The Ontological Argument

[slimshady2357]

Similarly, as I suggested earlier by way of example, the possible perfection of divine knowledge is limited, but it's a logical limit (once you know all the facts, it is logically impossible to increase your knowledgeability further).

Interesting

There is no limit to the number of true propositions though. Can one know all the facts? There is no end to the number of facts, how can one say that they 'know them all'?

It's like saying it's possible to 'know' all the integers. Is this really possible?

Just thinking out loud

Adam

 

[Ian Osborne]

1) God = greatest conceivable being
2) It is greater to exist in reality than just in the mind
3) God must exist in reality

It's been a long time since I studied propositional logic, but here, if we accept Premise 2, then Premise 1 is only valid if the conclusion is also true, thus the argument is not logical.

There's a term for such an argument, where one of the premies relies on the conclusion for its validity, but I can't remember what it is.

 

[ceo_esq]

Interesting

There is no limit to the number of true propositions though. Can one know all the facts? There is no end to the number of facts, how can one say that they 'know them all'?

It's like saying it's possible to 'know' all the integers. Is this really possible?

Just thinking out loud

Adam

Well, this is an interesting point. Upon reflection, I'm not certain that we should suppose that there is a "set" of all truths that is numerically limited. Some philosophers seem to agree with you: C. D. Broad, who coined the phrase "intrinsic maximum" in this context, did; a more contemporary figure is Patrick Grim. On the other hand, even if the notion of such a set is wrong, it's not clear that the idea of an intrinsically maximal degree of knowledge-perfection requires that such a set exist. Perhaps a more intuitive way of understanding omniscience is as follows:

• A being is omniscient if and only if, for every proposition, that being knows whether the proposition is true.

Looked at in this manner, it would seem that the there is a formal boundary to perfection of knowledge regardless of the number of propositions (finite or perhaps, even, infinite).

The best simple analogy I can think of - on short notice - to illustrate this principle is the one I evoked earlier of perfection in batting averages (for non-North American and non-Japanese readers, that's a baseball reference). We might say with justification:

• A ballplayer possesses the quality of perfection with respect to batting average if and only if, for every time at-bat, that ballplayer earns a hit.

Simultaneously, I think we would all agree that there is a logical, intrinsic maximum to batting averages: 1.000. This is true regardless of whether the number of at-bats is one hundred, one million or infinite.

Consider a hypothetical ballplayer who gets x number of hits in x times at-bat. Can we imagine greater perfection, strictly with respect to batting average, by positing a second ballplayer who gets 2x hits in 2x times at bat (the way we could imagine greater perfection in Gaunilo's island by simply doubling the number of coconuts and dancing girls)? No. We've reached the intrinsic maximum of the batting-average property, and so it goes, I submit, for the knowledge property.

 

[LW]

1. The sun is a star.
2. The sun exists.

Statement 1 makes a statement about the sun. Does statement 2 tell you anything more about the sun than statement 1 does?

Sure. See, for example:

1. Superman is a guy who flies around wearing his underwear topmost.
2. Superman exists.

It is possible to describe properties of entities that don't actually exist.

 

[LW]

Re: Re: The Ontological Argument

This is the same problem of definition I've discussed in relation to the .999... = 1 misunderstanding. You cannot define something, even a concept, into existence without looking at the coherence of its consequents.

I know that this is a pretty dead horse, but in that thread you didn't answer my question on whether there is an infinite number of natural numbers or not.

I have the feeling that your defnitions are either not particularly coherent or they throw out 99% of established number theory, but it is difficult to be sure as you haven't given them (or I haven't noticed them).

But anyway, if you want to reply to this, please do so in the original thread to avoid hijacking this one.

 

[ceo_esq]

Re: Re: The Ontological Argument

1) A subjective assertion based on personal incredulity. (In simpler terms, its a "personal opinion", not a valid premise)

It's not actually a premise or an assertion at all, it's an abbreviation - a definition used strictly for the purposes of the proof. Anselm is saying "Let God be used as shorthand for a being greater than which cannot be imagined." You can easily remove the term God, and the substance of Anselm's proof does not change because the definition is not technically part of the proof. I believe you're barking up the wrong tree here.

2) Another subjective assertion based on personal incredulity. There is no reason why being real is better than being a figment of the mind.

This is the real crux of it, I think, and I'd be interested to see some further discussion of this point. One issue to be dealt with is the fact that many thinking people find the proposition that real greatness is superior to imaginary greatness intuitively plausible, and it is, moreover, exceedingly difficult to set about proving the contrary proposition in a way that actually undermines Anselm's argument.

Doesn't it seem as though an actual being who shared all of Superman's great-making properties would in some meaningful (though perhaps hard to articulate) sense be greater than Superman the comic-book character?

Also, Regardless of how something is "defined", the definition of something is not enough to make it real. I could define a smurf as "A blue creature, humanoid, lives in fungi and tree stumps, is real in objective reality, commonly uses the word 'smurf' to prefix other words". By defining smurf as "real" is simply not enough to make it real.

True enough. However, as I pointed out in a previous post, Anselm could certainly agree with this. His version of the ontological argument doesn't depend on doing what you're describing above.

 

[Bookwyrm]

Let Dog be a malevolent, omnipotent entity, the being who is worst for human beings.

• 1. Dog exists in the understanding but not in reality.
  2. A being having all of Dog's properties plus existence in reality can be conceived.
  2. Dog's existence in reality would be worse for human beings than existence in the understanding alone.
  4. A being having all of Dog's properties plus existence in reality is worse for human beings than Dog.
  5. It is false that a being worse for human beings than Dog can be conceived.
  6. Hence it is false that Dog exists in the understanding but not in reality.
  7. This form of reasoning can show the existence of multiple omnipotent beings with opposing goals(see Ceo_esq's presentation of Anselm's argument)
  8. The existence of multiple omnipotent beings with opposing goals is incoherent
  9. This reasoning is therefore invalid

 

[Loki]

ceo_esq,

1. God exists in the understanding but not in reality.
2. Existence in reality is greater than existence in the understanding alone.
3. A being having all of God's properties plus existence in reality can be conceived.
4. A being having all of God's properties plus existence in reality is greater than God.
5. It is false that a being greater than God can be conceived.
6. Hence it is false that God exists in the understanding but not in reality

Nice summary! I like the ontological argument (in it's various stated forms) because it is a pretty tight proof. The key to unraveling it does seem to lie in the premise that "real existence" trumps "conceived". Certainly sounds reasonable at first that a real superman is "greater" that an imagined superman.

My best (so far) defense against this premise is that we can also conceive of things that it sounds just as reasonable are "lesser" if they were real than if they were imagined. For example, it would probably have been better if Hitler had been just an imaginary fictional character, rather than a real being. Well, better for humanity, worse for Hitler (I guess). So what's the benchmark we're determining "greater" by?

 

[69dodge]

Yahweh: There is no reason why being real is better than being a figment of the mind.
ceo_esq: This is the real crux of it, I think

I disagree. As I see it, the crux of the matter is the difference between words and what they refer to. It's easy to define a word which doesn't refer to anything that exists but then inadvertently use it as if its referent did exist. Doing so can result in unwarranted conclusions.

ceo_esq: Doesn't it seem as though an actual being who shared all of Superman's great-making properties would in some meaningful (though perhaps hard to articulate) sense be greater than Superman the comic-book character?

He would, if he existed. But since he doesn't exist, we can talk only about what would be true of him, not what is true of him. In reality, there is no Superman for anything to be true of.

ceo_esq:
1. God exists in the understanding but not in reality.
2. Existence in reality is greater than existence in the understanding alone.
3. A being having all of God's properties plus existence in reality can be conceived.
4. A being having all of God's properties plus existence in reality is greater than God.
5. It is false that a being greater than God can be conceived.
6. Hence it is false that God exists in the understanding but not in reality.

Let's focus on step 4. It talks about a being whose existence has not yet been established. So it really should not say, "the being is greater than God. Period." It should say, "if the being exists, it is greater than God. (If it doesn't exist, please ignore this step, and sorry for wasting your time.)" We can not, at this point in the proof, say that anything definitely is true of the being, because there might not be such a being for anything to be true of.

Therefore, any conclusion that relies on step 4 needs to be qualified with the proviso, "assuming the being mentioned in step 4 exists." So all the proof shows is that God exists assuming he exists. (yipee... ) Or, better said, the proof shows that, if a God-like being exists, then the word "God" (which is just shorthand for the phrase "a being greater than which cannot be imagined") refers to that existing being, rather than to a comic-book-character version of him.

If God doesn't exist, then the word "God," and the phrase "a being greater than which cannot be imagined," do not refer to anything at all, though people might pretend otherwise. I can say "Pink Unicorns That Exist" as often as I like; that doesn't mean any pink unicorns actually exist. I can stipulate, in my definition of it, that a word shall not refer to fictional entities, but doing so can't guarantee that any real entity exists to which it might refer. I can't conjure unicorns into existence simply by defining a word that refers only to real unicorns but not fictional ones. The possibility always remains that it doesn't refer to anything.

ceo_esq: Anselm does conclude that the idea the being than which none greater can be conceived is necessarily exemplified (in other words, the proposition God exists is true).

He has shown that God exists, only in the sense that Pink-Unicorns-That-Exist exist. Namely, that their names have been, directly or indirectly, defined to exist. But that implies nothing about their actual existence.

One cannot say anything about Superman; there is no Superman about which to say anything. If I say, "Superman can fly," what I really mean is, "people use the word 'Superman' to refer to a fictional superhero who can fly." That is, I am not talking about the characteristics of a person; I am talking about the definition of a word.

The proof talks about God before having demonstrated that God exists. Such talk cannot really be about God himself (as there might not be any God about which to talk); it is about the definition of the word "God." Any conclusion is therefore also about that definition.

God cannot be defined into existence.

 

[Loki]

69Dodge,

I disagree. As I see it, the crux of the matter is the difference between words and what they refer to. It's easy to define a word which doesn't refer to anything that exists but then inadvertently use it as if its referent did exist.

But the issue is whether "exists" is a necessary property (or a "greater/better/good" property). If god is considered to be "a being containing *all* good properties", and "existence" is "good", then god *must* exist.

1. God is *all* "good things"
2. Existence is a "good thing" (non existence is a "lesser thing" )
3. Therefore, god exists.

 

[Dorian Gray]

Much easier to refute the logic of the argument this way:
(Originally posted by metropolis_part_one)
1) God = greatest conceivable being
2) It is greater to exist in reality than just in the mind
3) God must exist in reality

Dorian Gray's refutation:
1) By process of elimination, a specific fantasy football team = the greatest conceivable football team
2) It is greater to exist in reality than just in the mind
3) The greatest conceivable football team must exist in reality

Plus, this refutation plays in America AND abroad.

 

[ceo_esq]

As I see it, the crux of the matter is the difference between words and what they refer to. It's easy to define a word which doesn't refer to anything that exists but then inadvertently use it as if its referent did exist.

Fair enough, but it's not clear to me that Anselm is guilty of this.

He would, if he existed. But since he doesn't exist, we can talk only about what would be true of him, not what is true of him. In reality, there is no Superman for anything to be true of.

Are you suggesting that no propositions are actually about nonexistent things? If so, this seems doubtful.

You appear to be saying that the proposition Merlin was able to cast magic spells is purely equivalent to saying If Merlin had existed, he would have been able to cast magic spells. By the same token, the proposition More movies have been made about Merlin than about Albert Einstein ought then to be equivalent to the proposition If Merlin had existed, more movies would have been made about him than about Albert Einstein - but clearly the two propositions are not equivalent. (For that matter, the proposition Merlin has abilities no actual person possesses is true, whereas if Merlin actually existed, the proposition would be false.) Something is wrong in your reasoning.

Let's focus on step 4. It talks about a being whose existence has not yet been established. So it really should not say, "the being is greater than God. Period." It should say, "if the being exists, it is greater than God. (If it doesn't exist, please ignore this step, and sorry for wasting your time.)" We can not, at this point in the proof, say that anything definitely is true of the being, because there might not be such a being for anything to be true of.

Step 4 refers to step 3's conception of a being greater than God. And if you accept step 3, then presumably you ought to agree that we can make propositions (whether true or false) about the idea it refers to - though maybe, in light of your earlier statement, you disagree. Interestingly, Anselm does not assume that the being in step 4 exists. He merely deduces a contradiction in the proposition contained in step 1.

I can say "Pink Unicorns That Exist" as often as I like; that doesn't mean any pink unicorns actually exist. I can stipulate, in my definition of it, that a word shall not refer to fictional entities, but doing so can't guarantee that any real entity exists to which it might refer. I can't conjure unicorns into existence simply by defining a word that refers only to real unicorns but not fictional ones. The possibility always remains that it doesn't refer to anything.

I agree with you, and there's no reason to believe that Anselm wouldn’t agree as well. To quote, once more, Alvin Plantinga from The Ontological Argument:

Schopenhauer describes the ontological argument as follows: "On some occasion or other someone excogitates a conception, composed out of all sorts of predicates, among which, however, he takes care to include the predicate actuality or existence, either openly or wrapped up for decency's sake in some other predicate, such as perfection, immensity, or something of the kind." If this were Anselm's procedure - if he started with some concept that has instances contingently if at all and then annexed existence to it - then indeed his argument would be subject to Kant’s criticism. But he didn't, and it isn't.

The proof talks about God before having demonstrated that God exists.

Actually, it begins by talking about a God that it assumes (in step 1) does not exist. I take it you think this is an equally illegitimate approach?

Turning the discussion in a slightly different direction, do you think there are any necessarily true existential propositions? If not, why not?

 

[69dodge]

Originally posted by ceo_esq
Are you suggesting that no propositions are actually about nonexistent things? If so, this seems doubtful.

You appear to be saying that the proposition Merlin was able to cast magic spells is purely equivalent to saying If Merlin had existed, he would have been able to cast magic spells.

No. I just said that we can't say, "Superman-the-real-person is greater than Superman-the-comic-book-character," because there is no Superman-the-real-person. On the other hand, if someone said, "Merlin was able to cast magic spells," he probably does not mean, "Merlin-the-real-person was able to cast magic spells." (That would indeed be meaningless, because there was no Merlin-the-real-person who might have been able, or unable, to cast spells.) Rather, he means, "Merlin-the-fictional-character was able to cast magic spells." And all that really means is, "Books of fiction have been written that contain sentences like 'Merlin cast a magic spell.' " So, even though the proposition, "Merlin was able to cast magic spells," appears to be a proposition about a nonexistent person, very similar to propositions we might make about real persons, in fact it is merely a proposition about (real) books.

By the same token, the proposition More movies have been made about Merlin than about Albert Einstein ought then to be equivalent to the proposition If Merlin had existed, more movies would have been made about him than about Albert Einstein - but clearly the two propositions are not equivalent. (For that matter, the proposition Merlin has abilities no actual person possesses is true, whereas if Merlin actually existed, the proposition would be false.) Something is wrong in your reasoning.

I understand what you mean by the original versions of all these propositions, and I agree that your rewritings of them are not equivalent. I'm not sure why you think I'd disagree. It's ok to talk about fictional people, as long as we keep in mind that fictional people aren't people; they're ideas in people's heads.

Step 4 refers to step 3's conception of a being greater than God.

Ok, that makes sense. I've thought about it some more, and I'm going to try a different approach.

[Anselm] . . . deduces a contradiction in the proposition contained in step 1.

Not exactly. He deduces a contradiction. That implies only that somewhere in the proof, something false was assumed to be true. If there were no other problems, it would have to be step 1. But there are other problems. Specifically, he uses the term "God" to refer to something that is most definitely not God. According to his definition of "God," nothing greater than God can be conceived. Now, a real deity can be conceived, and is greater than a fictional one. So, the term "God" cannot refer to a fictional diety; this is true even if no real diety exists to which it can refer. Yet he seems to think that, since he's assuming God doesn't exist, it's now ok to use "God" to mean the next best thing, namely, a fictional God, even though that usage contradicts his own definition of the term.

So, he has really made two assumptions:
1) God doesn't exist.
2) "God" means "a fictional diety" rather than "a real diety."

And therefore, when he finally reaches a contradiction, he is justified in concluding only that one of these assumptions is false. Guess which one it is?

Turning the discussion in a slightly different direction, do you think there are any necessarily true existential propositions? If not, why not?

If "necessarily true" means anything like "provable using no assumptions whatsoever," then, no, because I can't imagine what such a proof might look like.

 

[Hal 2001]

I could possibly understand the argument as long as we limit its significance.


1) If we say the god = the greatest conceivable beeing

2) Then one of the quality about him is his very existence.

It is of course debatable if existence is greater or not, or we could even debate what existence is.

3) Here comes the problem. The argument assumes that god then must exist. But this is a form of circular reasoning. We assume a concept that in its definition must exist and then we use that as a proof of it's very existance. Exactly like 69Dodges PUTE. This argument has no value whatsoever and is merely to be used as a mild amusement.

We are merely saying that if there was such a thing as a God he would have to exist.

Integrating another concept as necessity doesn't help because the the argument just rests on this so called necessity, and you have come no further.

As MP would say this argument is silly and I will have to close it.


Mss Hal

 

[Gregor]

{warning: off track}

CEO

I re-read my post and your well written response. I seem to have missed the crux of the ontological argument, and your response was both very courteous and non-confrontational in explaining my error. Thanks.

 

[ceo_esq]

No. I just said that we can't say, "Superman-the-real-person is greater than Superman-the-comic-book-character," because there is no Superman-the-real-person. On the other hand, if someone said, "Merlin was able to cast magic spells," he probably does not mean, "Merlin-the-real-person was able to cast magic spells." (That would indeed be meaningless, because there was no Merlin-the-real-person who might have been able, or unable, to cast spells.) Rather, he means, "Merlin-the-fictional-character was able to cast magic spells." And all that really means is, "Books of fiction have been written that contain sentences like 'Merlin cast a magic spell.' " So, even though the proposition, "Merlin was able to cast magic spells," appears to be a proposition about a nonexistent person, very similar to propositions we might make about real persons, in fact it is merely a proposition about (real) books.

Okay - this is getting semantically complex. But I'm intrigued the idea that a proposition like Robin Hood stole from the rich and gave to the poor could really mean something like Books of fiction have been written that contain sentences like "Robin Hood stole from the rich and gave to the poor". For one thing, the second proposition essentially restates the first, so it becomes kind of a weird semantic loop. And to complicate matters further, it would appear that the words "Robin Hood stole from the rich and gave to the poor" do not signify the same thing the second time around as they did in the initial proposition!

Does the meaning of a proposition change depending on whether the referents are instantiated in the real world? What if we don't know if they exist or not? This would arguably have serious implications for, among other things, any proof purporting to establish the existence of something. If propositions about things existing (possibly) only the understanding cannot validly be interpreted in a manner at least analogous to propositions about things that exist in reality, we're facing some major problems.

What about the proposition x plus x equals 2x?

Specifically, he uses the term "God" to refer to something that is most definitely not God. According to his definition of "God," nothing greater than God can be conceived. Now, a real deity can be conceived, and is greater than a fictional one. So, the term "God" cannot refer to a fictional diety; this is true even if no real diety exists to which it can refer. Yet he seems to think that, since he's assuming God doesn't exist, it's now ok to use "God" to mean the next best thing, namely, a fictional God, even though that usage contradicts his own definition of the term.

I hate to ask, but perhaps could you explain this another way?

If "necessarily true" means anything like "provable using no assumptions whatsoever," then, no, because I can't imagine what such a proof might look like.

Well, let me try to rephrase: Do you think there are any propositions of the sort "There really exists ..." which are logically impossible to be false (i.e. which are true in all conceivable worlds)? (And again - if not, how did you determine that there are no such propositions?)

 

[69dodge]

Originally posted by ceo_esq
Okay - this is getting semantically complex. But I'm intrigued [by] the idea that a proposition like Robin Hood stole from the rich and gave to the poor could really mean something like Books of fiction have been written that contain sentences like "Robin Hood stole from the rich and gave to the poor". For one thing, the second proposition essentially restates the first, so it becomes kind of a weird semantic loop. And to complicate matters further, it would appear that the words "Robin Hood stole from the rich and gave to the poor" do not signify the same thing the second time around as they did in the initial proposition!

I don't think there's any weird loop. The second proposition does restate the first, but within quotes; that's very different. "I typed 'qwertyuiop' " is a perfectly reasonable thing to say, even though "qwertyuiop" is meaningless.

I agree that "Robin Hood stole" means different things when someone in real life says it to you and when it appears in a work of fiction. If I told you "Robin Hood stole" and you weren't sure if my statement was true, how would you go about verifying it? Would you try to capture the alleged robber and interrogate him, or search for witnesses to interview, as if I had told you "my neighbor stole"? No, of course not. You'd go to the fiction section of your library and read the book entitled "Robin Hood" to see if it said anything like "Robin Hood stole." Because that's all I really meant to begin with.

Within the context of the book, Robin Hood is assumed to be a real person. So when the book says, "Robin Hood stole," it implicitly means, "There existed a real person named 'Robin Hood', and he stole." This is a meaningful statement; it just happens to be false. That's why we call the book containing it a work of fiction.

Does the meaning of a proposition change depending on whether the referents are instantiated in the real world? What if we don't know if they exist or not?

It can change, certainly. I wouldn't say the meaning depends, directly and only, on whether the referents exist. But there is always some context. Basically, what did the person who stated the proposition intend it to mean? What would most people who hear it think it means? In general, we can't determine its meaning just by looking at the words alone, with no knowledge of the context; language can be very imprecise.

What about the proposition x plus x equals 2x?

I'm not sure what you're asking here.

I hate to ask, but perhaps could you explain this another way?

We are using a definition of the term "God" which implies that nothing greater than God can be conceived. Therefore, a thing is, by definition, not God, if we can conceive of something else greater than it.

Step 1 of the proof asks us to assume that "God exists in the understanding but not in reality." It's fairly clear what this phrasing is intended to mean, but if we wish to be precise, we really should not use the term "God" for whatever it is that exists in our understanding, because, as the proof later shows, something greater can be conceived, namely, a deity that exists in reality. We might, instead, use the term "idea of God" for what exists in our understanding. So even if we assume that God doesn't exist in reality, it is still not the case that we can conceive of something greater than God; it is merely the case that we can conceive of something greater than the idea of God.

The contradiction arose, not because we assumed God doesn't exist in reality, but because we assumed he does exist in our understanding. (I do not deny, of course, that people think about God. In that sense, it may figuratively be said that God exists in our understanding. But only figuratively.)

When discussing an idea, we may want to refer to the idea as an idea, or we may want to refer to what the idea is about. The phrase, "the God that exists in our understanding," can reasonably be interpreted either way. However, if we claim that a real deity is greater than the God that exists in our understanding, because the former exists in reality while the latter doesn't, it is clear that we are interpreting the phrase to mean the idea of God, as an idea. (A deity that exists in reality is no greater than what our idea of God is about; our idea of God is about a-deity-that-exists-in-reality, too.) Certainly, a real god is greater than the idea of a god, but that's because the idea of a god is an idea, not a god. So we shouldn't call it "God." And if we do, we shouldn't be surprised when we run into contradictions.

Well, let me try to rephrase: Do you think there are any propositions of the sort "There really exists ..." which are logically impossible to be false (i.e. which are true in all conceivable worlds)? (And again - if not, how did you determine that there are no such propositions?)

The real, physical world and the world of mathematical or logical proofs seem so far removed from each other that I simply cannot imagine how one might go about logically proving that something existed in the real world. I do not mean "cannot imagine" in the sense of "I cannot imagine how one might go about proving Goldbach's Conjecture." I mean that it seems impossible in principle. As Einstein said:<blockquote>Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things? In my opinion the answer to this question is, briefly, this: As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.
</blockquote>

 

[whitefork]

Sure. See, for example:

1. Superman is a guy who flies around wearing his underwear topmost.
2. Superman exists.

It is possible to describe properties of entities that don't actually exist.

So, if existence is a property, then it is possible to describe the existence of something that doesn't exist.

I don't know if that statement makes any sense. It seems to be like describing the color of something that's invisible or the sound of something that makes no noise. Simon and Garfunkel notwithstanding, I'm not sure it can be done.

 

[Paul C. Anagnostopoulos]

This thread is an excellent example of how philosophy goes round in circles, never managing to converge on an answer.

~~ Paul

 

[whitefork]

Quoth Paul

This thread is an excellent example of how philosophy goes round in circles, never managing to converge on an answer.

I guess it depends on what kind of answer you're looking for.

I would like to add something to the "is existence a predicate?" discussion, from a slightly different point of view.

If it is, that is, if "X exists" adds something to the concept of X, then, we ought to be able to dispense with the backward-E existential quantifier of predicate logic. All such propositions would then be universals.

Say "there is at least one x such that Sx" where S is the predicate "is a star". How does one modify this to add "and X exists"? How does one write "there is at least one X such that X exists"?

Similarly, if "exists" is a predicate like others, oughtn't one be able to write any predicate symbol backwards and use it as a quantifier?


I'll take the position (probably lifted from G. E. Moore or somebody like him) that saying "the sun exists" is another way of saying that the statement "the sun is a star" is true.

So saying that God exists is just affirming that the stories about some god are true.