Modified Version of Anselm's Ontological Argument

Epicero April 19, 2023 at 11:44 7700 views 88 comments
Here is a modified version of Anselm's ontological argument for Gods existence and how it answers an objection from Kant. First I will list the original argument followed by its modified version.

Original:

1. That than which nothing greater can be conceived (TTWNGCBC) exists in thought.
2. It is greater to exist in thought and in actuality than to exist just in thought.
3. TTWNGCBC exists in actuality.
4. If TTWNGCBC exists in actuality, then God exists in actuality.
5. God exists in actuality

Modified:

1. If TTWNGCBC existed contingently, then there would be something greater than it (viz. a version of TTWNGCBC that existed necessarily).
2. Nothing is greater than TTWNGCBC.
3. Therefore, TTWNGCBC exists necessarily.
4. TTWNGCBC is God.
5. Therefore, God is necessarily existent.

Kant claims that existence is not a real predicate, meaning that existence cannot be a property or characteristic of something. He claims this because when we conceive of something in our minds, we conceive of it existing. There is no other way to conceive it or picture it if it lacks existence. Something has to exist in order to have the property of existence. Since what we conceive of has to have the property of existence, there is theoretically no meaning behind the property and it is an innate characteristic to anything. This is an issue for Anselm’s argument, because he claims that existence is a property of God as the perfect being must exist. If existence is not a property of God or the perfect being, then there is no conclusive claim about the existence of God.
The solution to this problem lies in the fact that more than one mode of existence exists. Even if existence is not a real predicate, God’s existence is. This is because God exists either necessarily or impossibly. He cannot exist contingently. We all exist contingently because we may or may not exist and have the ability to not exist. God on the other hand, cannot exist and have the potential for nonexistence (or not-exist and have the potential for existence). If that were the case, he would not be God. Therefore, Kant’s argument only applies to contingent existence. His argument is no threat to Anselm’s. To better define this we modified Anselm's argument in such a way.

Comments (88)

invicta April 19, 2023 at 11:55 #801108
Suppose I can think of a perfect pink unicorn and no better pink unicorn can be conceived via thought. It’s existence is not a necessity although it is contingent.

That is your modified argument in a nutshell.

It’s a good argument only in so far as we include it’s contingency as the necessity part of the argument is an unfounded conclusion right from the start.
Art48 April 19, 2023 at 13:44 #801183
My pet cat reasons as follows.
1. I can conceive of nothing greater than MO (my owner), who takes care of me, feeds me, provides me catnip and a comfortable place to live.
2. If MO existed contingently, there would be something greater
3. Nothing is greater than MO
4. Thererfore, MO exists necessarily
5. Therefore, MO is God.

The flaw is
2. Nothing is greater than TTWNGCBC
Any limitation in what we can conceive, doesn’t imply anything about what exists.
RogueAI April 19, 2023 at 13:54 #801189
Quoting invicta
Suppose I can think of a perfect pink unicorn and no better pink unicorn can be conceived via thought. It’s existence is not a necessity although it is contingent.


Isn't that perfect pink unicorn (PPU) eventually going to turn into god? For example, if the PPU isn't all-loving, I can think of a PPU that is. If the PPU isn't all-knowing, I can think of a PPU that is, etc. Eventually, the perfect PPU will be an omniobenevolent, omniscient, omnipotent necessarily existing thing. God, in other words.
180 Proof April 21, 2023 at 23:53 #802092
Reply to Epicero Neither are sound arguments.
Banno April 22, 2023 at 01:12 #802111
Reply to Epicero

Russell set Kant's objection out much more clearly. this is an oversimplification, but...

Existence is taken as a second-order predicate.

First-order predicates apply to (range over) individuals, and are written using the letters f,g,h... We write "f(a)" for the predication "a is f".

But if we want to say that something about the predicate, we need to move up a level. So if we want to say that something has the predicate f, we use an existential quantifier. So "Some thing has the predicate f" or "Something is f" have to be written:
?(x)f(x)

"There exists an x such that x is f".

Notice that the existential quantifier - the existential predicate, if you will - haas the predicate "f" within it's scope? It ranges over predicates. "f" is a first-order predicate, "?" is a second-order predicate.

The result, is that the formula ?(a) - "The individual a exists" - is ill-formed. It says nothing.

The upshot of all this is that it is pretty much impossible to set out the structure of the ontological argument in first-order logic. Or if you prefer, that the argument does not make sense.

Hence it is not valid.

Banno April 25, 2023 at 22:17 #803053
Reply to Epicero?

You only do OP's?
Art48 April 26, 2023 at 14:00 #803163
Quoting Banno
Russell set Kant's objection out much more clearly. this is an oversimplification, but...
Existence is taken as a second-order predicate.
First-order predicates apply to (range over) individuals, and are written using the letters f,g,h... We write "f(a)" for the predication "a is f".

I've seen this argument before but never fully understood it. Can you provide a reference which elaborates? Why can't existence be regarded as a first-order predicate?
Letting "a" stand for "exists" we have:
f(a) is false if f is "the first even prime number after 2"
f(a) is true if f is "the first odd prime number after 2"

Also, if "a" is "is green" then f(a) is true if f is "grass". But does that make "is a color" a second order predicate because we can say "green is a color"? i.e., "a" means "is a color" and f refers to green.
Michael April 26, 2023 at 14:16 #803164
Quoting Epicero
1. If TTWNGCBC existed contingently, then there would be something greater than it (viz. a version of TTWNGCBC that existed necessarily).
2. Nothing is greater than TTWNGCBC.
3. Therefore, TTWNGCBC exists necessarily.
4. TTWNGCBC is God.
5. Therefore, God is necessarily existent.


Your argument appears to be:

1. If God exists then God necessarily exists
2. Therefore, God (necessarily) exists

The conclusion doesn't follow.
Michael April 26, 2023 at 14:42 #803167
Quoting Epicero
1. That than which nothing greater can be conceived (TTWNGCBC) exists in thought.
2. It is greater to exist in thought and in actuality than to exist just in thought.
3. TTWNGCBC exists in actuality.
4. If TTWNGCBC exists in actuality, then God exists in actuality.
5. God exists in actuality


One of these is true:

1. I conceive of [an entity which is all powerful and all knowing and exists] and this entity doesn't exist
2. I conceive of [an entity which is all powerful and all knowing and exists] and this entity exists

The thing conceived (as shown in brackets) is the same in both cases. Anselm's argument makes a fallacious reinterpretation of these as something like:

3. I conceive of [an entity which is all powerful and all knowing and exists and doesn't exist]
4. I conceive of [an entity which is all powerful and all knowing and exists and exists]

He then claims that because the thing conceived (as shown in brackets) in 4) is "greater" than in 3) then 2) must be true, which again is a fallacious reinterpretation.
universeness April 26, 2023 at 15:24 #803172
I see no logical difference in proposing an ontological or teleological argument for god than the logic, of asking for the biggest possible number. Such has no existent.
Mww April 28, 2023 at 13:24 #803536
Quoting Michael
because the thing conceived (as shown in brackets) in 4) is "greater" than in 3)…..


“…. By whatever and by whatever number of predicates—even to the complete determination of it—I may cogitate a thing, I do not in the least augment the object of my conception by the addition of the statement: This thing exists.…”
(CPR A600/B628)

Quoting Michael
…..then 2) must be true, which again is a fallacious reinterpretation.


2) positing “and this entity exists”, is precisely the fallacy in the original argument expounded in the Kantian objection to it.

The OP is full of holes, but your breakdown is agreeable.



Banno April 28, 2023 at 23:03 #803715
Quoting Art48
Why can't existence be regarded as a first-order predicate?


It can. It's called Free Logic. But one of the results of free logic is that the existence of something cannot be the result of a deduction.

public hermit April 29, 2023 at 01:07 #803727
"The unconditioned necessity of judgments, however, is not an absolute necessity of things" Immanuel Kant Critique (A593/B621).

I took that from a recent article by Andrew Stephenson "Existence and Modality in Kant: Lessons from Barcan" in The Philosophical Journal. Is it the case that if something is possible then there must be something that possibly instantiates it? I don't know, but I'm gathering the de re/de dicto distinction might help show why the modified version won't work, @Epicero
Banno April 29, 2023 at 01:15 #803731
Quoting Banno
Here are two puzzles, from Frege and Russell, that must be explained if one is to treating "exists" as a property.

1. What is the difference between a sweet, juicy, red apple and a sweet, juicy red apple that exists? The difference between a red apple and a green apple, or a sweet apple and a sour apple, is pretty clear. But explaining clearly what is added to an apple by existing...?

2. It's not difficult to understand an apple that is not sweet, or an apple that is not red - but an apple that does not exist? What is it?

Michael April 29, 2023 at 10:10 #803805
Quoting Banno
It's not difficult to understand an apple that is not sweet, or an apple that is not red - but an apple that does not exist? What is it?


I don't quite get the issue. We seem to understand what we mean when we ask whether or not ghosts or aliens or tachyons exist.
hypericin April 29, 2023 at 17:51 #803936
Both versions conflate the thought of something and its existence.

In the first version:
2. It is greater to exist in thought and in actuality than to exist just in thought.

Here, "It" slides from the thought of (1) into a being. In some sense (though such arguments seem quaint to modern eyes), the thought of an existent being is "greater" than the thought of that same but nonexistent being. But whether or not the being exists in actuality does not impact the "greatness" of the thought. The thought remains identical across universes where the being exists and doesn't exist.

I think Reply to Michael is making this same point, but more clearly.


Quoting Banno
The upshot of all this is that it is pretty much impossible to set out the structure of the ontological argument in first-order logic. Or if you prefer, that the argument does not make sense.

Hence it is not valid.


This is not a refutation. So, it requires 2nd order logic. So what?




Banno April 29, 2023 at 19:44 #803958
Quoting hypericin
it requires 2nd order logic. So what?

So you can set it out in a second order formalism?

Go on, then.

Richard B May 02, 2023 at 03:20 #804516
Without assuming some underlying logic behind the language used by Anselm, what could Anslem be showing us with this argument, and why is it so unsatisfying to some. I think the passage before the main argument can shine some light.

“When a painter considers beforehand what he is going to paint, he has it in his understanding…” What is Anslem trying to say here, or how should one understand this? I think he would demonstrate that it is in his understanding by articulating or describing what he plans to paint. This shows what is “in his understanding”. If he was unable to articulate, this would demonstrate that nothing was “in his understanding.”

“But when he has painted it, he both has it in his understanding and understands that what he has now produced exists.” I do not think Anslem is saying that the painter is reporting on what he is perceiving (though it is implied that it happened), but more reflecting on what he has produced, and that he can say “it exists” whether he is perceiving it or not.

How did Anselm demonstrate his understanding of God. He provided us with definition, “God is a being than which none greater can be thought.” It must be accepted to get one started in the deductive reasoning like one does with geometric proofs (consider Euclid’s Elements, "A point is that which has position but not dimensions.") From a definition, Anselm concludes that “God exists” because to exist “in reality” is greater than just “existing in understanding.” Unlike the painting example, Anselm is not reflecting on an experience of God “in reality” like the painter did with his painting, but reflecting on the "ideas of God" that makes him understand "God exists." And this is where, to some, the argument is not satisfying. Anselm gets to “God exists” not by the example most would agree they understand by “to exist in reality” like the painting example.

So we are left with:

Chapter 2 (Proslogion)

“What exists exactly?” Answer, “A being than which none greater can be thought.”

“And what is that?” Answer, “a being that exists “in reality” as well as “in understanding.” This is greater than just "in understanding."

“And what being is that” Answer, “A being than which none greater can be thought.”

Chapter 3 (Proslogion)

“What exists exactly?” Answer, “A being than which none greater can be thought.”

“And what is that?” Answer, "A being that necessarily exists" This is greater than a being that contingently exists."

“And what being is that” Answer, “A being than which none greater can be thought.”

Hallucinogen May 03, 2023 at 19:07 #804871
Quoting Michael
1. If TTWNGCBC existed contingently, then there would be something greater than it (viz. a version of TTWNGCBC that existed necessarily).
2. Nothing is greater than TTWNGCBC.
3. Therefore, TTWNGCBC exists necessarily.
4. TTWNGCBC is God.
5. Therefore, God is necessarily existent. — Epicero

Your argument appears to be:

1. If God exists then God necessarily exists
2. Therefore, God (necessarily) exists


Could you lay out how you arrived at this representation please?

It does not begin with "if God exists", it begins with something equivalent to saying "that which there is nothing greater cannot be contingent". What falls into this category is God, and so the set-up connecting existence with non-contingency produces the conclusion. Denying that the category exists seems a contradiction in terms, as well as raises difficult questions about what the denier thinks. It is like saying "there's no greatest number".
Michael May 03, 2023 at 19:18 #804873
Reply to Hallucinogen

1), 2), 3) is simplified to:

a) If some X is TTWNGCBC then X necessarily exists

Given 4), replace "TTWNGCBC" with "God":

b) If some X is God then X necessarily exists

Or in other words:

1. If God exists then God necessarily exists

Hence why the argument is just:

1. If God exists then God necessarily exists
2. Therefore, God (necessarily) exists

Clearly a non sequitur.
Hallucinogen May 03, 2023 at 19:31 #804877
I think you are simplifying 1) too much.
Quoting Michael
a) If some X is TTWNGCBC then X necessarily exists


If TTWNGCBC existed contingently, then it would not exist necessarily, but something else would be TTWNGCBC.

Removing those parts is allowing you to make the argument look as if it's a non-argument.

Quoting Michael
Given 4), replace "TTWNGCBC" with "God:
b) If some X is God then X necessarily exists


No, the argument is "If some X is TTWNGCBC, then X necessarily exists".
Michael May 03, 2023 at 20:31 #804899
Quoting Hallucinogen
No, the argument is "If some X is TTWNGCBC, then X necessarily exists".


If some X is TTWNGCBC then X necessarily exists
If some X is TTWNGCBC then X is God
If some X is God then X necessarily exists

Therefore, God (necessarily) exists

This is what the argument amounts to. The conclusion is a non sequitur.
Hallucinogen May 03, 2023 at 20:46 #804904
Quoting Michael
If some X is TTWNGCBC then X necessarily exists
If some X is TTWNGCBC then X is God
If some X is God then X necessarily exists

Therefore, God (necessarily) exists

This is what the argument amounts to. The conclusion is a non sequitur.


I don't think that's a non sequitur, it's just not a fully formed argument. It's just 3 axioms followed by a conclusion. You could have switched "God" and "X" on the 3rd line though, that would've made it a valid and sound argument.

It could go:

If some X is TTWNGCBC, then X necessarily exists
God is an X.
Therefore, God (necessarily) exists.

Not a non sequitur.
Michael May 03, 2023 at 20:48 #804906
Quoting Hallucinogen
It could go:

If some X is TTWNGCBC, then X necessarily exists
God is an X.
Therefore, God (necessarily) exists.

Not a non sequitur.


Then this begs the question, as the second premise just asserts that God exists.
Hallucinogen May 03, 2023 at 20:50 #804908
Reply to Michael No it doesn't, it asserts God fits the definition of X.
Michael May 03, 2023 at 20:52 #804909
Reply to Hallucinogen You're misunderstanding the logic. Look at existential quantification.

I'll be more explicit with my terms to make this clearer:

1. If there exists something which is TTWNGCBC then this thing necessarily exists
2. If there exists something which is TTWNGCBC then this thing is God
3. If there exists something which is God then this thing necessarily exists
4. Therefore, God (necessarily) exists

This is the fallacious argument that the OP has given.
Hallucinogen May 03, 2023 at 21:07 #804916
Quoting Michael
You're misunderstanding the logic. Look at existential quantification.


Could you elaborate on what I'm misunderstanding? I see that quantifier being used in the article cited to argue for the existence of certain numbers. I don't see the difference to how it's being used in this argument.

TTWNGCBC is a concept, just like numbers are, so using a quantifier that means "there exists" to express the condition that something fits the definition of that concept should not beg the question, even if the conclusion is that that something exists.

Quoting Michael
1. If there exists something which is TTWNGCBC then this thing necessarily exists
2. If there exists something which is TTWNGCBC then this thing is God
3. If there exists something which is God then this thing necessarily exists
4. Therefore, God (necessarily) exists


3. in the above isn't in the original argument by the OP. They don't give the condition "if there exists God..." in the argument. It isn't necessary to include and I don't see a fallacy in the argument without it. All that is necessary is stating that God fits the definition of TTWNGCBC in some way, which the OP did in point 4.
Michael May 03, 2023 at 21:23 #804923
Quoting Hallucinogen
3. in the above isn't in the original argument by the OP. They don't give the condition "if there exists God..." in the argument. It isn't necessary to include and I don't see a fallacy in the argument without it. All that is necessary is stating that God fits the definition of TTWNGCBC in some way, which the OP did in point 4.


Then the argument is:

1. If there exists something which is TTWNGCBC then this thing necessarily exists
2. If there exists something which is TTWNGCBC then this thing is God
3. Therefore, God (necessarily) exists

Which again is invalid.
Hallucinogen May 03, 2023 at 22:01 #804942
Quoting Michael
Then the argument is:

1. If there exists something which is TTWNGCBC then this thing necessarily exists
2. If there exists something which is TTWNGCBC then this thing is God
3. Therefore, God (necessarily) exists


Actually it would be

1. If there exists something which is TTWNGCBC then this thing necessarily exists
2. If there exists something which is TTWNGCBC then this thing is God
3. TTWNGCBC is God (or vice versa).
4. Therefore, God (necessarily) exists.

Although it isn't optimal, it appears to be valid and sound.

Quoting Michael
Which again is invalid.


How so?
Michael May 03, 2023 at 22:07 #804947
Quoting Hallucinogen
1. If there exists something which is TTWNGCBC then this thing necessarily exists
2. If there exists something which is TTWNGCBC then this thing is God
3. TTWNGCBC is God (or vice versa).
4. Therefore, God (necessarily) exists.


How does 2 differ from 3?

Quoting Hallucinogen
How so?


Because the conclusion doesn't follow. You would need an additional premise such as:

1. If there exists something which is TTWNGCBC then this thing necessarily exists
2. If there exists something which is TTWNGCBC then this thing is God
3. There exists something which is TTWNGCBC
4. Therefore, God (necessarily) exists.

But 3) is an empirical claim that needs to be shown. It's not something that's true a priori.

The mistake the OP (and Anselm) makes is to derive 3) from 1), but that's a non sequitur.
Michael May 03, 2023 at 22:28 #804956
I think the modal ontological argument is a much stronger target of discussion.

1. If God exists then it is necessary that God exists
2. It is possible that God exists
3. Therefore, it is possible that it is necessary that God exists
4. If it is possible that it is necessary that God exists then it is necessary that God exists
5. Therefore, it is necessary that God exists

In formal logic:

[math]\exists xGx\to\Box\exists xGx\\\Diamond\exists xGx\\\therefore\Diamond\Box\exists xGx\\\Diamond\Box\exists xGx\to\Box\exists xGx\\\therefore\Box\exists xGx[/math]
Hallucinogen May 03, 2023 at 22:47 #804962
Quoting Michael
How does 2 differ from 3?


3 is not an axiom, just a definitional fact. 2. isn't necessary, I just left it there because you put it there. See:

Quoting Hallucinogen
If some X is TTWNGCBC, then X necessarily exists
God is an X.
Therefore, God (necessarily) exists.


Quoting Michael
1. If there exists something which is TTWNGCBC then this thing necessarily exists
2. If there exists something which is TTWNGCBC then this thing is God
3. There exists something which is TTWNGCBC
4. Therefore, God (necessarily) exists.

But 3) is an empirical claim that needs to be shown. It's not something that's true a priori.


Oh right. But I was assuming that by "If there exists something which is TTWNGCBC", you meant the same thing as "If some X is TTWNGCBC," in the arguments you gave when you were previously attacking it. I wouldn't try to defend this argument beginning with "If there exists something which is TTWNGCBC", because of the flaw you've pointed out, so I would have to insist on going back to the way you originally simplified it, to "If some X is TTWNGCBC (...)"

Showing that "there exists something which is TTWNGCBC" is the intent of the argument, so I suppose you would have to express it in a way that does not require the satisfaction of an empirical claim, as I have done above.
Michael May 03, 2023 at 23:25 #804973
Quoting Hallucinogen
But I was assuming that by "If there exists something which is TTWNGCBC", you meant the same thing as "If some X is TTWNGCBC," in the arguments you gave when you were previously attacking it.


Yes, they mean the same thing.

Quoting Hallucinogen
3 is not an axiom, just a definitional fact. 2. isn't necessary, I just left it there because you put it there.


Then the argument is invalid. To make your argument more precise:

1. If there exists something which is TTWNGCBC then this thing necessarily exists
2. God is defined as TTWNGCBC
3. Therefore, God (necessarily) exists

It's still missing the premise that asserts that there exists something which is TTWNGCBC, which as you say is the very intent of the argument.

To make this clearer by analogy:

1. If there exists something which is the greatest conceivable vampire then this thing necessarily exists
2. Dracula is defined as the greatest conceivable vampire
3. Therefore, Dracula exists

The conclusion doesn't follow. I'd need as a premise that the greatest conceivable vampire exists.
Banno May 03, 2023 at 23:55 #804989
Hallucinogen May 04, 2023 at 00:04 #804995
Quoting Michael
It's still missing the premise that asserts that there exists something which is TTWNGCBC


It doesn't need one; the argument is still valid.

Quoting Michael
1. If there exists something which is TTWNGCBC then this thing necessarily exists
2. God is defined as TTWNGCBC


Line 1 connects anything that fits the definition of TTWNGCBC (since you're allowing it to mean the same thing as "if some X is...") with it necessarily existing. So once a concept is identified as fitting that definition, it is shown to in fact exist.

Your objection seems to me to undermine the very capacity of logical and mathematical generalizations to prove anything about the world. All I need is for God to fit the definition of something which is a valid generalization of the logical and mathematical relationships between things that I already know to exist.

Quoting Michael
1. If there exists something which is the greatest conceivable vampire then this thing necessarily exists
2. Dracula is defined as the greatest conceivable vampire
3. Therefore, Dracula exists

The conclusion doesn't follow. I'd need as a premise that the greatest conceivable vampire exists.


It's a false analogy. Vampires aren't non-contingent entities.
Michael May 04, 2023 at 00:11 #805000
Quoting Hallucinogen
It's a false analogy. Vampires aren't non-contingent entities.


The greatest conceivable vampire is.

A vampire that exists is greater than a vampire that doesn’t exist.

A vampire that necessarily exists is greater than a vampire that non-necessarily exists.

Therefore, the greatest conceivable vampire is one that necessarily exists.

Replacing the word “vampire” with “intelligence” or “entity” or “thing” doesn’t change the logic.
Hallucinogen May 04, 2023 at 00:16 #805002
Reply to Michael If when you said "the greatest possible vampire" you ultimately didn't mean something uniquely vampiric, but just meant a non-contingent entity upon which everything else is contingent and we're calling it "Dracula", then your analogy is just the same argument and it is valid.
Michael May 04, 2023 at 00:31 #805006
Reply to Banno I don’t know how accurate that website is at parsing modal logics, but my understanding is that modal ontological arguments are commonly accepted to be valid, and so opponents must challenge the premise(s).

https://plato.stanford.edu/entries/ontological-arguments/#PlaOntArg

The “victorious” modal ontological argument of Plantinga 1974 goes roughly as follows: Say that an entity possesses “maximal excellence” if and only if it is omnipotent, omniscient, and morally perfect. Say, further, that an entity possesses “maximal greatness” if and only if it possesses maximal excellence in every possible world—that is, if and only if it is necessarily existent and necessarily maximally excellent. Then consider the following argument:

There is a possible world in which there is an entity which possesses maximal greatness.
(Hence) There is an entity which possesses maximal greatness.

Under suitable assumptions about the nature of accessibility relations between possible worlds, this argument is valid: from it is possible that it is necessary that p, one can infer that it is necessary that p. Setting aside the possibility that one might challenge this widely accepted modal principle, it seems that opponents of the argument are bound to challenge the acceptability of the premise.
Banno May 04, 2023 at 00:50 #805009
Quoting Michael
I don’t know how accurate that website is at parsing modal logics


The counter model looks right.

There might be something in the " suitable assumptions about the nature of accessibility relations between possible worlds", butI don't see it. It's invalid in all six, according to the tree proof generator.

So I'm left to supposing that it's down to how we pass
  • There is a possible world in which there is an entity which possesses maximal greatness.
  • (Hence) There is an entity which possesses maximal greatness.


??xGx??xGx looks invalid. there can be a world in which ??xGx is true, and yet ?xGx false - It is possible to have green cows, but there are no green cows.
Michael May 04, 2023 at 00:58 #805013
Quoting Banno
??xGx??xGx looks invalid.


Given the definition of “maximal greatness” as being necessarily “maximally excellent”, the argument is ?? ?xGx? ??xGx.

It is possible that something is necessarily maximally excellent, therefore it necessary that something is maximally excellent.
Michael May 04, 2023 at 01:01 #805015
Quoting Banno
The counter model looks right.


I think it’s interpreting this as an inference rather than as a premise:

?xGx ? ??xGx
Banno May 04, 2023 at 01:02 #805016
Quoting Michael
?? ?xGx? ??xGx.


But that's just an instance of ?p?p, which is pretty clearly invalid.

Quoting Michael
?xGx ? ??xGx


p??p. Invalid.
Michael May 04, 2023 at 01:18 #805018
Quoting Banno
But that's just an instance of ?p?p, which is pretty clearly invalid.


??p ? ?p is valid.

Quoting Banno
p??p. Invalid.


This is given as a premise, not an inference. It’s either true or false. If I gave this argument, would you reply by saying that 1) is invalid?

1. p?q
2. p
3. q
invicta May 04, 2023 at 01:18 #805019
I call bullshit on this badly constructed argument (Cosmological, Kalam, Contingent), it should go more like this.

Firstly it over complicates things, if cat, fish, dog is impossible (non-existent) then by fact of existence cat, fish, dog exist then cat, fish, dog exist.

Where does contingency come into it ?

Michael May 04, 2023 at 01:24 #805020
A simpler reformulation of the previous.

Either it is not possible that God exists or it is necessary that God exists
It is possible that God exists
Therefore, it is necessary that God exists

¬??xGx ? ??xGx
??xGx
??xGx
invicta May 04, 2023 at 01:27 #805021
Reply to Michael equivocation of necessity to possibility.

It’s like saying it’s possible that my next coin flip will be tail. So if I do flip it it will be tails. (By necessity)

Banno May 04, 2023 at 01:45 #805025
Reply to Michael That works.

https://www.umsu.de/trees/#((~3~9~7xGx~2~8~7xGx)~1~9~7xGx)~5~8~7xGx
Michael May 04, 2023 at 08:35 #805087
Reply to Banno

The question then is whether or not there is a satisfactory definition of God of which both ¬??xGx ? ??xGx and ??xGx are true.

The second premise is true if the definition doesn't contain a contradiction.

The first premise appears to be an application of the Buridan formula, ?x?Dx ? ??xDx, where Gx is defined as ?Dx, and Dx is defined as something like "x is the demiurge".

The full argument then is:

1. ?x?Dx ? ??xDx
2. ??x?Dx
3. ? ???xDx
4. ? ??xDx

What's interesting is that according to that website 1-3 is valid, 3-4 is valid, but 1-4 is invalid. That strikes me as a contradiction.

The countermodel is:

Worlds: { w0 }
Individuals: { 0 }
@: w0
D: { }
Banno May 04, 2023 at 09:27 #805096
Quoting Michael
The second premise is true if the definition doesn't contain a contradiction, which I think is an easy condition to satisfy.


If the definition is "a something a greater than which cannot be conceived", I'm not convinced. There's the obvious comparison of "A number a larger than which cannot be conceived" - the idea is not coherent.

Michael May 04, 2023 at 09:29 #805097
Quoting Banno
If the definition is "a something a greater than which cannot be conceived", I'm not convinced. There's the obvious comparison of "A number a larger than which cannot be conceived" - the idea is not coherent.


For the sake of argument I'm using the more simplistic definition "the demiurge of all possible worlds".
Banno May 04, 2023 at 09:33 #805100
Reply to Michael Hmm. The we are now a long way from Canterbury.

Michael May 04, 2023 at 09:41 #805105
Quoting Banno
The we are now a long way from Canterbury.


Yes, I've already argued with others that Anselm's argument is invalid. I'm now trying to find the strongest kind of ontological argument. It's a more worthy topic of discussion.
Banno May 04, 2023 at 09:47 #805109
Reply to Michael Yep.

But "the demiurge of all possible worlds" might need some work...

Michael May 04, 2023 at 09:55 #805111
Let Gx mean "x is God" and Fx mean "x created the world" (or anything else).

?xGx ? ?x?Fx
??x?Fx
? ?xGx

Proof

But given that ??x?Fx ? ?x?Fx is valid, ??x?Fx begs the question.

Also as a counterargument:

?xGx ? ?x?Fx
?¬?xFx
? ¬?xGx

Proof

But given that ?¬?xFx ? ¬?x?Fx is valid, ?¬?xFx also begs the question.

So at least with respect to the modal ontological argument there is no reason to believe either that God exists or that God doesn’t.
Sam26 May 04, 2023 at 13:37 #805187
Reply to Epicero

I'll use an argument formed from Anselm's text to show the argument isn't sound. It's taken from the English text of the Proslogion chapter 2. I think this is a better version of the argument, but it still doesn't work.

Premise (1) The fool hears and understands "a being than which none greater can be thought."

Premise (2) If the fool hears and understands, then it exists in his understanding.

Intermediate Conclusion: (3) The being than which none greater can be thought exists in the fool's understanding. Follows from (1) and (2) Modus Ponens

Premise (4) The being than which none greater can be thought exists in the understanding alone. (This would be the atheist's position according to Anselm.)

Premise (5) A being of which none greater can be thought can exist in reality.

Premise (6) A being that exists in reality is greater than a being existing in the understanding alone.

Intermediate Conclusion: (7) The being of which none greater can be thought existing in reality would be greater than the same being existing in the understanding alone. Follows from (5) and (6)

Final Conclusion: (8) A being than which none greater can be thought existing in reality would be greater than the same being existing in the mind/thought. Follows from (4) and (7)]

This presumably shows that the atheist position is contradictory, and therefore false. Why? Because the atheist's position is that a being than which none greater can be thought exists in the understanding alone. However, this cannot be so, because one could add a further attribute that would make it greater, viz., existing in reality. Thus, it can't exist in the understanding alone. It would be similar to saying that 10 is the greatest number. However, someone replies, no, I can add 1 to the number 10 and get 11, so 11 is the greatest number.

Since this argument is deductive it is valid. However, it must also be sound, i.e., the premises must be true, to be a good argument. The first premise with a problem is (2). How can a being exist in the understanding? Only a concept can exist in the understanding. We have the concept unicorn, but that doesn't mean unicorns are running around in my mind. Moreover, if you change the premise to only the concept existing in the understanding, then the argument is no longer valid. Why? Because if you add to the concept existing in reality you would still just have a concept existing in reality, not the being itself.

Finally, many find the argument dubious for other reasons, viz., trying to prove the existence of something from the concept alone, which others have pointed out in this thread, is very problematic to say the least.


EricH May 04, 2023 at 16:53 #805211
As a plain language person I can't get past the word "greater". To my way of thinking, "greatness" implies some mechanism to measure some observable or measurable property. But even this definition falls apart outside strictly defined parameters. Who is the greatest artist? Who is the greatest athlete of all time? Who (or what) is the greatest (fill in the blank)? Any criteria you choose to measure "greatness" in these examples is arbitrary.

Perhaps a naive question here, but does the word "greater" have some special meaning/usage in a philosophical discussion apart from the plain language meaning/usage?
Richard B May 05, 2023 at 16:33 #805425
Quoting Sam26
Why? Because if you add to the concept existing in reality you would still just have a concept existing in reality, not the being itself.

Finally, many find the argument dubious for other reasons, viz., trying to prove the existence of something from the concept alone, which others have pointed out in this thread, is very problematic to say the least.


I believe Anselm is trying to distinguish between two different ideas, "understanding that something exists in reality" and "experiencing that something exists in reality." As he says in Chapter 2 "And so. O lord, since thou givest understanding to faith, give me to understand-as far as thou knows it to be good for me-that thou exist, as we believe, and that thou art what we believe thee to be."

Unlike the painter and painting example, where producing a painting is the reason he understands the painting exists in reality, it is the idea of "a being than which none greater can be thought" and its deductive implication that Anselm understands such a concept of a being "exists in reality." So, when you say, "....you would still just have a concept exist in reality, not the being itself.", what is this idea trying to express? That the deductive argument should produce some experience of "the being of God"? Demonstrate some experience we had corresponds to this idea of "a being than which none greater can be thought."? It is a deductive argument, it is about ideas. Geometric proofs are about ideas, which does not mean it will have any successful application in reality.

Whether the argument is sound, how can we fairly access this? How does one evaluate the "truth" of "God is a being than which no greater can be thought", and "Existing in reality" is greater than "existing in understanding" in order to determine soundness. What should we do, take a poll on how many people agree with these premises?

Maybe what this argument ultimately demonstrates is the vacuousness of using general concepts and deductive reasoning whether one thinks something exist or not.

That experience is the final arbiter.
Banno May 05, 2023 at 22:44 #805519
Reply to Michael
Goats eat everything; therefore there is something that eats everything. therefore It is possible that something eats everything.

So you have a proof of the Great Goat:

Either it is not possible that something eats everything or it is necessary that something eats everything.
It is possible that something eats everything.
Therefore it is necessary that something eats everything.

And this we all call the Great Goat.

A few more small steps and we have that everything is a goat.
Michael May 06, 2023 at 10:10 #805571
Quoting Banno
Goats eat everything; therefore there is something that eats everything. therefore It is possible that something eats everything.

So you have a proof of the Great Goat:

Either it is not possible that something eats everything or it is necessary that something eats everything.
It is possible that something eats everything.
Therefore it is necessary that something eats everything.


Well, it's not a proof, but it is a valid argument.
fdrake May 10, 2023 at 14:15 #806904
Reply to Michael

I've never liked this one. Possibly necessary => necessary doesn't seem, to me, to be an adequate model of what a Godlike "necessary being" would look like.

Roughly, possibility means "exists in one (connected) possible world", and necessary means "exists in all (connected) possible worlds". It isn't exactly an account of what it would mean for a God to be a necessary existent in a world where they exist.

If you read premise one as "If god exists (in a world) then god exists in all worlds connected to that world", that's quite different from "If god exists (in a world), then their existence in that world is an essential property of it". If we take the sense of necessity of God's existence as "one whose essence includes existence", that sense of essentiality does not resemble necessity as a quantifier over possible worlds. Why? Essentiality concerns one entity in the world it's in - as a property of that entity. Necessity concerns one entity's behaviour in all worlds.

In other news, it doesn't tell you if the necessary existent is a god. Just that if a predicate behaves like premise 1, then it exists in all possible worlds. Could be the goat.
Michael May 10, 2023 at 14:54 #806913
Reply to fdrake

It does seem to trade on an ambiguous interpretation of the phrase "necessary". Modality is tricky. When I say that it is possible that it will rain tomorrow, I'm not simply saying that there is some possible world (e.g. parallel world) where it will rain tomorrow, but rather saying that the actual world might be such a world.

Is there a form of modal logic that can make this distinction?
fdrake May 10, 2023 at 15:48 #806944
Quoting Michael
Is there a form of modal logic that can make this distinction?


No idea. SEP has a related article.
Michael May 10, 2023 at 15:57 #806950
Reply to fdrake Although actually, I'm not sure this response is even warranted. Even if our "ordinary" concept of God is one that isn't to be interpreted as being modally necessary, the modal ontological argument does posit such a God, and their argument should be addressed on that premise.

Does it show that a modally necessary God exists? Is ???xGx true and does ???xGx entail ??xGx?
fdrake May 10, 2023 at 16:47 #806983
Quoting Michael
Does it show that a modally necessary God exists? Is ???xGx true and does ???xGx entail ??xGx?


First quibble: it isn't demonstrated to be any particular god, just an entity which satisfies G. The only thing which makes it god-ish is that G is associated with god. It would need to be argued that any given god has the property G, which is established independently (and is a theological thing, right). Moreover, it would need to be argued that an entity could, in principle, have that property.

Second quibble: possibly there exists x such that Gx is unsupported. Modal logics do lots of different things. You can say that 1 is possible for 2 under the accessibility relation "less than or equal to" in the integers. Whether the relevant sense of modality in the logic models an appropriate notion of metaphysical necessity is still something that you can quibble with. Why would you need something like an equivalence accessibility relation between worlds?

An example of that quibble: it was possibly physically necessary that the luminiferous aether existed, therefore it was physically necessary that the luminiferous aether existed, therefore the luminiferous aether existed. A sense of metaphysical necessity which lets you do this conjuring trick is... well, it needs a good argument to support.

Third quibble: you can always deny that it's possible that any particular god exists. And in that case the entity in question would not exist in any world.

Nevertheless, it might be the case that the underlying metaphysics that facilitates the argument is the correct one. It just still would have relatively little to do with a god. Or, as with other ontological arguments, you can perform the same conjuring trick where you posit an entity with G and then it suddenly exists. Like the aether example.
Michael May 10, 2023 at 16:52 #806987
Quoting fdrake
Nevertheless, it might be the case that the underlying metaphysics that facilitates the argument is the correct one. It just still would have relatively little to do with a god. Or, as with other ontological arguments, you can perform the same conjuring trick where you posit an entity with G and then it suddenly exists. Like the aether example.


I did offer a more substantial notion of God here. The argument attempts to show that there exists something which necessarily created the world.

But you are right that we can posit any entity. So if anything it's a reductio ad absurdum against the assumption that ??x?Fx is true for every logically consistent Fx.

Quoting fdrake
Second quibble: possibly there exists x such that Gx is unsupported. Modal logics do lots of different things. You can say that 1 is possible for 2 under the accessibility relation "less than or equal to" in the integers. Whether the relevant sense of modality in the logic models an appropriate notion of metaphysical necessity is still something that you can quibble with. Why would you need something like an equivalence accessibility relation between worlds?


The argument does depend on S5 where the accessibility relation is universal. From my reading there are good reasons to accept S5 so it would be shortsighted to deny it simply to dismiss the modal ontological argument, and special pleading to deny it only for the modal ontological argument.
Michael May 11, 2023 at 12:44 #807173
Quoting Michael
So if anything it's a reductio ad absurdum against the assumption that ??x?Fx is true for every logically consistent Fx.


On this point, consider this:

1. ?xFx ? ?x?y(Fy ? (x = y))
2. ??x?(Fx ? Ax) ? ?x?(Fx ? Ax)
3. ??x?(Fx ? ¬Ax) ? ?x?(Fx ? ¬Ax)

The first premise asserts that if there is an x such that Fx then there is exactly one x such that Fx. The second asserts that there is an x such that it is necessary that both Fx and Ax. The third asserts that there is an x such that it is necessary that both Fx and ¬Ax. Obviously this is a contradiction.

If we take Fx to mean something like "x is the sole creator of the world" then 1 is true, and as both 2 and 3 are valid under S5 it must be that one or both antecedents are false, and so one or both of these is true:

4. ¬??x?(Fx ? Ax)
5. ¬??x?(Fx ? ¬Ax)

Therefore we cannot assume that ??x?Px is true for any logically consistent Px, and so cannot assume that it is possible that something necessarily created the world.

Or we have to reject S5, but if we reject S5 then the modal ontological argument is invalid as “possibly necessary” wouldn’t entail “necessary”.
fdrake May 11, 2023 at 18:14 #807244
Quoting Michael
The argument does depend on S5 where the accessibility relation is universal. From my reading there are good reasons to accept S5 so it would be shortsighted to deny it simply to dismiss the modal ontological argument, and special pleading to deny it only for the modal ontological argument.


Eh, possibly necessary => necessary is reasonably easy to argue against. I don't like it for the above stated reasons. That lets you conjure up the luminiferous aether, assuming the "true logic of metaphysics" lets you do possibly necessary implies necessary. In that regard, either we'd have to rejected that the luminiferous aether isn't possibly physically necessary, or the law of logic which leads to the inference. I'm inclined to reject the latter, since I intuit that things like physical laws are "physically necessary" (whatever that means).

I wouldn't want to deny that S5 has applications, just that demonstrating it as the "true logic of metaphysics" is a project unto itself. That a logic applies to a domain isn't something that can be taken for granted, I think. The above argument regarding physical necessity is a reason to reject the application of any logic which allows the inference pattern (possibly necessary => necessary) to metaphysics in general.
Michael May 11, 2023 at 19:17 #807288
Quoting fdrake
In that regard, either we'd have to rejected that the luminiferous aether isn't possibly physically necessary, or the law of logic which leads to the inference. I'm inclined to reject the latter, since I intuit that things like physical laws are "physically necessary" (whatever that means).


Given my previous post that shows that under S5 we cannot assume that ??x?Px is true for any logically consistent Px, the third alternative is that “possibly necessary” under S5 means something different to what it means under other systems (or natural English).
fdrake May 11, 2023 at 19:18 #807290
Reply to Michael

Aye! Nothing tells you the meaning of the two modal operators other than the context they're applied to.
Jim Grossmann May 22, 2023 at 02:32 #809647
Every form of the ontological argument that I've ever heard of assumes that greatness is a property of some entity rather than a speaker evaluation of that entity.

I admit that whether the abstract property of greatness exists independently of speakers and their evaluations can be debated philosophically.

But this leaves the ontological argument, even if logically valid, only as sound as the notion that greatness exists independently of the evaluation of some rational being, rather than existing only as such an evaluation.

IMO, my evaluation of X is not a property of X.
EnPassant June 16, 2023 at 19:29 #815802
Existence is not a property of God. Existence IS God. All contingent things are properties of existence. Existence is what is from the beginning. It always is. Creation is when existence/God acquires properties.
Banno June 16, 2023 at 22:27 #815824
Reply to EnPassant Verbal fumbling.
Janus June 16, 2023 at 22:56 #815835
Quoting Banno
But explaining clearly what is added to an apple by existing...?


You can't add anything to or subtract anything from an apple that does not exist, except in thought.

Quoting Banno
It's not difficult to understand an apple that is not sweet, or an apple that is not red - but an apple that does not exist? What is it?


It is not an existent apple, but is merely the thought of an apple; am imagined or non-existent apple.

Banno June 16, 2023 at 23:10 #815839
Reply to Janus I have a regular supply of apples that don't exist, which I will happily on-sell.

Janus June 16, 2023 at 23:13 #815840
Reply to Banno To your non-existent friends? So you might think.
Banno June 16, 2023 at 23:15 #815843
Reply to Janus To you, if you like: there's a free sample next to you. I can provide as many as you need.
Janus June 16, 2023 at 23:16 #815845
Reply to Banno Yes, if I think so, although I don't need your free non-existent apples since I have as many of my own as I want.
EnPassant June 17, 2023 at 11:07 #815902
Reply to Banno Do you understand what existence is? What a positive existence, as opposed to nothingness, means? If you don't you will not understand what I'm saying.
Assume X has the property 'existence'.
Now ask; does X exist distinct from its property 'existence'?

Two answers:
1. X does not exist. Therefore it cannot have properties, let alone 'existence'.
2. X exists. This makes existence as a property superfluous, since X exists anyway, whence X is existence.

This proves existence cannot be a property.
Banno June 19, 2023 at 04:57 #816244
Reply to EnPassant Free logic allows us to talk of things that do not exist, hence treating existence as a property.
EnPassant June 19, 2023 at 16:29 #816308
Reply to Banno But I'm not talking about imaginary existences.
Banno June 19, 2023 at 22:26 #816356
Reply to EnPassant Free logic has wider application than just imaginary objects, addressing the difficulties you mention.
universeness June 20, 2023 at 09:52 #816421
Existence is a scientific state not a property:

A property can be physical or chemical etc, it can describe a change or variable attribute.
A state is an instantaneous observation, such as solid, liquid, gas. A property is variable and can cause movement from one state to another. Existence is a state that can change into a state of non-existence.
'State' and 'property' are not synonymous.
If god has an existent state then can that state change into a non-existent state?
Even cyclical or oscillating universe hypotheses still intuit a 'spark' to start the process that then becomes eternal. The eternal god posit suffers from the same problem, 'what sparked god?' and what sparked the spark. That's why it's called an 'infinite' regression.
An ontological argument for god has no significance at all, to theism as it is at it's best, a very poor argument for the existence of A god or first cause mind with an intent/need to create. It offers nothing to the theist by way of supporting evidence that their god flavour exists. Allah and Yahweh remain as likely, as the spider god or the energy god or any, from an infinity of potential god descriptions/properties.
Banno June 21, 2023 at 09:03 #816638
Love how folk just make shit up.

This ontology stuff is so easy!
Michael June 21, 2023 at 09:26 #816640
Quoting EnPassant
Existence IS God.


What does this mean? Are you saying that the words "existence" and "God" are synonyms? As a fluent English speaker I'd have to disagree. At the very least, "God" is proper noun and "existence" an improper noun, so clearly there is at least some distinction between the words.

What's the verb form of "God"? For "existence" it's "exists". So how would you rephrase the sentence "there exists more than one apple"? Maybe "there gods more than one apple"? Doesn't make much sense to me.

Or are you perhaps just asserting pantheism? If so then what evidence or reasoning leads you to believe that the universe is "divine" (or whatever it is that distinguishes a pantheistic universe from a non-pantheistic universe)?
EnPassant June 21, 2023 at 11:37 #816662
Reply to MichaelIn the 'beginning' existence and God are the same thing. Existence is not a verb, it is a noun. God becomes/creates. Contingent creation is a property of existence. Imagine a lump of bronze representing existence; it is. The bronze can be shaped into a horse, an eagle etc. 'Horse' and 'eagle' are properties.
The verb for God is 'becoming' ie. evolving properties.
More than one apple? There is existence and it can have many apples as properties. Pantheism? No. Existence is eternal. It becomes creation.
Michael June 21, 2023 at 12:39 #816672
Reply to EnPassant This doesn't seem to be saying anything.

Why use the word "God" at all? Why not just say that there was some inanimate, formless chaos that happened (without intention) to form into the space and time and matter and energy that we are familiar with?

Using the word "God" brings in all sorts of additional, religious baggage.
EnPassant June 21, 2023 at 14:42 #816706
Reply to Michael Well you can call it the source of all that is, if you want to avoid the religious. Personally I think the emergence of existence into being (life) is an intelligent evolution.
Banno June 22, 2023 at 02:53 #816895
Reply to EnPassant Obvious hypostatisation, verging on anthropomorphism.