Anselm argument and problem within

[bahman]

Here there is his argument:

1. It is a conceptual truth (or, so to speak, true by definition) that God is a being than which none greater can be imagined (that is, the greatest possible being that can be imagined).
2. God exists as an idea in the mind.
3. A being that exists as an idea in the mind and in reality is, other things being equal, greater than a being that exists only as an idea in the mind.
4. Thus, if God exists only as an idea in the mind, then we can imagine something that is greater than God (that is, a greatest possible being that does exist).
5. But we cannot imagine something that is greater than God (for it is a contradiction to suppose that we can imagine a being greater than the greatest possible being that can be imagined.)
6. Therefore, God exists.

God is believed to be omnipotent, omniscient, omniprenst,...

Let's focus on omnipotent for a moment. That means that God has to be extremely strong, or better to say infinitely strong. However, according to Cantor's theorem, the infinity is not the largest number. In fact, he shows that there is no largest infinity since there is always a number bigger than what you can imagine. Therefore, the strongest quality does not exist either. This questions the first premise. Therefore, his argument does not follow.

[Impenitent]

Muhammad Ali has left the building...

he was the greatest

-Imp

[mickthinks]

Anselm’s argument is flawed, but Cantor’s infinities have nothing to do with it.

Anselm shows why if you imagine God, you must imagine her existing. But that imagined existence doesn’t entail actual existence.

Cantor shows that there are infinities beyond the simple “countable” infinity, א° But even if we assume for the sake of argument that omnipotence etc. must be mathematically infinite, there’s no obvious reason to believe that א° isn’t infinite enough.

[Veritas Aequitas]

Here are 5 Formulation of St. Anselm's Ontological Argument
https://plato.stanford.edu/entries/onto ... tAnsOntArg

9.1 Formulation 1
God exists in the understanding but not in reality. (Assumption for reductio)

Existence in reality is greater than existence in the understanding alone. (Premise)

A being having all of God’s properties plus existence in reality can be conceived. (Premise)

A being having all of God’s properties plus existence in reality is greater than God. (From (1) and (2).)

A being greater than God can be conceived. (From (3) and (4).)

It is false that a being greater than God can be conceived. (From definition of “God”.)

Hence, it is false that God exists in the understanding but not in reality. (From (1), (5), (6).)

God exists in the understanding. (Premise, to which even the Fool agrees.)

Hence God exists in reality. (From (7), (8).)

See Plantinga 1967.

9.2 Formulation 2
The Fool understands the expression “the being than which no greater can be conceived”. (Premise)

If a person understands an expression “b”, then b is in that person’s understanding. (Premise)

If a thing is in a person’s understanding, then the person can conceive of that thing’s existing in reality. (Premise)

Each thing which exists in reality is greater than any thing which exists only in the understanding. (Premise)

If a person can conceive of something, and that thing entails something else, then the person can also conceive of that other thing. (Premise)

If a person can conceive that a specified object has a given property, then that person can conceive that something or other has that property. (Premise)

Hence the being than which no greater can be conceived exists in reality. (From (1)-(6), by a complex series of steps here omitted.)

See Barnes 1972.

9.3 Formulation 3
There is a thing x, and a magnitude m, such that x exists in the understanding, m is the magnitude of x, and it it not possible that there is a thing y and a magnitude n such that n is the magnitude of y and n>m. (Premise)

For any thing x and magnitude m, if x exists in the understanding, m is the magnitude of x, and it is not possible that there is a thing y and magnitude n such that n is the magnitude of y and n>m, then it is possible that x exists in reality. (Premise)

For any thing x and magnitude m, if m is the magnitude of x, and it it not possible that there is a thing y and a magnitude n such that n is the magnitude of y and n>m, and x does not exist in reality, then it is not possible that if x exists in reality then there is a magnitude n such that n is greater than m and n is the magnitude of x. (Premise)

(Hence) There is a thing x and a magnitude m such that x exist in the understanding, and x exists in reality, and m is the magnitude of x, and it it not possible that there is a thing y and a magnitude n such that n is the magnitude of y and n>m. (From 1, 2, 3)

See Adams 1971.

9.4 Formulation 4
For any understandable being x, there is a world w such that x exists in w. (Premise)

For any understandable being x, and for any worlds w and v, if x exists in w, but x does not exist in v, then the greatness of x in w exceeds the greatness of x in v. (Premise)

There is an understandable being x such that for no world w and being y does the greatness of y in w exceed the greatness of x in the actual world. (Premise)

(Hence) There is a being x existing in the actual world such that for no world w and being y does the greatness of y in w exceed the greatness of x in the actual world. (From (1)-(3).)

See Lewis 1970.

Lewis also suggests an alternative to (3) which yields a valid argument:

(3′) There is an understandable being x such that for no worlds v and w and being y does the greatness of y in w exceed the greatness of x in v.
and two alternatives to (3)—not presented here—which yield invalid arguments. (Of course, these further two alternatives are crucial to Lewis’ overall analysis of the passage: essentially, Lewis suggests that Anselm equivocates between an invalid argument with plausible premises and a valid argument with question-begging premises. In this respect, Lewis’ analysis is quite different from the other analyses currently under discussion.)

9.5 Formulation 5
There is (in the understanding) something than which there is no greater. (Premise)

(Hence) There is (in the understanding) a unique thing than which there is no greater. (From (1), assuming that the “greater-than” relation is connected.)

(Hence) There is (in the understanding) something which is the thing than which there is no greater. (From (2), by a theorem about descriptions.)

(Hence) There is (in the understanding) nothing which is greater than the thing than which there is no greater. (From (3), by another theorem about descriptions.)

If that thing than which there is no greater does not exist (in reality), then there is (in the understanding) something which is greater than that thing than which there is no greater. (Premise)

(Hence) That thing than which there is no greater exists (in reality). (From (4) and (5).)

(Hence) God exists. (From (6).)

See Oppenheimer and Zalta 1991.

Oppenheimer and Zalta 2011 provides a “simplified” version of this argument, in which the number of controversial assumptions is reduced. Since they also provide a clear reason for thinking that this new version of the argument is not persuasive, it won't be considered further here.

[Veritas Aequitas]

Critiques of ontological arguments.
Perhaps the best known criticisms of ontological arguments are due to Immanuel Kant, in his Critique of Pure Reason. Most famously, Kant claims that ontological arguments are vitiated by their reliance upon the implicit assumption that “existence” is a real predicate.
https://plato.stanford.edu/entries/onto ... arguments/

9.6 Critical Appraisal of St. Anselm Argument
https://plato.stanford.edu/entries/onto ... tAnsOntArg

Considered as interpretations of the argument presented in the Proslogion, these formulations are subject to various kinds of criticisms.

First, the modal interpretations of Lewis 1970 and Adams 1971 don’t square very well with the rest of the Proslogion: the claim that “being than which no greater can be conceived” should be read as “being than which no greater is possible” would have us render the claim of Proslogion 15 to be that God is a being greater than any which is possible. And that is surely a bad result.

Second, the Meinongian interpretations of Barnes 1972, Adams 1971 and Oppenheimer and Zalta 1991 produce arguments which, given the principles involved, could easily be much simplified, and which are obviously vulnerable to Gaunilo-type objections.

Consider, for example, the case of Oppenheimer and Zalta. They have Anselm committed to the claim that if anyone can understand the phrase “that than which F”, then there is something in the understanding such that F (see their footnote 25); and they also have him committed to the claim that if there is something which is the F-thing, then it—i.e., the F-thing—has the property F (see page 7). Plainly though, if Anselm is really committed to these principles, then he could hardly fail to be committed to the more general principles: (1) if anyone can understand the phrase “an F”, then there is at least one F-thing in the understanding; and (2) if there are some things which are the F-things, then they—i.e., the F-things—must have the property F. (It would surely be absurd to claim that Anselm is only committed to the less general principles: what could possibly have justified the restrictions to the special cases?)

But, then, mark the consequences. We all understand the expression “an existent perfect being”. So, by the first claim, there is at least one existent perfect being in the understanding. And, by the second claim, any existent perfect being is existent. So, from these two claims combined, there is—in reality—at least one existent perfect being.

This argument gives Anselm everything that he wants, and very much more briefly. (The Proslogion goes on and on, trying to establish the properties of that than which no greater can be conceived. How much easier if we can just explicitly build all of the properties which want to “derive” into the initial description.) So, if Anselm really were committed to the principles which Oppenheimer and Zalta appear to attribute to him, it is hard to understand why he didn’t give the simpler argument. And, of course, it is also hard to understand why he didn’t take Gaunilo’s criticism. After all, when it is set out in this way, it is obvious that the argument proves far too much.

Third, some of the arguments have Anselm committed to claims about greatness which do not seem to correspond with what he actually says. The natural reading of the text is that, if two beings are identical save that one exists only in the understanding and the other exists in reality as well, then the latter is greater than the former. But Barnes 1971, for example, has Anselm committed to the much stronger claim that any existing thing is greater than every non-existent thing.

Given these kinds of considerations, it is natural to wonder whether there are better interpretations of Proslogion II according to which the argument in question turns out NOT to be logically valid. Here is a modest attempt to provide such an analysis:

We start with the claim that the Fool understands the expression “being than which no greater can be conceived”, i.e., even the Fool can entertain the idea or possess the concept of a being than which no greater can be conceived. Now, entertaining this idea or possessing this concept requires the entertainer or possessor to recognise certain relationships which hold between given properties and the idea or concept in question. For example, given that you possess the concept of, or entertain the idea of, a smallest really existent Martian, it follows that you must recognise some kind of connection between the properties of being a Martian, really existing, and being smaller than other really existing Martians, and the concept or idea in question.

Following Anselm, we might say that, since you understand the expression “smallest really existent Martian”, there is, in your understanding, at least one smallest really existent Martian. (Or, apparently following Descartes, one might say that real existence is “part of”—or “contained in”—the idea of a smallest really existent Martian.) However, in saying this, it must be understood that we are not actually predicating properties of anything: we aren’t supposing that there is something which possesses the properties of being a Martian, really existing, and being no larger than any other Martian. (After all, we can safely suppose, we don’t think that any Martians really exist.) In other words, we must be able to have the concept of, or entertain the idea of, a smallest really existing Martian without believing that there really are any smallest Martians. Indeed, more strongly, we must be able to entertain the concept of a smallest really existent Martian—and to recognise that the property of “really existing” is part of this concept—while nonetheless maintaining that there are no smallest existent Martians.

It will be useful to introduce vocabulary to mark the point which is being made here. We could, for instance, distinguish between the properties which are encoded in an idea or concept, and the properties which are attributed in positive atomic beliefs which have that idea or concept as an ingredient. The idea “really existent Santa Claus” encodes the property of real existence; but it is perfectly possible to entertain this idea without attributing real existence to Santa Claus, i.e., without believing that Santa Claus really exists.

We can then apply this distinction to Anselm’s argument. On the one hand, the idea “being than which no greater can be conceived” encodes the property of real existence—this is what the reductio argument establishes (if it establishes anything at all). On the other hand, it is perfectly possible to entertain the idea of a being than which no greater can be conceived—and to recognise that this idea encodes the property of real existence—without attributing real existence to a being than which no greater can be conceived, i.e., without believing that a being than which no greater can be conceived really exists.

Of course, the argument which Anselm actually presents pays no attention to this distinction between encoding and attributing—i.e., between entertaining an idea and holding a belief—and nor does it pay attention to various other niceties. We begin from the point that the Fool entertains the idea of that than which no greater can be conceived (because the Fool understands the words “that than which no greater can be conceived”). From this, we move quickly to the claim that even the Fool is “convinced”—i.e., believes—that that than which no greater can be conceived possesses the property of existing in the understanding. And then the reductio argument is produced to establish that that than which no greater can be conceived cannot exist only in the understanding but must also possess the property of existing in reality as well (and all mention of the Fool, and what it is that the Fool believes, disappears).

As it stands, this is deeply problematic. How are we supposed to regiment the references to the Fool in the argument? Is the reductio argument supposed to tell us something about what even the Fool believes, or ought to believe? Are the earlier references to the Fool supposed to be inessential and eliminable? How are we so much as to understand the claim that even the Fool believes that that than which no greater can be conceived exists in the understanding? And how do we get from the Fool’s understanding the words “that than which no greater can be conceived” to his believing that that than which no greater can be conceived possesses the property of existing in the understanding?

Following the earlier line of thought, it seems that the argument might go something like this:

(Even) the Fool has the concept of that than which no greater can be conceived.

(Hence) (Even) the Fool believes that that than which no greater can be conceived exists in the understanding.

No one who believes that that than which no greater can be conceived exists in the understanding can reasonably believe that that than which no greater can be conceived exists only in the understanding.

(Hence) (Even) the Fool cannot reasonably deny that that than which no greater can be conceived exists in reality

(Hence) That than which no greater can be conceived exists in reality.

While this is not a good argument, it could appear compelling to one who failed to attend to the distinction between entertaining ideas and holding beliefs and who was a bit hazy on the distinction between the vehicles of belief and their contents. When the Fool entertains the concept of that than which no greater can be conceived he recognises that he is entertaining this concept (i.e., he believes that he is entertaining the concept of that than which no greater can be conceived—or, as we might say, that the concept is in his understanding). Conflating the concept with its object, this gives us the belief that than which no greater can be conceived possesses the property of existing in the understanding. Now, suppose as hypothesis for reductio, that we can reasonably believe that that than which no greater can be conceived possesses the property of existing only in the understanding. Ignoring the distinction between entertaining ideas and holding beliefs, this means that we when we entertain the idea of that than which no greater can be conceived, we entertain the idea of a being which exists only in the understanding. But that is absurd: when we entertain the idea of that than which no greater can be conceived, our idea encodes the property of existing in reality. So there is a contradiction, and we can conclude that, in order to be reasonable, we must believe that that than which no greater can be conceived exists in reality. But if any reasonable person must believe that that than which no greater can be conceived exists in reality, then surely it is the case that that than which no greater can be conceived exists in reality. And so we are done.

No doubt this suggestion about the interpretation of Anselm’s argument is deficient in various ways. However, the point of including it is illustrative rather than dogmatic. In the literature, there has been great resistance to the idea that the argument which Anselm gives is one which modern logicians would not hesitate to pronounce invalid. But it is very hard to see why there should be this resistance. (Certainly, it is not something for which there is much argument in the literature.) The text of the Proslogion is so rough, and so much in need of polishing, that we should not be too quick to dismiss the suggestion that Anselm’s argument is rather more like the argument most recently sketched than it is like the logically valid demonstrations provided by commentators such as Barnes, Adams, and Oppenheimer and Zalta. (For a more complex analysis of Proslogion II that has it yielding a valid argument, see Hinst 2014.)

[Age]

Here there is his argument:

1. It is a conceptual truth (or, so to speak, true by definition) that God is a being than which none greater can be imagined (that is, the greatest possible being that can be imagined).

Okay.

2. God exists as an idea in the mind.

Where is and what is 'the mind', exactly?

3. A being that exists as an idea in the mind and in reality is, other things being equal, greater than a being that exists only as an idea in the mind.

What is meant here by 'greater'.

If one imagines of 'a rat', for example, and imagines 'this rat is walking within a spinning wheel', and then comes upon 'this rat walking within a spinning wheel', then the existence of 'this rat', in reality, is not 'greater' than what was previously being imagined only. This is just a different scenario, or just 'a rat in real walking within a spinning wheel'. There is nothing amazing here to be nor get excited about. As there is nothing 'greater' nor 'lesser' than here.

4. Thus, if God exists only as an idea in the mind, then we can imagine something that is greater than God (that is, a greatest possible being that does exist).

This here does not logically follow.

If one is imagining that God is the so-called 'greatest', then there is no thing that one could imagine that is 'greater' than God. However, and for example, if one is imagining that there is some 'great' God, then, obviously, it would be very, very, simple to imagine of some thing 'greater' than 'this' God.

But, again, if one is imagining that God is the 'greatest being' of which there is none 'greater', then one could not imagine of some 'being' 'greater' than 'that' God. However, one could imagine some thing that is 'greater' than 'that' God. But this is just obvious also.

5. But we cannot imagine something that is greater than God (for it is a contradiction to suppose that we can imagine a being greater than the greatest possible being that can be imagined.)

So, if what is being said and claimed here now would be a contradiction, then why was some thing that did not logically follow and was just a contradiction anyway?

6. Therefore, God exists.

This arguments is not sound, not valid, does not even logically follow, and is completely and utterly nonsensical and absurd.

But as I continually say, and point out using the words and claims from the 'olden days' here, they really will say just about anything, in the hope that it would back up and support their currently held onto beliefs, even though what is said and claimed is Truly illogical and ridiculous.

God is believed to be omnipotent, omniscient, omniprenst,...

If you say so, and if this is what you believe, then this is okay with me.

Although you people would still want to believe somethings are true, prior to obtaining and gaining actual proof for them, I still question you as to why you would even begin to want to do this?

The answer by the way is very revealing, and enlightening.

Let's focus on omnipotent for a moment.

Okay.

That means that God has to be extremely strong, or better to say infinitely strong. However, according to Cantor's theorem, the infinity is not the largest number. In fact, he shows that there is no largest infinity since there is always a number bigger than what you can imagine.

Do you purposely twist and distort words around, to attempt to fool and deceive others, or are you completely oblivious to the fact that you are even doing this?

In other words, are you so fooled and deceived here that even you can still not yet see this?

Now, if you or anyone would like to know where and how the distortion and twisting of words here is taking place, then just let me know and i will inform you.

Therefore, the strongest quality does not exist either. This questions the first premise. Therefore, his argument does not follow.

How could the first premise be questioned?

It is just an idea, or just a definition, only.

There is no claim that there is anything other than just a concept or conceptual idea or definition, alone.

[Iwannaplato]

Here there is his argument:

1. It is a conceptual truth (or, so to speak, true by definition) that God is a being than which none greater can be imagined

I think that word imagine is very floppy. Can I really imagine God?
I can manage to have some fuzzy concept around which I associate other ideas, also fuzzy.

Let's take a more mundane example. Can I imagine my friend Jack?
I can certainly think the name, around which I have some immediate associations, whatever my idiosyncratic associations are - perhaps a fuzzy snapshot of his face and some feelings of warmth or humor. If I 'imagine' more then I get more images and ideas and perhaps facts.

But have I really imagined Jack???

There is so much even an hour long contemplation of Jack completely misses. Skills, experiences, attitudes, emotions, connections I forgot about or don't know about. The mass of things that Jack has access to about himself that I don't know. But then there are things JACK doesn't even know about himself or forgot. Facets others might or might not notice or know about and so on.

I think this idea of imagining (either the real Jack or some made up Jack or God) is a meaningless idea in this context.

One can't, I think, use such a floppy, idiosyncratic, contingent, vague verb in any meaningful way in a proof. We imagine portions/views of things. We imagine opinions. We don't even notice all that we imagine when we imagine.

I can think the word or some image of quark, black hole, Tommy's unconscious mind, Sally and Fred's relationship, The US economy, the ecosystem of the Tundra and so on. But that means...some kind of mental experience happened related to those things - at least, I think they relate in some way.

I don't think this means much in ways that lead to solid conclusions.

And if so, I could always, then think

God plus some other stuff. OK, that God plus some other stuff. More omniscient than omniscient cause the God I'm imagining knows about things that aren't or whatever idiotic clumping of thoughts I put together to rule out other people's Gods or prove yes or no about God.

[bahman]

Anselm’s argument is flawed, but Cantor’s infinities have nothing to do with it.

It has.

Anselm shows why if you imagine God, you must imagine her existing. But that imagined existence doesn’t entail actual existence.

So you have to deal with premise (3).

Cantor shows that there are infinities beyond the simple “countable” infinity, א° But even if we assume for the sake of argument that omnipotence etc. must be mathematically infinite, there’s no obvious reason to believe that א° isn’t infinite enough.

God is the greatest imaginable thing according to Anselm. I can imagine something greater but not the greatest. That is the whole message.

[Age]

Anselm’s argument is flawed, but Cantor’s infinities have nothing to do with it.

It has.

Anselm shows why if you imagine God, you must imagine her existing. But that imagined existence doesn’t entail actual existence.

So you have to deal with premise (3).

Cantor shows that there are infinities beyond the simple “countable” infinity, א° But even if we assume for the sake of argument that omnipotence etc. must be mathematically infinite, there’s no obvious reason to believe that א° isn’t infinite enough.

God is the greatest imaginable thing according to Anselm. I can imagine something greater but not the greatest. That is the whole message.

How could you possibly, logically and physically, imagine something greater than the greatest thing?

Maybe if you provide an example of how and/or when you can do this, then I, for one, could accept your claim here. Until then, I wait.

[bahman]

Here are 5 Formulation of St. Anselm's Ontological Argument
https://plato.stanford.edu/entries/onto ... tAnsOntArg

9.1 Formulation 1
God exists in the understanding but not in reality. (Assumption for reductio)

Existence in reality is greater than existence in the understanding alone. (Premise)

A being having all of God’s properties plus existence in reality can be conceived. (Premise)

A being having all of God’s properties plus existence in reality is greater than God. (From (1) and (2).)

A being greater than God can be conceived. (From (3) and (4).)

It is false that a being greater than God can be conceived. (From definition of “God”.)

Hence, it is false that God exists in the understanding but not in reality. (From (1), (5), (6).)

God exists in the understanding. (Premise, to which even the Fool agrees.)

Hence God exists in reality. (From (7), (8).)

See Plantinga 1967.

9.2 Formulation 2
The Fool understands the expression “the being than which no greater can be conceived”. (Premise)

If a person understands an expression “b”, then b is in that person’s understanding. (Premise)

If a thing is in a person’s understanding, then the person can conceive of that thing’s existing in reality. (Premise)

Each thing which exists in reality is greater than any thing which exists only in the understanding. (Premise)

If a person can conceive of something, and that thing entails something else, then the person can also conceive of that other thing. (Premise)

If a person can conceive that a specified object has a given property, then that person can conceive that something or other has that property. (Premise)

Hence the being than which no greater can be conceived exists in reality. (From (1)-(6), by a complex series of steps here omitted.)

See Barnes 1972.

9.3 Formulation 3
There is a thing x, and a magnitude m, such that x exists in the understanding, m is the magnitude of x, and it it not possible that there is a thing y and a magnitude n such that n is the magnitude of y and n>m. (Premise)

For any thing x and magnitude m, if x exists in the understanding, m is the magnitude of x, and it is not possible that there is a thing y and magnitude n such that n is the magnitude of y and n>m, then it is possible that x exists in reality. (Premise)

For any thing x and magnitude m, if m is the magnitude of x, and it it not possible that there is a thing y and a magnitude n such that n is the magnitude of y and n>m, and x does not exist in reality, then it is not possible that if x exists in reality then there is a magnitude n such that n is greater than m and n is the magnitude of x. (Premise)

(Hence) There is a thing x and a magnitude m such that x exist in the understanding, and x exists in reality, and m is the magnitude of x, and it it not possible that there is a thing y and a magnitude n such that n is the magnitude of y and n>m. (From 1, 2, 3)

See Adams 1971.

9.4 Formulation 4
For any understandable being x, there is a world w such that x exists in w. (Premise)

For any understandable being x, and for any worlds w and v, if x exists in w, but x does not exist in v, then the greatness of x in w exceeds the greatness of x in v. (Premise)

There is an understandable being x such that for no world w and being y does the greatness of y in w exceed the greatness of x in the actual world. (Premise)

(Hence) There is a being x existing in the actual world such that for no world w and being y does the greatness of y in w exceed the greatness of x in the actual world. (From (1)-(3).)

See Lewis 1970.

Lewis also suggests an alternative to (3) which yields a valid argument:

(3′) There is an understandable being x such that for no worlds v and w and being y does the greatness of y in w exceed the greatness of x in v.
and two alternatives to (3)—not presented here—which yield invalid arguments. (Of course, these further two alternatives are crucial to Lewis’ overall analysis of the passage: essentially, Lewis suggests that Anselm equivocates between an invalid argument with plausible premises and a valid argument with question-begging premises. In this respect, Lewis’ analysis is quite different from the other analyses currently under discussion.)

9.5 Formulation 5
There is (in the understanding) something than which there is no greater. (Premise)

(Hence) There is (in the understanding) a unique thing than which there is no greater. (From (1), assuming that the “greater-than” relation is connected.)

(Hence) There is (in the understanding) something which is the thing than which there is no greater. (From (2), by a theorem about descriptions.)

(Hence) There is (in the understanding) nothing which is greater than the thing than which there is no greater. (From (3), by another theorem about descriptions.)

If that thing than which there is no greater does not exist (in reality), then there is (in the understanding) something which is greater than that thing than which there is no greater. (Premise)

(Hence) That thing than which there is no greater exists (in reality). (From (4) and (5).)

(Hence) God exists. (From (6).)

See Oppenheimer and Zalta 1991.

Oppenheimer and Zalta 2011 provides a “simplified” version of this argument, in which the number of controversial assumptions is reduced. Since they also provide a clear reason for thinking that this new version of the argument is not persuasive, it won't be considered further here.

Thanks for sharing other versions of the argument. I had a quick look at them and found them interesting to discuss. I, however, do not have time to discuss them all right now. Could we please work on the version that I posted? What is your opinion about my counterargument?

[bahman]

Critiques of ontological arguments.
Perhaps the best known criticisms of ontological arguments are due to Immanuel Kant, in his Critique of Pure Reason. Most famously, Kant claims that ontological arguments are vitiated by their reliance upon the implicit assumption that “existence” is a real predicate.
https://plato.stanford.edu/entries/onto ... arguments/

9.6 Critical Appraisal of St. Anselm Argument
https://plato.stanford.edu/entries/onto ... tAnsOntArg

Considered as interpretations of the argument presented in the Proslogion, these formulations are subject to various kinds of criticisms.

First, the modal interpretations of Lewis 1970 and Adams 1971 don’t square very well with the rest of the Proslogion: the claim that “being than which no greater can be conceived” should be read as “being than which no greater is possible” would have us render the claim of Proslogion 15 to be that God is a being greater than any which is possible. And that is surely a bad result.

Second, the Meinongian interpretations of Barnes 1972, Adams 1971 and Oppenheimer and Zalta 1991 produce arguments which, given the principles involved, could easily be much simplified, and which are obviously vulnerable to Gaunilo-type objections.

Consider, for example, the case of Oppenheimer and Zalta. They have Anselm committed to the claim that if anyone can understand the phrase “that than which F”, then there is something in the understanding such that F (see their footnote 25); and they also have him committed to the claim that if there is something which is the F-thing, then it—i.e., the F-thing—has the property F (see page 7). Plainly though, if Anselm is really committed to these principles, then he could hardly fail to be committed to the more general principles: (1) if anyone can understand the phrase “an F”, then there is at least one F-thing in the understanding; and (2) if there are some things which are the F-things, then they—i.e., the F-things—must have the property F. (It would surely be absurd to claim that Anselm is only committed to the less general principles: what could possibly have justified the restrictions to the special cases?)

But, then, mark the consequences. We all understand the expression “an existent perfect being”. So, by the first claim, there is at least one existent perfect being in the understanding. And, by the second claim, any existent perfect being is existent. So, from these two claims combined, there is—in reality—at least one existent perfect being.

This argument gives Anselm everything that he wants, and very much more briefly. (The Proslogion goes on and on, trying to establish the properties of that than which no greater can be conceived. How much easier if we can just explicitly build all of the properties which want to “derive” into the initial description.) So, if Anselm really were committed to the principles which Oppenheimer and Zalta appear to attribute to him, it is hard to understand why he didn’t give the simpler argument. And, of course, it is also hard to understand why he didn’t take Gaunilo’s criticism. After all, when it is set out in this way, it is obvious that the argument proves far too much.

Third, some of the arguments have Anselm committed to claims about greatness which do not seem to correspond with what he actually says. The natural reading of the text is that, if two beings are identical save that one exists only in the understanding and the other exists in reality as well, then the latter is greater than the former. But Barnes 1971, for example, has Anselm committed to the much stronger claim that any existing thing is greater than every non-existent thing.

Given these kinds of considerations, it is natural to wonder whether there are better interpretations of Proslogion II according to which the argument in question turns out NOT to be logically valid. Here is a modest attempt to provide such an analysis:

We start with the claim that the Fool understands the expression “being than which no greater can be conceived”, i.e., even the Fool can entertain the idea or possess the concept of a being than which no greater can be conceived. Now, entertaining this idea or possessing this concept requires the entertainer or possessor to recognise certain relationships which hold between given properties and the idea or concept in question. For example, given that you possess the concept of, or entertain the idea of, a smallest really existent Martian, it follows that you must recognise some kind of connection between the properties of being a Martian, really existing, and being smaller than other really existing Martians, and the concept or idea in question.

Following Anselm, we might say that, since you understand the expression “smallest really existent Martian”, there is, in your understanding, at least one smallest really existent Martian. (Or, apparently following Descartes, one might say that real existence is “part of”—or “contained in”—the idea of a smallest really existent Martian.) However, in saying this, it must be understood that we are not actually predicating properties of anything: we aren’t supposing that there is something which possesses the properties of being a Martian, really existing, and being no larger than any other Martian. (After all, we can safely suppose, we don’t think that any Martians really exist.) In other words, we must be able to have the concept of, or entertain the idea of, a smallest really existing Martian without believing that there really are any smallest Martians. Indeed, more strongly, we must be able to entertain the concept of a smallest really existent Martian—and to recognise that the property of “really existing” is part of this concept—while nonetheless maintaining that there are no smallest existent Martians.

It will be useful to introduce vocabulary to mark the point which is being made here. We could, for instance, distinguish between the properties which are encoded in an idea or concept, and the properties which are attributed in positive atomic beliefs which have that idea or concept as an ingredient. The idea “really existent Santa Claus” encodes the property of real existence; but it is perfectly possible to entertain this idea without attributing real existence to Santa Claus, i.e., without believing that Santa Claus really exists.

We can then apply this distinction to Anselm’s argument. On the one hand, the idea “being than which no greater can be conceived” encodes the property of real existence—this is what the reductio argument establishes (if it establishes anything at all). On the other hand, it is perfectly possible to entertain the idea of a being than which no greater can be conceived—and to recognise that this idea encodes the property of real existence—without attributing real existence to a being than which no greater can be conceived, i.e., without believing that a being than which no greater can be conceived really exists.

Of course, the argument which Anselm actually presents pays no attention to this distinction between encoding and attributing—i.e., between entertaining an idea and holding a belief—and nor does it pay attention to various other niceties. We begin from the point that the Fool entertains the idea of that than which no greater can be conceived (because the Fool understands the words “that than which no greater can be conceived”). From this, we move quickly to the claim that even the Fool is “convinced”—i.e., believes—that that than which no greater can be conceived possesses the property of existing in the understanding. And then the reductio argument is produced to establish that that than which no greater can be conceived cannot exist only in the understanding but must also possess the property of existing in reality as well (and all mention of the Fool, and what it is that the Fool believes, disappears).

As it stands, this is deeply problematic. How are we supposed to regiment the references to the Fool in the argument? Is the reductio argument supposed to tell us something about what even the Fool believes, or ought to believe? Are the earlier references to the Fool supposed to be inessential and eliminable? How are we so much as to understand the claim that even the Fool believes that that than which no greater can be conceived exists in the understanding? And how do we get from the Fool’s understanding the words “that than which no greater can be conceived” to his believing that that than which no greater can be conceived possesses the property of existing in the understanding?

Following the earlier line of thought, it seems that the argument might go something like this:

(Even) the Fool has the concept of that than which no greater can be conceived.

(Hence) (Even) the Fool believes that that than which no greater can be conceived exists in the understanding.

No one who believes that that than which no greater can be conceived exists in the understanding can reasonably believe that that than which no greater can be conceived exists only in the understanding.

(Hence) (Even) the Fool cannot reasonably deny that that than which no greater can be conceived exists in reality

(Hence) That than which no greater can be conceived exists in reality.

While this is not a good argument, it could appear compelling to one who failed to attend to the distinction between entertaining ideas and holding beliefs and who was a bit hazy on the distinction between the vehicles of belief and their contents. When the Fool entertains the concept of that than which no greater can be conceived he recognises that he is entertaining this concept (i.e., he believes that he is entertaining the concept of that than which no greater can be conceived—or, as we might say, that the concept is in his understanding). Conflating the concept with its object, this gives us the belief that than which no greater can be conceived possesses the property of existing in the understanding. Now, suppose as hypothesis for reductio, that we can reasonably believe that that than which no greater can be conceived possesses the property of existing only in the understanding. Ignoring the distinction between entertaining ideas and holding beliefs, this means that we when we entertain the idea of that than which no greater can be conceived, we entertain the idea of a being which exists only in the understanding. But that is absurd: when we entertain the idea of that than which no greater can be conceived, our idea encodes the property of existing in reality. So there is a contradiction, and we can conclude that, in order to be reasonable, we must believe that that than which no greater can be conceived exists in reality. But if any reasonable person must believe that that than which no greater can be conceived exists in reality, then surely it is the case that that than which no greater can be conceived exists in reality. And so we are done.

No doubt this suggestion about the interpretation of Anselm’s argument is deficient in various ways. However, the point of including it is illustrative rather than dogmatic. In the literature, there has been great resistance to the idea that the argument which Anselm gives is one which modern logicians would not hesitate to pronounce invalid. But it is very hard to see why there should be this resistance. (Certainly, it is not something for which there is much argument in the literature.) The text of the Proslogion is so rough, and so much in need of polishing, that we should not be too quick to dismiss the suggestion that Anselm’s argument is rather more like the argument most recently sketched than it is like the logically valid demonstrations provided by commentators such as Barnes, Adams, and Oppenheimer and Zalta. (For a more complex analysis of Proslogion II that has it yielding a valid argument, see Hinst 2014.)

I read this wall of text once but I have to read a few times more to understand what it is saying. Could you please summarize it?

[bahman]

Here there is his argument:

1. It is a conceptual truth (or, so to speak, true by definition) that God is a being than which none greater can be imagined (that is, the greatest possible being that can be imagined).

Okay.

I have a problem with the first premise.

2. God exists as an idea in the mind.

Where is and what is 'the mind', exactly?

Read it that God exists as an idea in the understanding.

3. A being that exists as an idea in the mind and in reality is, other things being equal, greater than a being that exists only as an idea in the mind.

What is meant here by 'greater'.

If one imagines of 'a rat', for example, and imagines 'this rat is walking within a spinning wheel', and then comes upon 'this rat walking within a spinning wheel', then the existence of 'this rat', in reality, is not 'greater' than what was previously being imagined only. This is just a different scenario, or just 'a rat in real walking within a spinning wheel'. There is nothing amazing here to be nor get excited about. As there is nothing 'greater' nor 'lesser' than here.

By greater I believe he means better quality.

4. Thus, if God exists only as an idea in the mind, then we can imagine something that is greater than God (that is, a greatest possible being that does exist).

This here does not logically follow.

If one is imagining that God is the so-called 'greatest', then there is no thing that one could imagine that is 'greater' than God. However, and for example, if one is imagining that there is some 'great' God, then, obviously, it would be very, very, simple to imagine of some thing 'greater' than 'this' God.

But, again, if one is imagining that God is the 'greatest being' of which there is none 'greater', then one could not imagine of some 'being' 'greater' than 'that' God. However, one could imagine some thing that is 'greater' than 'that' God. But this is just obvious also.

It follows if you accept (3).

5. But we cannot imagine something that is greater than God (for it is a contradiction to suppose that we can imagine a being greater than the greatest possible being that can be imagined.)

So, if what is being said and claimed here now would be a contradiction, then why was some thing that did not logically follow and was just a contradiction anyway?

What do you mean?

6. Therefore, God exists.

This arguments is not sound, not valid, does not even logically follow, and is completely and utterly nonsensical and absurd.

But as I continually say, and point out using the words and claims from the 'olden days' here, they really will say just about anything, in the hope that it would back up and support their currently held onto beliefs, even though what is said and claimed is Truly illogical and ridiculous.

Where is the problem?

God is believed to be omnipotent, omniscient, omniprenst,...

If you say so, and if this is what you believe, then this is okay with me.

Although you people would still want to believe somethings are true, prior to obtaining and gaining actual proof for them, I still question you as to why you would even begin to want to do this?

The answer by the way is very revealing, and enlightening.

You have to wait for it.

Let's focus on omnipotent for a moment.

Okay.

If you waited longer then you wouldn't ask the previous question.

That means that God has to be extremely strong, or better to say infinitely strong. However, according to Cantor's theorem, the infinity is not the largest number. In fact, he shows that there is no largest infinity since there is always a number bigger than what you can imagine.

Do you purposely twist and distort words around, to attempt to fool and deceive others, or are you completely oblivious to the fact that you are even doing this?

In other words, are you so fooled and deceived here that even you can still not yet see this?

Now, if you or anyone would like to know where and how the distortion and twisting of words here is taking place, then just let me know and i will inform you.

There is no twist of distortion here.

Therefore, the strongest quality does not exist either. This questions the first premise. Therefore, his argument does not follow.

How could the first premise be questioned?

It is just an idea, or just a definition, only.

There is no claim that there is anything other than just a concept or conceptual idea or definition, alone.

It follows from Cantor's theorem. Like it or not.

[bahman]

Here there is his argument:

1. It is a conceptual truth (or, so to speak, true by definition) that God is a being than which none greater can be imagined

I think that word imagine is very floppy. Can I really imagine God?
I can manage to have some fuzzy concept around which I associate other ideas, also fuzzy.

Let's take a more mundane example. Can I imagine my friend Jack?
I can certainly think the name, around which I have some immediate associations, whatever my idiosyncratic associations are - perhaps a fuzzy snapshot of his face and some feelings of warmth or humor. If I 'imagine' more then I get more images and ideas and perhaps facts.

But have I really imagined Jack???

There is so much even an hour long contemplation of Jack completely misses. Skills, experiences, attitudes, emotions, connections I forgot about or don't know about. The mass of things that Jack has access to about himself that I don't know. But then there are things JACK doesn't even know about himself or forgot. Facets others might or might not notice or know about and so on.

I think this idea of imagining (either the real Jack or some made up Jack or God) is a meaningless idea in this context.

One can't, I think, use such a floppy, idiosyncratic, contingent, vague verb in any meaningful way in a proof. We imagine portions/views of things. We imagine opinions. We don't even notice all that we imagine when we imagine.

I can think the word or some image of quark, black hole, Tommy's unconscious mind, Sally and Fred's relationship, The US economy, the ecosystem of the Tundra and so on. But that means...some kind of mental experience happened related to those things - at least, I think they relate in some way.

I don't think this means much in ways that lead to solid conclusions.

And if so, I could always, then think

God plus some other stuff. OK, that God plus some other stuff. More omniscient than omniscient cause the God I'm imagining knows about things that aren't or whatever idiotic clumping of thoughts I put together to rule out other people's Gods or prove yes or no about God.

I think you can imagine the idea of God who is omni-whatever and the creator of the world. Couldn't you? I think that is all he asks.

[bahman]

Anselm’s argument is flawed, but Cantor’s infinities have nothing to do with it.

It has.

Anselm shows why if you imagine God, you must imagine her existing. But that imagined existence doesn’t entail actual existence.

So you have to deal with premise (3).

Cantor shows that there are infinities beyond the simple “countable” infinity, א° But even if we assume for the sake of argument that omnipotence etc. must be mathematically infinite, there’s no obvious reason to believe that א° isn’t infinite enough.

God is the greatest imaginable thing according to Anselm. I can imagine something greater but not the greatest. That is the whole message.

How could you possibly, logically and physically, imagine something greater than the greatest thing?

Maybe if you provide an example of how and/or when you can do this, then I, for one, could accept your claim here. Until then, I wait.

Read Cantor's theorem, please.

[Iwannaplato]

I think you can imagine the idea of God who is omni-whatever and the creator of the world. Couldn't you? I think that is all he asks.

I can have those words in my brain, but I don't know what 'imagine' means, in this context.

I can close my eyes and imagine a red horse - and even this is an extremely partial, unstable 'rendition' in my mind.
To 'imagine' and omni deity....what have I really done?