@@NeverTalkToCops1 I don't believe the argument is meant to do so, nor such a Beings particular identity; only necessary attributes and existence. The rest is our homework! ;-)
@@NeverTalkToCops1 No, the argument demonstrates the existence of at least one such entity. At this point, one may simply appeal to Occam's razor which states that one ought not multiply entities beyond necessity.
Professor Bonevac, your channel is a lantern in the darkness. A flower growing in a garbage pile. Glad I found it all those years ago, and thank you for making your videos.
@@PhiloofAlexandria Wow, you're very welcome and thanks for the reply! Your classes have been life-changing for me. I consider you one of the great philosophy teachers, and I've listened to many others, including Hubert Dreyfus when he was still alive.
Thank you for this video that sharpens the arguments of Anselm and Descartes using the powerful logic of Godel. I would greatly appreciate if you can comment on Nagarjuna's Tetralemma and whether that is a refutation of the logic of Anselm/Dscartes/Godel.
The same objection to Anselm's argument applies: Existence and nonexistence cannot be properties of a thing, because a thing by definition exists and cannot not exist (or it would not be a thing, indeed it would not BE).
No it doesn’t. There’s a difference between virtual existence and mental existence Quine On What there Is). Pegasus exists mentally but not virtually. He still exists though. Something has existence if it is a member of a set.
@@tim2muntu954 If we take your definition of property: an essential or distinctive attribute or quality of a thing, then replace the word thing with a definition that includes the necessity for existence then Kant's criticism becomes more clear. "An essential or distinctive attribute or quality of a concept with existence" or "An essential or distinctive attribute or quality of an entity that exists." The problem stems less from assigning existence to things but rather that non-existence would disallow the addition of a property to an object. We can reimagine this conversation with a unicorn. Person A can say they are imagining a unicorn with a red horn while person B says that no unicorns have a red horn. Person A then comes back with a painting of their red horned unicorn to showcase that at least one unicorn has a red horn. Now is where Kant's criticism comes in, person B states (in true surrealism fashion) that what Person A is holding is actually a painting not a unicorn, thus does not have a red horn. Neither Person A nor Person B deny the existence of unicorns (and Person B heavily implies a shift in the burden of proof), but Person B will not accept the addition of an attribute unless it is not a painting. That is to say, Kant expresses that existence is a perquisite for all other attributes to be applied and that attributes that are applied to things seeming to be non-existent are rather applied to the object that carries its existence (The painting of the unicorn or the human mind thinking of god). So the ontological argument would boil down to "The mind can hold the thought of god therefor the mind exists." To specifically look at Gödel's proof most either criticize the axioms by applying David Hilbert's remark about the interchangeability of the primitives' names, where one can replace "positive" and "God-Like" to create an entity that one wishes without changing how the conclusion follows from the axioms, or one points to Jordan Howard Sobel's work showcasing an implication of modal collapse that would not only remove our understanding of free will but also remove any possibility of a "sovereign god," that is to say the being stated in the proof would themselves lack any discernable method of choice (All actions that are taken must have been taken and could have been the only actions taken).
@@25chrishall To be a "thing" is to exist. And to be existing is to be a "thing". The use of the verb "to be" is always an assertion of existence. There is no such thing as a nonexistent thing. Existence is not a property that a thing may or may not possess. It is rather the essence of "thingness".
How do you define a “thing”? Existence proofs are fundamental to mathematics. For example we can prove that there exists infinitely many primes. We can take “infinitely many primes” as the “thing”. It is an intuitive concept that can be grasped and understood from definitions (what constitutes a thing), but its existence is not guaranteed at face value and must be demonstrated from more fundamental (intuitive) principles. So a “thing” does not by definition exists necessarily.
This is an important argument. It leads directly to the question of what is and isn't in the domain of human determinability. The lack of facts or lack of logical formulation, that this argument brings up, should be directly looked at. In this way new facts or new relations of ideas will be inferred. This realm of inference could then be confronted. In this way light will be shed on the abyss of ignorance. No? The reasons and evidence, or lack thereof, why we can or can't "explain" God should all have inverse suppositions. We would gain knowledge were we to extrapolate these inverse suppositions to their inverse logical relations wouldn't we?
Hello sir! How are you i watch your videos regularly.Please answer my question a person here is using godels incompleteness theorem on contingency argument.Does it make any sense? plz answer thank you
This ontological argument seems to have the same problems as the other ontological arguments. Namely, it's completely formal and therefore tells us very little about the properties this "god" must have necessarily. The common objection, which you will find here in the comments, is that the concept of positive is subjective. This objection comes from the fact that the argument is formal and in order to give it any content whatsoever, human ideas of what is good and bad must enter into it, thereby introducing subjectivity. I have a slightly more original objection, which is that the content of the argument can point in the exact opposite direction because the argument is purely formal, it doesn't dictate what kind of content goes into it. For instance, if we talk about _negative_ properties rather than positive properties, we can arrive at a very startling and worrying conclusion. Consider things like doing harm, being evil, being hateful. These are negative properties. But in order to do harm, for instance, you must be powerful enough to do harm. Therefore, being powerful is a negative property (our version of Axiom 2). And furthermore existence is a negative property, and necessary existence as well. Following Godel's argument to its conclusion we find that a being which contains every negative property must necessarily exist, and of course it has these properties to the maximal degree. It is all-powerful so that it can do as much harm as logically possible. I doubt Godel (or any christian) would accept this argument for a god of pure evil.
At either extreme it argues for the existence of both God and Satan. But that leaves people where they began, with unclear questions. Since people are divorced from the old dialogical methods, and barely aware of the congealing new dialectics, this ontological argument is only helpful for those seeking the strongest arguments for and against faith. And only after significant hours invested in the training of logic, inquisitiveness, and fallacy spotting. But going at it all by oneself is a recipe for self-congratulation and circular reasoning, so it takes two people *at minimum.*
Negative properties don't exist, is what any theologian would respond to your inversion of the ontological argument. Classical and medieval philosophy doesn't view evil as having any properties, but rather as being made of a lack, as being defined as deficiency of properties. Any given thing's existence is considered good, and evil is a disturbance of the order by which something exists. A rotten apple is bad, not because of any specific property of the apple, but rather because the rot takes away from the apple's existence, and deprives it from it's properties of being edible and tasty.
@@rubeng9092 Well, I think that's a pretty bad argument, for a lot of reasons. The main reason is that it goes against our everyday experience of negative things. Pain is not merely the lack of pleasure, bitterness is not merely the lack of sweetness, and so on. And of course if you want to push the argument that far, I can easily go that far in the opposite direction (positive properties don't exist, they are merely a lack), so I don't really see how it solves anything.
@@APaleDot Isn't it that when we encounter something bad we seek it's remedy? Whereas when we encounter something positive we cherish it for what it is? Pain on it's own isn't bad, many people wake up after day of intense exercise, with muscles feeling quite sore, yet they are content and happy about it, since they know their muscles are growing and their capability is increasing. Whereas someone having a serious injury has to put up with not being able to move without crutches or having his arm not function properly, which objectively entails a decrease in that arm's ability to be an arm - which is bad, because it's a negation, and that's where the word negative get's its meaning.
@@APaleDot Pain and bitterness aren't evil. Pain is a necessary signal for survival, but those who enjoy inflicting it are evil. Bitterness is a taste enjoyed by many.
Thank you for your video. One thing that comes to mind to me when reading Axiom 5 is the myth of Sibyl, of which you talked about at the beginning of your T.S. Eliot and The Wasteland lecture. Can we say that for old Sibyl, existence is still a positive property?
What if a society existed that sacrificed it’s most intellectual person every year? Is intellect itself a negative in that society or is it the society that’s a negative?
Essentially, this and Anselm's argument are very precise formulations of the intuitive concept that humanity's conception of God must flow from His will.
Do we need a deeper understanding of reality to have this argument? Positive and negative charge is an innate part of all matter, all objects. A sphere has one perfect surface the same positive curvature everywhere. If the Universe is based on a process of spherical symmetry forming and breaking, then we would be the imperfect broken symmetry. You explained this difficult subject very well!!!
Thank you! I’ve been looking for a video explaining Godel’s Ontological Argument for over a year! I’m still not sure I get it, but I’ll watch it a few more times. I just wish you’d also explained the symbols used. But this is a great help!
Thank you VERY much for making this presentation! I do not understand it very well. Maybe I should take some classes on this, LOL! But I think whatever it is you are talking about would be very helpful for me when it comes to studying the Bible. The Bible is quite a bit of reading and I am really interested to find out if there is some way to evaluate whether or not the Bible is logically consistent. I have read Genesis through Revelation about three times now and am amazed at how few obvious contradictions there are in the whole account (when seen rightly). There are some passages that seem to conflict in the English translations. But I think it is probably due to misunderstandings or poor translations that lead to these apparent contradictions. Hmmm... maybe "God does not contradict Himself" is a positive property?? Is it possible to feed the Bible into a computer in such a way that it could extract from the text all statements indicating "A is true" and then find any statements that indicate "A is not true"? This would be very helpful in finding those trouble spots and get into examining possible meaning or interpretations of the text. And if nothing else, that would be instructive just from a "weight of the evidence" perspective. Often, when reading the Bible, i find myself asking, "does x mean this or does x mean that?" If x means this, is that logically consistent with the rest of Scripture? If x means that, is that logically consistent with the rest of Scripture?
Again, I very much appreciate your explanation of essences. A is an essence of x if and only if it is a property of x and entails the necessary properties of x and only the necessary properties of x. That makes sense. But when I read Godel's original proof, it seems to say something different. It seems to say A is an essence of x if and only if it is a property of x and entails all the properties of x. Am I misreading Godel's argument? Or does this reflect a change in Anthony Anderson's revision of the argument? If it is a change, I'd say it is an improvement. I don't see why an essence of x should imply non-necessary properties of x.
So when it is said that "it is possible that necessarily something is godlike" in theorem 3 is that referring back to "necessary existence" as in the positive property of exemplified essences in all possible situations?
I actually enjoyed this presentation. It’s a nice argument, with a clear structure. As someone interested in mathematics and formal logic, I’m pleasantly surprised to see an argument in the language of modal logic. It was nice to research and find out that this axiomatic system is consistent. However, it seem to not be applicable in the real world, as this system implies a modal collapse. Also, since “positive” property is not defined constructively, we can not infer any real-world properties of this maximal object, so it might as well be referring to a rabbit in my back yard. Due to the same limitations, we don’t get a strategy to find out which properties are positive, or a way to find or determine if any given object is maximal in this regard.
I used Anderson’s reconstruction to avoid the modal collapse problem. I also agree with Koons that “is self-identical and such that the cat is on the mat” is not a real property.
@@TeaParty-qh1py I would suggest that the "facts of reality without contradiction" of which logic can help derive and describe, does not exclude the metaphysical.
Wonderful video, thank you! I love the "round square" example at 15:30 that segues into Leibnitz's approach. The explanation of Leibnitz's approach appears to share similarities to showing that a space is complete. If it is, then it is spanned by a linearly independent set of basis (or "properties", in this context) which must be consistent with each other because they are independent (or "primitive", in this context). Properties of all objects in this space must therefore be consistent too. Thanks for the video!
This is an engaging puzzle wish I encountered when I had more time to play and learn. Would you or someone please enlighten me on how this proof relates to Godel's other work on the properties of formal systems (like logic) in regard to being complete and/or consistent. At my level of ignorance, I'm also interested relation between logic and science.
I would like to add another important notion: if something exists that is maximum, then it must necessarily contain all that exists and not be separate from it, for that implies restriction.
Could you possibly say for that second modal principle mentioned, that it boils down to the belief that every universe shares the same contingent matters of fact, so that they can be discounted when discussing necessity
As a Muslim I loved the ending. The final discussion about "Maximal Nature Of God" translates very nicely to the concept of "Allah-u-Akbar" (God is Greater) in Islam.
The question is not what lens to look through, but what to look at through the lens. I think this is a brilliant lens, the problem is that most people are afraid to point the lens where is needs to be in order to see. A hint: What is the difference between God and God-like?
I can imagine a Flying Spaghetti Monster that created the universe. But it would not be perfect without existing, because existence is a positive property. And nobody is more positive than him! Therefore the Monster exists.
Good video and your positive ability of lecturing. Why don't you make videos on different conceptualizations of God in Islam, Christianity and Judaism?
I'm excited to learn you have a background in mathematics. We are all familiar with the idea of using different axioms concerning accessibility relations for possible worlds models to model different kinds of modality. But have you heard that a better way to do so is to use topology (at least for the case of S4 and beyond)? Consider the axioms of S4 modal logic. A proposition is possible if and only if it is possible it is possible. If P implies Q, then P is possible implies Q is possible. If P is true, then P is possible. “P or Q” is possible, if and only if either P is possible or Q is possible. Now consider the closure axioms for a topological space. The closure of the closure of a set equals the closure of the set. If P is a subset of Q, then closure of P is a subset of the closure of Q. P is a subset of the closure of P. The closure of the union of A and B is equal to the union of the closure of A with the closure of B. The axioms of the possibility operator of modal logic in S4 coincide precisely with the axioms for the closure operator of a topological space! In the same way, the axioms of the necessity operator of modal logic in S4 coincide precisely with the axioms of the interior operator in a topological space! I’m still astonished by this. So we can model a system of S4 modal logic using a topological space. The points of the topological space represent possible worlds. Propositions are represented by sets of possible world (sets in which the proposition is true). If a proposition P is represented by a set of possible worlds S, then possibly P is represented by the closure of S (it makes sense that the set of worlds in which P is possibly true is a superset of the worlds in which P is true). Necessarily P is represented by the interior of S (it makes sense that the set of worlds in which necessarily P is true is a subset of the set of worlds in which P is true). A proposition P is represented by an open set if and only if "P is true" implies that "P is necessarily true." A proposition P is represented by a closed set if and only if "possibly P is true" implies that "P is true." For example, since a MGB is defined in part to be a being that exists necessarily, if the proposition "A MGB exists" is true, the proposition "It is necessarily true a MGB exists" is true. So "A MGB exists" is represented by an open set. Furthermore "No MGB exists" is represented by a closed set. If it is possible no MGB exists, then no MGB exists. What would an S5 topological space be? It would be one where every open set was a closed set, and vice versa. An S5 space could be represented as a discrete union of closed-open set, where any set was closed-open if and only it was a union of a sub-collection of these discrete sets. The interior of a set would be the largest closed-open subset of that set, and the closure of a set would be the smallest closed-open set containing that set. Above we noted that "A MGB exists" is represented by an open set. Working in S5, the set representing “a MGB exists” must be a closed set as well, so if it is possible a MGB exists then a MGB exists. Given any topology T on a set, we can take the minimal refinement of T that satisfies the conditions of S5 in the obvious way (show the intersection of any collection of S5 topologies is S5, etc.). Therefore, it would seem given any S4 modal logic, there is in a sense a minimal extension of that logic to an S5 modal logic. Perhaps this is what Richard Swinburne was referring to when he talked about metaphysical necessity being a sort of idealized version of epistemic necessity.
That is really nice. Contemporary philosophers underutilize topological concepts; they're often very illuminating as well as elegant. One of my regrets is that, in my last semester of graduate school, I didn't at least audit a course being offered on topological logic. I feared it would distract me from finishing my dissertation. But it was an opportunity I haven't had since to study the links.
@@PhiloofAlexandria Let’s define a Goldbach number to be an even integer greater than 2 that cannot be written as the sum of two primes. Then the Goldbach conjecture asserts that there is no Goldbach number. Let us assume, for the sake of argument, that the Goldbach conjecture is undecidable; that it is true there is no Goldbach number, but it is impossible to prove that. In an S4 logic modelling provability, it’s possible a Goldbach number exists (because we cannot prove no such number exists). But in a metaphysical modality, it is impossible a Goldbach number exists (because in reality no such number exists). Now given any positive integer, it is in principle possible to verify through a finite process that that integer is not a Goldbach number. So in the modality of provability modelled by S4, it is not possible 4 is a Goldbach number, it is not possible 6 is a Goldbach number, it is not possible 8 is a Goldbach number, etc. Yet at the same time it is possible there exists a positive even Goldbach number. It’s not clear how we would model this situation using possible worlds with a transitive reflexive accessibility relation. There would have to be a world accessible from the actual world in which 4 was not a Goldbach number, 6 was not a Goldbach number, and so on, but there was a Goldbach integer. That’s not helpful. But we can model this using topology as follows. We assume there exist possible worlds, 4, 6, 8, 10, etc., in which 4 is a Goldbach number in 4, 6 is a Goldbach number in 6, and so on. Since all of these assertions are demonstrably impossible, they are not possible in the actual world. What that means is, topologically speaking, there is an open neighbourhood of the actual world that excludes world 2, another open neighbourhood that excludes world 4, another open neighbourhood that excludes world 6, and so on. Since open sets are closed under finite intersection, there is an open neighbourhood containing the actual world that excludes any given finite set of these worlds. This reflects the fact that given any finite set of positive even integers, we can in principle verify they are not Goldbach numbers in a finite amount of time. Now however, imagine that the actual world is a limit point of the set {2,4,6,8,. . .}. This reflects the fact that while no particular such world is possible from the perspective of the actual world, the collection of all of these worlds is possible. This reflects the fact that while we can prove any finite subset of the positive even integers contains no Goldbach numbers, we cannot prove the set of all positive even integers does not contain a Goldbach integer. Now let’s go to the S5-topology generated by this S4 topology. This topology includes all the open and closed sets from the S4-topology. In this topology, open sets are closed sets and vice versa. So in this S5 topology, open sets are now closed under arbitrary intersections. So in this topology, the intersection of the open sets containing the actual world and excluding 2, 4, 6, 8, etc. is an open set. And so it is metaphysically impossible a Goldbach number exists.
As the video demonstrates the power of Godel’s argument hangs on the meaning of modal language. The only way I can make sense of modal language in the context of metaphysical philosophy is this: There is the actual reality in which we live and which has a particular nature. Given that nature there are many ways reality could have been but isn’t (or in other words many facts of the actual reality are contingent). Let us call the set of all realities that could have been the “set of metaphysically possible worlds”. Then we define that “X is metaphysically possible” iff X obtains in at least one element of the set of metaphysically possible worlds”, and we define that “X is metaphysically necessary” iff X obtains in all elements of the set of metaphysically possible worlds. But then the expression “X is necessarily possible” (or, to be precise, “it is metaphysically necessary that X is metaphysically possible” turns out to be meaningless, for there are no different kinds of metaphysical possibility. Either X does obtain in some element of the set of metaphysically possible worlds or it doesn’t. If it does then in it is metaphysically possible simpliciter. If it doesn’t then it is not metaphysically possible. Thus to speak of “necessary possibility” as if it were something distinct is to speak nonsense, and to use that non-existing distinction in an argument is to build on thin air. I suspect that Godel’s error is to uncritically apply modal logic to metaphysical reasoning. In the realm of logic perhaps it makes sense to speak of X being necessarily possible, but that’s irrelevant to the practical business of metaphysical philosophy. After all it is not like one can map the set of all logically possible worlds to the set of all metaphysically possible worlds. So, for example, the set of all logically possible worlds (that is in the set of all internally logically consistent realities) there are some worlds which are theistic and some that aren’t. For example a by definition logically possible world is the empty world in which nothing exists, which is a non theistic world. But it is easy to prove (see Plantinga) that if it is metaphysically possible that theism is true then it it metaphysically necessary that it is true. Or, applying my meaning of modal language, if theism is true in one metaphysically possible world then it is true in all of them. One can see why this is so without actually following Plantinga’s proof: Theism is a claim about the very nature of reality. If the nature of reality is theistic then all ways reality could have been will be theistic also (it’s not like the nature of reality is a contingent fact or that God might remove himself from reality). Incidentally for the same reason Plantinga’s result can be turned on its head: If it is metaphysically possible that theism is false then it it metaphysically necessary that it is false.
This is very good, but it depends on how God is defined. If God is defined as the set of all metaphysical possibilities, then it is not possible to remove this from the sets, because all such sets depend on this by definition. As to your point, the reason I agree is that I'd go another step and say that because there is no way to prove that anything can be metaphysically impossible, including even basics like logic itself, any technical talk of such is incoherent. For me, this means the problem reduces to what God is in respect to existence. If there is a truth about this (which there is no reason to be particularly skeptical about that I can see), then the focus must be on finding the true answer to this question, which will, in my view, require some kind of empiricism (including the subjective kind in this special case where existence can only be experienced subjectively in the final analysis.. in other words, this is not a pragmatic empirical issue that can be tested and verified locally).
@@konberner170 The definition of God that everybody accepts is that God is the greatest conceivable thing. This is a clear definition as proven by the fact that even atheists can engage in intelligent and indeed sophisticated theological argumentation. Now the greatest conceivable being will certainly be prior to everything. That is, God will not need to stand on something else, or conform to something else. Therefore God is what philosophers call the "metaphysical ultimate", the ground on which everything else stands. (Incidentally metaphysical naturalism - which is the worldview of most atheists - also entails a metaphysical ultimate, namely mechanical nature.) But the metaphysical ultimate is the same in all metaphysically possible worlds. Therefore if it is possible that some metaphysical theory (whether theism or naturalism) is true then it is necessarily true. As for what God is in respect to existence, the answer is pretty straightforward: Existence itself is not prior to God, thus God does not only make what exists (or may exist) but makes existence itself. Theists commonly say that "God exists", but this is a linguistic shortcut which is misleading when understood literally. Strictly speaking "God exists" is an incoherent proposition. Theism's claim is *not* that among the many things that exist God also exists. Theism's claim is rather that existence itself is created by God. As for other existents, both theists and atheists agree with the proposition "apples exist" but mean something different, because atheists and theists understand differently what it is for something to exist. The understand differently what existence itself is. So naturalists believe that the existence of, say, elementary particles and their mechanical nature is implicit and autonomous. Theists believe that their existence is not autonomous but depends on God's will; they are created and remain around as long as God wills it.
@@DianelosGeorgoudis Atheists don't all agree with that. Theists don't all agree with that. And "great" is substantially subjective. Who decides what is greater than something else? Maybe start over?
@@DianelosGeorgoudis 🕉 सर्वं खल्विदं ब्रह्म 🕉 Chandogya Upanishad 3.14 (‘sarvam khalvidam brahma’ teaches that ‘All this is indeed Brahman’. “Brahman” is a Sanskrit word referring to the TOTALITY of existence. There is nothing but Eternal Being, Consciousness, Bliss!).
I know next nothing about logic, but am I right in suspecting that Gödel’s proof of God’s existence is essentialist in its metaphysics as opposed to relationalist?
Sorry but my argument is, isn't positive or necessarily positive property a relative matter of fact ? If we got two or more negative numbers lying on different coordinates of the negative side of number line, then would we not get a positive property between the more and less negative numbers? Then how positive property can be compared with all perfectness ? Please answer.
That's the thing. I think they should be relative to zero not to each other. Because we are going to look at the big picture to directly reach the fundamental nature of reality not small inter-negative pictures. Because the moment you look at inter-negative relations you are not treating them as negative anymore but as numbers.
For all of us that are taken by the beauty of saint Anselm's ontological argument, Gottfried Leibniz' phrase sums it up best: "if God is possible then God is (exists)". Incidentally, the syllogism is correct, pursuant to classical Aristotelian logic.
It reminds me of something I heard recently (I don't remember who said it) about physics. "Anything not prohibited is mandatory." Some people assume that magnetic monopoles and cosmic strings must exist unless there is a still-undiscovered reason they don't exist. It is at odds with Occam's razor and the concept of "burden of proof." This probably explains why they can't agree whether negative energy or sterile neutrinos are real despite some good circumstantial evidence.
The problem with this and many other ontological style arguments is that they treat "existence" as a property. Strictly speaking it isn't, at least not in the way that we typically use it linguistically. If I say that an apple exists, I'm treating "exists" as a property of the apple, and linguistically as a predicate. But technically I've got it backwards when I do that. What I'm _actually_ saying with that statement is "In the reality in which I occupy, there exists an apple." The apple existing is a property of the context (in this case "the reality I occupy") in which it is invoked. In other words, existence isn't a property of the apple, it's a property of the reality in which I occupy. To look at it another way, the concept of an apple isn't changed if I specify that it exists, or that it doesn't exist. It's fundamentally still the same concept. To say an apple exists (in reality) is like saying that an apple is a fruit eaten by man. It's confusing the nature of the relationship between the two. That apples are eaten by man isn't a property of the apple, it's a property of man. An apple would still be an apple, totally absent the concept of eating, or man. The concept of an apple is the same whether you tack on existence, or you don't. So when we start talking about existence as a perfection, it's just begging the question. As already demonstrated, existence doesn't change the concept of an apple, so it's not coherent to say that the concept is improved by the addition of "existence." If we're not talking about the concept then that just leaves us with discussing an _actual_ (extant) apple, but that's just a tautology. To say that an existent apple that exists is better than an existent apple that doesn't exist, is silly. One option is simply incoherent and self contradictory, and the other is tautological. Don't get me wrong. I love me some Kurt Gödel, but I think he was a little out of his wheelhouse when making this argument.
If the property 'maximal' or 'perfect' is positive then what requirement decides whether 'maximal good or 'maximal evil is ''God-like'' (if not arbitrarily by definition)?
The very idea of 'positive properties' is totally subjective; there is no way to test a property to see if it is positive or negative, it is open to the interpretation of the speculator. Gödel' should have realized this when he had to revise it to 'some properties are positive'. As an attempted argument for an objective god, this doesn't cut it. Excellent presentation in the video though!
This question might prove I didn't understand a thing here, but isn't the conclusion that for those who believe in God anyway as well as those who now a accept Goedel's proof, necessarily each person identifies their own god and that it is possible that no two people identify the same god?
Godel's whole thesis was an exercise as to how Modal Logic ( possibility> necessity) might be applied to Anselm's ontological proof. Here, it's important to understand that ML as such was created during Godel's active years; he seemed to have had a lot of fun with it--much like his famous argument during his citizenship Q&A about contradictions in the Constitution...my dream is to have been a fly on the wall during his conversations with einstein at Princeton... which is to say that theologians shouldn't take his 'proofs' so seriously!
I don’t understand how existence (whether necessary or not) can be declared a positive property. Nothing but human feeling may provoke that assumption, and the only reason that non-existence has negative implications is because the living fear it. But isn’t the one as positive or negative or indeed meaningless as the other?
I don't get it, how can a property ever be positive or negative? I mean, it seems easy to respond if you're a human, but it's not like our reason is necessarily an accurate representation of independent objects, how do we know if something is positive, or going even further, how do we know if something is necessarily positive?
I could never feel the strength of Axiom 5 (Necessary existence is positive / existence is a perfection / existence is an improving quality). There's just nothing compelling me to accept it. Why is existence necessarily "better" than non-existence? Why do so many accept it without any justification as something obvious? Not only do I not find it obvious, it sounds to me like a category mistake. Is there something I don't see? Note that this isn't the same as Kant's critique, who would deny that existence is a predicate. I'm fine with it being a predicate (at least for the sake of argument). I claim that these are two different predicates that aren't related the way that the axiom states.
It being stronger doesn't mean it's more compelling, it simply means it's a more substantial claim. "All swans are white" is stronger than "Some swans are white".
@@cynicviper You're not wrong, but that doesn't make my choice of words a mistake. Note that we also call compelling arguments "strong" and we conceptualize arguments as resting on "strong" or "weak" foundations. "Strong(1) claims require strong(2) evidence". When we say that a self-evident axiom is "strong", do we mean (1) or (2)? Does it even make sense for self-evident axioms to be stronger(1) or weaker?
@@luszczi It absolutely doesn't make you wrong, I apologize if that is how it came across. Without wanting to sound pretentious, I was merely trying to explain what I thought was a misunderstanding. You are certainly right, and I as well, don't agree with the Axiom. To Gödel, who perhaps cared about logical rigor this whole endeavor matters, but to me, it is still nonsensical to Analytically grant existence to anything.
"Meaningfulness" is the why. An existing thing affects the state of reality; a non-existent thing does not. Being effects things. Non-being does not. Being is therefore greater than non-being.
@@ansaz14 pen > sword sometimes. Sometimes the concept of god is all thats needed to change the world. Since all that needs is a concept to change, then being real doesnt matter
Boltzman's "entropy" implies a complex system dissipating into 'consistent' randomness; Ervin Schrodinger's "negative entropy" 1943 'What is Life?' infers a system tending to randomness re-asserts itself into further complexity that tends towards persistence extracting what it needs from its ambience to accumulate, sustain, recreate and increase its 'essential' complexity. Thus, Godlike consistent randomness as a 'necessary property' per Godel so God's negation is the known Universe. Like the death of Jesus? Help Anselm! Help, Spinoza! Think Spring!
So with necessary possibility at the end there, I don't understand the argument against the axiom of "if it is possible that it is necessary, then it is necessary." Based on contingent matters of fact. Couldnt you argue if some property has contingent matters of fact that dispute it's necessary existence, then it is simply a property that isnt necessarily existent?
So for example for the weightlifting, could you not say that, though it was possible for you to lift 300lbs, it was not necessarily so, on the basis of that event not occuring?
It is fascinating that Goedel, who committed suicide by starving himself to death, should argue that existence is a positive property. Nonsense can get out of hand, it seems.
But how are we determining that it is better to exist than to not exist, surely there’s not much evidence for that. I’m thinking of some eastern philosophy or Schopenhauer or someone saying existence is pain and bad, not necessarily agreeing with that just wondering how to resolve this
Thank you so very much for your videos. I’m a 65 year old photographer with a love for philosophy because I have a love for God. I’ve always liked the Ontological Argument as a starting point - followed by Contingency and on to cosmological and morals arguments. I’ve been working on an argument from beauty (as an artist) which seems to me to be somewhat like the moral argument but is also a design argument. Anyway, thank you. I greatly enjoyed your presentation and appreciate Godel’s model ontological argument.
Interesting comment. I want to hear more about this design from beauty argument (from artists pov). I'm a lover of the beauty of nature. I always think mountains/forests, fields and oceans untouched by mankind has beauty. Once arrange and rearrange, we make it ugly.
l second that request, that you expand on this idea of beauty if you feel like sharing. As l child growing up on the edge of a grimy industrial landscape, with factories, coal mines, hundreds of smoke stacks across the horizon, the ugliness overwhelmed me and l would squint and minimise my visual field until l could fixate on something beautiful like a tiny patch of cloud in the sky or reflections in puddle. These moments literally gave a crushing childhood meaning and uplift, it was the nearest thing to numinous for me. l detest the axiom "that beauty is truth" however beauty is definitely some kind of harbinger,and reprieve, for sure.
@@veronica_._._._ I plan on posting later this week. Both my parents were born and raised in West Virginia so coal mining was very much part of my family. To me, just as darkness is the absence of light, so ugliness is the absence of beauty. In art we know that art/beauty has properties. The same is true with the beauty we find in nature. And, just as art needs an artist - so the beauty we find in nature needs an artist (Psalms 19). Van Gogh used paint and canvas to re-create a Starry Night, but God does it ever night.
Strange argument. For starters, it is based on questionable axioms. It leaves undefined which properties are necessarily positive, other than the property of existence and the property of being God-like, which is also not very clear. If I understand correctly, to be "God-like" is to possess all positive properties? (All necessarily positive properties, not those that are contingent on circumstances). But we don't know what those properties are, other than the property of existence. So if the logic holds and the axioms are in fact valid, we still don't know the nature of this being we call "God"?
If you look into eastern Theosophy, similar conclusions have been reached : the existence of Divinity/ a Divine Being, can be inferred from the existence of it's attributes ( omniscience, omnipotence, etc ) but not fully known, by any part of it's creation : nature, cosmos, humans. Peace
Gödel's ontological proof is just a formalization of a pre-existing ontological argument. He just "translated" to the mathematical language - using modal first-order logic - the argument, with no merit of the validity of the axioms of whether the conclusion really means the existence of God. I think Gödel himself didn't intend to "prove God's existence".
We do not know if there is necessary existence outside mere arbitrarily defined terms of a language
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Existence is not a property of the subject. It is a property of the concept. "My spaceship" is not a thing that exists, but it's not the spaceship that has this negated property, because, well, it doesn't exist. Instead, the concept "my spaceship" has a negation of a reifying property. Can't believe how much people trip on this simple language pitfall.
If one is Omnipotent, then one is capable of doing good (as well as everything else). If one is Good, then one intends to do good. If one intends to good and one is capable of doing good, then one does good. The only thing left is: Is it good to eliminate evil?
I don't know if it's true and the source is questionable but funny but I like Norm Macdonald's thought on this matter. He thinks if God made everything good he would simply be expanding himself. He wants a family therefore he had to make not good who now in a cool turn of events has the capability to do good and join in him
What if being god like involves killing or destruction? Does this mean that killing and destruction are positive and necessary properties? And these oppose being as a necessary property?
I did not know that Godel presented a variant on the ontological argument. However his incompleteness theorem has radical implications for the philosophy and foundations of rational or formal symbolic systems of thought. One of these implications is that no system that has the power to include self referential statements or outputs that describe the system itself, can be proven to be both consistent and complete. What this means is that any attempt to construct a rational system will not be able to be entirely a closed system where strange and paradoxical statements and possibilities can be expunged and excluded from the system. It means that whether we like it or not we live in a radically and inescapably mysterious, paradoxical and open reality and cosmos. Where all kinds of transcendent possibilities that are super rational may not only, but may in fact have to, exist. Even though this is not a positive proof of God, it is a negative proof against any arguments that deny that such a reality and being, that escapes being fully defined within a rational order and system, can't exist. In essence reason has debunked its own pretentions to ever being able to offer a full and complete, self contained and sufficient, description of all the manifold aspects of reality. This makes rationally inexplicable intuitive leaps of faith inescapable and inevitable for the fullness of human knowledge to be revealed, discovered, made known and manifest. And yes it is a rather strange spooky synchronistic coincidence that Godel has the word God in his name! Almost like God has a weird mischievous sense of humor! Oh by the way he does, but the jokes can be quite deep and subtle. For example the very ability to ask the question is God real, actually itself suggests that more than mere animal existence is required to understand human existence. Of course there are many people who will hate such a conclusion but so what the joke of them pulling the wool over their own eyes and not knowing it, is always going to be on them, isn't it? As it stares them in the face and they never see it, and passes completely over their supposedly intellectually superior heads.
I think a bit more work is needed for an objective definition of “positive”. The definition here is very dependent on things we value as a species, like being alive vs. being dead, or “it’s preferable to be God than to not be God”. Of course a living species would value living over not, but this is an ontological argument so it needs to be ontologically positive. “Positive” needs to be something defined by its presence, & negated by its absence, like heat or strength vs. cold or weakness. Knowledge should be positive, not because we prefer to have it than to not have it, but because it is something that can be had, while ignorance is merely the lack of having knowledge. The thing is, we may conceive of a possible world where the creatures evolved to prefer ignorance to knowledge, but there should be no possible world where ignorance is ontologically “positive” even if it is valued or preferred.
Those are similar to my thoughts...it seems those dependencies without adequate definitions indicate assumptions aka implied yet unacknowledged axioms.
🐟 03. CONCEPTS Vs THE TRUTH: The term “TRUTH” is a grossly misused word. Anything which has ever been written or spoken, by even the greatest sage or Avatar (incarnation of Divinity), including every single postulation within this Holy Scripture, is merely a CONCEPT and not “The Truth”, as defined further down. A concept is either accurate or inaccurate. Virtually all concepts are inaccurate to a degree. However, some concepts are far more accurate than others. A belief is an unhealthy and somewhat problematic relationship one has with a certain concept, due to misapprehension of life as it is, objectively-speaking. Attachment to beliefs, particularly in the presumption of individual free-will, is the cause of psychological suffering. For example, the personal conception of the Ultimate Reality (God or The Goddess) is inaccurate to a large extent (see Chapter 07). The concept of Ultimate Reality being singular (“All is One”) is far more accurate. The transcendence of BOTH the above concepts (non-duality) is excruciatingly accurate. However, none of these concepts is “The Truth” as such, since all ideas are relative, whilst The Truth is absolute. It is VITALLY important to distinguish between relative truth and Absolute Truth. Relative truth is temporal, mutable, subjective, dependent, immanent, differentiated, conditioned, finite, complex, reducible, imperfect, and contingent, whilst Absolute Truth is eternal, immutable, objective, independent, transcendent, undifferentiated, unconditional, infinite, non-dual (i.e. simple), irreducible, perfect, and non-contingent. Absolute Truth is the ground of all being (“Brahman”, in Sanskrit), and is prior to any mind, matter, name, form, intent, thought, word, or deed. Good and bad are RELATIVE - what may be good or bad can vary according to temporal circumstances and according to personal preferences. For example, there is absolutely no doubt that citrus fruits are a good source of nutrients for human beings. However, it may be bad to consume such beneficial foods when one is experiencing certain illnesses, such as chronic dysentery. 'One man's food is another man's poison.' Because of the relative nature of goodness, anything which is considered to be good must also be bad to a certain degree, since the extent of goodness is determined by the purpose of the object in question. As demonstrated, citrus fruits can be either good or bad, depending on its use. Is drinking arsenic good or bad? Well, if one wishes to remain alive, it is obviously bad, but for one who wishes to die, it is obviously good. However, beyond the dichotomy of good and bad, is the Eternal Truth, which transcends mundane relativism. Therefore, the goal of life is to rise above the subjective “good” and “bad”, and abide in the transcendental sphere. A qualified spiritual preceptor is able to guide one in the intricacies of such transcendence. Such a person, who has transcended mundane relative truth, is said to be an ENLIGHTENED soul. When making moral judgments, it is more appropriate to use the terms “holy/evil” or “righteous/unrighteous”, rather than “good/bad” or “right/wrong”. As the Bard of Avon so rightly declared in the script for one of his plays, there is nothing which is intrinsically either good or bad but “thinking makes it so”. At the time of writing (early twenty-first century), especially in the Anglosphere, most persons seem to use the dichotomy of “good/evil” rather than “good/bad” and “holy/evil”, most probably because they consider that “holiness” is exclusively a religious term. However, the terms “holy” and “righteous” are fundamentally synonymous, for they refer to a person or an act which is fully in accordance with pure, holy, and righteous principles (“dharma”, in Sanskrit). So a holy person is one who obeys the law of “non-harm” (“ahiṃsā”, in Sanskrit), and as the ancient Sanskrit axiom states: “ahiṃsa paramo dharma” (non-violence is the highest moral virtue or law). The ONLY real (Absolute) Truth in the phenomenal manifestation is the impersonal sense of “I am” (“ahaṃ”, in Sanskrit). Everything else is merely transient and unreal (“unreal” for that very reason - because it is ever-mutating, lacking permanence and stability). This sense of quiddity is otherwise called “Infinite Awareness”, “Spirit”, “God”, “The Ground of Being”, “Necessary Existence“, “The Higher Self”, as well as various other epithets, for it is the very essence of one's being. Chapters 06 and 10 deal more fully with this subject matter. Of course, for one who is fully self-realized and enlightened, the subject-object duality has collapsed. Therefore, a fully-awakened individual does not perceive any REAL difference between himself and the external world, and so, sees everything in himself, and himself in everything. If it is true that there are none so blind as those who don’t WANT to see, and none so deaf as those who don’t WANT to hear, then surely, there are none so ignorant as those who don’t WANT to learn the truth. OBVIOUSLY, in the previous paragraph, and in most other references to the word “truth” within this booklet, it is meant “the most accurate concept possible”, or at least “an extremely accurate fact”. For example, as clearly demonstrated in Chapters 21 and 22, it is undoubtedly “true” that a divinely-instituted monarchy is the most beneficial form of national governance, but that is not the Absolute Truth, which is the impersonal, never-changing ground of all being. So, to put it succinctly, all “truths” are relative concepts (even if they are very accurate) but the Universal Self alone is REAL (Absolute) Truth. “In the absence of both the belief 'I am the body' and in the absence of the belief that 'I am not the body', what is left is what we really are. We don't need to define what we really are. We don't need to create a thought to tell us what we are. What we are is what TRUTH is." ************* “God is not something 'out-there', 'looking-in', but God (or Source) has BECOME all of This. So, God is the Underlying Principle of all of this - the Energy or the Consciousness. The (psycho-physical) manifestation has arisen within Consciousness as an imagination in the mind of Source.” Roger Castillo, Australian Spiritual Teacher, 15/07/2015. “I am the TRUTH...” “...and the TRUTH shall set you free”. Lord Jesus Christ, John 14:16 and 8:32.
@@ReverendDr.Thomas Seriously, are you a bot?? A giant wall of unreadable text that's completely irrelevant to the comment thread...I'm not going to read that. It's apparently copypasted from a (I imagine _much_) larger text. If you value your own ideas (and are not a bot) why not take some effort and actually contribute to the conversation?
exactly my thoughts, positive is relative and completely inseparable from negative aspects. How can there be anything positive without negative? both of which are human constructs. For example as a thought experiment you could say death is a negative so lets keep everything that is "alive" and discard everything that is "dead". Well, people, plants, puppies, lemurs, trees are all alive so they can stay, but rocks, mountains, stars, black holes and dead people are all "dead" so let's get rid of those. So you'd end up with people, plants, puppies etc just floating in empty space, which is ridiculous. Death as a thing is jsut a state of matter; it it necessary for things to become or turn into a state of matter of being alive. It's the same thing. We as humans provide the property of positive and negative, so to me there really isn't such a things as Positive or a being that is only positive; it would be impossible to percieve it because it wouldn't have a contrast.
Well said. It was Kant who won the argument of why "existence cannot be a predicate" for the reasons @cvdevol 2 yrs ago cited--but sometimes I wonder... "Existence and nonexistence cannot be properties of a thing, because a thing by definition exists and cannot not exist for it would not be a thing, indeed it would not BE." How persuasive is that, really? If Bernardo Kastrup is right in that experience is what truly is, said experience being qualia of mentation, such that measurable quanta of experience is also mentation, then it makes sense to think of that which is experienced to have the property of existence by virtue of being thought--since mentation is for us what it is. Kant's argument presupposes the veridical experience of 'matter' to be there as phenomena such that it is a mere tautology of sorts to say ofcan existing thing it exists: or not, since if it does not one could not predicate as property anything about it since it is not there. But how could one even do that WITHOUT first giving the thought of the inexistent thing the salient feature of nonexistence as an intrinsic property. Therefore if X exists it, X, must have the property of being actual, i.e., existing.
Does Gödel define this God at all? He’s talking about ‘God’, but there doesn’t seem to be a clear definition of what this God is or if he’s referring to any one god in particular. How can he argue for something that is ill defined? Any ideas?
I am certainly no logician (and am having some trouble with the nesting of possibility and necessity), but I am troubled by at least two things here. 1) I doubt that self-identity is a property any more than existence itself is a property. 2) I understand that metaphysical modality differs from material modality; but there are also epistemological and intensional aspects to the modality as applied in issues like this, and I think Godel would need to explicate that as well. If I say, "Such-and-such MIGHT be necessary, but it might also be merely possible - I just don't know," I apparently acknowledge the possibility of the thing, but it does not follow that it is necessarily possible, nor that I believe it to be necessarily possible.
You don't need logic to see what's really happening with this stupid argument. It's called equivocation or ambiguous use of terms. Forget the logic form (syllogism), it's perfect. However, using terms like "god-like" and assuming premises like "existing is a positive property" and hence not existing is negative, is preposterous.
Axiom 2... If you can't feel pain and its positive as a super hero yet you can't feel the touch of a lover... that is a duality both negative and positive. Surely I'm missing something.
Presumably God's existence is free of the troubles that afflict us. But that doesn't remove the worry. Whether necessary existence limits God's power is a deep and rather puzzling question. Also, if we take 'positive' as meaning something strictly logical, definable without negation, it's not clear that necessary existence is positive; it seems to mean something like 'invulnerable' or 'indestructible' or 'contingent on nothing,' all of which contain negation. So, I think you're right to think that this is a potential trouble spot.
@@PhiloofAlexandria It wouldn't be as much of an issue if it wasn't an axiom that didn't need to be an axiom if it was explicitly true thanks to the other axioms. creates a bit of a logic loop by using it as an independent factor whereas any other positive trait is proven by the other axioms. I would love to see someone tackle the problem without that. I'm open to it, because of definition 3. You could argue that something with suffering is not God. I don't think Christians would like that definition very much, though - they may argue that the ability to withstand suffering is positive and necessary as suffering is innate? that might be another loop actually.
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This has made me question the existence of Gödel.
Godel exists. Proof:
We established that God exists and is good.
Godel entails God (phonetically). By axiom 2, Godel exists and is good.
Been looking forward to this! Thanks!
thank you, daniel. I've been researching this recently and your video cleared up some confusion I was having! cheers, friend.
Glad it was helpful!
Beautiful. Gödel's elegant and simple ontological argument is really underrated. Thank you professor.
You're very welcome!
And yet, it demonstrates how many gods? One, two? OH...EXACTLY ZERO.
@@NeverTalkToCops1 *tips fedora respectfully towards you*
@@NeverTalkToCops1 I don't believe the argument is meant to do so, nor such a Beings particular identity; only necessary attributes and existence. The rest is our homework! ;-)
@@NeverTalkToCops1 No, the argument demonstrates the existence of at least one such entity. At this point, one may simply appeal to Occam's razor which states that one ought not multiply entities beyond necessity.
I love this video. Thank you!
Professor Bonevac, your channel is a lantern in the darkness. A flower growing in a garbage pile. Glad I found it all those years ago, and thank you for making your videos.
Wow, thanks!
@@PhiloofAlexandria Wow, you're very welcome and thanks for the reply! Your classes have been life-changing for me. I consider you one of the great philosophy teachers, and I've listened to many others, including Hubert Dreyfus when he was still alive.
I've been looking for this!
Thank you Dr. For sharing.
Superbly done, especially for those of us without the topology of modern logics in our heads!
Stop speaking smart!!????$$456
Lol I was not disappointed at all. Thank God for Gödel and also for this incredible and easy to follow video!
Beautiful! Beautifully presented, with the passion of the truth seeker and the strength and ease in conveyance of the teacher and academician.
When listening to philosophers, and thinkers in general, one realizes how difficult it is to take nothing for granted,
They like the sound of their own voice too much and say too little.
The outdoor setting is really good
🤯🧠 This is something I'm going to have to watch five times to wrap my head around.
Thank you for this video that sharpens the arguments of Anselm and Descartes using the powerful logic of Godel. I would greatly appreciate if you can comment on Nagarjuna's Tetralemma and whether that is a refutation of the logic of Anselm/Dscartes/Godel.
Great Video, I also like the references to predecessors like Descartes and Leibniz.
The same objection to Anselm's argument applies: Existence and nonexistence cannot be properties of a thing, because a thing by definition exists and cannot not exist (or it would not be a thing, indeed it would not BE).
No it doesn’t. There’s a difference between virtual existence and mental existence Quine On What there Is). Pegasus exists mentally but not virtually. He still exists though. Something has existence if it is a member of a set.
@@tim2muntu954 If we take your definition of property: an essential or distinctive attribute or quality of a thing, then replace the word thing with a definition that includes the necessity for existence then Kant's criticism becomes more clear. "An essential or distinctive attribute or quality of a concept with existence" or "An essential or distinctive attribute or quality of an entity that exists." The problem stems less from assigning existence to things but rather that non-existence would disallow the addition of a property to an object. We can reimagine this conversation with a unicorn. Person A can say they are imagining a unicorn with a red horn while person B says that no unicorns have a red horn. Person A then comes back with a painting of their red horned unicorn to showcase that at least one unicorn has a red horn. Now is where Kant's criticism comes in, person B states (in true surrealism fashion) that what Person A is holding is actually a painting not a unicorn, thus does not have a red horn. Neither Person A nor Person B deny the existence of unicorns (and Person B heavily implies a shift in the burden of proof), but Person B will not accept the addition of an attribute unless it is not a painting. That is to say, Kant expresses that existence is a perquisite for all other attributes to be applied and that attributes that are applied to things seeming to be non-existent are rather applied to the object that carries its existence (The painting of the unicorn or the human mind thinking of god). So the ontological argument would boil down to "The mind can hold the thought of god therefor the mind exists." To specifically look at Gödel's proof most either criticize the axioms by applying David Hilbert's remark about the interchangeability of the primitives' names, where one can replace "positive" and "God-Like" to create an entity that one wishes without changing how the conclusion follows from the axioms, or one points to Jordan Howard Sobel's work showcasing an implication of modal collapse that would not only remove our understanding of free will but also remove any possibility of a "sovereign god," that is to say the being stated in the proof would themselves lack any discernable method of choice (All actions that are taken must have been taken and could have been the only actions taken).
@@25chrishall To be a "thing" is to exist. And to be existing is to be a "thing". The use of the verb "to be" is always an assertion of existence. There is no such thing as a nonexistent thing. Existence is not a property that a thing may or may not possess. It is rather the essence of "thingness".
How do you define a “thing”? Existence proofs are fundamental to mathematics. For example we can prove that there exists infinitely many primes. We can take “infinitely many primes” as the “thing”. It is an intuitive concept that can be grasped and understood from definitions (what constitutes a thing), but its existence is not guaranteed at face value and must be demonstrated from more fundamental (intuitive) principles. So a “thing” does not by definition exists necessarily.
@@faustianfellaheen Can you name a thing that does not exist?
amazing video
Thank you!
I need to watch this a few times over.
Dude was top shelf!
This is an important argument. It leads directly to the question of what is and isn't in the domain of human determinability.
The lack of facts or lack of logical formulation, that this argument brings up, should be directly looked at. In this way new facts or new relations of ideas will be inferred. This realm of inference could then be confronted. In this way light will be shed on the abyss of ignorance. No?
The reasons and evidence, or lack thereof, why we can or can't "explain" God should all have inverse suppositions. We would gain knowledge were we to extrapolate these inverse suppositions to their inverse logical relations wouldn't we?
no
@Josip Ivesic 😂
Hello sir! How are you i watch your videos regularly.Please answer my question a person here is using godels incompleteness theorem on contingency argument.Does it make any sense? plz answer thank you
This ontological argument seems to have the same problems as the other ontological arguments. Namely, it's completely formal and therefore tells us very little about the properties this "god" must have necessarily.
The common objection, which you will find here in the comments, is that the concept of positive is subjective. This objection comes from the fact that the argument is formal and in order to give it any content whatsoever, human ideas of what is good and bad must enter into it, thereby introducing subjectivity.
I have a slightly more original objection, which is that the content of the argument can point in the exact opposite direction because the argument is purely formal, it doesn't dictate what kind of content goes into it. For instance, if we talk about _negative_ properties rather than positive properties, we can arrive at a very startling and worrying conclusion.
Consider things like doing harm, being evil, being hateful. These are negative properties. But in order to do harm, for instance, you must be powerful enough to do harm. Therefore, being powerful is a negative property (our version of Axiom 2). And furthermore existence is a negative property, and necessary existence as well.
Following Godel's argument to its conclusion we find that a being which contains every negative property must necessarily exist, and of course it has these properties to the maximal degree. It is all-powerful so that it can do as much harm as logically possible. I doubt Godel (or any christian) would accept this argument for a god of pure evil.
At either extreme it argues for the existence of both God and Satan. But that leaves people where they began, with unclear questions.
Since people are divorced from the old dialogical methods, and barely aware of the congealing new dialectics, this ontological argument is only helpful for those seeking the strongest arguments for and against faith. And only after significant hours invested in the training of logic, inquisitiveness, and fallacy spotting. But going at it all by oneself is a recipe for self-congratulation and circular reasoning, so it takes two people *at minimum.*
Negative properties don't exist, is what any theologian would respond to your inversion of the ontological argument. Classical and medieval philosophy doesn't view evil as having any properties, but rather as being made of a lack, as being defined as deficiency of properties. Any given thing's existence is considered good, and evil is a disturbance of the order by which something exists. A rotten apple is bad, not because of any specific property of the apple, but rather because the rot takes away from the apple's existence, and deprives it from it's properties of being edible and tasty.
@@rubeng9092
Well, I think that's a pretty bad argument, for a lot of reasons. The main reason is that it goes against our everyday experience of negative things. Pain is not merely the lack of pleasure, bitterness is not merely the lack of sweetness, and so on.
And of course if you want to push the argument that far, I can easily go that far in the opposite direction (positive properties don't exist, they are merely a lack), so I don't really see how it solves anything.
@@APaleDot Isn't it that when we encounter something bad we seek it's remedy? Whereas when we encounter something positive we cherish it for what it is? Pain on it's own isn't bad, many people wake up after day of intense exercise, with muscles feeling quite sore, yet they are content and happy about it, since they know their muscles are growing and their capability is increasing. Whereas someone having a serious injury has to put up with not being able to move without crutches or having his arm not function properly, which objectively entails a decrease in that arm's ability to be an arm - which is bad, because it's a negation, and that's where the word negative get's its meaning.
@@APaleDot Pain and bitterness aren't evil. Pain is a necessary signal for survival, but those who enjoy inflicting it are evil. Bitterness is a taste enjoyed by many.
thanks, this video helped me doing a research about Gödel for school! You explained very well the argument
Thank you for your video.
One thing that comes to mind to me when reading Axiom 5 is the myth of Sibyl, of which you talked about at the beginning of your T.S. Eliot and The Wasteland lecture. Can we say that for old Sibyl, existence is still a positive property?
Good point!
What if a society existed that sacrificed it’s most intellectual person every year? Is intellect itself a negative in that society or is it the society that’s a negative?
@@James-ms2mx Pol Pot got there first.
Essentially, this and Anselm's argument are very precise formulations of the intuitive concept that humanity's conception of God must flow from His will.
Do we need a deeper understanding of reality to have this argument? Positive and negative charge is an innate part of all matter, all objects. A sphere has one perfect surface the same positive curvature everywhere. If the Universe is based on a process of spherical symmetry forming and breaking, then we would be the imperfect broken symmetry. You explained this difficult subject very well!!!
Positive and negative are just names given to charges. They could've been called anything.
Thank you! I’ve been looking for a video explaining Godel’s Ontological Argument for over a year! I’m still not sure I get it, but I’ll watch it a few more times. I just wish you’d also explained the symbols used. But this is a great help!
Check out Plantingas ontological argument
@@LucicPower Are you a THEIST? 🤔
If so, what are the reasons for your BELIEF in God? 🤓
@@ReverendDr.Thomas nobody knows and if you say you do you could be wrong . Lol 😆
why does it have to be a video?
@@crossman3940 nobody knows WHAT? 🤔
Thank you VERY much for making this presentation! I do not understand it very well. Maybe I should take some classes on this, LOL! But I think whatever it is you are talking about would be very helpful for me when it comes to studying the Bible. The Bible is quite a bit of reading and I am really interested to find out if there is some way to evaluate whether or not the Bible is logically consistent. I have read Genesis through Revelation about three times now and am amazed at how few obvious contradictions there are in the whole account (when seen rightly). There are some passages that seem to conflict in the English translations. But I think it is probably due to misunderstandings or poor translations that lead to these apparent contradictions. Hmmm... maybe "God does not contradict Himself" is a positive property??
Is it possible to feed the Bible into a computer in such a way that it could extract from the text all statements indicating "A is true" and then find any statements that indicate "A is not true"? This would be very helpful in finding those trouble spots and get into examining possible meaning or interpretations of the text. And if nothing else, that would be instructive just from a "weight of the evidence" perspective.
Often, when reading the Bible, i find myself asking, "does x mean this or does x mean that?" If x means this, is that logically consistent with the rest of Scripture? If x means that, is that logically consistent with the rest of Scripture?
Try the Yale University Open classes on new and old testaments.
Again, I very much appreciate your explanation of essences. A is an essence of x if and only if it is a property of x and entails the necessary properties of x and only the necessary properties of x. That makes sense.
But when I read Godel's original proof, it seems to say something different. It seems to say A is an essence of x if and only if it is a property of x and entails all the properties of x.
Am I misreading Godel's argument? Or does this reflect a change in Anthony Anderson's revision of the argument? If it is a change, I'd say it is an improvement. I don't see why an essence of x should imply non-necessary properties of x.
So when it is said that "it is possible that necessarily something is godlike" in theorem 3 is that referring back to "necessary existence" as in the positive property of exemplified essences in all possible situations?
What does "better" mean?
I actually enjoyed this presentation. It’s a nice argument, with a clear structure.
As someone interested in mathematics and formal logic, I’m pleasantly surprised to see an argument in the language of modal logic. It was nice to research and find out that this axiomatic system is consistent.
However, it seem to not be applicable in the real world, as this system implies a modal collapse. Also, since “positive” property is not defined constructively, we can not infer any real-world properties of this maximal object, so it might as well be referring to a rabbit in my back yard. Due to the same limitations, we don’t get a strategy to find out which properties are positive, or a way to find or determine if any given object is maximal in this regard.
I used Anderson’s reconstruction to avoid the modal collapse problem. I also agree with Koons that “is self-identical and such that the cat is on the mat” is not a real property.
Or if somethings positive it's real lol 😆
Logic is mans method of identifying the facts of reality without contradiction, not a mystical revelation.
@@TeaParty-qh1py I would suggest that the "facts of reality without contradiction" of which logic can help derive and describe, does not exclude the metaphysical.
thanks!!!!!!!!!!!!!!!!
Wonderful video, thank you! I love the "round square" example at 15:30 that segues into Leibnitz's approach. The explanation of Leibnitz's approach appears to share similarities to showing that a space is complete. If it is, then it is spanned by a linearly independent set of basis (or "properties", in this context) which must be consistent with each other because they are independent (or "primitive", in this context). Properties of all objects in this space must therefore be consistent too.
Thanks for the video!
thanks
This is an engaging puzzle wish I encountered when I had more time to play and learn. Would you or someone please enlighten me on how this proof relates to Godel's other work on the properties of formal systems (like logic) in regard to being complete and/or consistent.
At my level of ignorance, I'm also interested relation between logic and science.
There is no connection between the two.
I would like to add another important notion: if something exists that is maximum, then it must necessarily contain all that exists and not be separate from it, for that implies restriction.
Could you possibly say for that second modal principle mentioned, that it boils down to the belief that every universe shares the same contingent matters of fact, so that they can be discounted when discussing necessity
Fascinating!
It makes me investigate one of God's potential new proof of existence.
I will share once i have more convictions.
Thank you
As a Muslim I loved the ending. The final discussion about "Maximal Nature Of God" translates very nicely to the concept of "Allah-u-Akbar" (God is Greater) in Islam.
The question is not what lens to look through, but what to look at through the lens. I think this is a brilliant lens, the problem is that most people are afraid to point the lens where is needs to be in order to see. A hint: What is the difference between God and God-like?
I can imagine a Flying Spaghetti Monster that created the universe. But it would not be perfect without existing, because existence is a positive property. And nobody is more positive than him! Therefore the Monster exists.
I do exist, I'm positive
Personally, I find Godel's language easier to understand than the rephrasing, but I appreciate the video.
Not sure I completely buy it, but I'm going to save this video to return to the subject
Being positive and negative depends on the system of values we choose.
I wonder how hard the reaction from other members of the Vienna Circle would be should they have been exposed to such a prove by Goedel.
Good video and your positive ability of lecturing. Why don't you make videos on different conceptualizations of God in Islam, Christianity and Judaism?
Arguing from the conclusion.
I'm excited to learn you have a background in mathematics. We are all familiar with the idea of using different axioms concerning accessibility relations for possible worlds models to model different kinds of modality. But have you heard that a better way to do so is to use topology (at least for the case of S4 and beyond)?
Consider the axioms of S4 modal logic. A proposition is possible if and only if it is possible it is possible. If P implies Q, then P is possible implies Q is possible. If P is true, then P is possible. “P or Q” is possible, if and only if either P is possible or Q is possible.
Now consider the closure axioms for a topological space. The closure of the closure of a set equals the closure of the set. If P is a subset of Q, then closure of P is a subset of the closure of Q. P is a subset of the closure of P. The closure of the union of A and B is equal to the union of the closure of A with the closure of B.
The axioms of the possibility operator of modal logic in S4 coincide precisely with the axioms for the closure operator of a topological space! In the same way, the axioms of the necessity operator of modal logic in S4 coincide precisely with the axioms of the interior operator in a topological space! I’m still astonished by this.
So we can model a system of S4 modal logic using a topological space. The points of the topological space represent possible worlds. Propositions are represented by sets of possible world (sets in which the proposition is true). If a proposition P is represented by a set of possible worlds S, then possibly P is represented by the closure of S (it makes sense that the set of worlds in which P is possibly true is a superset of the worlds in which P is true). Necessarily P is represented by the interior of S (it makes sense that the set of worlds in which necessarily P is true is a subset of the set of worlds in which P is true).
A proposition P is represented by an open set if and only if "P is true" implies that "P is necessarily true." A proposition P is represented by a closed set if and only if "possibly P is true" implies that "P is true." For example, since a MGB is defined in part to be a being that exists necessarily, if the proposition "A MGB exists" is true, the proposition "It is necessarily true a MGB exists" is true. So "A MGB exists" is represented by an open set. Furthermore "No MGB exists" is represented by a closed set. If it is possible no MGB exists, then no MGB exists.
What would an S5 topological space be? It would be one where every open set was a closed set, and vice versa. An S5 space could be represented as a discrete union of closed-open set, where any set was closed-open if and only it was a union of a sub-collection of these discrete sets. The interior of a set would be the largest closed-open subset of that set, and the closure of a set would be the smallest closed-open set containing that set.
Above we noted that "A MGB exists" is represented by an open set. Working in S5, the set representing “a MGB exists” must be a closed set as well, so if it is possible a MGB exists then a MGB exists.
Given any topology T on a set, we can take the minimal refinement of T that satisfies the conditions of S5 in the obvious way (show the intersection of any collection of S5 topologies is S5, etc.). Therefore, it would seem given any S4 modal logic, there is in a sense a minimal extension of that logic to an S5 modal logic. Perhaps this is what Richard Swinburne was referring to when he talked about metaphysical necessity being a sort of idealized version of epistemic necessity.
That is really nice. Contemporary philosophers underutilize topological concepts; they're often very illuminating as well as elegant. One of my regrets is that, in my last semester of graduate school, I didn't at least audit a course being offered on topological logic. I feared it would distract me from finishing my dissertation. But it was an opportunity I haven't had since to study the links.
@@PhiloofAlexandria Let’s define a Goldbach number to be an even integer greater than 2 that cannot be written as the sum of two primes. Then the Goldbach conjecture asserts that there is no Goldbach number.
Let us assume, for the sake of argument, that the Goldbach conjecture is undecidable; that it is true there is no Goldbach number, but it is impossible to prove that. In an S4 logic modelling provability, it’s possible a Goldbach number exists (because we cannot prove no such number exists). But in a metaphysical modality, it is impossible a Goldbach number exists (because in reality no such number exists).
Now given any positive integer, it is in principle possible to verify through a finite process that that integer is not a Goldbach number. So in the modality of provability modelled by S4, it is not possible 4 is a Goldbach number, it is not possible 6 is a Goldbach number, it is not possible 8 is a Goldbach number, etc. Yet at the same time it is possible there exists a positive even Goldbach number.
It’s not clear how we would model this situation using possible worlds with a transitive reflexive accessibility relation. There would have to be a world accessible from the actual world in which 4 was not a Goldbach number, 6 was not a Goldbach number, and so on, but there was a Goldbach integer. That’s not helpful.
But we can model this using topology as follows. We assume there exist possible worlds, 4, 6, 8, 10, etc., in which 4 is a Goldbach number in 4, 6 is a Goldbach number in 6, and so on. Since all of these assertions are demonstrably impossible, they are not possible in the actual world. What that means is, topologically speaking, there is an open neighbourhood of the actual world that excludes world 2, another open neighbourhood that excludes world 4, another open neighbourhood that excludes world 6, and so on. Since open sets are closed under finite intersection, there is an open neighbourhood containing the actual world that excludes any given finite set of these worlds. This reflects the fact that given any finite set of positive even integers, we can in principle verify they are not Goldbach numbers in a finite amount of time.
Now however, imagine that the actual world is a limit point of the set {2,4,6,8,. . .}. This reflects the fact that while no particular such world is possible from the perspective of the actual world, the collection of all of these worlds is possible. This reflects the fact that while we can prove any finite subset of the positive even integers contains no Goldbach numbers, we cannot prove the set of all positive even integers does not contain a Goldbach integer.
Now let’s go to the S5-topology generated by this S4 topology. This topology includes all the open and closed sets from the S4-topology. In this topology, open sets are closed sets and vice versa. So in this S5 topology, open sets are now closed under arbitrary intersections. So in this topology, the intersection of the open sets containing the actual world and excluding 2, 4, 6, 8, etc. is an open set. And so it is metaphysically impossible a Goldbach number exists.
As the video demonstrates the power of Godel’s argument hangs on the meaning of modal language.
The only way I can make sense of modal language in the context of metaphysical philosophy is this: There is the actual reality in which we live and which has a particular nature. Given that nature there are many ways reality could have been but isn’t (or in other words many facts of the actual reality are contingent). Let us call the set of all realities that could have been the “set of metaphysically possible worlds”. Then we define that “X is metaphysically possible” iff X obtains in at least one element of the set of metaphysically possible worlds”, and we define that “X is metaphysically necessary” iff X obtains in all elements of the set of metaphysically possible worlds.
But then the expression “X is necessarily possible” (or, to be precise, “it is metaphysically necessary that X is metaphysically possible” turns out to be meaningless, for there are no different kinds of metaphysical possibility. Either X does obtain in some element of the set of metaphysically possible worlds or it doesn’t. If it does then in it is metaphysically possible simpliciter. If it doesn’t then it is not metaphysically possible. Thus to speak of “necessary possibility” as if it were something distinct is to speak nonsense, and to use that non-existing distinction in an argument is to build on thin air.
I suspect that Godel’s error is to uncritically apply modal logic to metaphysical reasoning. In the realm of logic perhaps it makes sense to speak of X being necessarily possible, but that’s irrelevant to the practical business of metaphysical philosophy. After all it is not like one can map the set of all logically possible worlds to the set of all metaphysically possible worlds. So, for example, the set of all logically possible worlds (that is in the set of all internally logically consistent realities) there are some worlds which are theistic and some that aren’t. For example a by definition logically possible world is the empty world in which nothing exists, which is a non theistic world. But it is easy to prove (see Plantinga) that if it is metaphysically possible that theism is true then it it metaphysically necessary that it is true. Or, applying my meaning of modal language, if theism is true in one metaphysically possible world then it is true in all of them. One can see why this is so without actually following Plantinga’s proof: Theism is a claim about the very nature of reality. If the nature of reality is theistic then all ways reality could have been will be theistic also (it’s not like the nature of reality is a contingent fact or that God might remove himself from reality). Incidentally for the same reason Plantinga’s result can be turned on its head: If it is metaphysically possible that theism is false then it it metaphysically necessary that it is false.
I say you did better on this than Scott on the "Theoretical Bullshit" channel.
This is very good, but it depends on how God is defined. If God is defined as the set of all metaphysical possibilities, then it is not possible to remove this from the sets, because all such sets depend on this by definition. As to your point, the reason I agree is that I'd go another step and say that because there is no way to prove that anything can be metaphysically impossible, including even basics like logic itself, any technical talk of such is incoherent. For me, this means the problem reduces to what God is in respect to existence. If there is a truth about this (which there is no reason to be particularly skeptical about that I can see), then the focus must be on finding the true answer to this question, which will, in my view, require some kind of empiricism (including the subjective kind in this special case where existence can only be experienced subjectively in the final analysis.. in other words, this is not a pragmatic empirical issue that can be tested and verified locally).
@@konberner170 The definition of God that everybody accepts is that God is the greatest conceivable thing. This is a clear definition as proven by the fact that even atheists can engage in intelligent and indeed sophisticated theological argumentation.
Now the greatest conceivable being will certainly be prior to everything. That is, God will not need to stand on something else, or conform to something else. Therefore God is what philosophers call the "metaphysical ultimate", the ground on which everything else stands. (Incidentally metaphysical naturalism - which is the worldview of most atheists - also entails a metaphysical ultimate, namely mechanical nature.) But the metaphysical ultimate is the same in all metaphysically possible worlds. Therefore if it is possible that some metaphysical theory (whether theism or naturalism) is true then it is necessarily true.
As for what God is in respect to existence, the answer is pretty straightforward: Existence itself is not prior to God, thus God does not only make what exists (or may exist) but makes existence itself. Theists commonly say that "God exists", but this is a linguistic shortcut which is misleading when understood literally. Strictly speaking "God exists" is an incoherent proposition. Theism's claim is *not* that among the many things that exist God also exists. Theism's claim is rather that existence itself is created by God. As for other existents, both theists and atheists agree with the proposition "apples exist" but mean something different, because atheists and theists understand differently what it is for something to exist. The understand differently what existence itself is. So naturalists believe that the existence of, say, elementary particles and their mechanical nature is implicit and autonomous. Theists believe that their existence is not autonomous but depends on God's will; they are created and remain around as long as God wills it.
@@DianelosGeorgoudis Atheists don't all agree with that. Theists don't all agree with that. And "great" is substantially subjective. Who decides what is greater than something else? Maybe start over?
@@DianelosGeorgoudis
🕉 सर्वं खल्विदं ब्रह्म 🕉
Chandogya Upanishad 3.14
(‘sarvam khalvidam brahma’ teaches that ‘All this is indeed Brahman’.
“Brahman” is a Sanskrit word referring to the TOTALITY of existence.
There is nothing but Eternal Being, Consciousness, Bliss!).
I know next nothing about logic, but am I right in suspecting that Gödel’s proof of God’s existence is essentialist in its metaphysics as opposed to relationalist?
Una explicación muy clara. Saludos desde Perú.
Sorry but my argument is, isn't positive or necessarily positive property a relative matter of fact ? If we got two or more negative numbers lying on different coordinates of the negative side of number line, then would we not get a positive property between the more and less negative numbers? Then how positive property can be compared with all perfectness ? Please answer.
That's the thing. I think they should be relative to zero not to each other. Because we are going to look at the big picture to directly reach the fundamental nature of reality not small inter-negative pictures. Because the moment you look at inter-negative relations you are not treating them as negative anymore but as numbers.
I wish i get it, this guy is sensational!
What a peaceful background!
For all of us that are taken by the beauty of saint Anselm's ontological argument, Gottfried Leibniz' phrase sums it up best: "if God is possible then God is (exists)". Incidentally, the syllogism is correct, pursuant to classical Aristotelian logic.
It reminds me of something I heard recently (I don't remember who said it) about physics. "Anything not prohibited is mandatory." Some people assume that magnetic monopoles and cosmic strings must exist unless there is a still-undiscovered reason they don't exist. It is at odds with Occam's razor and the concept of "burden of proof." This probably explains why they can't agree whether negative energy or sterile neutrinos are real despite some good circumstantial evidence.
The problem with this and many other ontological style arguments is that they treat "existence" as a property. Strictly speaking it isn't, at least not in the way that we typically use it linguistically. If I say that an apple exists, I'm treating "exists" as a property of the apple, and linguistically as a predicate. But technically I've got it backwards when I do that. What I'm _actually_ saying with that statement is "In the reality in which I occupy, there exists an apple." The apple existing is a property of the context (in this case "the reality I occupy") in which it is invoked. In other words, existence isn't a property of the apple, it's a property of the reality in which I occupy. To look at it another way, the concept of an apple isn't changed if I specify that it exists, or that it doesn't exist. It's fundamentally still the same concept. To say an apple exists (in reality) is like saying that an apple is a fruit eaten by man. It's confusing the nature of the relationship between the two. That apples are eaten by man isn't a property of the apple, it's a property of man. An apple would still be an apple, totally absent the concept of eating, or man. The concept of an apple is the same whether you tack on existence, or you don't.
So when we start talking about existence as a perfection, it's just begging the question. As already demonstrated, existence doesn't change the concept of an apple, so it's not coherent to say that the concept is improved by the addition of "existence." If we're not talking about the concept then that just leaves us with discussing an _actual_ (extant) apple, but that's just a tautology. To say that an existent apple that exists is better than an existent apple that doesn't exist, is silly. One option is simply incoherent and self contradictory, and the other is tautological.
Don't get me wrong. I love me some Kurt Gödel, but I think he was a little out of his wheelhouse when making this argument.
If the property 'maximal' or 'perfect' is positive then what requirement decides whether 'maximal good or 'maximal evil is ''God-like'' (if not arbitrarily by definition)?
The very idea of 'positive properties' is totally subjective; there is no way to test a property to see if it is positive or negative, it is open to the interpretation of the speculator. Gödel' should have realized this when he had to revise it to 'some properties are positive'. As an attempted argument for an objective god, this doesn't cut it. Excellent presentation in the video though!
So what is the definition of "positive"? I missed that somewhere.
"first we approximate god as a integer ...."
This question might prove I didn't understand a thing here, but isn't the conclusion that for those who believe in God anyway as well as those who now a accept Goedel's proof, necessarily each person identifies their own god and that it is possible that no two people identify the same god?
Basically it says: Because we exist and it's a positive thing or property, God exists as a positive.
Godel's whole thesis was an exercise as to how Modal Logic ( possibility> necessity) might be applied to Anselm's ontological proof. Here, it's important to understand that ML as such was created during Godel's active years; he seemed to have had a lot of fun with it--much like his famous argument during his citizenship Q&A about contradictions in the Constitution...my dream is to have been a fly on the wall during his conversations with einstein at Princeton... which is to say that theologians shouldn't take his 'proofs' so seriously!
What about the simple kantian objection to the ontological argument? Existence is not a predicate? Does that not undermine the entire argument?
I don’t understand how existence (whether necessary or not) can be declared a positive property. Nothing but human feeling may provoke that assumption, and the only reason that non-existence has negative implications is because the living fear it. But isn’t the one as positive or negative or indeed meaningless as the other?
I don't get it, how can a property ever be positive or negative? I mean, it seems easy to respond if you're a human, but it's not like our reason is necessarily an accurate representation of independent objects, how do we know if something is positive, or going even further, how do we know if something is necessarily positive?
This demonstrates why Hume, Kant, all the way to Popper, have to assassinate induction.
I could never feel the strength of Axiom 5 (Necessary existence is positive / existence is a perfection / existence is an improving quality). There's just nothing compelling me to accept it. Why is existence necessarily "better" than non-existence? Why do so many accept it without any justification as something obvious? Not only do I not find it obvious, it sounds to me like a category mistake. Is there something I don't see?
Note that this isn't the same as Kant's critique, who would deny that existence is a predicate. I'm fine with it being a predicate (at least for the sake of argument). I claim that these are two different predicates that aren't related the way that the axiom states.
It being stronger doesn't mean it's more compelling, it simply means it's a more substantial claim. "All swans are white" is stronger than "Some swans are white".
@@cynicviper You're not wrong, but that doesn't make my choice of words a mistake.
Note that we also call compelling arguments "strong" and we conceptualize arguments as resting on "strong" or "weak" foundations.
"Strong(1) claims require strong(2) evidence". When we say that a self-evident axiom is "strong", do we mean (1) or (2)? Does it even make sense for self-evident axioms to be stronger(1) or weaker?
@@luszczi It absolutely doesn't make you wrong, I apologize if that is how it came across. Without wanting to sound pretentious, I was merely trying to explain what I thought was a misunderstanding.
You are certainly right, and I as well, don't agree with the Axiom. To Gödel, who perhaps cared about logical rigor this whole endeavor matters, but to me, it is still nonsensical to Analytically grant existence to anything.
"Meaningfulness" is the why. An existing thing affects the state of reality; a non-existent thing does not. Being effects things. Non-being does not. Being is therefore greater than non-being.
@@ansaz14 pen > sword sometimes. Sometimes the concept of god is all thats needed to change the world. Since all that needs is a concept to change, then being real doesnt matter
Properties are positive depending on the point of view and the circumstances.
It seems to reduce to saying that we define God as that which is perfect and necessarily exists. That is, so much hot air.
Boltzman's "entropy" implies a complex system dissipating into 'consistent' randomness; Ervin Schrodinger's "negative entropy" 1943 'What is Life?' infers a system tending to randomness re-asserts itself into further complexity that tends towards persistence extracting what it needs from its ambience to accumulate, sustain, recreate and increase its 'essential' complexity. Thus, Godlike consistent randomness as a 'necessary property' per Godel so God's negation is the known Universe. Like the death of Jesus? Help Anselm! Help, Spinoza! Think Spring!
BleSsings To You
So with necessary possibility at the end there, I don't understand the argument against the axiom of "if it is possible that it is necessary, then it is necessary." Based on contingent matters of fact. Couldnt you argue if some property has contingent matters of fact that dispute it's necessary existence, then it is simply a property that isnt necessarily existent?
So for example for the weightlifting, could you not say that, though it was possible for you to lift 300lbs, it was not necessarily so, on the basis of that event not occuring?
What does he mean by necessary properties ?
It is fascinating that Goedel, who committed suicide by starving himself to death, should argue that existence is a positive property. Nonsense can get out of hand, it seems.
He didn't starve himself on purpose, his wife was in hospital and he didn't trust anyone else to cook his meals for him.
The title should go as "Gödel's RECIPE for GOD"🥴
But ofcourse the ingredients were inconsistent. 😅
But how are we determining that it is better to exist than to not exist, surely there’s not much evidence for that. I’m thinking of some eastern philosophy or Schopenhauer or someone saying existence is pain and bad, not necessarily agreeing with that just wondering how to resolve this
Probably believing that existence is better than non-existence is the real leap of faith.
Thank you so very much for your videos. I’m a 65 year old photographer with a love for philosophy because I have a love for God. I’ve always liked the Ontological Argument as a starting point - followed by Contingency and on to cosmological and morals arguments. I’ve been working on an argument from beauty (as an artist) which seems to me to be somewhat like the moral argument but is also a design argument. Anyway, thank you. I greatly enjoyed your presentation and appreciate Godel’s model ontological argument.
Interesting comment. I want to hear more about this design from beauty argument (from artists pov). I'm a lover of the beauty of nature. I always think mountains/forests, fields and oceans untouched by mankind has beauty. Once arrange and rearrange, we make it ugly.
@@SH-bl9wh The new fallen snow is "beautiful"...
unless you are unprepared or unprotected.
In which case you will be dead in a day.
l second that request, that you expand on this idea of beauty if you feel like sharing.
As l child growing up on the edge of a grimy industrial landscape, with factories, coal mines, hundreds of smoke stacks across the horizon, the ugliness overwhelmed me and l would squint and minimise my visual field until l could fixate on something beautiful like a tiny patch of cloud in the sky or reflections in puddle.
These moments literally gave a crushing childhood meaning and uplift, it was the nearest thing to numinous for me.
l detest the axiom "that beauty is truth" however beauty is definitely some kind of harbinger,and reprieve, for sure.
@@SH-bl9wh thank you for your response. I will plan on posting later this week my syllogism from beauty.
@@veronica_._._._ I plan on posting later this week. Both my parents were born and raised in West Virginia so coal mining was very much part of my family. To me, just as darkness is the absence of light, so ugliness is the absence of beauty. In art we know that art/beauty has properties. The same is true with the beauty we find in nature. And, just as art needs an artist - so the beauty we find in nature needs an artist (Psalms 19). Van Gogh used paint and canvas to re-create a Starry Night, but God does it ever night.
Strange argument. For starters, it is based on questionable axioms. It leaves undefined which properties are necessarily positive, other than the property of existence and the property of being God-like, which is also not very clear. If I understand correctly, to be "God-like" is to possess all positive properties? (All necessarily positive properties, not those that are contingent on circumstances). But we don't know what those properties are, other than the property of existence. So if the logic holds and the axioms are in fact valid, we still don't know the nature of this being we call "God"?
Bingo.
If you look into eastern Theosophy, similar conclusions have been reached : the existence of Divinity/ a Divine Being, can be inferred from the existence of it's attributes ( omniscience, omnipotence, etc ) but not fully known, by any part of it's creation : nature, cosmos, humans. Peace
Gödel's ontological proof is just a formalization of a pre-existing ontological argument. He just "translated" to the mathematical language - using modal first-order logic - the argument, with no merit of the validity of the axioms of whether the conclusion really means the existence of God. I think Gödel himself didn't intend to "prove God's existence".
H8rz b h8tn'.
My thought exactly - Descartes, but in mathematical formulars.
How we can define a "positive" property? Why is better to be powerful instead weak?
We do not know if there is necessary existence outside mere arbitrarily defined terms of a language
Existence is not a property of the subject. It is a property of the concept. "My spaceship" is not a thing that exists, but it's not the spaceship that has this negated property, because, well, it doesn't exist. Instead, the concept "my spaceship" has a negation of a reifying property. Can't believe how much people trip on this simple language pitfall.
Since in a perfect Universe you would have a spacecraft, you must have a spacecraft!
Makes me wonder if both good and omnipotence are positive properties. One can’t be because if both were, then there would be no problem of evil right?
Omnipotence is a matter of ability, I think, not of what one actually does.
If one is Omnipotent, then one is capable of doing good (as well as everything else). If one is Good, then one intends to do good. If one intends to good and one is capable of doing good, then one does good. The only thing left is: Is it good to eliminate evil?
@@bimsherwood7006 Ultimately.
@@bimsherwood7006 A better question, though, is whether or not it's good to allow evil in the first place.
I don't know if it's true and the source is questionable but funny but I like Norm Macdonald's thought on this matter. He thinks if God made everything good he would simply be expanding himself. He wants a family therefore he had to make not good who now in a cool turn of events has the capability to do good and join in him
What if being god like involves killing or destruction? Does this mean that killing and destruction are positive and necessary properties? And these oppose being as a necessary property?
Bertrand Russell killed the ontological argument by remarking that only conclusions are necessary, not objects.
Oooo, this is good. I need to read BR again!
The best argument is the current argument , Plantinga's Warrant
Besides, {cf. Carlos D. here} , a negation of a positive, whether a polar or nullar negative, may be positive just as often \\
I did not know that Godel presented a variant on the ontological argument. However his incompleteness theorem has radical implications for the philosophy and foundations of rational or formal symbolic systems of thought. One of these implications is that no system that has the power to include self referential statements or outputs that describe the system itself, can be proven to be both consistent and complete. What this means is that any attempt to construct a rational system will not be able to be entirely a closed system where strange and paradoxical statements and possibilities can be expunged and excluded from the system. It means that whether we like it or not we live in a radically and inescapably mysterious, paradoxical and open reality and cosmos. Where all kinds of transcendent possibilities that are super rational may not only, but may in fact have to, exist. Even though this is not a positive proof of God, it is a negative proof against any arguments that deny that such a reality and being, that escapes being fully defined within a rational order and system, can't exist. In essence reason has debunked its own pretentions to ever being able to offer a full and complete, self contained and sufficient, description of all the manifold aspects of reality. This makes rationally inexplicable intuitive leaps of faith inescapable and inevitable for the fullness of human knowledge to be revealed, discovered, made known and manifest. And yes it is a rather strange spooky synchronistic coincidence that Godel has the word God in his name! Almost like God has a weird mischievous sense of humor! Oh by the way he does, but the jokes can be quite deep and subtle. For example the very ability to ask the question is God real, actually itself suggests that more than mere animal existence is required to understand human existence. Of course there are many people who will hate such a conclusion but so what the joke of them pulling the wool over their own eyes and not knowing it, is always going to be on them, isn't it? As it stares them in the face and they never see it, and passes completely over their supposedly intellectually superior heads.
Could you conceptualize necessity as being exemplified in all possible worlds, and possibility as being exemplified in at least one possible world?
Are we therefore forced to assume that all logically possible worlds in some way exist, for this formulation to work?
Positive is just a defined term. A matter of opinion not a fact.
I think a bit more work is needed for an objective definition of “positive”. The definition here is very dependent on things we value as a species, like being alive vs. being dead, or “it’s preferable to be God than to not be God”. Of course a living species would value living over not, but this is an ontological argument so it needs to be ontologically positive. “Positive” needs to be something defined by its presence, & negated by its absence, like heat or strength vs. cold or weakness.
Knowledge should be positive, not because we prefer to have it than to not have it, but because it is something that can be had, while ignorance is merely the lack of having knowledge. The thing is, we may conceive of a possible world where the creatures evolved to prefer ignorance to knowledge, but there should be no possible world where ignorance is ontologically “positive” even if it is valued or preferred.
Those are similar to my thoughts...it seems those dependencies without adequate definitions indicate assumptions aka implied yet unacknowledged axioms.
🐟 03. CONCEPTS Vs THE TRUTH:
The term “TRUTH” is a grossly misused word.
Anything which has ever been written or spoken, by even the greatest sage or Avatar (incarnation of Divinity), including every single postulation within this Holy Scripture, is merely a CONCEPT and not “The Truth”, as defined further down.
A concept is either accurate or inaccurate. Virtually all concepts are inaccurate to a degree. However, some concepts are far more accurate than others. A belief is an unhealthy and somewhat problematic relationship one has with a certain concept, due to misapprehension of life as it is, objectively-speaking. Attachment to beliefs, particularly in the presumption of individual free-will, is the cause of psychological suffering.
For example, the personal conception of the Ultimate Reality (God or The Goddess) is inaccurate to a large extent (see Chapter 07). The concept of Ultimate Reality being singular (“All is One”) is far more accurate. The transcendence of BOTH the above concepts (non-duality) is excruciatingly accurate. However, none of these concepts is “The Truth” as such, since all ideas are relative, whilst The Truth is absolute.
It is VITALLY important to distinguish between relative truth and Absolute Truth. Relative truth is temporal, mutable, subjective, dependent, immanent, differentiated, conditioned, finite, complex, reducible, imperfect, and contingent, whilst Absolute Truth is eternal, immutable, objective, independent, transcendent, undifferentiated, unconditional, infinite, non-dual (i.e. simple), irreducible, perfect, and non-contingent.
Absolute Truth is the ground of all being (“Brahman”, in Sanskrit), and is prior to any mind, matter, name, form, intent, thought, word, or deed.
Good and bad are RELATIVE - what may be good or bad can vary according to temporal circumstances and according to personal preferences. For example, there is absolutely no doubt that citrus fruits are a good source of nutrients for human beings. However, it may be bad to consume such beneficial foods when one is experiencing certain illnesses, such as chronic dysentery. 'One man's food is another man's poison.'
Because of the relative nature of goodness, anything which is considered to be good must also be bad to a certain degree, since the extent of goodness is determined by the purpose of the object in question. As demonstrated, citrus fruits can be either good or bad, depending on its use. Is drinking arsenic good or bad? Well, if one wishes to remain alive, it is obviously bad, but for one who wishes to die, it is obviously good.
However, beyond the dichotomy of good and bad, is the Eternal Truth, which transcends mundane relativism. Therefore, the goal of life is to rise above the subjective “good” and “bad”, and abide in the transcendental sphere. A qualified spiritual preceptor is able to guide one in the intricacies of such transcendence. Such a person, who has transcended mundane relative truth, is said to be an ENLIGHTENED soul.
When making moral judgments, it is more appropriate to use the terms “holy/evil” or “righteous/unrighteous”, rather than “good/bad” or “right/wrong”. As the Bard of Avon so rightly declared in the script for one of his plays, there is nothing which is intrinsically either good or bad but “thinking makes it so”. At the time of writing (early twenty-first century), especially in the Anglosphere, most persons seem to use the dichotomy of “good/evil” rather than “good/bad” and “holy/evil”, most probably because they consider that “holiness” is exclusively a religious term. However, the terms “holy” and “righteous” are fundamentally synonymous, for they refer to a person or an act which is fully in accordance with pure, holy, and righteous principles (“dharma”, in Sanskrit). So a holy person is one who obeys the law of “non-harm” (“ahiṃsā”, in Sanskrit), and as the ancient Sanskrit axiom states: “ahiṃsa paramo dharma” (non-violence is the highest moral virtue or law).
The ONLY real (Absolute) Truth in the phenomenal manifestation is the impersonal sense of “I am” (“ahaṃ”, in Sanskrit).
Everything else is merely transient and unreal (“unreal” for that very reason - because it is ever-mutating, lacking permanence and stability).
This sense of quiddity is otherwise called “Infinite Awareness”, “Spirit”, “God”, “The Ground of Being”, “Necessary Existence“, “The Higher Self”, as well as various other epithets, for it is the very essence of one's being. Chapters 06 and 10 deal more fully with this subject matter.
Of course, for one who is fully self-realized and enlightened, the subject-object duality has collapsed. Therefore, a fully-awakened individual does not perceive any REAL difference between himself and the external world, and so, sees everything in himself, and himself in everything.
If it is true that there are none so blind as those who don’t WANT to see, and none so deaf as those who don’t WANT to hear, then surely, there are none so ignorant as those who don’t WANT to learn the truth.
OBVIOUSLY, in the previous paragraph, and in most other references to the word “truth” within this booklet, it is meant “the most accurate concept possible”, or at least “an extremely accurate fact”.
For example, as clearly demonstrated in Chapters 21 and 22, it is undoubtedly “true” that a divinely-instituted monarchy is the most beneficial form of national governance, but that is not the Absolute Truth, which is the impersonal, never-changing ground of all being.
So, to put it succinctly, all “truths” are relative concepts (even if they are very accurate) but the Universal Self alone is REAL (Absolute) Truth.
“In the absence of both the belief 'I am the body' and in the absence of the belief that 'I am not the body', what is left is what we really are.
We don't need to define what we really are. We don't need to create a thought to tell us what we are. What we are is what TRUTH is."
*************
“God is not something 'out-there', 'looking-in', but God (or Source) has BECOME all of This.
So, God is the Underlying Principle of all of this - the Energy or the Consciousness.
The (psycho-physical) manifestation has arisen within Consciousness as an imagination in the mind of Source.”
Roger Castillo,
Australian Spiritual Teacher, 15/07/2015.
“I am the TRUTH...” “...and the TRUTH shall set you free”.
Lord Jesus Christ,
John 14:16 and 8:32.
@@ReverendDr.Thomas Seriously, are you a bot?? A giant wall of unreadable text that's completely irrelevant to the comment thread...I'm not going to read that. It's apparently copypasted from a (I imagine _much_) larger text.
If you value your own ideas (and are not a bot) why not take some effort and actually contribute to the conversation?
@@j3ffn4v4rr0 Kindly repeat that in ENGLISH, Miss.☝️
exactly my thoughts, positive is relative and completely inseparable from negative aspects. How can there be anything positive without negative? both of which are human constructs. For example as a thought experiment you could say death is a negative so lets keep everything that is "alive" and discard everything that is "dead". Well, people, plants, puppies, lemurs, trees are all alive so they can stay, but rocks, mountains, stars, black holes and dead people are all "dead" so let's get rid of those. So you'd end up with people, plants, puppies etc just floating in empty space, which is ridiculous. Death as a thing is jsut a state of matter; it it necessary for things to become or turn into a state of matter of being alive. It's the same thing. We as humans provide the property of positive and negative, so to me there really isn't such a things as Positive or a being that is only positive; it would be impossible to percieve it because it wouldn't have a contrast.
Daniel Bonevac, can there be no positive properties?
Well said. It was Kant who won the argument of why "existence cannot be a predicate" for the reasons @cvdevol 2 yrs ago cited--but sometimes I wonder...
"Existence and nonexistence cannot be properties of a thing, because a thing by definition exists and cannot not exist for it would not be a thing, indeed it would not BE."
How persuasive is that, really?
If Bernardo Kastrup is right in that experience is what truly is, said experience being qualia of mentation, such that measurable quanta of experience is also mentation, then it makes sense to think of that which is experienced to have the property of existence by virtue of being thought--since mentation is for us what it is.
Kant's argument presupposes the veridical experience of 'matter' to be there as phenomena such that it is a mere tautology of sorts to say ofcan existing thing it exists: or not, since if it does not one could not predicate as property anything about it since it is not there.
But how could one even do that WITHOUT first giving the thought of the inexistent thing the salient feature of nonexistence as an intrinsic property. Therefore if X exists it, X, must have the property of being actual, i.e., existing.
It is a Kataphatic (Cataphatic) reasoning.
Does Gödel define this God at all? He’s talking about ‘God’, but there doesn’t seem to be a clear definition of what this God is or if he’s referring to any one god in particular. How can he argue for something that is ill defined? Any ideas?
I am certainly no logician (and am having some trouble with the nesting of possibility and necessity), but I am troubled by at least two things here. 1) I doubt that self-identity is a property any more than existence itself is a property. 2) I understand that metaphysical modality differs from material modality; but there are also epistemological and intensional aspects to the modality as applied in issues like this, and I think Godel would need to explicate that as well. If I say, "Such-and-such MIGHT be necessary, but it might also be merely possible - I just don't know," I apparently acknowledge the possibility of the thing, but it does not follow that it is necessarily possible, nor that I believe it to be necessarily possible.
You don't need logic to see what's really happening with this stupid argument.
It's called equivocation or ambiguous use of terms.
Forget the logic form (syllogism), it's perfect. However, using terms like "god-like" and assuming premises like "existing is a positive property" and hence not existing is negative, is preposterous.
Axiom 2... If you can't feel pain and its positive as a super hero yet you can't feel the touch of a lover... that is a duality both negative and positive.
Surely I'm missing something.
as someone who has been suicidal, necessary existence being positive is a deal-breaker.
Presumably God's existence is free of the troubles that afflict us. But that doesn't remove the worry. Whether necessary existence limits God's power is a deep and rather puzzling question. Also, if we take 'positive' as meaning something strictly logical, definable without negation, it's not clear that necessary existence is positive; it seems to mean something like 'invulnerable' or 'indestructible' or 'contingent on nothing,' all of which contain negation. So, I think you're right to think that this is a potential trouble spot.
@@PhiloofAlexandria It wouldn't be as much of an issue if it wasn't an axiom that didn't need to be an axiom if it was explicitly true thanks to the other axioms. creates a bit of a logic loop by using it as an independent factor whereas any other positive trait is proven by the other axioms. I would love to see someone tackle the problem without that. I'm open to it, because of definition 3. You could argue that something with suffering is not God. I don't think Christians would like that definition very much, though - they may argue that the ability to withstand suffering is positive and necessary as suffering is innate? that might be another loop actually.