may be all three, but more importantly it is impossible to determine which. Ergo this proof is irrelevant, except as a means to con the gullible.
5) Finally, I will not that your accusation that my beliefs are based on prejudice is simply argumentum ad hominem.
Lol! You're all over the place pal.
I do teach Logic, and you can find the full course here: czcams.com/play/PLJWhXkxQzDF58EHPCuxHS-iaMpom9qTqg.html
Every proof in Logic/Math is only valid and can never be considered sound (the concept does not make sense in the context of Logic and Math as most premises are validated via inductive reasoning which is not permitted in these fields). You are conflating some other field (likely Science) with Logic.
The only way you can invalidate an axiom in an axiomatic system is to demonstrate the axioms are not consistent, which you most certainly did not do. You are simply applying an interpretation to the axiomatic system (and I mean that in the technical sense as covered in the given Logic course), and then showing that your intuition for your own interpretation is inconsistent. Outside of that you'd have to show that the axioms don't entail the conclusion, which you appear to have made an attempt at.
It was nice of you to do some googling around to put together that extremely incoherent response; reading it was much like listening to a toddler reciting the dictionary to sound smart. If you understand half those words you googled, then you should understand that the proof has been computationally validated (so the axioms for sure entail the conclusion, which is all the proof demonstrates).
Anyways, thanks for laughs and thanks for the comments. It's been fun!
@@donaldtimpson4320, you seem only to be able to argue by ad hominem. Consequently, you are of no further interest to me - though I do recommend your students ask for a refund.
@@tom_curtis you cannot be this dense
It is of course nonsense, on at least two levels. Level 1: The above assumes Reductionism (the Greek one), i.e.: That ultimate reality, aka Ontology, can be wholly graspable by its properties / attributes / categories / features. But that's of course not true. Quantum Physics demonstrates that there are regions where categories do not exist, e.g.: below the Planck scale. (The proton is both larger than, and smaller than, its components, depending on how you measure it.) And God can of course be outside the realm of attributes, as is the wave function, before it goes pffft. Level 2: "Positive" and "Negative" properties are from the PoV of a human, i.e. an Observer. So, no Observer, no God. Is this how it's supposed to work?... Saying all that, Godel was certainly smart, but since his main work was showing the limitation of categories-dependent math, the above "proof," dependent as it is on categories-dependent math symbols, comes up as, well, beneath him.