Gödel's Ontological Proof(en.wikipedia.org)
en.wikipedia.org
Gödel's Ontological Proof
https://en.wikipedia.org/wiki/Gödel%27s_ontological_proof
130 comments
> unlike Russell's papers, where — as you may know — large segments are embargoed
That's surprising. I wonder what was embargoed from Russell's papers.
That's surprising. I wonder what was embargoed from Russell's papers.
From a quick skimming online, it sounds like there's a policy to embargo private correspondence until all involved haven't been around for at least 5 years.
In this case, it seems that Russell took a much younger woman as his third wife: [Patricia Russell, Countess Russell](https://en.wikipedia.org/wiki/Patricia_Russell,_Countess_Rus...). Wikipedia lists her as passing in 2004, so presumably there was an embargo on their correspondence until 2009.
In this case, it seems that Russell took a much younger woman as his third wife: [Patricia Russell, Countess Russell](https://en.wikipedia.org/wiki/Patricia_Russell,_Countess_Rus...). Wikipedia lists her as passing in 2004, so presumably there was an embargo on their correspondence until 2009.
It's really is quite strange that scholars would hesitate to show this, I don't know of many examples of similar behaviour around other subjects.
Fun fact: the proof is formalised in TPTP (a standard benchmark library for automated theorem provers). It is considered of average difficulty.
http://www.tptp.org/cgi-bin/SeeTPTP?Category=Problems&Domain...
http://www.tptp.org/cgi-bin/SeeTPTP?Category=Problems&Domain...
Is it related to the GoedelGod project (which was an open source project on attempting to formalize Godel's Ontological Proof, was in GSoC 2017)?
https://github.com/FormalTheology/GoedelGod
https://github.com/FormalTheology/GoedelGod
I believe not. This was the citation given in the problem: https://arxiv.org/abs/1308.4526
Silly me, we're talking about the same thing :p
A lot of comments here are making counter-arguments by showing that some other improbable entity would exist by the same logic. This is fine, but be aware that Gödel was just formalizing a 1000 year old argument, and the first counter-argument using this form is also 1000 years old: https://en.wikipedia.org/wiki/Ontological_argument#Gaunilo
The argument basically comes down to if you can define something into existence. If the definition of X implies that X exists...then X must exist?
The argument basically comes down to if you can define something into existence. If the definition of X implies that X exists...then X must exist?
Also, it looks like those who don't understand Kant are doomed to reinvent him haphazardly.
Is that such a bad thing? It's like a framework: if it's not necessary to download a thousand pages of Kant in order to arrive at the correct conclusion, is it really all that important to get the rigorous version instead?
It would however save many people a lot of time if they understood that logical reasoning cannot tell you facts about the world with are not already implied by the premises or definitions chosen.
You cannot prove the existence of gravity or the platypus purely by logic. Neither can you prove the existence of "God", unless you define "God" in such a vague way that it doesn't tell you anything about reality.
You cannot prove the existence of gravity or the platypus purely by logic. Neither can you prove the existence of "God", unless you define "God" in such a vague way that it doesn't tell you anything about reality.
[deleted]
Succinct form:
“God, by definition, is that for which no greater can be conceived. God exists in the understanding. If God exists in the understanding, we could imagine Him to be greater by existing in reality. Therefore, God must exist.”
I’m having a hard time following the “modal” logic. I’d appreciate if someone could please expand on it.
“God, by definition, is that for which no greater can be conceived. God exists in the understanding. If God exists in the understanding, we could imagine Him to be greater by existing in reality. Therefore, God must exist.”
I’m having a hard time following the “modal” logic. I’d appreciate if someone could please expand on it.
Let's separate it up, with this argument, people often do follow the logic, but do not accept the premises.
Premise 1: God is defined as the greatest thing that we can possibly concieve ("that for which no greater can be conceived")
Premise 2: real things are better than imaginary things
We can imagine God (he exists in understanding). A real God is better than an imaginary God (2).
Then, if God does not exist, we can concieve a greater thing (a real God) this leads to a contradiction with respect to (1). Therefore by proof of contradiction, God must exist
Premise 1: God is defined as the greatest thing that we can possibly concieve ("that for which no greater can be conceived")
Premise 2: real things are better than imaginary things
We can imagine God (he exists in understanding). A real God is better than an imaginary God (2).
Then, if God does not exist, we can concieve a greater thing (a real God) this leads to a contradiction with respect to (1). Therefore by proof of contradiction, God must exist
Premise 1: Pennywise The Dancing Clown is defined as the scariest clown that could possibly exist ("that for which no greater horror can be conceived" EDIT: "that clown for which no more horrifying clown could be conceived").
("Pennywise the Dancing Clown" is usually defined as "the clown from It". I'm repurposing the name for the sake of this argument. We need a name for "scariest possible clown"; I'm choosing "Pennywise".)
Premise 2: real things are scarier than imaginary things.
We can imagine Pennywise The Dancing Clown (he exists in understanding---you're welcome). A real Pennywise is scarier than an imaginary Pennywise (2).
Then, if Pennywise The Dancing Clown does not exist, we can conceive a scarier clown (a real Pennywise). This leads to a contradiction with respect to (1). Therefore by proof of contradiction, Pennywise the Dancing Clown must exist.
Where's the flaw in this argument? Does the same flaw apply in the theological argument?
("Pennywise the Dancing Clown" is usually defined as "the clown from It". I'm repurposing the name for the sake of this argument. We need a name for "scariest possible clown"; I'm choosing "Pennywise".)
Premise 2: real things are scarier than imaginary things.
We can imagine Pennywise The Dancing Clown (he exists in understanding---you're welcome). A real Pennywise is scarier than an imaginary Pennywise (2).
Then, if Pennywise The Dancing Clown does not exist, we can conceive a scarier clown (a real Pennywise). This leads to a contradiction with respect to (1). Therefore by proof of contradiction, Pennywise the Dancing Clown must exist.
Where's the flaw in this argument? Does the same flaw apply in the theological argument?
Some variety of this is in fact the classical reply to Anselm's version of the ontological argument. A contemporary of Anselm's, Gaunilo, published a satirical proof that a maximally excellent lost island must exist: https://en.wikipedia.org/wiki/Gaunilo_of_Marmoutiers#The_%22...
This is the same as Anselm's argument. If the Lord of Hosts is not scarier to you than Pennywise, you have not thought very hard about the implications of an omnipotent, omniscient being. He isn't going to spook you like a movie clown; no, He is far more existentially terrifying, as befits Someone beyond Whom no greater horror can be conceived. And, after all, "The fear of the Lord is the beginning of wisdom."
The more common formulation of your counterargument is something like imagining the most perfect possible ice cream sandwich, to which I would also say, is God not better than any ice cream sandwich? Are the splendors of heaven not far beyond any earthly dessert?
The more common formulation of your counterargument is something like imagining the most perfect possible ice cream sandwich, to which I would also say, is God not better than any ice cream sandwich? Are the splendors of heaven not far beyond any earthly dessert?
> If the Lord of Hosts is not scarier to you than Pennywise, [...]
I don't mean to define Pennywise as the scariest possible being. I mean to define Pennywise as the scariest possible clown. The Lord is, I imagine you will agree, not literally a clown.
I don't mean to define Pennywise as the scariest possible being. I mean to define Pennywise as the scariest possible clown. The Lord is, I imagine you will agree, not literally a clown.
Doesn't the fact that He's not a clown make it particularly unnerving that He's in fact the scariest possible clown?
Or, in what sense is God not a clown when He created not only every clown but the entire concept of clowning?
Or, being a little more serious, that constraint isn't compatible with the problem Anselm stated. There's no reason for the scariest possible clown to exist: there's no reason that, of the clowns both real and imaginary, the scariest real one should be scarier than the scariest imaginary one. (I think we could argue quite convincingly that, say, Pennywise has scared more people than any real clown.) So the argument "A clown is scarier if it exists" isn't obviously true.
Or put yet another way, the greatest possible mortal (existent or not) is obviously not immortal, but you could plausibly argue that the greatest possible being is.
If you want to maximize on one axis the most superlative being, though, you can probably get to God. I suspect Anselm's conception of God is the ultimate realization of any axis of comparison we can think of: the supreme delight, the supreme fear, the most resplendent, the most hidden, etc. And in particular I think Anselm's axis of greatness is much more defensible, that is, "A being is greater if it exists" sounds much more like a reasonable assumption (even if I'm not sure I accept it) than "A being is scarier if it exists."
Or, in what sense is God not a clown when He created not only every clown but the entire concept of clowning?
Or, being a little more serious, that constraint isn't compatible with the problem Anselm stated. There's no reason for the scariest possible clown to exist: there's no reason that, of the clowns both real and imaginary, the scariest real one should be scarier than the scariest imaginary one. (I think we could argue quite convincingly that, say, Pennywise has scared more people than any real clown.) So the argument "A clown is scarier if it exists" isn't obviously true.
Or put yet another way, the greatest possible mortal (existent or not) is obviously not immortal, but you could plausibly argue that the greatest possible being is.
If you want to maximize on one axis the most superlative being, though, you can probably get to God. I suspect Anselm's conception of God is the ultimate realization of any axis of comparison we can think of: the supreme delight, the supreme fear, the most resplendent, the most hidden, etc. And in particular I think Anselm's axis of greatness is much more defensible, that is, "A being is greater if it exists" sounds much more like a reasonable assumption (even if I'm not sure I accept it) than "A being is scarier if it exists."
>the implications of an omnipotent, omniscient being
There is nothing in the premise or conclusion about omnipotent or omniscient. Just "most powerful". If there is nothing which is omnipotent then the most powerful being is not omnipotent.
said another way: while I can (sort of) imagine omnipotentence, it does not follow that there is an omnipotent being in the same way. That is to say, there is necessarily a most powerful object in existence but there is not necessarily an omnipotent object in existence.
Indeed we can infer no attributes of this most powerful object except its power: we may just be talking about the largest black hole or something.
There is nothing in the premise or conclusion about omnipotent or omniscient. Just "most powerful". If there is nothing which is omnipotent then the most powerful being is not omnipotent.
said another way: while I can (sort of) imagine omnipotentence, it does not follow that there is an omnipotent being in the same way. That is to say, there is necessarily a most powerful object in existence but there is not necessarily an omnipotent object in existence.
Indeed we can infer no attributes of this most powerful object except its power: we may just be talking about the largest black hole or something.
Anselm's argument was about "greater," not "more powerful." Specifically, was about the existence of "a being than which nothing greater can be conceived." Since you just conceived of a potential being with omnipotence, it follows that Anselm's being must have omnipotence, at least if we assume having omnipotence is greater than not having it.
More practically, Anselm was thinking within the Christian tradition, which also attributes omniscience, omnipotence, and fearworthiness to God. Had Anselm understood his argument to refer to a "greater" entity that potentially lacked these characteristics, he would not have called that being "God." I do generally agree that the argument is not particularly useful because it doesn't describe interesting properties of God and God's relationship with / desires for humanity, but at least for understanding the argument as Anselm understood it, we can fairly easily conclude that Anselm saw nothing in the being of the argument that was inconsistent with the God of his religion.
More practically, Anselm was thinking within the Christian tradition, which also attributes omniscience, omnipotence, and fearworthiness to God. Had Anselm understood his argument to refer to a "greater" entity that potentially lacked these characteristics, he would not have called that being "God." I do generally agree that the argument is not particularly useful because it doesn't describe interesting properties of God and God's relationship with / desires for humanity, but at least for understanding the argument as Anselm understood it, we can fairly easily conclude that Anselm saw nothing in the being of the argument that was inconsistent with the God of his religion.
Very true, Anselm refers to greater, not more powerful. And is describing God entirely in the Christian tradition. But another problem is, the conclusion does not follow from the premises.
1) Imagine/conceive of the greatest possible thing. (This premise is more than true, it's a directive.) 2) Real things are greater than imaginary things. (This premise is un-controversially true.)
So we can imagine an extraordinary being omnipotent and great. And we must imagine him existing because if we imagine he does not exist, we're imagining something less great.
The problem is, in his own premise, _any_ existing being is greater than _any_ imagined being. So it's very true that a real God is greater than an imagined God. But, from premise 2, so is any physical real thing including the most humble being.
At the risk of wandering outside of my expertise, I would think this would not bother the faithful either way since I understand faith is central to the religion. I'm guessing that Anselm's argument is a "nice to have" but if it fails it does not disturb anyone. And incidentally, I hope I have not said anything offensive.
1) Imagine/conceive of the greatest possible thing. (This premise is more than true, it's a directive.) 2) Real things are greater than imaginary things. (This premise is un-controversially true.)
So we can imagine an extraordinary being omnipotent and great. And we must imagine him existing because if we imagine he does not exist, we're imagining something less great.
The problem is, in his own premise, _any_ existing being is greater than _any_ imagined being. So it's very true that a real God is greater than an imagined God. But, from premise 2, so is any physical real thing including the most humble being.
At the risk of wandering outside of my expertise, I would think this would not bother the faithful either way since I understand faith is central to the religion. I'm guessing that Anselm's argument is a "nice to have" but if it fails it does not disturb anyone. And incidentally, I hope I have not said anything offensive.
> But, from premise 2, so is any physical real thing including the most humble being.
This doesn't invalidate the argument. A real person is certainly better than his imaginations of what God might be. But the real God is still greater than even that.
This doesn't invalidate the argument. A real person is certainly better than his imaginations of what God might be. But the real God is still greater than even that.
> Where's the flaw in this argument? Does the same flaw apply in the theological argument?
You've matched the argument pretty well and I think it does serve as a useful analogy
> Therefore by proof of contradiction, Pennywise the Dancing Clown must exist.
I see no problem with this: We know that Pennywise exists. We don't know much else about Pennywise, but we do know that if we are postulating a candidate for Pennywise it must be a clown that is postulated as existing.
To see this, examine this rephrasing that more closely matches the original:
> A Pennywise understood as real is scarier than a Pennywise understood as imaginary (2).
Thus, if you grant the truth of "Pennywise The Dancing Clown is that clown for which no more horrifying clown could be conceived", you cannot be a Pennywise atheist. If you use the term "Pennywise" to refer to something that you believe doesn't exist, you are deliberately misusing the term.
Note, that even this definition does not preclude the existence of a "Super Pennywise is the scariest clown that could ever exist" which has as potential candidates all the potentially real clowns whose true horror cannot be conceived.
You've matched the argument pretty well and I think it does serve as a useful analogy
> Therefore by proof of contradiction, Pennywise the Dancing Clown must exist.
I see no problem with this: We know that Pennywise exists. We don't know much else about Pennywise, but we do know that if we are postulating a candidate for Pennywise it must be a clown that is postulated as existing.
To see this, examine this rephrasing that more closely matches the original:
> A Pennywise understood as real is scarier than a Pennywise understood as imaginary (2).
Thus, if you grant the truth of "Pennywise The Dancing Clown is that clown for which no more horrifying clown could be conceived", you cannot be a Pennywise atheist. If you use the term "Pennywise" to refer to something that you believe doesn't exist, you are deliberately misusing the term.
Note, that even this definition does not preclude the existence of a "Super Pennywise is the scariest clown that could ever exist" which has as potential candidates all the potentially real clowns whose true horror cannot be conceived.
Premise 1 is false. A clown is not "that for which no greater horror can be conceived". In order to be so, he would have to be omnipotent (less powerful = less scary), eternal (able to induce constant horror), necessarily self-existing (can't be killed), etc -- in short, God.
This is actually proof for God and the doctrine of Hell.
This is actually proof for God and the doctrine of Hell.
> A clown is not "that for which no greater horror can be conceived"
I don't know, some people are really scared of clowns.
Also as a reminder, your "proof" is something made up throughout history along with thousands of other denominations of thousands of other religions of thousands of other gods people have conceived through thousands of years. I can imagine many great things and it doesn't mean it exists, that's where this "proof" fails. Calling this "proof" is, if not a lie, but a big detriment to the notion of proofs already tested and held dear.
As an addendum, if you follow your logic then you're still left with the old 'who created God' argument because although you might imagine some great entity, any entity that god can imagine should surely be greater than the god you imagine so their god must be true. You still have the infinite egress problem diluting your "proof".
I don't know, some people are really scared of clowns.
Also as a reminder, your "proof" is something made up throughout history along with thousands of other denominations of thousands of other religions of thousands of other gods people have conceived through thousands of years. I can imagine many great things and it doesn't mean it exists, that's where this "proof" fails. Calling this "proof" is, if not a lie, but a big detriment to the notion of proofs already tested and held dear.
As an addendum, if you follow your logic then you're still left with the old 'who created God' argument because although you might imagine some great entity, any entity that god can imagine should surely be greater than the god you imagine so their god must be true. You still have the infinite egress problem diluting your "proof".
> Where's the flaw in this argument? Does the same flaw apply in the theological argument?
The only thing scarier than the scariest clown that could possibly exist anywhere, is that clown right here and now.
Therefore Pennywise is under your desk right now. But if you check, I'm guessing you'll find he's not. Disproved by contradiction!
Edit: Wait, unless clowns are scarier when they're invisible... :S
The only thing scarier than the scariest clown that could possibly exist anywhere, is that clown right here and now.
Therefore Pennywise is under your desk right now. But if you check, I'm guessing you'll find he's not. Disproved by contradiction!
Edit: Wait, unless clowns are scarier when they're invisible... :S
The argument leaves unspecified where "Pennywise the Dancing Clown" must exist, or in what form, or in what places. Even though we say that it is real, it may not exist in any form that we recognize.
This is as much an argument for a Lovecraftian reality as the original argument is for God.
This is as much an argument for a Lovecraftian reality as the original argument is for God.
I don't understand the problem here. There is a scariest clown and you chose to name him Pennywise.
There is something that is greater than everything else, and you chose to call it "God."
Great. What else can be said about this "God?"
Great. What else can be said about this "God?"
The problem is that anything which would make this scary clown scarier would necessarily be true. So if having claws and being able to fly would make this scary clown scarier, then a flying clown with claws would necessarily exist. At least if you follow the logic of the ontological argument.
How does defining God a certain way lead to the idea that God must exist? That doesn't work for any other definitions. A lot is being packed into the words "greatest" and "better".
Premise 1: I define "Foo" to refer to the "blorgest" possible thing: a real situation where I'm the richest person alive.
Premise 2: A real "Foo" would be even "blorger" than a hypothetical "Foo".
We can imagine a hypothetical Foo, but a real Foo is blorger than an imaginary Foo, so if you accept the existence of hypothetical Foos, you also accept the even blorger real Foo. QED I'm the richest person alive.
The ability to conceive of something more extreme in some quality than what exists in reality can't obligate reality to change at all.
Premise 1: I define "Foo" to refer to the "blorgest" possible thing: a real situation where I'm the richest person alive.
Premise 2: A real "Foo" would be even "blorger" than a hypothetical "Foo".
We can imagine a hypothetical Foo, but a real Foo is blorger than an imaginary Foo, so if you accept the existence of hypothetical Foos, you also accept the even blorger real Foo. QED I'm the richest person alive.
The ability to conceive of something more extreme in some quality than what exists in reality can't obligate reality to change at all.
Very interesting. I was trying to think on how to refute premise 2, and came up with:
- A real catastrophe is worse than an imaginary catastrophe
Then not all real things are better than imaginary things
- An imaginary outcome in which my country's team wins the world cup is greater than a real outcome in which it doesn't
Then not all real things are greater than imaginary thins
Not sure if these are valid, since I'm not familiar with philosophical reasoning.
- A real catastrophe is worse than an imaginary catastrophe
Then not all real things are better than imaginary things
- An imaginary outcome in which my country's team wins the world cup is greater than a real outcome in which it doesn't
Then not all real things are greater than imaginary thins
Not sure if these are valid, since I'm not familiar with philosophical reasoning.
Yes, those are valid arguments! Maybe I should have reformulated it to "a real god is better than an imaginary god" directy, then that does not work anymore. But I am no expert either ;)
The real way to break it down is by attacking (1). One common answer is that this does not prove the existence of the "biblical god" at all. Nothing about an omniscient creator God in heaven. It just proves there is a "best" thing. For all we know it could be a potato.
Another way is to say that by accepting (1), we basically already assume a God exists. So, nothing new was concluded by proving he does. This logical flaw is called "begging the question". Although not everyone agrees if that is the case here.
The real way to break it down is by attacking (1). One common answer is that this does not prove the existence of the "biblical god" at all. Nothing about an omniscient creator God in heaven. It just proves there is a "best" thing. For all we know it could be a potato.
Another way is to say that by accepting (1), we basically already assume a God exists. So, nothing new was concluded by proving he does. This logical flaw is called "begging the question". Although not everyone agrees if that is the case here.
> a real god is better than an imaginary god
Cthulhu. Or pretty much any god from or inspired by Lovecraft really.
> For all we know it could be a potato.
Or a jelly donut.
Cthulhu. Or pretty much any god from or inspired by Lovecraft really.
> For all we know it could be a potato.
Or a jelly donut.
This is where you have to get into the nuts and bolts of Godel's proof. Godel axiomized "positive properties" into the proof. A positive property is such that either it or its negation is positive, never both. So a catastrophe is a negative property, it's absence is the positive.
He then goes on to define God as the most positive thing imaginable. So a real catastrophe is not more positive than an imagined one.
He then goes on to define God as the most positive thing imaginable. So a real catastrophe is not more positive than an imagined one.
The argument blurs two things:
1. "in order to imagine the most powerful thing possible then you must imagine it exists"
and 2. "anything which exist is more powerful than anything which is just imagined"
In the case of number 1, there is nothing requiring it to exist just how you are allowed to imagine it.
For number 2, even very simple objects will be stronger than the most powerful thing you can imagine.
To rescue the argument a third interpretation is often given: god is the most powerful thing in existence. But this provides no details and could be a very uninteresting but powerful natural phenomenon.
1. "in order to imagine the most powerful thing possible then you must imagine it exists"
and 2. "anything which exist is more powerful than anything which is just imagined"
In the case of number 1, there is nothing requiring it to exist just how you are allowed to imagine it.
For number 2, even very simple objects will be stronger than the most powerful thing you can imagine.
To rescue the argument a third interpretation is often given: god is the most powerful thing in existence. But this provides no details and could be a very uninteresting but powerful natural phenomenon.
> Premise 1: God is defined as the greatest thing that we can possibly concieve ("that for which no greater can be conceived")
The problem starts here though. Aristotle/Aquinas showed by God could not be a thing, even the largest thing. God is not a being but rather Being Itself (ipsum esse subsistens).
* https://www.youtube.com/watch?v=1zMf_8hkCdc
The problem starts here though. Aristotle/Aquinas showed by God could not be a thing, even the largest thing. God is not a being but rather Being Itself (ipsum esse subsistens).
* https://www.youtube.com/watch?v=1zMf_8hkCdc
I think the issue is premise 2. Real things implies it is possible for it to exist.
The moment you can concieve of a thing which can't be real, 2 is invalid.
The moment you can concieve of a thing which can't be real, 2 is invalid.
Couldn't one satisfy the argument simply by believing that God is real, regardless of whether he does or not?
Here is my favorite snarky rebuttal to Anselm’s ontological argument:
“The worst proof, by definition, is worse than any other proof that could possibly be conceived. If such a proof exists in understanding, then surely it must be an even worse proof if it exists in reality. Therefore, the worst proof must already exist in reality”
“The worst proof, by definition, is worse than any other proof that could possibly be conceived. If such a proof exists in understanding, then surely it must be an even worse proof if it exists in reality. Therefore, the worst proof must already exist in reality”
My preferred version of this (which so far as I know is original to me; see http://www.mccaughan.org.uk/g/log/2009/ontological.html):
Consider a proof of God's existence than which no worse can be conceived. Proofs that are merely wrong (bad logic, false premises, etc.) are two a penny; clearly the worst possible proof would in fact have to conclusively refute the proposition it was trying to prove.
As St Anselm has taught us, clearly a worst-possible proof "exists in the understanding". But a proof so bad that it actually refutes its intended conclusion is clearly much worse if it actually exists in reality. Hence such a proof that exists only in the understanding is not worst-possible after all.
Hence, there exists (in reality, not merely "in the understanding") a proof of God's existence so bad that it conclusively proves that there is no God.
And, of course, if there is a conclusive proof that there is no God, there is in fact no God. Hence, there is no God. Thanks, St Anselm!
Consider a proof of God's existence than which no worse can be conceived. Proofs that are merely wrong (bad logic, false premises, etc.) are two a penny; clearly the worst possible proof would in fact have to conclusively refute the proposition it was trying to prove.
As St Anselm has taught us, clearly a worst-possible proof "exists in the understanding". But a proof so bad that it actually refutes its intended conclusion is clearly much worse if it actually exists in reality. Hence such a proof that exists only in the understanding is not worst-possible after all.
Hence, there exists (in reality, not merely "in the understanding") a proof of God's existence so bad that it conclusively proves that there is no God.
And, of course, if there is a conclusive proof that there is no God, there is in fact no God. Hence, there is no God. Thanks, St Anselm!
See the Wikipedia page of Ontological Argument.
https://en.wikipedia.org/wiki/Ontological_argument
It belongs to the long tradition in Western Philosophy and has been proposed by many great philosophers in different variations, Godel's proof can simply be seen as the same metaphysical argument rigorously expressed in modal logic. And of course, this argument, like many other issues in philosophy and theology, is not without its controversy. It has been criticized by many people in the past 1000 years, including some high-profile theologians as technically flawed, which is also covered by this Wikipedia article.
https://en.wikipedia.org/wiki/Ontological_argument
It belongs to the long tradition in Western Philosophy and has been proposed by many great philosophers in different variations, Godel's proof can simply be seen as the same metaphysical argument rigorously expressed in modal logic. And of course, this argument, like many other issues in philosophy and theology, is not without its controversy. It has been criticized by many people in the past 1000 years, including some high-profile theologians as technically flawed, which is also covered by this Wikipedia article.
There is a nice book by Melvin Fitting: Types, Tableaus, and Gödel’s God, Kluwer 2002. It introduces some fairly standard typed higher order logic and then formalizes Gödel's proof in it. Although I personally like it a bit less than Mendelsohn and Fitting's book on first order modal logic, it's a good read (if you like logic and have had some basic course in logic sometime).
Modal logic adds two new operators: ◻ -- necessity; and ◇ -- possibility. For example, a triangle's angles necessarily add up to 180, but it's merely a possibility that it will rain tomorrow.
That's all there is to it, but things can get very complex when you start adding negations and the other logical connectives.
That's all there is to it, but things can get very complex when you start adding negations and the other logical connectives.
That’s not Gödel’s ontological argument. You’re confusing it with something else.
That is not Godel's ontological argument, that's Saint Anselm's.
Now do the same for the devil:
"The devil, by definition, is that for which no greater evil can be conceived. The devil exists in the understanding. If the devil exists in the understanding, we could imagine him to be greater by existing in reality. Therefore, the devil must exist."
From which it also follows that:
"If the devil doesn't destroy god, we could imagine him to be a greater evil by destroying god. Therefore, the devil must have destroyed god."
At which point we must conclude that it is a shame that theology has captured the minds of so many brilliant people.
"The devil, by definition, is that for which no greater evil can be conceived. The devil exists in the understanding. If the devil exists in the understanding, we could imagine him to be greater by existing in reality. Therefore, the devil must exist."
From which it also follows that:
"If the devil doesn't destroy god, we could imagine him to be a greater evil by destroying god. Therefore, the devil must have destroyed god."
At which point we must conclude that it is a shame that theology has captured the minds of so many brilliant people.
> At which point we must conclude that it is a shame that theology has captured the minds of so many brilliant people.
Or that the brilliant people whom it captured were more brilliant than arm chair philosophers of the modern age. Even Aquinas didn't like Godel/Anselm's argument:
* https://en.wikipedia.org/wiki/Ontological_argument#Thomas_Aq...
And this is not specifically theology, but philosophy generally. Aristotle espoused these views in 300 BC:
* https://en.wikipedia.org/wiki/Aristotle#Metaphysics
And I think you'd be hard pressed to call Aristotle "religious", and yet the (Catholic) Church took up worldview with few qualms:
* https://en.wikipedia.org/wiki/Five_Ways_(Aquinas)
When universities were established in the middle ages, they certainly had theology as a specific course of study, but a good portion of the curriculum was about Aristotle's view of the natural world:
* https://en.wikipedia.org/wiki/Corpus_Aristotelicum
Or that the brilliant people whom it captured were more brilliant than arm chair philosophers of the modern age. Even Aquinas didn't like Godel/Anselm's argument:
* https://en.wikipedia.org/wiki/Ontological_argument#Thomas_Aq...
And this is not specifically theology, but philosophy generally. Aristotle espoused these views in 300 BC:
* https://en.wikipedia.org/wiki/Aristotle#Metaphysics
And I think you'd be hard pressed to call Aristotle "religious", and yet the (Catholic) Church took up worldview with few qualms:
* https://en.wikipedia.org/wiki/Five_Ways_(Aquinas)
When universities were established in the middle ages, they certainly had theology as a specific course of study, but a good portion of the curriculum was about Aristotle's view of the natural world:
* https://en.wikipedia.org/wiki/Corpus_Aristotelicum
>If the devil exists in the understanding, we could imagine him to be greater by existing in reality.
That, like with God, is a logical jump. Who said reality > understanding? Reality could be == understanding (e.g. all, including what we conceive as matter, is just thought), or understanding could be discreet but greater than reality (and e.g. reality being a fossilized, realized, and constrained version of one path in the realm of understanding).
>At which point we must conclude that it is a shame that theology has captured the minds of so many brilliant people.
What you cited is based philosophy and logical argumentation, one of the cornerstones of civilization. And theology had quite a role in shaping it, along with the rest of civilization. Just because the starting points and assumptions are bad, it doesn't make the mechanism bad. For that matter, just because a mechanism is bad, it doesn't make it less useful (e.g. a population could be more agreeable, civilized, and moral when believing in a higher power, even if that higher power is BS, not to mention other benefits at the civic and personal level. See [1] for an example of such thinking).
[1] https://www.npr.org/templates/story/story.php?storyId=129528...
That, like with God, is a logical jump. Who said reality > understanding? Reality could be == understanding (e.g. all, including what we conceive as matter, is just thought), or understanding could be discreet but greater than reality (and e.g. reality being a fossilized, realized, and constrained version of one path in the realm of understanding).
>At which point we must conclude that it is a shame that theology has captured the minds of so many brilliant people.
What you cited is based philosophy and logical argumentation, one of the cornerstones of civilization. And theology had quite a role in shaping it, along with the rest of civilization. Just because the starting points and assumptions are bad, it doesn't make the mechanism bad. For that matter, just because a mechanism is bad, it doesn't make it less useful (e.g. a population could be more agreeable, civilized, and moral when believing in a higher power, even if that higher power is BS, not to mention other benefits at the civic and personal level. See [1] for an example of such thinking).
[1] https://www.npr.org/templates/story/story.php?storyId=129528...
I am not aware of any claim that the devil is the largest evil that could be imagined. Further, such a definition would not make sense in for example traditional Christianity where evil is defined as a privation on good, not something that exists in itself.
Having God and the devil as evenly matched but opposite powers is not something you would find in theology. Learn the basics of it before thinking you have created a proper critique.
Having God and the devil as evenly matched but opposite powers is not something you would find in theology. Learn the basics of it before thinking you have created a proper critique.
> I am not aware of any claim that the devil is the largest evil that could be imagined.
That is completely irrelevant. The ontological proof claims to deduce the existence of an entity from a definition of that entity. It does not matter whether this definition happen to match some current religious dogma or not.
That is completely irrelevant. The ontological proof claims to deduce the existence of an entity from a definition of that entity. It does not matter whether this definition happen to match some current religious dogma or not.
Anselm defined God as "that which nothing greater can be thought." Introducing a devil into this mix doesn't change this reasoning, and basically boils down to "is evil greater than good?", which I don't think anyone can reasonably argue.
It's not the most interesting argument for God I've encountered, but it's not trivially invalidated by elevating evil to the same status as good. That hasn't been a serious element of any real theology since long before the ancient Hebrews.
Theology is the art of imagination, the same way that politics is the art of the possible. Imagining absolute evil is only interesting when you want to attack the idea of absolute good. Absolute good remains interesting without a foil. So therefore people will be willing to believe in it.
It's not the most interesting argument for God I've encountered, but it's not trivially invalidated by elevating evil to the same status as good. That hasn't been a serious element of any real theology since long before the ancient Hebrews.
Theology is the art of imagination, the same way that politics is the art of the possible. Imagining absolute evil is only interesting when you want to attack the idea of absolute good. Absolute good remains interesting without a foil. So therefore people will be willing to believe in it.
The point is that if the ontological argument is valid then you can define all kinds of things into existence also. The devil is just an example, it could also be The Most Perfect Island, The Real Santa Claus and so on. So it is a reductio ad absurdum.
I'm not saying the ontological argument is correct, just that your reasoning doesn't sufficiently refute it.
It doesn't refute it per se. It just shows that The Real Santa Claus also exists by the same token. Which is not really a logical contradiction so if you want to believe that, more power to you.
More generally, you can't attack the reasoning with any amount of imaginary horrors or delights. This is because the ontological argument doesn't try to argue imaginary things that are not God exist. Just that the imagination we have of God does exist, as the greatest thing ever. This is because of God's special property, that of being the greatest thing ever, that any imagination greater would just become the new God.
This property is not shared by things that are not God, such as Santa Claus. So you can't use the ontological argument for God to also show that Santa Claus exists. Santa Claus isn't the greatest thing ever, so Santa Claus isn't bound by the rules of logic to exist.
This property is not shared by things that are not God, such as Santa Claus. So you can't use the ontological argument for God to also show that Santa Claus exists. Santa Claus isn't the greatest thing ever, so Santa Claus isn't bound by the rules of logic to exist.
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The real Santa Claus did exist, the one the current myth is based on.
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Fair enough, but that is totally beside the point.
Maybe sibling comment is more to your liking.
That sounds as if it were a fact that can be measured. Everything can be conjured into existence by false assumptions.
"The spaghetti monster, by definition, is that for which no more delicious thing can be conceived. The spaghetti monster exists in the understanding. If the spaghetti monster exists in the understanding, we could imagine it to be even more delicious by existing in reality. Therefore, the spaghetti monster must exist."
"The spaghetti monster, by definition, is that for which no more delicious thing can be conceived. The spaghetti monster exists in the understanding. If the spaghetti monster exists in the understanding, we could imagine it to be even more delicious by existing in reality. Therefore, the spaghetti monster must exist."
You could just as easily adjust the axioms to require that both a god and devil must exist in perfect balance.
In any case, your argument is an informal one - turn it into a formal refutation of Goedel's modal logic proof, and it'd be more relevant to this post.
In any case, your argument is an informal one - turn it into a formal refutation of Goedel's modal logic proof, and it'd be more relevant to this post.
He doesn't have to. He can use the same argument to prove that a formal logical proof exists.
Ontological argument for the nonexistence of God.
1. It is more great to do something with a greater handicap.
2. Not existing is the greatest possible handicap.
3. The greatest possible being is thus one who could create the universe despite not existing.
1. It is more great to do something with a greater handicap.
2. Not existing is the greatest possible handicap.
3. The greatest possible being is thus one who could create the universe despite not existing.
You have not proved step 1 or step 2. In fact I'm quite sure your step two is false, and your step one would be quite hard to prove.
Did Gödel even prove step 1?. In Gödel's argument, it's relying on very arbitrary definitions of what many have defined as a god and that their god is "great". OP defined what is "great" to him, it's not necessarily what's great to you or me.
I think OP here is meaning "great" in some intellectual capacity, that you are just as powerful or great if you can make up your lack of greatness in one area with another form of greatness, something I don't see as greater but equally great. Is it greater to be successful by bootstrapping off the success of your forebearer or greater to be as successful when starting from nothing? It's a classical argument but to me it stands on just as rational ground as Gödel's argument.
I think OP here is meaning "great" in some intellectual capacity, that you are just as powerful or great if you can make up your lack of greatness in one area with another form of greatness, something I don't see as greater but equally great. Is it greater to be successful by bootstrapping off the success of your forebearer or greater to be as successful when starting from nothing? It's a classical argument but to me it stands on just as rational ground as Gödel's argument.
Maybe you can prove step 1, but step 2 is clearly false - a much greater difficulty is having an adversary unmaking what you make.
> 2. Not existing is the greatest possible handicap.
I would argue that impossiblity, rather than non-existence is the greatest handicap.
I would argue that impossiblity, rather than non-existence is the greatest handicap.
This (very nice) argument is due to Douglas Gasking: https://en.wikipedia.org/wiki/Ontological_argument#Douglas_G....
Thanks, I'd never found the original source! I'll add that to my saved version.
Well, what is existence and nonexistence in this sense? Something which we can measure and see or something which we do not know of because we cannot measure it?
For Polish speakers, I highly recommend this book:
https://www.ccpress.pl/produkt/Dowody_ontologiczne._W_900._r...
It has multiple formalisations of both Anselm's and Gaunilo's arguments, and critiques of each approach
https://www.ccpress.pl/produkt/Dowody_ontologiczne._W_900._r...
It has multiple formalisations of both Anselm's and Gaunilo's arguments, and critiques of each approach
>Hence, it must follow from Godlikeness. Moreover, Godlikeness is an essence of God, since it entails all positive properties, and any non-positive property is the negation of some positive property, so God cannot have any non-positive properties.
Counter argument: Of course he can.
God isn't constrained by formal logic constraints -- in fact God created logic and can break it at will (e.g. by being two contradicting things at once).
We, as humans (or even as all of the universe), might not be able to conceive these, but then again, why should why? We're not gods!
In other words: when one is considering a God-like figure, there's no reason to consider one bound by the same restrictions we have, our Kantian "a prioris", or even basic consistency. If you do give your God such restrictions you might be able to prove this or that theorem, but only as regards to that lesser God, not the concept of God in general.
Counter argument: Of course he can.
God isn't constrained by formal logic constraints -- in fact God created logic and can break it at will (e.g. by being two contradicting things at once).
We, as humans (or even as all of the universe), might not be able to conceive these, but then again, why should why? We're not gods!
In other words: when one is considering a God-like figure, there's no reason to consider one bound by the same restrictions we have, our Kantian "a prioris", or even basic consistency. If you do give your God such restrictions you might be able to prove this or that theorem, but only as regards to that lesser God, not the concept of God in general.
The ontological argument is about a specific definition of "God" as having certain properties. You cannot counter that argument by assuming a different definition of "God".
Your "God" can be two contradictory things at once which seems fundamentally different than the "God" defined in the ontological proof. So basically you are talking about two different things. (But OK, if logic doesn't exist then who cares?)
Your "God" can be two contradictory things at once which seems fundamentally different than the "God" defined in the ontological proof. So basically you are talking about two different things. (But OK, if logic doesn't exist then who cares?)
>The ontological argument is about a specific definition of "God" as having certain properties. You cannot counter that argument by assuming a different definition of "God".
Of course you can.
The ontological argument arrived at the "specific definition" (of axioms about God) under the assumption that those are required and true attributes of any entity that can be called God.
If those are just a random selection of attributes merely thought necessary by Anselm (or Godel here), and not inherently necessarily tied to the notion of God in general, then the whole argument is moot, nothing more than a logical deduction based on some arbitrary axioms that tells us nothing about God existing or not.
The purpose of Anselm and Godel is not to show that (a) "a specific definition of God having [those] certain properties exists".
It is to assert that "those certain properties" are necessary properties of a God entity, and (b) "a God having those properties must exist", (c) "God exists".
>Your "God" can be two contradictory things at once which seems fundamentally different than the "God" defined in the ontological proof. So basically you are talking about two different things.
No, we're just talking about two different assertions of what properties God can and cannot have. God as a notion pre-exists any attributes assigned to it in a specific logical argument (for example, Godel and Anselm have both heard about the notion of God before they've picked their axioms).
When trying to match an existing notion it's not enough that one picks axioms: they should also make sure those axioms are the proper ones to capture the notion properly.
Else it's just a new arbitrary definition of an entity, which they called "God" but could just as easily have called "Bob" or "Jane".
Of course you can.
The ontological argument arrived at the "specific definition" (of axioms about God) under the assumption that those are required and true attributes of any entity that can be called God.
If those are just a random selection of attributes merely thought necessary by Anselm (or Godel here), and not inherently necessarily tied to the notion of God in general, then the whole argument is moot, nothing more than a logical deduction based on some arbitrary axioms that tells us nothing about God existing or not.
The purpose of Anselm and Godel is not to show that (a) "a specific definition of God having [those] certain properties exists".
It is to assert that "those certain properties" are necessary properties of a God entity, and (b) "a God having those properties must exist", (c) "God exists".
>Your "God" can be two contradictory things at once which seems fundamentally different than the "God" defined in the ontological proof. So basically you are talking about two different things.
No, we're just talking about two different assertions of what properties God can and cannot have. God as a notion pre-exists any attributes assigned to it in a specific logical argument (for example, Godel and Anselm have both heard about the notion of God before they've picked their axioms).
When trying to match an existing notion it's not enough that one picks axioms: they should also make sure those axioms are the proper ones to capture the notion properly.
Else it's just a new arbitrary definition of an entity, which they called "God" but could just as easily have called "Bob" or "Jane".
You are talking past the comment you are replying to, and Goedel's argument altogether. That is, you are referring to an entity that may have contradictory properties in the way you mentioned, but Goedel's philosophical God isn't such an entity.
> Else it's just a new arbitrary definition of an entity, which they called "God" but could just as easily have called "Bob" or "Jane".
It exactly is arbitrary. The argument works for every referent that satisfies the properties.
> Else it's just a new arbitrary definition of an entity, which they called "God" but could just as easily have called "Bob" or "Jane".
It exactly is arbitrary. The argument works for every referent that satisfies the properties.
>You are talking past the comment you are replying to, and Goedel's argument altogether. That is, you are referring to an entity that may have contradictory properties in the way you mentioned, but Goedel's philosophical God isn't such an entity.
Which is the point exactly. Even if Goedel's argument didn't have logical jumps based on non-essential assumptions, it still doesn't prove the existence of God per se, only the existence of something Goedel calls God, which satisfies Goedel's axioms ("every referent that satisfies the properties").
But the problem is that Goedel doesn't say he tries to prove the existence of "any referent that satisfies the properties" but of God.
Well, who (apart from Goedel himself) said that those are the properties of God, and not others?
Which is the point exactly. Even if Goedel's argument didn't have logical jumps based on non-essential assumptions, it still doesn't prove the existence of God per se, only the existence of something Goedel calls God, which satisfies Goedel's axioms ("every referent that satisfies the properties").
But the problem is that Goedel doesn't say he tries to prove the existence of "any referent that satisfies the properties" but of God.
Well, who (apart from Goedel himself) said that those are the properties of God, and not others?
> it still doesn't prove the existence of God
You mean the God of your religion. If Goedel believed his argument that would make him a kind of deist.
> Even if Goedel's argument didn't have logical jumps based on non-essential assumptions
Goedel's argument is tight given the axioms, though. It's been formally verified.
The God that you mention that may have contradictory properties isn't that interesting for logical analysis, since it's likely that logicians only want to consider "Gods" whose existence do not render useless their logical system (contradiction leads to the principle of explosion). Hence you won't find primarily logical works discussing such a God.
> which satisfies Goedel's axioms
to be pedantic, his "God" doesn't satisfy Goedel's axioms, his "God" satisfies his definition of "God". Then the argument has that you accept its existence once you accept the axioms of the argument.
> Well, who (apart from Goedel himself) said that those are the properties of God, and not others?
Well, in most cultures, you call a kind of sufficiently magical or spiritual or ineffable entity a god. Nobody has a monopoly on the word "God", and many cultures use the word to refer to entities unrecognizable as the one you call God.
You mean the God of your religion. If Goedel believed his argument that would make him a kind of deist.
> Even if Goedel's argument didn't have logical jumps based on non-essential assumptions
Goedel's argument is tight given the axioms, though. It's been formally verified.
The God that you mention that may have contradictory properties isn't that interesting for logical analysis, since it's likely that logicians only want to consider "Gods" whose existence do not render useless their logical system (contradiction leads to the principle of explosion). Hence you won't find primarily logical works discussing such a God.
> which satisfies Goedel's axioms
to be pedantic, his "God" doesn't satisfy Goedel's axioms, his "God" satisfies his definition of "God". Then the argument has that you accept its existence once you accept the axioms of the argument.
> Well, who (apart from Goedel himself) said that those are the properties of God, and not others?
Well, in most cultures, you call a kind of sufficiently magical or spiritual or ineffable entity a god. Nobody has a monopoly on the word "God", and many cultures use the word to refer to entities unrecognizable as the one you call God.
You've left the realm of rationalism and are firmly seated in theology. The correct theological interpretation here isn't that God can't do something illogical, but rather that God can remain strictly logical, and still be God. God isn't constrained by formal logic, but chooses to be because it suits Him. In fact, the entire field of theology is built on this. Theologies are imagined descriptions of God, these imaginations are accepted by God because God wants us to believe in Him.
The problem of evil is the same way, ascribing a kind of logic to God. Theologians think a lot about theodicy, and have broken away from their churches over it.
One interesting way to think about it is that God has three basic attitudes about the things humans do. God either wills a thing, accepts it, or tolerates it. If God wills it, it creates more goodness in the world than it takes away. If God accepts it, then the balance is roughly equal. If He tolerates it, then that means God has to balance the scales personally. This can happen through the mechanism we call karma.
A rationally-aware theologian would state that God accepts any rational regime you want to put on him, and the Book of Job puts this into story form. Just because God is rational and good doesn't mean He's going to appear that way all the time to all the people.
The problem of evil is the same way, ascribing a kind of logic to God. Theologians think a lot about theodicy, and have broken away from their churches over it.
One interesting way to think about it is that God has three basic attitudes about the things humans do. God either wills a thing, accepts it, or tolerates it. If God wills it, it creates more goodness in the world than it takes away. If God accepts it, then the balance is roughly equal. If He tolerates it, then that means God has to balance the scales personally. This can happen through the mechanism we call karma.
A rationally-aware theologian would state that God accepts any rational regime you want to put on him, and the Book of Job puts this into story form. Just because God is rational and good doesn't mean He's going to appear that way all the time to all the people.
>You've left the realm of rationalism and are firmly seated in theology.
Nope, except in the sense that I'm talking about God. But assuming God exists (or can exist) it's perfectly rational to consider him unbounded by logical or physical constraints.
>The correct theological interpretation here isn't that God can't do something illogical, but rather that God can remain strictly logical, and still be God.
There's no "correct theological interpretation". That's just one interpretation (e.g. augustinian). Orthodox Christianity, for one, as many other religions, doesn't bound God to be "strictly logical".
So, this "God [that] can remain strictly logical, and still be God" is just one constrained conception of God. One can also argue for a God that can be illogical or beyond logic (such us that logical and illogical make no sense as restrictions to him).
Nope, except in the sense that I'm talking about God. But assuming God exists (or can exist) it's perfectly rational to consider him unbounded by logical or physical constraints.
>The correct theological interpretation here isn't that God can't do something illogical, but rather that God can remain strictly logical, and still be God.
There's no "correct theological interpretation". That's just one interpretation (e.g. augustinian). Orthodox Christianity, for one, as many other religions, doesn't bound God to be "strictly logical".
So, this "God [that] can remain strictly logical, and still be God" is just one constrained conception of God. One can also argue for a God that can be illogical or beyond logic (such us that logical and illogical make no sense as restrictions to him).
> There's no "correct theological interpretation".
Theology is more correct the closer it gets to God. God is the greatest thing imaginable. Theology is an imagination of God. If God is real then there must exist more correct theologies.
So more correct theology will more descriptive of God's greatness. And a God that can be rational is greater than a God that strictly stays outside of rationality.
Theology is more correct the closer it gets to God. God is the greatest thing imaginable. Theology is an imagination of God. If God is real then there must exist more correct theologies.
So more correct theology will more descriptive of God's greatness. And a God that can be rational is greater than a God that strictly stays outside of rationality.
>Theology is more correct the closer it gets to God.
Only if God wants it so. The "thelema" (will) of God is more important in this regard to what aspirations self-professed thelogicians have. God for one haven't even said that he likes or approves of theologicians! In fact in several religions attempting to get "closer to god" or "learn God's secrets" is a blaspheme.
>And a God that can be rational is greater than a God that strictly stays outside of rationality.
That's just an arbitrary axiom. One could just as easily posit the opposite: "A god that isn't bounded by rationality is greater than a God that strictly stays inside of rationality" (in fact, e.g. the Eastern Orthodox church posits exactly that, and other non-Christian religions as well).
Only if God wants it so. The "thelema" (will) of God is more important in this regard to what aspirations self-professed thelogicians have. God for one haven't even said that he likes or approves of theologicians! In fact in several religions attempting to get "closer to god" or "learn God's secrets" is a blaspheme.
>And a God that can be rational is greater than a God that strictly stays outside of rationality.
That's just an arbitrary axiom. One could just as easily posit the opposite: "A god that isn't bounded by rationality is greater than a God that strictly stays inside of rationality" (in fact, e.g. the Eastern Orthodox church posits exactly that, and other non-Christian religions as well).
> That's just an arbitrary axiom.
No it's not. It's saying that a God that can do two things, i.e. be rational and be irrational, is greater than a God that can just do one thing, be irrational. Your opposite isn't an actual opposite, it's just a comparison between a God that can do a thing and a God that can do some things but not others.
No it's not. It's saying that a God that can do two things, i.e. be rational and be irrational, is greater than a God that can just do one thing, be irrational. Your opposite isn't an actual opposite, it's just a comparison between a God that can do a thing and a God that can do some things but not others.
>No it's not. It's saying that a God that can do two things, i.e. be rational and be irrational, is greater than a God that can just do one thing, be irrational.
Actually, the God that "can do two things, i.e. be rational and be irrational" is my description -- I was supporting that (e.g. see above: "unbounded by logical or physical constraints", "God that can be illogical or beyond logic (such us that logical and illogical make no sense as restrictions to him)", "God created logic and can break it at will" -- which means can also follow it at will, etc.).
You were going by a more restricted God that can only be rational.
Not to mention your own comparison is based on rationality. Even ignoring what I wrote above, from the standpoint of God "a God that can do two things" might not be greater than a "God that can only do one".
God himself defines not just physical laws and logic, but also the very meaning of notions like "greater" (that is, works on a meta level). "More if greater" is our undestanding of what's greater, not necessarily God's (like a child thinks more sugar in food is greater, but a parent knows better). It would be constraining to assume of God the constrains of greatness than we are bound to.
Actually, the God that "can do two things, i.e. be rational and be irrational" is my description -- I was supporting that (e.g. see above: "unbounded by logical or physical constraints", "God that can be illogical or beyond logic (such us that logical and illogical make no sense as restrictions to him)", "God created logic and can break it at will" -- which means can also follow it at will, etc.).
You were going by a more restricted God that can only be rational.
Not to mention your own comparison is based on rationality. Even ignoring what I wrote above, from the standpoint of God "a God that can do two things" might not be greater than a "God that can only do one".
God himself defines not just physical laws and logic, but also the very meaning of notions like "greater" (that is, works on a meta level). "More if greater" is our undestanding of what's greater, not necessarily God's (like a child thinks more sugar in food is greater, but a parent knows better). It would be constraining to assume of God the constrains of greatness than we are bound to.
> God isn't constrained by formal logic constraints -- in fact God created logic and can break it at will (e.g. by being two contradicting things at once).
Not in the (Catholic) Christian tradition:
* https://en.wikipedia.org/wiki/Omnipotence_paradox#Other_vers...
Not in the (Catholic) Christian tradition:
* https://en.wikipedia.org/wiki/Omnipotence_paradox#Other_vers...
Whenever this makes top of HN, it remains one of the most contentiously misunderstood pieces of formal logic -- much like some of Gödel's other famous results. The proof is basically a formalizing of Anselm's Ontological Argument[1]. The proof doesn't "prove" there is a God, it just shows that the argument, written in S5[2] (a type of modal logic), is correct -- more specifically, that if the premises are true, then the conclusion follows.
Alvin Plantinga also did a lot of work refining these kinds of modal ontological arguments in the 70s and 80s; of note is his famous "victorious" ontological argument[3] -- still hotly cited to this day. Modal logic, for the uninitiated, essentially adds two new operators to the "usual" logical operators we might have seen in college (negation, implication, conjunction, disjunction, quantifiers):
The historical context is also very interesting. It was somewhat unknown how valid Anselm's argument was, and it took almost a millennium before we could satisfactorily formalize the ontological argument (although many non-modal and Aristotelian proofs had been written).
What does it mean for non-logicians? Well, if you buy the premises (which is key!), it shows that it's not irrational to believe in God (as defined by the argument). Again, it doesn't prove the existence of God, but it does show that the logic of the argument makes sense.
[1] https://plato.stanford.edu/entries/ontological-arguments/#St...
[2] https://plato.stanford.edu/entries/logic-modal-origins/
[3] https://plato.stanford.edu/entries/ontological-arguments/#Pl...
Alvin Plantinga also did a lot of work refining these kinds of modal ontological arguments in the 70s and 80s; of note is his famous "victorious" ontological argument[3] -- still hotly cited to this day. Modal logic, for the uninitiated, essentially adds two new operators to the "usual" logical operators we might have seen in college (negation, implication, conjunction, disjunction, quantifiers):
Necessity: ◻P -- P is true in all worlds
Possibility: ◇Q -- Q is true in some (or no) worlds
~◻P -- P cannot be true in any world!
The historical context is also very interesting. It was somewhat unknown how valid Anselm's argument was, and it took almost a millennium before we could satisfactorily formalize the ontological argument (although many non-modal and Aristotelian proofs had been written).
What does it mean for non-logicians? Well, if you buy the premises (which is key!), it shows that it's not irrational to believe in God (as defined by the argument). Again, it doesn't prove the existence of God, but it does show that the logic of the argument makes sense.
[1] https://plato.stanford.edu/entries/ontological-arguments/#St...
[2] https://plato.stanford.edu/entries/logic-modal-origins/
[3] https://plato.stanford.edu/entries/ontological-arguments/#Pl...
> What does it mean for non-logicians? Well, if you buy the premises (which is key!), it shows that it's not irrational to believe in God (as defined by the argument). Again, it doesn't prove the existence of God, but it does show that the logic of the argument makes sense.
This understates what the proof shows. It shows that if you buy the premises it's not rational to believe God doesn't exist (as defined by the argument).
This understates what the proof shows. It shows that if you buy the premises it's not rational to believe God doesn't exist (as defined by the argument).
The proof shows precisely that a conclusion follows from axioms.
That doesn't settle anything though, all it means is that anyone disagreeing with the conclusion must also disagree with one or more of the axioms. Particularly, if someone believes it is irrational to believe in God they would also believe it is irrational to accept all the axioms of the proof.
My personal complaint is that "for each positive property, either it or its negation must be positive". Assuming that a property is uniquely positive or negative requires the assumption of a universal moral value system, which in turn really would require require something godlike to set the standards. I accept that there are properties that are sometimes positive and sometimes negative, so I don't agree with the argument.
That doesn't settle anything though, all it means is that anyone disagreeing with the conclusion must also disagree with one or more of the axioms. Particularly, if someone believes it is irrational to believe in God they would also believe it is irrational to accept all the axioms of the proof.
My personal complaint is that "for each positive property, either it or its negation must be positive". Assuming that a property is uniquely positive or negative requires the assumption of a universal moral value system, which in turn really would require require something godlike to set the standards. I accept that there are properties that are sometimes positive and sometimes negative, so I don't agree with the argument.
"Rationality" is not a (meta-)logical property. You're right that the proof shows that, logically speaking, if one buys the premises, God must exist. But more colloquially, it shows that by accepting some premises that are reasonable, one reaches the conclusion that God exists. Ergo, there's an argument a rational person would accept whose conclusion is the necessity of God.
> But more colloquially, it shows that by accepting some premises that are reasonable, one reaches the conclusion that God exists. Ergo, there's an argument a rational person would accept whose conclusion is the necessity of God.
I think that is a very weak conclusion, there are an infinite number of proofs for god that are valid so long as you accept their particular premises. It is the specific plausibility of the premises and definitions implied in St. Anselm’s Ontological Argument that make it of interest.
What this shows colloquially is that if you are arguing against god, you must either reject this definition of god or one of the other premises. If you don't your argument is self-contradictory.
I think that is a very weak conclusion, there are an infinite number of proofs for god that are valid so long as you accept their particular premises. It is the specific plausibility of the premises and definitions implied in St. Anselm’s Ontological Argument that make it of interest.
What this shows colloquially is that if you are arguing against god, you must either reject this definition of god or one of the other premises. If you don't your argument is self-contradictory.
> I think that is a very weak conclusion ...
That's kind of my point. It's not some knock-down argument, but it's a very nuanced result that achieved a few very neat things:
1) Formalized Anselm's "greatest of which can be conceived of" notion.
2) The concept of "accidental" (contingent) and "non-accidental" (necessary) properties had existed since antiquity, but modal logic essentially formalized the idea.
3) Showed that Anselm's argument was indeed valid. Again, this project took around 1000 years.
Plantinga did a lot of work in trying to make the premises more palatable, but of course, the argument for the existence of God still rages on. (As I'm sure it will far after we're gone.)
That's kind of my point. It's not some knock-down argument, but it's a very nuanced result that achieved a few very neat things:
1) Formalized Anselm's "greatest of which can be conceived of" notion.
2) The concept of "accidental" (contingent) and "non-accidental" (necessary) properties had existed since antiquity, but modal logic essentially formalized the idea.
3) Showed that Anselm's argument was indeed valid. Again, this project took around 1000 years.
Plantinga did a lot of work in trying to make the premises more palatable, but of course, the argument for the existence of God still rages on. (As I'm sure it will far after we're gone.)
Seems to me it’s a reductio ad absurdem argument against the premises.
This sort of thing casts doubt on the formal logic in question more than it makes a case for God.
It it not really the formal logic that is at fault. In logic you are basically allowed to make any assumption or definition you want.
The problem is thinking a proof can tell you anything about reality which isn't already implicit in those premises.
If we define that X exists, then it is logically true X exists. But this doesn't prove that X exist in the real world.
The problem is thinking a proof can tell you anything about reality which isn't already implicit in those premises.
If we define that X exists, then it is logically true X exists. But this doesn't prove that X exist in the real world.
I'll take the First Way of Aristotle/Aquinas:
* http://tofspot.blogspot.com/2014/07/first-way-some-backgroun...
* http://tofspot.blogspot.com/2014/08/first-way-moving-tale.ht...
* http://tofspot.blogspot.com/2014/09/first-way-part-ii-two-le...
> Some things in the world are changing. (Observation)
> Whatever is changing is being changed by another. (Lemma 1) See Part I.
> There cannot be an infinite regress of instrumental changers. (Lemma 2) See Part II.
> Therefore, there must be a changer that is not itself being changed by another.
* http://tofspot.blogspot.com/2014/10/first-way-part-iii-big-k...
* http://tofspot.blogspot.com/2014/07/first-way-some-backgroun...
* http://tofspot.blogspot.com/2014/08/first-way-moving-tale.ht...
* http://tofspot.blogspot.com/2014/09/first-way-part-ii-two-le...
> Some things in the world are changing. (Observation)
> Whatever is changing is being changed by another. (Lemma 1) See Part I.
> There cannot be an infinite regress of instrumental changers. (Lemma 2) See Part II.
> Therefore, there must be a changer that is not itself being changed by another.
* http://tofspot.blogspot.com/2014/10/first-way-part-iii-big-k...
> Whatever is changing is being changed by another
> Therefore, there must be a changer that is not itself being changed by another.
A proof that contains its own refutation :-)
> Therefore, there must be a changer that is not itself being changed by another.
A proof that contains its own refutation :-)
I think you're misunderstanding "changing" here. It is being applied to the object of change, not the subject that is effecting the change.
Whatever is changing is being changed by another. God is not changing, therefore does not need to be changed by another. Immutability is one of the Divine Attributes (Aquinas talks about this as well).
Whatever is changing is being changed by another. God is not changing, therefore does not need to be changed by another. Immutability is one of the Divine Attributes (Aquinas talks about this as well).
> Whatever is changing is being changed by another
It started off good :)
Makes me wonder about the technical details of what hardware God runs on and how that was created?
I got interested in Sethianism, since Seth is my given name, and it has a fun creation mythos. You get a little backstory leading up to the garden of eden.
https://en.wikipedia.org/wiki/Sethianism
It started off good :)
Makes me wonder about the technical details of what hardware God runs on and how that was created?
I got interested in Sethianism, since Seth is my given name, and it has a fun creation mythos. You get a little backstory leading up to the garden of eden.
https://en.wikipedia.org/wiki/Sethianism
> Makes me wonder about the technical details of what hardware God runs on and how that was created?
If it is created, then it cannot be God by definition. If we are talking about creation and existence (and not change), then we are getting into the Second Way:
> 1. Everything which has come to exist has been caused to come to exist.
> 2. Nothing which has come to exist can be the cause of its own existence.
> 3. Everything which has come to exist is caused to exist by something other than itself. (follows from 1,2)
> 4. It is impossible for a chain of causes of this kind to go on to infinity.
> C. There must be a first cause, which causes other things to come into existence but did not itself come into existence. (follows from 3,4)
* https://www3.nd.edu/~jspeaks/courses/mcgill/201/aquinas-cosm...
NB: the argument is not "everything has a cause", which, if it is your starting proposition, tends to leads to problems:
* https://en.wikipedia.org/wiki/Kalam_cosmological_argument
If it is created, then it cannot be God by definition. If we are talking about creation and existence (and not change), then we are getting into the Second Way:
> 1. Everything which has come to exist has been caused to come to exist.
> 2. Nothing which has come to exist can be the cause of its own existence.
> 3. Everything which has come to exist is caused to exist by something other than itself. (follows from 1,2)
> 4. It is impossible for a chain of causes of this kind to go on to infinity.
> C. There must be a first cause, which causes other things to come into existence but did not itself come into existence. (follows from 3,4)
* https://www3.nd.edu/~jspeaks/courses/mcgill/201/aquinas-cosm...
NB: the argument is not "everything has a cause", which, if it is your starting proposition, tends to leads to problems:
* https://en.wikipedia.org/wiki/Kalam_cosmological_argument
I'm not really sure about any of these premises. Maybe there is some reflexivity in there. Maybe there are causes as far back as anyone cares to look and we'll never know for sure if there are loops or starting point(s).
How is anything caused, what does it mean for a cause to not exist, what hardware does God run on and so on?
How is anything caused, what does it mean for a cause to not exist, what hardware does God run on and so on?
Let us examine premise 2: Something does not exist. How can it then cause itself to exist?
I would love to hear how you think this is not logical.
> How is anything caused, what does it mean for a cause to not exist, what hardware does God run on and so on?
You were caused by your parents, they were caused by your grandparents. Before you existed your parents needed to exist. When your parents did not exist, neither did you.
That's one way (though not the only way) "for a cause to not exist". (Called per accidens sequences by Aquinas/Aristotle.)
The thing that we call "God" runs on no hardware, but is the hardware that everything else is built on. Strictly speaking, in the (Catholic) Christian thinking, God is not a thing or a being (not even the Supreme Being), but rather Being Itself: God is the act of to be itself.
* https://en.wikipedia.org/wiki/Aseity
* https://www.youtube.com/watch?v=1zMf_8hkCdc
I would love to hear how you think this is not logical.
> How is anything caused, what does it mean for a cause to not exist, what hardware does God run on and so on?
You were caused by your parents, they were caused by your grandparents. Before you existed your parents needed to exist. When your parents did not exist, neither did you.
That's one way (though not the only way) "for a cause to not exist". (Called per accidens sequences by Aquinas/Aristotle.)
The thing that we call "God" runs on no hardware, but is the hardware that everything else is built on. Strictly speaking, in the (Catholic) Christian thinking, God is not a thing or a being (not even the Supreme Being), but rather Being Itself: God is the act of to be itself.
* https://en.wikipedia.org/wiki/Aseity
* https://www.youtube.com/watch?v=1zMf_8hkCdc
I can imagine inquisitive minds today might want to know more about how the God "hardware" works.
We have amazing computers today that can simulate worlds. We use them to simulate and learn about this one. It's almost inconceivable in the past, but now someone might say that this world is a simulation and that our creator may have created along with the hardware our world runs on. Perhaps it seems unlikely, but we have new ideas to explore and I like to leave a little room for them.
I suppose that's why I'm not so sure about the premises. The world has turned out to be really amazing and strange.
To answer your question, I imagine something may exist at one time, then not exist, but have put in motion the events to cause it to exist again. So things that get into a causal loop like a mushrooms and fungal spores, a cutting or someday perhaps digital copy of a physical person, or some speculate even the whole universe gets recycled.
We have amazing computers today that can simulate worlds. We use them to simulate and learn about this one. It's almost inconceivable in the past, but now someone might say that this world is a simulation and that our creator may have created along with the hardware our world runs on. Perhaps it seems unlikely, but we have new ideas to explore and I like to leave a little room for them.
I suppose that's why I'm not so sure about the premises. The world has turned out to be really amazing and strange.
To answer your question, I imagine something may exist at one time, then not exist, but have put in motion the events to cause it to exist again. So things that get into a causal loop like a mushrooms and fungal spores, a cutting or someday perhaps digital copy of a physical person, or some speculate even the whole universe gets recycled.
> I can imagine inquisitive minds today might want to know more about how the God "hardware" works.
Again, this is a category error. God (in the Catholic/Christian theological tradition) is not, strictly speaking, an individual or a being. Not even the Supreme Being. God is the act of to be. What you mean when you refer to "God" and what theologians mean when they refer to "God" are two different things:
* https://www.youtube.com/watch?v=1zMf_8hkCdc
> The world has turned out to be really amazing and strange.
Stranger than you thing. Expanding:
> Of every created entity, we may ask two questions: what is its nature, and does it actually exist? Answering the first question does not give us an answer to the second. Consider the question “What is ____?” [...] If, for example, we ask, “What is a human being?” we might reasonably reply, “A rational animal.” We need not add the phrase “that exists.” It does not improve or clarify our response to the request for a definition. We can grasp the “what-it-is” of an entity, in other words, without having to determine whether it exists.
[...]
> This distinction between essence and existence also applies to imaginary entities. If you ask me, “What are elves?” I will explain that they are rational children of Ilúvatar, but unlike human beings, they are immortal and exist as long as the world lasts. [Per Tolkien.]
[...]
> Commenting on the above passage from the Summa Theologiae, Bauerschmidt writes: “Existence is not a part of the definition of any created thing; even more, it cannot be derived from that definition, as the ability to laugh can be derived from the definition of human beings as rational animals, for the existence of a particular thing’s essence presupposes that the thing exist”
> But not so with the eternal Creator, who is perfect simplicity. If God is God—that is to say, the ultimate and final answer to the question “Why does anything exist rather than nothing?” (the burden of the Five Ways)—then he cannot suffer from essence/existence composition. God does not potentially exist; he necessarily exists. Deity is the mystery where the ontological buck finally stops. Here is perhaps Thomas’s most important contribution to Christian reflection upon divinity. The eternal Creator and first mover must exist in and of himself. He cannot derive existence from some other source; otherwise the question of “why” would continue ad infinitum. But not only must God exist, he is his existence: the whatness of God is identical to his act of existing (ipsum essendi).
* https://afkimel.wordpress.com/2016/05/25/god-simply-is-the-s...
> To answer your question, I imagine something may exist at one time, then not exist, but have put in motion the events to cause it to exist again.
And what caused the thing to come into existence in the first place? It did not exist, at all, at one point it time. It then did. Then it went away, but came back. I'm talking about the first nothing-to-something instantiation.
Further, when it does exist, why does it continue to exist?
When theologians say "God creates the world", they don't just mean in the past. Yes, you could say "God created the world" via the Big Bang, but they also mean in the here-and-now. Just as Yo-Yo Ma created recordings of Bach's Cello Suites (that will continue to exist after he dies), he also creates the sound of the Cello Suites during a concert: and the music stops when he stops moving the bow.
The first ("created") sense is what is called accidentally ordered creation, while the latter ("creates") is called essentially ordered creation:
* http://tofspot.blogspot.com/2014/09/first-way-part-ii-two-le...
Again, this is a category error. God (in the Catholic/Christian theological tradition) is not, strictly speaking, an individual or a being. Not even the Supreme Being. God is the act of to be. What you mean when you refer to "God" and what theologians mean when they refer to "God" are two different things:
* https://www.youtube.com/watch?v=1zMf_8hkCdc
> The world has turned out to be really amazing and strange.
Stranger than you thing. Expanding:
> Of every created entity, we may ask two questions: what is its nature, and does it actually exist? Answering the first question does not give us an answer to the second. Consider the question “What is ____?” [...] If, for example, we ask, “What is a human being?” we might reasonably reply, “A rational animal.” We need not add the phrase “that exists.” It does not improve or clarify our response to the request for a definition. We can grasp the “what-it-is” of an entity, in other words, without having to determine whether it exists.
[...]
> This distinction between essence and existence also applies to imaginary entities. If you ask me, “What are elves?” I will explain that they are rational children of Ilúvatar, but unlike human beings, they are immortal and exist as long as the world lasts. [Per Tolkien.]
[...]
> Commenting on the above passage from the Summa Theologiae, Bauerschmidt writes: “Existence is not a part of the definition of any created thing; even more, it cannot be derived from that definition, as the ability to laugh can be derived from the definition of human beings as rational animals, for the existence of a particular thing’s essence presupposes that the thing exist”
> But not so with the eternal Creator, who is perfect simplicity. If God is God—that is to say, the ultimate and final answer to the question “Why does anything exist rather than nothing?” (the burden of the Five Ways)—then he cannot suffer from essence/existence composition. God does not potentially exist; he necessarily exists. Deity is the mystery where the ontological buck finally stops. Here is perhaps Thomas’s most important contribution to Christian reflection upon divinity. The eternal Creator and first mover must exist in and of himself. He cannot derive existence from some other source; otherwise the question of “why” would continue ad infinitum. But not only must God exist, he is his existence: the whatness of God is identical to his act of existing (ipsum essendi).
* https://afkimel.wordpress.com/2016/05/25/god-simply-is-the-s...
> To answer your question, I imagine something may exist at one time, then not exist, but have put in motion the events to cause it to exist again.
And what caused the thing to come into existence in the first place? It did not exist, at all, at one point it time. It then did. Then it went away, but came back. I'm talking about the first nothing-to-something instantiation.
Further, when it does exist, why does it continue to exist?
When theologians say "God creates the world", they don't just mean in the past. Yes, you could say "God created the world" via the Big Bang, but they also mean in the here-and-now. Just as Yo-Yo Ma created recordings of Bach's Cello Suites (that will continue to exist after he dies), he also creates the sound of the Cello Suites during a concert: and the music stops when he stops moving the bow.
The first ("created") sense is what is called accidentally ordered creation, while the latter ("creates") is called essentially ordered creation:
* http://tofspot.blogspot.com/2014/09/first-way-part-ii-two-le...
Eh, if there are problems with the proof, it isnt because of that. All proofs by contradiction eventually claim the negation of their premise must be true. That's the point.
The weaknesses in these proofs are in the premises.
For example:
> Whatever is changing is being changed by another
Asian philosophers would have pointed out that self causation seems to be true. Most things that appear persistent cause themselves to change state. They even had the concepts of two things changing or creating each other at the same time "dependent co-arising". "conditioned existence". Thing might exist conditionally. When condition arises thing starts to exist, when it goes away it ceases to to exist.
For example:
> Whatever is changing is being changed by another
Asian philosophers would have pointed out that self causation seems to be true. Most things that appear persistent cause themselves to change state. They even had the concepts of two things changing or creating each other at the same time "dependent co-arising". "conditioned existence". Thing might exist conditionally. When condition arises thing starts to exist, when it goes away it ceases to to exist.
> Asian philosophers would have pointed out that self causation seems to be true.
This is more along the lines of the Second Way:
> 1. Everything which has come to exist has been caused to come to exist.
> 2. Nothing which has come to exist can be the cause of its own existence.
> 3. Everything which has come to exist is caused to exist by something other than itself. (follows from 1,2)
> 4. It is impossible for a chain of causes of this kind to go on to infinity.
> C. There must be a first cause, which causes other things to come into existence but did not itself come into existence. (follows from 3,4)
* https://www3.nd.edu/~jspeaks/courses/mcgill/201/aquinas-cosm...
Note that Aquinas has not (just|necessarily) talking about 'horizontal' causes (going back in time), but 'vertical' causes.
Up until the Big Bang Theory was formulated (by a Belgian priest no less)†, the accepted cosmology was that the universe had always existed eternally with no beginning. So Aquinas talking about what caused things (to continue) to exist in the here and now.
> A sequence is ordered essentially if each changer in the sequence possesses the power to change another only if a preceding changer is acting concurrently upon it. For example, a clarinet does not have the power to play Mozart's Clarinet Concerto in A in and of itself. It will only play if Sharon Kam is playing upon it concurrently.
* http://tofspot.blogspot.com/2014/09/first-way-part-ii-two-le...
For a fuller treatment on the subject, I highly recommend the book Aquinas by Edward Feser.
† The fact that it was initially put forward by a priest supposedly stunted its spread a bit, because folks thought that he just wanted to give "scientific" grounding to the Biblical account of creation in the book of Genesis.
This is more along the lines of the Second Way:
> 1. Everything which has come to exist has been caused to come to exist.
> 2. Nothing which has come to exist can be the cause of its own existence.
> 3. Everything which has come to exist is caused to exist by something other than itself. (follows from 1,2)
> 4. It is impossible for a chain of causes of this kind to go on to infinity.
> C. There must be a first cause, which causes other things to come into existence but did not itself come into existence. (follows from 3,4)
* https://www3.nd.edu/~jspeaks/courses/mcgill/201/aquinas-cosm...
Note that Aquinas has not (just|necessarily) talking about 'horizontal' causes (going back in time), but 'vertical' causes.
Up until the Big Bang Theory was formulated (by a Belgian priest no less)†, the accepted cosmology was that the universe had always existed eternally with no beginning. So Aquinas talking about what caused things (to continue) to exist in the here and now.
> A sequence is ordered essentially if each changer in the sequence possesses the power to change another only if a preceding changer is acting concurrently upon it. For example, a clarinet does not have the power to play Mozart's Clarinet Concerto in A in and of itself. It will only play if Sharon Kam is playing upon it concurrently.
* http://tofspot.blogspot.com/2014/09/first-way-part-ii-two-le...
For a fuller treatment on the subject, I highly recommend the book Aquinas by Edward Feser.
† The fact that it was initially put forward by a priest supposedly stunted its spread a bit, because folks thought that he just wanted to give "scientific" grounding to the Biblical account of creation in the book of Genesis.
I have seen Aquinas's proof written somewhere. It is like what you wrote: Something that is moved is moved by someone else, but there cannot be a infinite regress, therefore God is the unmoved mover. But that is illogical: The conclusion contradicts the premise. Rather, if something that is moved is moved by someone else that is before it (rather than a loop), then it necessarily is a infinite regress (and this infinite regress is like what is God, I suppose).
> Rather, if something that is moved is moved by someone else that is before it (rather than a loop), then it necessarily is a infinite regress (and this infinite regress is like what is God, I suppose).
Read the series posts. The use of the word "motion" in the day-to-day colloquial sense is not the way "motion" is being used in the technical/philosophical sense in these arguments:
> What's in a name? If "motion" is more than the thin concept used in modern physics, that raises the question³ of whether we ought to call it "motion" anymore. Because motion is defined as "the reduction potency to act," we might call it "actualization," but this would earn blank stares [see left]. So would kinesis, although that sounds agreeably scientificalistic. The word change captures the greater scope of kinesis, but comes off as rather bland. It's kinetic change, after all.
[...]
> 3. "Motion" begins when the many potencies a thing possesses collapse onto a single potency (the "actual" potency). The act of building commences.
> 4. "Motion" ceases when the potency has been fully actualized (or the actualizing force has been removed!) The building has been completed (or abandoned).
> 5. "Motion" means that a thing is both what it is now and what it is going to be, as of now.
> 6. "Motion" is a change to something a thing already possesses. If the thing already possesses motion, then it would be a change in that motion (i.e., an acceleration)
[...]
> 8. "Inertia" (lit. "laziness") is a principle of resistance to change, not a principle of motion. "Motion" ["Change"] must overcome this resistance. A body does not continue to move because of inertia, but because of momentum. If friction changes the motion, it must overcome resistance to change.
> 9. "Motion" that is continuous and unchanging is actually "rest" (equilibrium). This includes orbiting planets, Belousov–Zhabotinsky reactions, etc.
* http://tofspot.blogspot.com/2014/08/first-way-moving-tale.ht...
Read the series posts. The use of the word "motion" in the day-to-day colloquial sense is not the way "motion" is being used in the technical/philosophical sense in these arguments:
> What's in a name? If "motion" is more than the thin concept used in modern physics, that raises the question³ of whether we ought to call it "motion" anymore. Because motion is defined as "the reduction potency to act," we might call it "actualization," but this would earn blank stares [see left]. So would kinesis, although that sounds agreeably scientificalistic. The word change captures the greater scope of kinesis, but comes off as rather bland. It's kinetic change, after all.
[...]
> 3. "Motion" begins when the many potencies a thing possesses collapse onto a single potency (the "actual" potency). The act of building commences.
> 4. "Motion" ceases when the potency has been fully actualized (or the actualizing force has been removed!) The building has been completed (or abandoned).
> 5. "Motion" means that a thing is both what it is now and what it is going to be, as of now.
> 6. "Motion" is a change to something a thing already possesses. If the thing already possesses motion, then it would be a change in that motion (i.e., an acceleration)
[...]
> 8. "Inertia" (lit. "laziness") is a principle of resistance to change, not a principle of motion. "Motion" ["Change"] must overcome this resistance. A body does not continue to move because of inertia, but because of momentum. If friction changes the motion, it must overcome resistance to change.
> 9. "Motion" that is continuous and unchanging is actually "rest" (equilibrium). This includes orbiting planets, Belousov–Zhabotinsky reactions, etc.
* http://tofspot.blogspot.com/2014/08/first-way-moving-tale.ht...
OK, what you write makes sense, although my argument is not about motion, but rather about Aquinas's argument, so the meaning of "motion" is not relevant to my argument (whether that premise is true or false is also not relevant); rather, I am commenting on the form of the argument being illogical.
> God, by definition, is that for which no greater can be conceived.
This axiom is very questionable to people who don't already believe in God, so the proof is worthless. For example, I'd define God as a social construct created to cope with existential dread. By that definition God doesn't exist.
This axiom is very questionable to people who don't already believe in God, so the proof is worthless. For example, I'd define God as a social construct created to cope with existential dread. By that definition God doesn't exist.
By your definition God does exist.
Thread from 2014: https://news.ycombinator.com/item?id=8806293
2009: https://news.ycombinator.com/item?id=417917
Others?
2009: https://news.ycombinator.com/item?id=417917
Others?
Seems like it's made the rounds a few times. Still, 2014 was 5 years ago and 2009 was 10 years ago. It's likely that many of us either weren't on HN at the time or several years is sufficient for us to have forgotten.
Oh yes, reposts are fine after about a year—this is in the FAQ: https://news.ycombinator.com/newsfaq.html. The reason for linking to past discussions is just that some readers find them interesting.
I think that it is difficult to define what is meant by "God"; and maybe even by "exists" in such a context, too. So, many people will disagree. Also, even if a proof may be mathematically valid, it may be misapplied, or have invalid premises, or misuse of words (which can be a kind of misapplication, I suppose).
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Something I like about this is that whatever number you imagine as the greatest number signifying god, your conception is still much lower than Graham’s number. Graham’s number is the terrifying giant that reminds you that the limits of your conception are that of a weak human mind.
No I don’t care to debate technicalities :)
No I don’t care to debate technicalities :)
If you are postulating that "greatness" is infinitely conceivable, then defining "God is the greatest thing that can be conceived" would mean that god, like the largest number, does not exist.
No actually the opposite. I’m saying we have a finite capacity to imagine magnitude, though it’s not readily apparent. Infinite is easy conceptually, but most people’s pragmatic place holder for “basically infinite” is going to be a really big number. Very big to be sure. But Graham’s number is so large it’s beyond the scope of numbers you’re likely to have conceived could exist. It’s not something you can quite fit in your head even reading about it, like something out of Lovecraft.
Whatever you imagined in imagining God as the greatest thing, Graham’s number is inconceivably larger still.
And that is why Cthulhu wins.
Whatever you imagined in imagining God as the greatest thing, Graham’s number is inconceivably larger still.
And that is why Cthulhu wins.
> Whatever you imagined in imagining God as the greatest thing, Graham’s number is inconceivably larger still.
And despite that, there are still more numbers between 0 and 1 than increments required to reach Graham's number.
It seems to me like you are assuming that conceptions of god and integers share the same cardinality when I'm not so sure that is clearly the case.
And despite that, there are still more numbers between 0 and 1 than increments required to reach Graham's number.
It seems to me like you are assuming that conceptions of god and integers share the same cardinality when I'm not so sure that is clearly the case.
> I think God is the greatest jelly donut in existence.
Mmm, applied theology.
0: http://machall.com/view.php?date=2003-04-21
Mmm, applied theology.
0: http://machall.com/view.php?date=2003-04-21
If God wanted to be 'provable', we wouldn't we have anything left to prove (it would already be proved...). The option to doubt (or to believe) the existence of God, leaves an opportunity for love. Choice is essential to love. If we saw God, we would lose that choice. Though it's interesting to attempt to prove God; I'm currently reading "The Physics of Christianity" [0]. I can't say I stand behind it completely, but it's a fascinating effort.
[0] - https://www.amazon.com/Physics-Christianity-Frank-J-Tipler/d...
[0] - https://www.amazon.com/Physics-Christianity-Frank-J-Tipler/d...
This proof exploits an edge case in dualistic human reasoning which occurs at the intersection of ontology and epistemology.
Lets do some term re-writing, so we can move away from the emotional trigger that is the God-word.
1. God, by definition, is that for which no greater can be conceived.
This conception of God is equivalent to what we call 'The Universe'.
Rewritten: The Universe, by definition, is that for which no greater can be conceived.
2. God exists in the understanding.
The Universe itself doesn't exist in the same way a planet, or a galaxy exists. The Universe is ALL things that exist. Conceptually it's the set of all sets.
Planets, stars and galaxies exist ontologically as members of the set. The Universe exists only epistemologically as a category in your head.
Rewritten: The Universe exists in the understanding.
3. If God exists in the understanding, we could imagine Him to be greater by existing in reality.
Rewritten: If The Universe exists in the understanding, we could imagine The Universe to be greater by existing in reality.
Uh what? We could imagine The Universe to exist within The Universe?
From a contradiction anything follows.
It's simply a case of Equivocation fallacy. Godel uses the word 'exists' in multiple senses throughout the argument.
The premises could have been about anything.
Lets do some term re-writing, so we can move away from the emotional trigger that is the God-word.
1. God, by definition, is that for which no greater can be conceived.
This conception of God is equivalent to what we call 'The Universe'.
Rewritten: The Universe, by definition, is that for which no greater can be conceived.
2. God exists in the understanding.
The Universe itself doesn't exist in the same way a planet, or a galaxy exists. The Universe is ALL things that exist. Conceptually it's the set of all sets.
Planets, stars and galaxies exist ontologically as members of the set. The Universe exists only epistemologically as a category in your head.
Rewritten: The Universe exists in the understanding.
3. If God exists in the understanding, we could imagine Him to be greater by existing in reality.
Rewritten: If The Universe exists in the understanding, we could imagine The Universe to be greater by existing in reality.
Uh what? We could imagine The Universe to exist within The Universe?
From a contradiction anything follows.
It's simply a case of Equivocation fallacy. Godel uses the word 'exists' in multiple senses throughout the argument.
The premises could have been about anything.
About this proof, quoting from a talk by John W. Dawson Jr., an internationally recognized authority on the life and work of Kurt Gödel:
"And a final example of this sort of unfashionable pursuit is Gödel's proof of the existence of God, which is a formalization in modal logic of an argument — traces all the way back to Anselm — but in particular an argument due to Leibniz. Gödel was very much interested in Leibniz's philosophy, and so he felt that it would be possible to formalize some of Leibniz's ideas. But because this was a theological subject he was very cautious about this. Said very little about it during his lifetime. And although word of it sort of leaked out, it was only after his death that the details were really made public.
"In fact, when I was cataloging Gödel's papers, I realized that there was some concern among the triumvirate of mathematicians that were in charge of my work [...] that there might be some things in Gödel's Nachlass that needed to be restricted, that scholars would not be allowed access to. And it quickly became apparent that this was the primary thing they were thinking of. And it took some persuasion on my part to convince them that while mathematicians may think it's silly to try to prove that God exists, philosophers certainly don't, and that this was something of real interest in philosophy. And so, eventually, unlike Russell's papers, where — as you may know — large segments are embargoed [...] you can see everything in Gödel's Nachlass, there aren't any restrictions on that."
Source: https://youtu.be/4vpTFZdyjKM?t=2179