5 ms·

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 coul

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.

bcaa7f3a8bbc 7y ago
See the Wikipedia page of Ontological Argument. https://en.wikipedia.org/wiki/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.
Saturn_V 7y ago
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
- tcgv 7y ago
  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.
  - Saturn_V 7y ago
    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.
    - a1369209993 7y ago
      > 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.
  - vinceguidry 7y ago
    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.
- justinpombrio 7y ago
  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?
  - ARandomerDude 7y ago
    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.
    - 481092 7y ago
      > 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".
  - 7y ago
- AgentME 7y ago
  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.
- TomMckenny 7y ago
  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.
- throw0101a 7y ago
  > 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 https://www.youtube.com/watch?v=1zMf_8hkCdc
- myrryr 7y ago
  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.
- elihu 7y ago
  Couldn't one satisfy the argument simply by believing that God is real, regardless of whether he does or not?
reggehid 7y ago
That’s not Gödel’s ontological argument. You’re confusing it with something else.
13415 7y ago
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).
andrepd 7y ago
That is not Godel's ontological argument, that's Saint Anselm's.
zwkrt 7y ago
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”
- gjm11 7y ago
  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 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!
dvt 7y ago
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.

bcaa7f3a8bbc 7y ago

See the Wikipedia page of Ontological Argument. https://en.wikipedia.org/wiki/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.

Saturn_V 7y ago

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

tcgv 7y ago
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.
- Saturn_V 7y ago
  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.
  - a1369209993 7y ago
    > 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.
- vinceguidry 7y ago
  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.
justinpombrio 7y ago
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?
- ARandomerDude 7y ago
  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.
  - 481092 7y ago
    > 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".
- 7y ago
AgentME 7y ago
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.
TomMckenny 7y ago
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.
throw0101a 7y ago
> 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 https://www.youtube.com/watch?v=1zMf_8hkCdc
myrryr 7y ago
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.
elihu 7y ago
Couldn't one satisfy the argument simply by believing that God is real, regardless of whether he does or not?

reggehid 7y ago

That’s not Gödel’s ontological argument. You’re confusing it with something else.

13415 7y ago

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).

andrepd 7y ago

That is not Godel's ontological argument, that's Saint Anselm's.

zwkrt 7y ago

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”

gjm11 7y ago
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 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!

dvt 7y ago

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.