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.

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.

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. — invicta

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.

Neither are sound arguments.

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.

?

You only do OP's?

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". — Banno

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.

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

The conclusion doesn't follow.

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 — Epicero

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.

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.

because the thing conceived (as shown in brackets) in 4) is "greater" than in 3)….. — Michael

“…. 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)

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

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.

Why can't existence be regarded as a first-order predicate? — Art48

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.

"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

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? — 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? — Banno

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.

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 is making this same point, but more clearly.

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

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

it requires 2nd order logic. So what? — hypericin

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

Go on, then.

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.”

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 — Michael

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".

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.

I think you are simplifying 1) too much.

a) If some X is TTWNGCBC then X necessarily exists — Michael

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.

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

No, the argument is "If some X is TTWNGCBC, then X necessarily exists".

No, the argument is "If some X is TTWNGCBC, then X necessarily exists". — Hallucinogen

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.

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. — Michael

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.

It could go:

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

Not a non sequitur. — Hallucinogen

Then this begs the question, as the second premise just asserts that God exists.

No it doesn't, it asserts God fits the definition of X.

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.

You're misunderstanding the logic. Look at existential quantification. — Michael

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.

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 — Michael

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.

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. — Hallucinogen

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.

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 — Michael

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.

Which again is invalid. — Michael

How so?

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. — Hallucinogen

How does 2 differ from 3?

How so? — Hallucinogen

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.