Can Anselm be proven wrong?

[Euphrates]

There are many arguments for the existence of God. These arguments have been mulled over by untold numbers of people through the years. Do any of these arguments show us that God exists?... or can they all be refuted by the beautiful minds at DC&R?

I want to focus on Anselm's Ontological Argument for the existence of God (as formalized and summarized on wikipedia):

1. If I am thinking of the Greatest Being Thinkable, then I can think of no being greater
1a. If it is false that I can think of no being greater, it is false I am thinking of the Greatest Being Thinkable
2. Being is greater than not being
3. If the being I am thinking of does not exist, then it is false that I can think of no being greater.
4. If the being I am thinking of does not exist, then it is false that I am thinking of the Greatest Being Thinkable

Anselm said, "God is that, than which nothing greater can be conceived." He then argues that, based on that definition, God must exist.

That argument has frustrated many atheists and philosophers, including Bertrand Russell, who at one point said that the argument seems flawed, but the flaw is hard to find, and at another point said the argument is sound.

If Anselm is right, God exists. So... is Anselm right?

[Abraxas]

Abraxas, from what I can tell, you think the argument is flawed because it slipped something in there somewhere, but it's hard to see where and what exactly happened.

I think what was slipped in was the assumption that the properties of thought up beings can be considered identical with properties of actual beings, something necessary for the argument to work.

Nothing about the greatest possible thought up being allows it to make the transition to greatest possible real being, as up to the last point, we were dealing only with thought up beings.

The greatest being you can imagine must be real because, otherwise, anything real would be greater than it.

Not relevant. Anything real is in an independent class, real beings. All we can get through imagination is thought up beings, the greatest thought up being is perfectly capable of being the greatest of all thought up beings, imagined to be real, while not corresponding to anything in the real world. It is making that leap from the class of imaginary beings we start with to real beings where the argument falls apart.

Why does existence in the real world make something a greater thought up being? It doesn't.

Being is greater than not being. I've given arguments as to why that's true. You're simply claiming it to be false. And... calling it a "thought up being" is question begging.

Being is greater than not being for real world entities. For thought up entities, only imagined to exist, being is not greater than not being. Or, more accurately, being for such entities is having been thought up whereas not being is not having been thought up. I have a sneaking suspicion that this is an equivocation fallacy.

"Though up being" is not question begging. The fact the every entity in the argument is asked to be imagined until the very last point where it assumes God exists puts them in an independent class from beings which actually exist. This is related to what thatoneguy has been posting about the argument not actually asserting anything exists, the beings described are "ifs", not "thats". The argument functions as either a thought experiment or a linguistic construct, depending on phrasing, but either way it makes everything up to the last point non-real entities for the purpose of argument then for the conclusion treats those non-real entities as though they have real traits. Yes, now I am certain this is an equivocation fallacy.

[Euphrates]

Here is your argument in Symbolic logic:

Tx - x is being thought about
Gx - x is the greatest thing thinkable
Rxy - y is greater than x
Bx - x is being (exists in reality)

1. (x) {(Tx & Gx) > ~(Ey)[(Ty) & (Rxy)]}
2. [(x)(y)] [(Bx & ~By) > ~ (Rxy)]
3. (x) {(Tx & ~Bx) > ~(Ey) [(Ty & Rxy)]}
4. (x) [(Tx & ~Bx) > (Tx & ~ Gx)]

/ (Ex) (Gx & Bx)

Rather then expand this and assign values, which would take forever, I'd rather just explain the flaw. You said you took a logic class, so I'll assume you understand the notation, since this is all introductory-level.

I'm afraid I am no longer able to parse and symbolize everything and do the appropriate operations to show validity, but I know how logic works and I know what would be required of a successful refutation. If you are trying to show me that there is an error in the logic itself, all you need to do is give me a scenario where the premises are true but the conclusion is false.

Basically, the problem is simply that nothing in any of your 4 premises is affirmed to exist. It's a set of universal if-then statements. It is logically impossible to get an existential statement out of strictly universal premises.

Why do you think that it logically impossible? Can you demonstrate? The argument purports to do exactly what you are (roughly) claiming is impossible. Saying that it is impossible just sounds like an unsupported assumption. If it is logically impossible, it should be fairly easy to locate the error, name it, and give a counterexample that shows the argument to be invalid.

Do you deny that I translated your premises correctly? Short of that, I can see no possible rebuttal.

I really don't know if you translated them correctly. I'm willing to give you the benefit of the doubt, but you have not made an argument showing anything. You translated Anselm's premises into symbolic logic then simply said "it's impossible to do that". I can see no possible rebuttal either, because I honestly don't see anything to rebut.

3. For any given x, if x is both being thought and not being (non-existent in the real world), then there does not exist even a single y such that y is both being thought and is greater then x.

You think this is Anselm's third premise? You've basically translated it to say "If you're thinking of something, but it only exists in your mind (not in reality), there's nothing else that is greater than it." Am I reading that correctly? That is pretty far from anything Anselm said.

The reason I did not quibble over "greater" was because regardless of what it mean the argument was logically invalid, and I considered the invalidity to be the important part.

And you think you have proven Anselm's argument to be logically invalid? Care to venture a guess as to why you could even though great philosophers like Russell have acknowledged that it is valid? They don't typically teach invalid philosophical arguments in college philosophy classes, but the ontological argument is a staple in philosophy classes around the world.

[Euphrates]

I think what was slipped in was the assumption that the properties of thought up beings can be considered identical with properties of actual beings, something necessary for the argument to work.

I don't see anything like that going on. But if you think you've proven the argument to be unsound (false), can you tell me which premise you are arguing against and what, exactly, is your argument proving that premise to be false?

Because at this point, it sounds like you generally disagree with the argument, but it's not clear how your disagreement proves the argument wrong.

Not relevant. Anything real is in an independent class, real beings. All we can get through imagination is thought up beings...

An independent class? Now you're just making things up. Independent of what? What are all the classes? Are there dependent classes? Are independent classes mutually exclusive?... why? Are all real things in the same class? What about things that are historically real? Are they in the same class as current real things?

If I look at a bunny, and I close my eyes and think about (imagine) that bunny, according to you, that bunny isn't real. I'm thinking about my sister. Is she not real? Is my sister a thought up being?

It is making that leap from the class of imaginary beings we start with to real beings where the argument falls apart.

Like I said before, what you need to be concerned about is the thing that you're thinking of. The thought is not the key. The thing is the key.

You can't think of something that is greater than K. You can't. It is impossible. Are we talking about a thought? No. We're talking about a something. You can think of a lot of other somethings. Some of those somethings are real. Some of those somethings are only imaginary.

Are we talking about the thought being greater? No. We're talking about the thing being thought.

Being is greater than not being for real world entities. For thought up entities, only imagined to exist, being is not greater than not being.

If they are only imagined, being is not an option. But we are trying to determine if it must be real (which the argument concludes). Assuming that they are only imagined, begs the question.

Yes, now I am certain this is an equivocation fallacy.

Great! Prove it. What word/phrase am I equivocating and where have I used that word/phrase to mean two different things in order to make a point?

Of course, most words are ambiguous, but context usually makes a univocal meaning clear. Also, equivocation alone is not fallacious, though it is a linguistic boobytrap which can trip people into committing a fallacy. The Fallacy of Equivocation occurs when an equivocal word or phrase makes an unsound argument appear sound. Consider the following example:

All banks are beside rivers.
Therefore, the financial institution where I deposit my money is beside a river.

In this argument, there are two unrelated meanings of the word "bank":

1. A riverside: In this sense, the premiss is true but the argument is invalid, so it's unsound.
2. A type of financial institution: On this meaning, the argument is valid, but the premiss is false, thus the argument is again unsound.

[thatoneguy]

You think this is Anselm's third premise? You've basically translated it to say "If you're thinking of something, but it only exists in your mind (not in reality), there's nothing else that is greater than it." Am I reading that correctly? That is pretty far from anything Anselm said.

Good point. It should have been:

3. (x) {(Tx & ~Bx) > (Ey) [(Ty & Rxy)]}

Now it translates to If you're thinking of something, but it only exists in your mind (not in reality), there's something else that is greater than it.

That's correct now, right? It doesn't make a lick of difference. Unfortunately, it looks like I actually have to do the required work to make my point. Sigh.

[thatoneguy]

Euphrates, I hear-by rescind all previous statements I have made, except those explicitly quoted in this post. It's easier for me to just prove my point with this single argument. This post will be extremely technical, and I open it up for anyone with a working knowledge of first-order logic to correct me, though I checked over this post much more thoroughly then anything else I've posted here. For everyone else, if you have no idea what the stuff I'm saying means, skip to the bottom.

Before starting, I want to make a quick distinction. I will be referring to two different types of existence. The first is existence in the sense of predicate logic. This is a conceptual existence that may refer to anything, whether it is a thought or existent in reality. The second is the idea that an object is being. This refers exclusively to a physical entity that exists in reality (holy spirits count too). (Ex) refers to the first kind of existence, Bx to the latter.

I will now take your premises and symbolize them (you were also correct regarding my mistranslation of premise 3. I have fixed it.)

Tx - x is a thought
Gx - x is the greatest thing thinkable
Rxy - y is greater than x
Bx - x is being (exists in reality)

1. (x) {(Tx & Gx) > ~(Ey)[(Ty) & (Rxy)]}
2. (x) {Bx > [(y) (~By > ~ Rxy)]}
3. (x) {(Tx & ~Bx) > (Ey) [(Ty & Rxy)]}
4. (x) [(Tx & ~Bx) > (Tx & ~ Gx)]

/ (Ex) (Gx & Bx)

Taking just this, your argument is invalid. If I were to instantiate everything as follows:

1. (Ta & Ga) > ~(Ey)[(Ty) & (Ray)]
2. Ba > [(y) (~By > ~ Ray)]
3. (Ta & ~Ba) > (Ey) [(Ty & Ray)]
4. (Ta & ~Ba) > (Ta & ~ Ga)

/ Ga & Ba

Then simply assigning Ta as false invalidates the entire argument.

Obviously, this isn't satisfactory. If the argument were that simple to disprove, no one would have ever had any trouble with it. So, I asked myself what unsaid premise had been forgotten. I concluded it was

5. (Ex) (Tx & Gx)
[There exists at least one x such that x is both a thought and the greatest thing thinkable]

I disagree with this, and I'll get to why later, but for now I'll accept it. Basically, what this says is that the greatest thought possible exists as a thought. It assumes that it is possible that the greatest thing thinkable can be thought. Depending on your interpretation, it also might imply that someone is actually thinking it, but I'm willing to overlook that because the from a symbolic standpoint it changes nothing.

Now, with this new premise, the argument is valid. This, too, I found unsatisfactory. It just didn't seem right. Even ignoring the vague definition of "greater," proving God could not be that easy. Again, I believed that something must be missing. Then I remembered an exchange I had with you in another thread about the same topic:

Euphrates, do things that exist only in your imagination exist by the definition of "existence" used in premise 2?

No. I was trying to avoid the ambiguity of "existence" by not talking about things "existing" only in your imagination. Anselm says that if you think about something it exists in your mind. That is one kind of "existence".

If that is how we are defining existence (in the sense of being/reality), then we must add a premise to clarify that we are working under this definition:

6. (x) (Tx > ~Bx)
[For any given x, if x is a thought then x is not being (does not exist in reality).

You accepted this, but even if you hadn't I consider this to be fundamental. A thought and the thing being thought about are two different things. Just because you are thinking about something concrete does not make the thought itself concrete. I would think this is unarguable.

So, now we get the following:

1. (x) {(Tx & Gx) > ~(Ey)[(Ty) & (Rxy)]}
2. (x) {Bx > [(y) (~By > ~ Rxy)]}
3. (x) {(Tx & ~Bx) > (Ey) [(Ty & Rxy)]}
4. (x) [(Tx & ~Bx) > (Tx & ~ Gx)]
5. (Ex) (Tx & Gx)
6. (x) (Tx > ~Bx)

/ (Ex) (Gx & Bx)

This statement is, from a purely technical standpoint, valid. The conclusion is unfalsifiable given the premises. Yet, upon further examination, the argument is still very much fallacious:

7. Ta & Ga___________________________EI 5
8. (Ta & ~Ba) > (Ta & ~ Ga)______________UI 4
9. Ta > ~Ba__________________________UI 6
10. Ta______________________________simplification 7
11. Ta > (Ta & ~Ba)____________________absorption 9
12. Ta & ~Ba_________________________Modus Ponens 10,11
13. Ta & ~Ga_________________________MP 8, 12
14. ~Ga_____________________________simp 13
15. Ga______________________________simp 7

The problem, it seems, is that a contradiction is created. In case anyone does not know, when a contradiction exists in a formal argument it is impossible to make literally any conclusion falsifiable. Contradictions are also impossible in the real world, as it is impossible for something to be both true and false at the same time.

This contradiction only exists because of the simultaneous addition of premises 5 and 6. Remove one, and the contradiction disappears. Since it is virtually impossible to deny that a thought and the thing being thought about are two separate things (of which the object may exist in reality but the thought does not), it is the other premise (which had never been established to begin with) that we must assume false. Doing so, we can instantiate to:

1. (Ta & Ga) > ~(Ey)[(Ty) & (Ray)]
2. Ba > [(y) (~By > ~ Ray)]
3. (Ta & ~Ba) > (Ey) [(Ty & Ray)]
4. (Ta & ~Ba) > (Ta & ~ Ga)
5. Ta > ~Ba

/ Ga & Ba

And now the argument becomes invalid again. If Ba is true (and it has to be to reach the conclusion), then Ta is false. With Ta false, we run into the same problem we had before. This entire argument is nothing but if-then statements that hinge on the greatest thought thinkable actually being a thought. As long as Ta is false, the argument proves nothing.

Conclusion For Everyone Else:
Anselm's Ontological argument is valid if and only if you accept the following premises: 1) The greatest thought thinkable exists (as a thought) and 2) It is false that a thought, even if it is of something real, cannot exist in reality. Basically, premise 2 asks you to deny that internal thoughts and external entities are, by necessity, two separate things.

I disagree with premise 1, however I consider premise 2 to be fundamentally false.

[Euphrates]

Euphrates, do things that exist only in your imagination exist by the definition of "existence" used in premise 2?

No. I was trying to avoid the ambiguity of "existence" by not talking about things "existing" only in your imagination. Anselm says that if you think about something it exists in your mind. That is one kind of "existence".

If that is how we are defining existence (in the sense of being/reality), then we must add a premise to clarify that we are working under this definition:

6. (x) (Tx > ~Bx)
[For any given x, if x is a thought then x is not being (does not exist in reality).

You accepted this, but even if you hadn't I consider this to be fundamental. A thought and the thing being thought about are two different things.

I really appreciate the time and effort you put into this. My first order logic skills are rusty at best, so I'm glad you were thorough and honest about the argument.

I think you have added an element of mutual exclusivity to existence. When I think about my sister, the thought of her exists and she exists also... because I really do have a sister. She and my thought of her are different, but connected. You could say that she (in reality) enables my thought of her.

I was trying to avoid the dual ways of "existing" because the only one that matters is "exists in reality". The greatest thing thinkable can't only be a thought. My real rollercoaster beats your imaginary rollercoaster any day. I think that's obvious.

Conclusion For Everyone Else:
Anselm's Ontological argument is valid if and only if you accept the following premises: 1) The greatest thought thinkable exists (as a thought) and...

I don't think that premise is important to the argument.

2) It is false that a thought, even if it is of something real, cannot exist in reality. Basically, premise 2 asks you to deny that internal thoughts and external entities are, by necessity, two separate things.

This premise is not part of Anselm's argument. I admit that I'm a little lost by all the Ty and Ga stuff, but Anselm never argues that the thought exists in the same way as the thing being thought of. Like I said before, the thing and the thought are connected. Aren't they?

Think of some thing that exists. If that thing did not exist, you would not be able to think of it. You could imagine something similar, but not it.

I think the problem is that you're starting off with a thought, whereas the argument starts with a thing. It's probably my fault for using the wikipedia formalization of the argument, which uses "Greatest Being Thinkable" and makes it sound like it's a thought. In fact, the argument is saying that you can't imagine something or identify something (real) with your mind (which would be a thought) that is greater than God. You can't think of something greater than X. This is a thing, not a thought. Anselm is saying you can't beat X. Whatever "X" identifies is God. It may not be what you think it is, or have the qualities you were hoping for, but it exists. There must be some thing that no conception can be greater than.

[Crazy Ivan]

I was trying to avoid the dual ways of "existing" because the only one that matters is "exists in reality". The greatest thing thinkable can't only be a thought. My real rollercoaster beats your imaginary rollercoaster any day. I think that's obvious.

Only to you. This is as much an unsubstantiated opinion as the first time you said it. Does a real gun "beat" an imaginary gun any day? It's "better"? "Greater"? The real ability to take life beats an imaginary one any day? A real pedophile is "better", "greater"? I could go on considerably longer here. Just imagine anything anyone as ever wished to be just a "concept" and not "real". By all means, continue ignoring the fact that there's nothing inherently "greater" or "better" in "real existence" as opposed to "conceptual existence".

[thatoneguy]

I think you have added an element of mutual exclusivity to existence. When I think about my sister, the thought of her exists and she exists also... because I really do have a sister. She and my thought of her are different, but connected. You could say that she (in reality) enables my thought of her.

Connected is insignificant. If you want, I could add a premise saying that if a thought is of an object that exists in reality then they are connected. You'll find nothing changes with that premise. In order for the proof to work, the thought and the being must be the same thing. That is not arguable. It's a simple logical fact.

Your sister and the thought of your sister are two separate things. That is fact.

I was trying to avoid the dual ways of "existing" because the only one that matters is "exists in reality". The greatest thing thinkable can't only be a thought. My real rollercoaster beats your imaginary rollercoaster any day. I think that's obvious

.

I got that. You seem to have missed my point. I understand that you did not follow what I did logically, but at the very least you should read my conclusion. If you disagree, then I am sorry that you lack the expertise to counter my arguments.

Conclusion For Everyone Else:
Anselm's Ontological argument is valid if and only if you accept the following premises: 1) The greatest thought thinkable exists (as a thought) and...

I don't think that premise is important to the argument.

It is absolutely vital. I have shown that beyond a shadow of a doubt. As your argument stands, you have committed the fallacy of existential assumption (http://fallacyfiles.org/existent.html). You have given me four if-then premises but forgotten to actually affirm that anything exists.

I have tried to reconcile this. I attempted to allow for a world with an infinite number of items, some being and some not being, but without any connection between thoughts and beings, all I could do was affirm that somethings were greater than others. There is nothing I can actually do with the premises as they stand. Even asserting just a thought proves useless. In order to make the conclusion valid, you must add the premise that the greatest thought thinkable exists as a thought. Again, though, this contradicts an important premise that, though not mentioned in your argument, is in fact a fundamental fact of reality. Which is that a thought and the thing being thought of, no matter how similar, are two different things. Hence:

2) It is false that a thought, even if it is of something real, cannot exist in reality. Basically, premise 2 asks you to deny that internal thoughts and external entities are, by necessity, two separate things.

This premise is not part of Anselm's argument. I admit that I'm a little lost by all the Ty and Ga stuff, but Anselm never argues that the thought exists in the same way as the thing being thought of. Like I said before, the thing and the thought are connected. Aren't they?

I know it is not part of Anselm's argument, it's part of reality. Anselm's conclusion does not follow from his premises. I have shown which premise must be added to make his conclusion follow. I then showed that this real world premise makes his assumed premise impossible.

Think of some thing that exists. If that thing did not exist, you would not be able to think of it. You could imagine something similar, but not it.

If I am thinking of my car, then my thought is not my car. It is of my car, but unless they are the same thing you have no argument.

I think the problem is that you're starting off with a thought, whereas the argument starts with a thing. It's probably my fault for using the wikipedia formalization of the argument, which uses "Greatest Being Thinkable" and makes it sound like it's a thought. In fact, the argument is saying that you can't imagine something or identify something (real) with your mind (which would be a thought) that is greater than God. You can't think of something greater than X. This is a thing, not a thought. Anselm is saying you can't beat X. Whatever "X" identifies is God. It may not be what you think it is, or have the qualities you were hoping for, but it exists. There must be some thing that no conception can be greater than.

It is clear that you don't understand my logical syllogisms. I did not necessitate that the greatest thing thinkable was a thought. I simply said it must be in order for the conclusion to follow.

And x is not God, not even close. x is anything. x is only God is if it happens to be an x that is both the greatest thing thinkable and doesn't exist.

[Euphrates]

Your sister and the thought of your sister are two separate things. That is fact.

Absolutely. Let me try to be clearer about what I'm trying to say.

My sister's name is Katie. When I think about her, Katie is a thought in my mind. When I take inventory of the real world, Katie really exists also. You're sixth premise (the one you added that makes the argument invalid) makes this untrue, which I consider to be an absurd proposition.

6. (x) (Tx > ~Bx)
[For any given x, if x is a thought then x is not being (does not exist in reality).

Let's say x is my sister, Katie. For any given Katie, if Katie is a thought (and she is, by definition, when I think about her), then Katie doesn't exist in reality.

I think you want to say: For any given Katie, if Katie is a thought, then the thought of Katie doesn't exist in reality. But that is not what is captured by the premise. Your premise, unless I'm mistaken, accidentally implies that things aren't real if you think about them.

As your argument stands, you have committed the fallacy of existential assumption (http://fallacyfiles.org/existent.html). You have given me four if-then premises but forgotten to actually affirm that anything exists.

That's only because such a premise is always implied. You added the existential premise (thank you) when you started symbolizing the argument. It's not a fallacy. It's an omission.

In order to make the conclusion valid, you must add the premise that the greatest thought thinkable exists as a thought.

But the problem is that some thing can be a thought and be real. My sister, for example. The thought of her and the real her are two different things, but they both exist. That fact is not captured by the symbolic logic you've created. I'm sorry I don't have the expertise to fix it, but I recognize the problem.

Also, you often call it the greatest thought thinkable. It is the greatest thing thinkable. Your phrasing makes it a thought. The actual argument makes it a thing. But then you turn around and say it doesn't have to be a thought. That's why I have been saying that the thought doesn't have to exist for the argument to hold its ground. When I have a little more time, I might be able to show some equivocation there.

[thatoneguy]

Euphrates, you seem to have misunderstood the concept of quantifiers and instantiation. If I instantiate a statement, then I am referring to one single thing. If there are two things that fit a certain criteria (such as being Katie), then we can still only apply the rules to one at a time. The Katie that is a thought is one Katie, then the Katie that is real is another Katie. In order for your conclusion to work, the greatest thing thinkable must be both a thought and exist in reality at the same time.

Your sister and the thought of your sister are two separate things. That is fact.

Absolutely. Let me try to be clearer about what I'm trying to say.

My sister's name is Katie. When I think about her, Katie is a thought in my mind. When I take inventory of the real world, Katie really exists also. You're sixth premise (the one you added that makes the argument invalid) makes this untrue, which I consider to be an absurd proposition.

You are wrong. You have misunderstood my 6th premise. I said that for any thing, that thing, and that thing alone, cannot exist in the real world and as a thought at the same time, as the same entity.

x refers to only a single thing at a time. It could be anything, but if you are going to instantiate it (call it Katie), then you can only apply all further logic to that instance of Katie. If that Katie is a thought, then Katie the not-thought is going to be a separate instance, to which you must assign a different letter.

6. (x) (Tx > ~Bx)
[For any given x, if x is a thought then x is not being (does not exist in reality).

Let's say x is my sister, Katie. For any given Katie, if Katie is a thought (and she is, by definition, when I think about her), then Katie doesn't exist in reality.

I think you want to say: For any given Katie, if Katie is a thought, then the thought of Katie doesn't exist in reality. But that is not what is captured by the premise. Your premise, unless I'm mistaken, accidentally implies that things aren't real if you think about them.

The premise distinctly and unquestionably states that anything that is a thought does not exist in reality. The thing being referred to may be a thought of a person which exists in the real world, but the thought itself does not.

As your argument stands, you have committed the fallacy of existential assumption (http://fallacyfiles.org/existent.html). You have given me four if-then premises but forgotten to actually affirm that anything exists.

That's only because such a premise is always implied. You added the existential premise (thank you) when you started symbolizing the argument. It's not a fallacy. It's an omission.

Correct. That is why I did not simply declare fallacy at your 4 premises, and instead added the implied premise. But this premise is a big one, and not easily accepted. The unstated premise is that there is a thought which is the greatest thing thinkable. There is no other premise I could think of that would validate your argument (that wouldn't be completely arbitrary).

For example, if I declare a world with any number of thoughts, then without my premise 6 I have no way to decide which thoughts are "being" and which are not, so there is no way to declare which are greater. If I declare a world where there is something that is being, then I can not characterize that something in any way. If I declare a world where something exists and something else does not, then I can only assert that one thing is greater than the other. Etc.

In fact, the only time I can assert any relation between thought and being is with my added premise. And, upon doing so, I still only find that I have the ability to assert that being in reality is greater than being a thought, and nothing else.

But the problem is that some thing can be a thought and be real. My sister, for example. The thought of her and the real her are two different things, but they both exist. That fact is not captured by the symbolic logic you've created. I'm sorry I don't have the expertise to fix it, but I recognize the problem.

"The thought of her and the real her are two different things"

And thus the problem is solved. This is symbolic logic. The rules are very strict. Only one of those two things can be referred to at a time. It's that simple.

but they both exist. That fact is not captured by the symbolic logic you've created.

Nonsense. Nothing about my syllogism prevents the possibility that the two exist. It simply prevents the possibility that they are the same thing. It also states that they are not, by necessity, both existent. The Katie that is a thought does not exist in reality, and the Katie that exists in reality is not a thought. That is literally all that is says.

Also, you often call it the greatest thought thinkable. It is the greatest thing thinkable. Your phrasing makes it a thought. The actual argument makes it a thing. But then you turn around and say it doesn't have to be a thought. That's why I have been saying that the thought doesn't have to exist for the argument to hold its ground. When I have a little more time, I might be able to show some equivocation there.

Calling it a thought is a mistake that I probably made carelessly form typing it too many times. In my syllogism, it is clearly labelled as the greatest thing thinkable.

But that's the beauty of symbolic logic, and one of the reasons I chose to symbolize. It doesn't matter what the technical definition of G is, it will always mean the same thing. G could mean made of cheese, and the logic would remain either valid or invalid. I used the term the way that it was used in the premises, whatever it means doesn't have the slightest effect on how I construct my proof.