Anselm's Ontological Argument: A Guide for the Perplexed | Hacker News Reader

Anselm's Ontological Argument: A Guide for the Perplexed

philosophicaldisquisitions.blogspot.com

56 pointstintinnabula117 comments

Emmanuel Kant reflected deeply on the ontological argument, as did Godel, Decartes, Spinoza, and Plantinga among others. Perhaps a bit of intellectual openness and a touch of humility would benefit the conversation in this thread? The Stanford Encyclopedia of Philosophy has a lengthy discussion on the history of the ontological argument, together with various attempts to refute it and reformulate it.

I find Kant's refutation most convincing. His claim is: "Existence is not a predicate." My intuition on his point is this. Let's consider the following statement: "Imagine a unicorn, with the property that it happens to be brown." There is an implicit and unstated assertion at the beginning of the above statement, that we are for the moment imagining that that the unicorn exists. We might rephrase as follows: "Imagine for the moment that a particular unicorn exists, and that it has the property that it is brown." Now we attempt to attribute to this unicorn the "property" of non-existence: "Imagine that a particular unicorn exists, and that it has the property that it does not exist." The statement is logically ill-formed, since we assert of a hypothetical entity that it simultaneously has and does not have a "property", namely that of existence. Hence, "existence" cannot be considered to be a property whose presence or absence can be attributed to a hypothetical entity. Kant argues that since Anselm's Ontological Argument depends on this logical fallacy, it is shown to be invalid.

Has anyone evaluated Godel's reformulation of the Ontological Argument to see if it avoids Kant's critique? I can't help but imagine that Godel was aware of Kant's (and others') analysis of the Ontological Argument.

I think the multiple meanings of the symbol "existence" should be taken into consideration in any such discussion:

https://en.m.wikipedia.org/wiki/Semiotics

https://en.m.wikipedia.org/wiki/Ontology

https://en.m.wikipedia.org/wiki/Consciousness

And Popper has an interesting relevant theory:

https://en.m.wikipedia.org/wiki/Popper%27s_three_worlds

And of course:

https://en.m.wikipedia.org/wiki/Reality

I know you’re not allowed to say this, but I’m not sure many people here actually read the article. Many people are responding to the argument itself in ways that were already addressed in the article (for example, there’s a whole section outlining two rebuttals to the “perfect island” parody).

This should be in bold face type at the top of every comment page of HN.

RTFA before replying. Paging Emanuel Lasker...

Didn't read the article, but existence is obviously not a property. It is an operator, and it takes a property (e.g. "x => x is a brown unicorn"), and then searches the whole universe for something with that property.

Philosophy is a funny thing. You need some word to describe what you are doing when you are thinking about something you haven't fully grasped yet, and which is on shaky foundations. That word might as well be Philosophy. But all too often Philosophy gets lost in intellectual games which make no sense. I have to read the article to see if that is one of those cases.

Just skimmed the article. Yep, this is obviously one of those meaningless intellectual games. Nothing to see there.

Does God exist? Well, something makes logic, the mathematical universe, and the physical universe work. We might as well call that something God. That doesn't mean that God is a conscious being. But then again, it becomes increasingly difficult to define what a conscious being is.

> Didn't read the article, but existence is obviously not a property.

It is "obviously" also a property.

> But all too often Philosophy gets lost in intellectual games which make no sense.

Did you consider how "makes sense" is implemented?

> Philosophy is a funny thing.

If you think philosophy is weird, you should check out reality!

> It is "obviously" also a property.

Nope, it is not. If it was a property, if would be everywhere true, and that's not really interesting, is it?

> Did you consider how "makes sense" is implemented?

You are the implementation. Does most of Philosophy make sense to you?

> Nope, it is not.

Yes it is.

> If it was a property, if would be everywhere true

It would only need to be true sometimes.

> and that's not really interesting, is it?

I think how humans generate and then perceive reality is extraordinarily interesting actually.

>> Did you consider how "makes sense" is implemented?

> You are the implementation.

Then why are you acting if your implementation is correct?

>Does most of Philosophy make sense to you?

I've only read tiny portions, so no. How about yourself?

Gödel does the usual Gödel thing - he just breaks modal logic. Modal logic is higher order, but there's logic above modal, and property "exists in all possible worlds" is such supermodal property that doesn't obey modal logic and is supposed to be output of modal logic, but Gödel uses it as input as a normal modal property. Modal property should be limited to one world and circumstances around it should be a priori variable across worlds, then we can expect those circumstances to vary by switching between worlds, but supermodal properties aren't like that and shouldn't be used like that.

Anseml's argument isn't really an argument, but a hypothesis: it concludes with "a greater thing can be thought to exist in reality", which is obviously a hypothesis.

This argument is somewhat related to Russell's Paradox.[1] "Suppose that we can form a class of all classes (or sets) that, like the null class, are not included in themselves. The paradox arises from asking the question of whether this class is in itself." Trouble comes from trying to force a set into existence by defining a predicate and then claiming that there is a set of all things for which that predicate is true. The mathematicians of the era eventually got out of that mess by adding a type theory. That broke the philosophical recursion loop.

When Russell was working on this, set theory was an abstract hobby, not the basis of industrial-strength systems. Now that computers routinely deal with types, recursion, sets, and groups for practical purposes, this sort of thing is better understood. We know you can get yourself into a definitional mess, and that there are useful systems which lack that flaw.

[1] https://iep.utm.edu/par-russ/

There's a (non-religious) form of it in the start of Spinoza's (rationalist) Ethica, too, where he posits the existence of a singular "substance" through a similar sort of intellectual trick.

> When Russell was working on this, set theory was an abstract hobby, not the basis of industrial-strength systems

I don’t think that’s true is it? People were doing very serious mathematics with sets before Russell. For example Richard Dedekind (finally) provided the rigorous construction of the real numbers using Dedekind cuts (specially defined subsets of the Rationals) in 1858.

Russell’s paradox required some rethinking of the axioms of set theory which brought about ZF and ZFC set theory but those weren’t really very different from what came before - just better defined.

Just to explain myself perhaps a little better.

Set theory since at least the mid 19th century has been fundamental to the basis of mathematics. The natural numbers are defined starting fromthe empty set and a successor operation that given a set a returns a U {a}, then the integers are defined as infinite sets of pairs from the cartesian product of the natural numbers with a particular common property[1], and rationals as infinite sets of pairs of integers[2].

Then Dedekind constructed the reals from the rationals and proved the least upper bound property. His construction is essentially to cut the numberline of the Rationals into two sets with specific properties (but essentially one less than and one greater than or equal to a particular real number, with the lower set having no largest element).

There is an excellent pair of youtube videos explaining how number systems are defined using sets https://youtu.be/dKtsjQtigag?si=3JFgz2YTUqB7EAv3 and https://youtu.be/IzUw53h12wU?si=D0lx1vCiy5FwjlwC

[1] Which you could think of as being that everything in the set [(a,b)] has a-b equal to some common integer which is what we think of as that particular integer. So the set [(2,0)] contains (2,0), (4,2) (-4,-6) and so on to infinitiy in both directions and that entire set of pairs we think of as the integer “2”

[2] where the common property is a division rather than a subtraction

Dedekinds paper is I believe 1872 actually and this is more in line with the set theory research explosion as cantor had published his results by this point. Plus him and Dedekind were close friends so they would have known of eachother’s research.

Russell’s paradox is not until like 1900 in response to I believe Frege’s own publication. This is why Hilbert then includes questions around the foundations of mathematics in his list because of these issues with sets and logic, while also offering up the famous phrase “we shall not be chased from the paradise cantor has created for us”.

My favorite rebuttal for this argument is https://www.machall.com/comic/things-to-think-about which uses applied theology and the ontological argument to summon a jelly donut.

One way to disconvince yourself of Anselm's OA is to look at it as a variant of Quine's "Platonic beard": formulation (1) is equivalent to asserting that the intelligibility of an object is a precursor to its necessary existence, which isn't true in non-logic settings.

Put another way: you can replace "God" with "a Unicorn that necessarily exists" in the OA and the proof is no less correct. But the Unicorn still does not necessarily exist.

That’s the real nail in the coffin for the argument. You don’t need to pick apart all the specific things wrong with it to tell it’s trash, because it’s easy to see that you can use it to “prove” all kinds of arbitrary bullshit. It’s clearly just useless.

The ontological argument works just as well to "prove" the nonexistence of God.

Let the greatest possible being be called "God".

Creating the universe is the most difficult possible task. (Unproven assertion).

Completing a task with a handicap is more difficult than without, so a being capable of creating the universe with a handicap is greater than one which could only do it without a handicap.

Not existing is the strongest handicap possible for any task.

Thus, any being worthy of being called God must not exist.

I've picked this one over throughout the years, and every step of the argument is chock full of bad assumptions. My favourite has always been with the final step: "If God exists in the mind, a greater version of God would be one that existed in reality, therefore God must exist in reality." OR, far more likely, as Anselm lacked sufficient other proof that he had to try out this little logical rope-a-dope, the understanding of "God" that lives in his mind is flawed.

There's this old maths joke about the proof that Santa exists:

We will prove a stronger statement, namely that existing Santa exists. There are two mutually exclusive possibilities:

1. Existing Santa exists. 2. Existing Santa does not exist.

2. Is self-contradictory, therefore Santa exists.

Clever and clear formulation. Why isn't this seen as a rebuttal of the ontological argument?

I think this joke is covered by the "existence is not a property" line of critique.

Of course it's a property, but we shouldn't omit the assumption "assume an existing santa exists" when starting an argument. If you make that explicit, it becomes clearer that you assume the thing you're trying to prove. There is nothing magical or non-property like about existing afaik.

I believe consensus for a long time has been that existence is not a property. I am inclined to view existence as being the possessor of a property.

Can you briefly explain what the definition is of a 'property' and why 'existing' doesn't fit in it? The way I use the word property I don't see how it wouldn't apply to 'existing' or any other adjective for that matter

So what exactly a property is would also naturally be up for debate, but an example property would be say having a mass of 13kg. Or being pink. Most adjectives presumably are corresponding to properties, some would word my formulation as to exist is to be the subject of a predicate.

There are also relational properties, like being ten meters away from the Eiffel tower.

Some would call existence a second order property.

The Stanford encyclopedia of philosophy gives s good overview of the issues around existence. https://plato.stanford.edu/entries/existence/

Thanks for the link. It would seem to me that it's all a matter of how you define the word property. Since words are part of a natural language, there is no one given true definition, so one has to be chosen before starting an argument, like an axiom if you are mathematically inclined. But still, it doesn't feel relevant for the question at hand, which is, how to prove an existing Santa exists? This clearly is an instance of assuming the thesis before proving it. The same can be done for any property, like proving that a blue santa is blue. I suppose that the premise of proving that an "existing santa exists" is not really a stronger statement after all than the original question of whether just "santa exists".

> Existence exists. — Ayn Rand

> Existence does not exist. — Thomas Cajetan

* https://edwardfeser.blogspot.com/2014/01/does-existence-exis...

> And that is why modern readers typically do not understand the argument. For example, they often think it is an attempt to “define God into existence,” as if Anselm believed that arbitrarily attaching certain meanings to certain words could tell us something about objective reality. But this is to confuse what Scholastics call a nominal definition – an explanation of the meaning of a word – with what they call a real definition – an explanation of the nature or essence of the objective reality a word refers to. Anselm is ultimately concerned with the latter, not the former. While he no doubt thinks that any reflective language user will agree that the notion of “that than which nothing greater can be conceived” is implicit in his use of the word “God,” the more important point he is driving at is that being that than which nothing greater can be conceived must as a matter of objective fact be of the essence or nature of being divine, just as (to use a stock modern example) being a compound of hydrogen and oxygen is of the essence of water.

* https://edwardfeser.blogspot.com/2010/11/anselms-ontological...

Which also has the stronger critique of the argument:

> The lesson is not that Anselm’s argument is unsound so much as that it presupposes knowledge (i.e. of God’s essence) that we cannot have. Moreover, the idea that reason points us to the existence of that than which there can be nothing greater is something Aquinas himself endorses as long as it is developed in an a posteriori fashion, as it is in Aquinas’s Fourth Way.

* Ibid

I've stumbled on the ontological argument without knowing that it's called that myself - not as an argument for god, but for multiple universes. Namely, one can conceive a universe so powerful that one of its properties is that it must necessarily exist, even if it doesn't yet and even if there is currently only one universe - a universe so powerful that it is capable of breaking the isolation inherent of a multiverse and will itself into existence.

I suppose you could argue for anything with this reasoning.

> I suppose you could argue for anything with this reasoning.

Yes. It's the divide-by-zero error of philosophy.

That's why the ontological framing is important- notice that 'powerful' doesn't mean anything inherently. Being, on the other hand, is necessary and inescapable for any metaphysical framework. To have anything, being must exist, necessarily. Therefore, to imagine the greatest possible being, seems not so much a stretch, compared to an arbitrary characteristic, such as 'power'. That there is a must 'powerful universe' does not seem a priori necessary, whereas insofar as existance exists, there is necessarily a greatest possible being. That is not to say that you can get to any meaningful conception of a God from that ontological framework, only that the it is only an argument when it is framed ontologically- once you stretch it to other domains, the inherent strength of the argument fails.

It's been a long time since I've studied any of this, but I immediately wonder if there's a difference between "thinking something" and stating that one is "thinking something". Surely(?), I can claim to be thinking one thing, while not thinking of that thing at all.

I added the (?) after the initial comment because I'm not certain that certainty can be certain.

And what does it mean to be "greater". That implies some set of qualities to judge greatness by. What are these qualities?

Apologies. I was lazy and jumped into the argument before reading the article. It says, "where greatness is usually cashed out in terms of the traditional “omni”-properties (omnipotence, omnibenevolence, omniscience etc)"

For those who are interested, there are much better arguments than this nowadays. The so-called cosmological arguments, particularly Kalaam, are much more convincing.

https://en.wikipedia.org/wiki/Cosmological_argument#Argument...

These get us at least as far as accepting that something beyond human comprehension brought the universe into being, and IMO give a hint of the nature of that cause.

Singularity brought the universe into being.

> For those who are interested, there are much better arguments than this nowadays.

There were better argument even in his day. See:

* https://www.goodreads.com/book/show/35592365-five-proofs-of-...

Which covers pre-Anselm arguments from Aristotle, Plotinus, Augustine (and post-Anselm: Aquinas, Leibniz). For Aristotle, the author goes over it in this podcast (first 30m; after which some objections are covered):

* https://www.youtube.com/watch?v=SfQldsGrMfk

(3) It is possible for God to exist.

Actually, no, it's not, at least not a God which is both omniscient and omnipotent. Omniscience and omnipotence cannot co-exist; they are logically incompatible. If there is an omniscient being, then all action must be in accordance with what that being foresees. Anything not foreseen by an omniscient being is impossible, ergo omnipotence is impossible in the face of omniscience.

Given such a being was subject to time and logic in this universe.

I’m a programmer, I create a universe that is a single round of the game of pong. I can trivially have knowledge of every single thing that happens in the history of this universe, I can change any of it, I can know precisely how it will play out beginning to end. Nothing is unknowable, nothing is unchangable.

If your god is outside the confines of your universe, there’s no contradiction.

That is the standard apologetic but it doesn't work. Complete knowledge of a finite domain like pong is not omniscience. Omniscience is full knowledge of everything, including the future. To know the future, you have to be able to solve the halting problem (among other challenges).

Of course we can postulate that God has (or is) an oracle for the halting problem, but that still doesn't make him omniscient, it just pushes the problem one level higher. An oracle for the halting problem can (by definition) solve the halting problem for ordinary Turing machines, but it cannot solve the halting problem for Turing machines augmented with an oracle for the halting problem for ordinary Turing machines. Such machines (let's call them meta-TMs) have their own halting problem which cannot be solved by a meta-TM. We can hypothesize a meta-oracle which solves the halting problem for meta-TMs, yielding a meta-meta-TM, and so on. But at every level there is still an unsolvable halting problem. It is not possible to close this loop for the same reason that it is not possible to enumerate the real numbers by repeated diagonalization, or to enumerate the transfinite ordinals. So in fact it is a much weaker condition that makes God impossible, namely, that omniscience is impossible. (It immediately follows that omnipotence is also impossible.) But that's a harder case to make because it requires an understanding of the halting problem.

You might enjoy reading this:

https://blog.rongarret.info/2018/01/a-multilogue-on-free-wil...

> Omniscience is full knowledge of everything, including the future.

Speaking of "the future" with respect to an eternal being† is non-sensical, as it is outside of time.

† Strictly speaking God is not a [bB]eing (not even the Supreme Being), but Being itself: see the term/concept of "ipsum esse subsistens".

The being (or whatever you want to call this thing) might be outside of time, but to be omniscient it still has to know about things that happen in time.

From Five Proofs of the Existence of God, Edward Feser (2017), Chapter 6 (§Omniscience), pp. 212f:

> Recall that I emphasized that God can hardly be mistaken about the cat being on the mat, insofar as he is the cause of the cat's being on the mat in thefirst place. I compared this to an author's knowledge of the characters and events of the story he has come up with. Now, the way an author knows these characters and events is not by observering them. It is not a kind of perceptual knowledge. Rather, the ahtor knows them by virtue of knowing himself, by virtue of knowing his own thoughts and intentions as author. And that is precisely the way in which God knows the world. His knowledge is not the result of a kind of observation of that happens as history unfolds. God is not, after all, in time, and thus he does not need to wait until something happens in order to know that it happens. Nor does he have a perceptual organs by which he comes to know things, since he is incorporeal. Nordoes he learn anything in any other way, since learning is a kind of change and God is immutable. As I said above, it is in a single, timeless act that God causes to exist everything that has been and will be. And it is in knowing himself as so acting that God knows everything that is, has been, and will be. His knowledge of the world is a consequence of his self-knowledge.[48]

> [48] See Katherin A. Rogers, Anselm on Freedom (Oxford: Oxford University Press, 2008), pp. 158f.

Following pages go into free will and such.

If you think you've come up with some clever objection(s), that have not been considered over the centuries by folks that are probably smarter than both of us put together, you're probably wrong. :)

I'd recommend this book for steelman coverage of the topic:

* * https://www.goodreads.com/book/show/35592365-five-proofs-of-...

I've actually never seen my objection seriously considered by theologians. (Non-religious people of course just acknowledge it as self-evidently true.) And I've done a lot of reading on this. Nothing in the passage you quoted is new to me, and nothing in it refutes my argument. I make no assumptions about God's nature at all. I don't even require that the omniscient entity be God (though it certainly could be). I am merely pointing out that omniscience logically precludes certain things, namely, the things that are known to the omniscience to be false, and therefore logically precludes omnipotence.

This is still quite hinged on the assumption that there are a set of rules omnipotence must follow which is a contradiction in terms. Could you not create a simulation that had rules that didn't apply to you? Who says turing machines or halting problems even make sense at all outside our reality. Who says time has any meaning outside our reality?

What difference does it make what happens outside of our reality? Omniscience and omnipotence need not be limited to our reality, but they do have to include our reality, and that it all that is required to make them logically incompatible.

> Omniscience and omnipotence cannot co-exist; they are logically incompatible.

Aquinas, in his Summa Contra Gentiles, for one would disagree. See Theorem 11 (and corollaries):

* https://tofspot.blogspot.com/2014/11/first-way-part-iv-casca...

Aquinas is transparently wrong.

> As the singular First Mover (§2), the BPA is the common source of all powers.

No. At best the BPA is the common source of all powers that actually exist. Some powers cannot exist because they are logically impossible, and acting against the predictions of an omniscience is, by the definition of omniscience, logically impossible. Nothing, not even God, can act against the predictions of an omniscience for the same reason that nothing, not even God, can create a four-sided triangle.

The classic example is could an omnipotent God create a state where it is not omniscient? If not then God is not omnipotent, and if so then God is only omnipotent. If God is only omnipotent could it create a rock it could not lift? Both answers cancel God's omnipotence, and no God remains.

Yes, exactly. The standard answer for this is to exclude the logically impossible from the definition of omnipotence. I'm pointing out that if there is an omniscient entity, then anything not known to that entity is logically impossible -- that is what omniscience means.

One parody I expected to see, but didn’t, is the notion that instead of modifying the predicates on the “greatest possible X”, we can instead modify the word greatest.

For instance, suppose I define a custom quality “Quux”. An object is more quux the more purple it is, the more it resembles a unicorn, the more it exists, and the closer it is to the center of Time Square.

We can certainly conceive of a maximally quux object — imagine a purple unicorn in the middle of time square. Therefore, by Anselm’s argument, since quuxness is increasing with existence, there must actually be a purple unicorn in the middle of Time Square.

Is there also a Premise (0) that goes unstated, namely that being "great" has a partial ordering (a necessary condition for a being-none-greater to be a coherent formulation), or does Anselm address this? I find it difficult to judge, for example, whether this cup of tea is greater than that palm tree, or whether this composer is greater than that wristwatch; yet Anselm seems to consider it obvious that I could conceive of a being or thing strictly "greater" than all of them. I don't know what that would even mean!

I don't get how we can reason about God existence (or not) using plain logic. First we should define what God(s) is/are. For example, If God = The Universe then God exists, even if the Universe is an hologram.

> First we should define what God(s) is/are.

It's a good turn because it's the quickest path toward dealing with apophatic/cataphatic problem.

For the uninitiated, cataphatic definitions of God involve saying "God is..." and attaching positive claims to God. You can see this assumption in the article's quote

> Now we believe that [God is] something than which nothing greater can be thought…

The use of "greater" should key you in that we're using cataphatic theology. The issue is that when you start to add these positive claims, they start to conflict. God is the reddest and the bluest and the heaviest or the lightest and becomes a big ball of mud.

Apophatic definitions of God try to solve this, but using negetive attributes eg: God is not evil, God is ineffable, &c. The issue with that is that all you sort of have left is that "God is." Which isn't much at all.

The sort of third way out of this are various forms of pantheism which you've identified, but ultimately aren't very satisfying to adherents to world religions for reasons that are outside of the topic of this discussion.

Personally if someone wants to ontologically argue for the conclusion that God is reality, or God is the universe, more power to them. It's a perfectly logical conclusion, and while beautiful in its own way, eschews conventionally theological normativity in ways that again, I don't think are palatable to adherents of world religions. Note: they are rather palatable to cannabis users however :)

I am Muslim and the universe is what I identify God with. It seems "natural" to me and what I feel is actually being conveyed. Now I wonder how other adherents of world religions actually see God.

I'm ignorant, and feel like I have something to learn. Is this related to waḥdat al-wujūd and waḥdat ash-shuhūd?

A Muslim, don't you believe God created the Universe? If so, how can he be the universe?

> I don't get how we can reason about God existence (or not) using plain logic.

Aristotle has you covered:

* https://tofspot.blogspot.com/2014/07/first-way-some-backgrou...

* https://tofspot.blogspot.com/2014/08/first-way-moving-tale.h...

* https://tofspot.blogspot.com/2014/09/first-way-part-ii-two-l...

* https://tofspot.blogspot.com/2014/10/first-way-part-iii-big-...

* https://tofspot.blogspot.com/2014/11/first-way-part-iv-casca...

* First 30m of this podcast: https://www.youtube.com/watch?v=SfQldsGrMfk

Book which covers arguments from Aristotle, Plotinus, Augustine, Aquinas, Leibniz:

* https://www.goodreads.com/book/show/35592365-five-proofs-of-...

The TL; DR is:

1. Some things in the world are changing. (Observation)

2. Whatever is changing† is being changed by another. (Lemma 1) https://docs.google.com/file/d/0B7SKlRTfkUieN3dGVkhNTi1SQUU/...

3. There cannot be an infinite regress of instrumental changers. (Lemma 2) http://www.academia.edu/4415427/There_Must_Be_A_First_Why_Th...

4. Therefore, there must be a changer that is not itself being changed by another.

† From kinēsis in Aristotle's Greek.

Change can happen as inertial motion, interaction isn't necessary for it, but yeah, Aristotle and Aquinas didn't know that inertial motion can last for long.

> Change can happen as inertial motion […]

That is one type of change; from Five Proofs (2017), Edward Feser, Chapter 1: The Aristotelean Proof (p. 17):

> These examples illustrate four kinds of change: qualitative change (the coffee cools down); change with respect to location (the leaf falls from the tree); quantitative change (the puddle increases in size): and substantial change (a living things gives way to dead matter). That changes of these sorts occur is evident from our sensory experience of the world outside our minds.

> […], interaction isn't necessary for it, […]

Newton would disagree.

According to Newton's first law inertial motion happens without interaction. What moves the inertially moving object?

In Aristotelian mechanics inertial motion stops shortly after beginning, so for sustained motion the object must be moved by another. Falling leaf is not inertial motion, it's pulled by gravity, Aristotle didn't know about gravity, but Aquinas probably did as round Earth theory required the concept of gravity.

Just defending Herr Gödel as I see his and Leibniz names being bandied about. His proof said nothing on existence. It only said if god did exist god _must_ be perfect. That’s a very different argument.

You’d still have to accept the axioms though, one of which is kinda that god even exists. And Gödel certainly believed in a God of sorts so to him this logical system was a proof.

I think this website is trying to make the ontological argument for this debate

In fact, no serious philosophers are curious about this question because it’s not a current line of inquiry in any serious philosophical journal or other work of contemporary philosophers.

Being able to imagine something impossible is not proof that it is possible in fact. This mathematically dead end of a theory has no avenues for serious inquiry

Yet there are still Christian theologians and philosophers who actual philosophers have to spend time debating and refuting, and they invoke arguments like this. Anselm's argument is also set in exams for philosophy students, as something to find problems with.

> Anselm's argument is also set in exams for philosophy students, as something to find problems with.

Yes, because the well-known (to people who aren't first year philosophy students) problems with it are a good intro and lead in to various concepts, notably the distinction between existence in intellectu and existence in re the idea that existence is not a predicate.

Its not taught as an argument that is particularly influential currently, but because it is both historically important and pedagogically useful in coning yo concepts that are of more current relevance.

Why do they have to debate and refute?

Because William Lane Craig does lecture tours.

Existence is not a boolean property.

https://blog.rongarret.info/2015/02/31-flavors-of-ontology.h...

Various modal formulations of the ontological argument do lead to an interesting and I think correct conclusion that falls short of God’s existence. That is the conclusion that God must either necessarily exist or necessarily fail to exist. Anything that merely happened not to exist would not, if it did exist, be worthy of worship (as it would be something that merely happened to exist).

I am just stating the result here rather than arguing for it. Norman Malcolm expressed it very clearly in a 1960 paper. The original paper is on JSTOR, but there’s a decent summary of it here: https://s3-eu-west-1.amazonaws.com/s3-euw1-ap-pe-ws4-cws-doc...

Malcolm wanted to go all the way and show that God does indeed exist. I think that’s where the argument runs into problems.

While an excellent proof, the comments here are evidence it is not fool proof.

1. A nonexistent god able to conceive, create, and maintain all that exists is greater by far than a god unable to accomplish anything unless it exists.

2. A god which necessarily exists is perforce an inferior being, from 1.

3. Ergo God does not exist.

Seems riddled with holes.

"The concept of God". I reject God as a concept. Done. If you can speak God into existence by defining it, then I can speak it out of existence by calling BS.

"It is possible for God to exist". No it's laughably impossible. Done.

Why is it impossible for God to exist?

Doesn't matter. He gets to assert that it's possible, so I get to assert that it's not.

In a logic setting, this is a much harder position to hold: it's much easier to assert the possibility of existence than the non-possibility of existence (which requires universal qualification).

The OA isn't a good argument for various reasons that others have noted above, but the possible existence of God (or Unicorns, or Colorless Green Ideas) isn't one of them.

One way to show non-possibility, leveraging universality, is to show that for all A's, one can prove both B and something contradicting B.

Example:

    ∀(G ∈ gods . card(G) = 3) ∧ ∀(G ∈ gods . card(G) < 3)

Whether or not people have "proved" contradictory attributes for gods is left as an exercise for the reader...

cf https://en.wikipedia.org/wiki/Sic_et_Non

It's much easier to not exist than to exist.

Clever!

Do you have enough control over your mind to command it to contemplate what the truth of the matter is?

An all-powerful, omniscient being invites some paradoxes/problems:

Homer Simpson's version was "Could Jesus microwave a burrito so hot that he himself could not eat it?"

Also - if you're omniscient and you already know your future, does that imply that you do not have free will?

The first is not a paradox but a nonsensical statement. Omnipotent, (by definition), does not include breaking logic because at its core something illogical is nonsense.

As to free will, well that's something only Catholics and Orthodox hold onto. I don't believe Muslims or many Protestants (Calvin?) adhere to that.

That kind of deity can not be restricted by logical paradoxes, it is beyond their reach so to speak.

That of course raises the question why even attempt logical proofs, but here we are.

You can just claim that omniscience and omnipotence do not require that you can do logically impossible things. For instance, God couldn't will that 2+2=5, or that he could create something so heavy that he could not move it.

> An all-powerful, omniscient being invites some paradoxes/problems:

Not really:

* https://edwardfeser.blogspot.com/2010/02/dawkins-on-omnipote...

> If you can speak God into existence by defining it, then I can speak it out of existence by calling BS.

Yeah:

* https://edwardfeser.blogspot.com/2010/11/anselms-ontological...

Which also has the stronger critique of the argument:

* Ibid

For a better argument, and summary of that argument, see Aristotle:

* https://tofspot.blogspot.com/2014/07/first-way-some-backgrou...

* https://tofspot.blogspot.com/2014/08/first-way-moving-tale.h...

* https://tofspot.blogspot.com/2014/09/first-way-part-ii-two-l...

* https://tofspot.blogspot.com/2014/10/first-way-part-iii-big-...

* https://tofspot.blogspot.com/2014/11/first-way-part-iv-casca...

* First 30m of this podcast: https://www.youtube.com/watch?v=SfQldsGrMfk

Book which covers arguments from Aristotle, Plotinus, Augustine, Aquinas, Leibniz:

* https://www.goodreads.com/book/show/35592365-five-proofs-of-...

Anselm's argument did not stand the test of time. Plato's and Aquinas' did, though :)

The term "existing" in the mind kind of covers up a lot of details. You can actually estimate the bounds of everything that can possibly exist within someones mind.

It's similar to thinking about what are all the possible things that can exist in computer memory? It's basically the total permutations of 1s and 0s.

The same thing goes on with the human brain, only the primitives are not 1 and 0. The primitives are much more complex but they are finite. One turing-complete-esque model for the human brain is the ML neuron with weights. It may be possible to model the entire human brain as just a composition of all these primitives. If not, then maybe some additional primitives to complicate things may work as well. The key here is to realize that it's more complex than binary memory but like binary memory the amount of things that can "exist" in a human brain is finite and countable.

So it's a combinatorics permutation problem of the state of all primitives in the brain.

When you bring the concept closer to actual formalization by technically modelling what the brain is, the rest of the philosophical question requires formalization as well.

Clearly when something "real" exists in your mind it is data compression. A fewer number of primitives is symbolically representing an actual thing that exists. What are all the possible things that can actually exists?

Well that's another combinatorics problem. Take all fundamental particles and compose them in all the ways possible and that's your total.

So essentially it's using high level primitives in memory to symbolically compress data in the real universe represented as atomic particle primitives.

Once all the details are in a way formalized and actualized in your brain you can easily disprove this "argument". Right? It's simply large compositions of primitives (atoms) being represented by a smaller amount of primitives (neurons) in the exact SAME way a computer represents say a world in an open world game. The whole thing is a linguistic trick. You need to visualize this problem as a physical actualization: Data and atoms (the data is the state of neurons in a neural net but in the end that's just made up of atoms too so it's technically atoms representing atoms).

This helps you get past all the bullshit word play in the original question. Not all chunks of data in a computer/brain represents compressed data from something that actually exists. It's all a matter of interpretation too. I can have a single bit represent the entire concept of god if I wanted to.

Anyway this isn't even a refutation of the argument. It's just a detailed description showing that people aren't even sure about what they should be asking here.

Is a certain stream of data in the brain a compressed version of an actual combination of atoms that exists? Or maybe is it a compressed version of something that isn't atoms but "god" or some other bs? Well the point of my whole argument was that what the "data" represents here is irrelevant. I can interpret 1010101010101 to mean understanding of god, you can interpret it to mean your sock drawer. How can someones interpretation of something influence whether or not it's compressed data of something that actually exists? No. It's not, it's like asking a someone the color of music... completely irrelevant, like Anslems entire argument... not even asking the right question.

I'm afraid I'm still perplexed. The argument is just plain bad. Even the most steelmanned versions of it are bad.

That's fine. Anselm doesn't really need to prove the existence of God. Christians don't need to prove it; they have a Bible that they take as fundamental revelation. They know that this argument isn't going to convert anybody on its own.

What I'm perplexed by is why philosophers keep treating it as if its worth steelmanning. It's not going to get any better. The "better-than-all-other-things" definition is meaningless and doesn't tell us anything we want to know about God. Nor is it Biblical; it doesn't prove anything at all about the Bronze-Age-Middle-East deity Anselm believed in.

It feels like philosophers really enjoy beating a dead horse.

Yes, when I first encountered this argument I was indeed perplexed because it seemed so incoherent I thought I must not be understanding it. Only after reading a some different formal explications was I able to conclude, "Nope, I understood it correctly the first time!"

The argument is indeed so bad, all it proves is that the church was so powerfull at the time that they could spout any ludicrous nonsense and still have people bow in obedience.

The argument was created by a churchman for churchmen, it wasn't intended or used as a popular argument, but it's worth understanding that c. 1000 CE this argument seemed compelling to literate folks who were introduced to it. If people had thought it was ludicrous nonsense they actually were free to say this, this is a philosophical argument, not doctrine, and the Church didn't have too much to do with supporting/opposing such things other than opposing philosophical arguments seen as heretical.

And even Aquinas, who did not think Anselm's argument worked, thought it worthy enough to engage.

At the time, in Europe, atheism was simply not a permitted intellectual path to take. It was basically inconceivable. So nobody truly needed to "prove" God, and the argument "works" for some thinkers because its presupposition and ends confirm what they already "know" to be true.

I feel that it's the kind of argument you devise when you think language is the fundamental basis of reality rather than a (flawed) way to model it. There are many logical deductions you can make that only tell you things about language, but nothing about reality.

> I feel that it's the kind of argument you devise when you think language is the fundamental basis of reality rather than a (flawed) way to model it.

I think it's both - unless ~everyone is secretly playing a gag and joking about everything they say (as opposed to being mostly sincere about their claims, as I believe the case to be, and I've never once encountered someone mentioning it), I can't see how it is otherwise.

Indeed, it makes sense in the philosophical mindset of the time, because they seriously really believed this, or a form of it.

"In the beginning was the Word (Logos), and the Word (Logos) was with God, and the Word (Logos) was God"

It's the bread and butter of the Neo-Platonism of the time. And to the Christians of the time, Jesus Christ was the literal embodiment of the Word of God.

Isn't "logos" a term with quite a few different translations? It also seems to mean "reason", "argument" and "law". Perhaps the word "Word" has a special meaning here. "In the beginning was the Word" - what does that mean? Which word?

You can ask a similar quesion about the phrase "the Word of God": did he really only ever utter a single word? Or does the phrase really refer to the entirety of Christian teaching? Is that barking street-preacher with a megaphone speaking the Word of God when he declares me to be a sinner? But the things he's saying are his words, they are not scripture.

I think "In the beginning was the Word" is the most mysterious passage in the Bible. I used to think Revelation was mysterious. But Revelation is explicitly a description of a hallucination; the author doesn't claim to know what it means, or even that it means anything. The opening passage of John's gospel, on the other hand, purports to be stating unqualified facts.

Hold on there. You've conflated a number of things here.

> Anselm doesn't really need to prove the existence of God.

I cannot comprehend this statement.

> Christians don't need to prove it; they have a Bible that they take as fundamental revelation.

Why trust the Bible? Its authority must rest on extra-biblical knowledge (in Catholicism called Tradition). The Catholic Church compiled the text in light of Tradition. It didn't fall from the sky. But regardless, the point is that knowledge of the existence of God is not a matter of revelation. Indeed, the Catechism of the Catholic Church (a kind of summary of the beliefs of the Church, not a didactic manual or comprehensive text) teaches as much [0]:

  Our holy mother, the Church, holds and teaches that God, the first principle and last end of all things, can be known with certainty from the created world by the natural light of human reason. [...] Without this capacity, man would not be able to welcome God's revelation. Man has this capacity because he is created "in the image of God".

If you're going to write a check like that, you better be ready to cash it! And there are many ways to cash it (like these, to name a few [1]).

> They know that this argument isn't going to convert anybody on its own.

While many people aren't persuaded by proofs about most things, this does not make proofs worthless. First, those who are moved by proofs will benefit. Second, proofs can lead to greater clarity of what we mean by "God". This is because in order to understand a proof, one often needs to discuss presuppositions and ancillary propositions to appreciate it. You are also given a point of departure for further discussion that can deepen your grasp of the subject matter. Third, those who aren't moved by proofs can still benefit from some reassurance that such proofs do, in fact, exist. This is still true for those who do not know or understand them, just as one need not have a comprehension of medicine to take comfort in the claims of one's doctor.

> The "better-than-all-other-things" definition is meaningless and doesn't tell us anything we want to know about God.

You're confusing the question of whether God exists with what God is like. Why? Knowing about God is certainly desirable, but to establish God's existence through reason alone is a worthy enough exercise. I don't understand the compulsion to dismiss the value of establishing existence. It's not either/or, it's both. Existence and essence. (Of course, we come to understand that God's essence just is existence: Ipsum Esse Subsistens.)

> Nor is it Biblical; it doesn't prove anything at all about the Bronze-Age-Middle-East deity Anselm believed in.

I have no idea how you arrived at this claim. How is it not Biblical? This frankly sounds like some strange 20th century concoction of Protestantism. Reason has always been central to Christianity, certainly in the Catholic tradition. This is just basic knowledge ("fides et ratio"). As reason is what is the most essential and definitive characteristic of human beings, and the basis for understanding anything, it would be absurd to assent to any faith that opposes it. Not only that, but the very first verse of the Gospel of John, for all intents and purposes, equates Christ with Reason itself (the Incarnate Logos). The God we're talking about here is not some mere "Bronze-Age-Middle-East deity", one being among many, one ubermensch among many pagan alternatives, but Being Itself.

(Also, here's a take on Anselm [2] that you may find will clarify things.)

[0] https://www.vatican.va/archive/ENG0015/__PB.HTM

[1] https://a.co/d/7SnyEST

[2] https://edwardfeser.blogspot.com/2010/11/anselms-ontological...

>Why trust the Bible?

Mystics have inclination for mysticism, and bible provides that.

>can be known with certainty

Doubtful.

Romans 11:33 "O the depth of the riches both of the wisdom and knowledge of God! how unsearchable are his judgments, and his ways past finding out!"

Isaiah 55:9 "For as the heavens are higher than the earth, so are my ways higher than your ways, and my thoughts than your thoughts."

I think it's fun to think about.

Start from the premise that Anselm was serious, and wasn't an idiot. How must he have seen the world for this argument to make sense? (This is, very loosely, the approach of the Cambridge School in the history of ideas.)

Looking back from several centuries, we can think the argument is obviously bad. (We might have heard, for example, that "existence is not a predicate" so you can't just talk about existence as something that God may or may not possess.) But Anselm didn't have that. His argument was a step on the way to where we are now.

And sometimes if you squint hard enough at it, you come to see why and how it might make sense, and the arguments don't seem so stupid. Plato does that to you sometimes, for example.

I think of the ontological argument as a kind of pointless philosophical roundabout which only connects in a circle for some because they already believe God exists and can't -- emotionally or physically -- truly posit a world where He doesn't.

The argument "works" because they simply can't/won't think of atheism as a legitimate position. I've had exactly that kind of "debate" with the religious where in the end it falls down to either "how can you actually think that?!", or, worse, "you're crazy/silly."

In that mindset, the argument seems self-evident. Or something.

And I tend to think of the intricacies of the words of Anselm and others of his era like this:

We sit on these forums debating programming languages, or go off and write code, or play with mathematics, or etc. because our human brains love intellectual puzzles.

However in the middle ages, dark ages, whole swathes of intellectual paths were essentially off limits, or not even imaginable.

So if you were of the intellectual bent, and love brain puzzles, you naturally engage in the form available to you in the dominant ideology and permitted by society at the time. Theology, theological philosophy, religious music, poetry, and art. They had all sorts of fun reinterpreting (pre-Christian) Aristotle and Plato to try to puzzle a way to get a Christian spin on them, for example.

I remember in my 2nd year philosophy of religion class going through all the theodicies, and in the end summarized with: there are profound holes and problems with all of these. But in the end the only real argument for religion and God that works is the argument from experience. If people feel they experience God ... I can't really argue or debate that. That's for them. Which is why I leave my heavily religious sister and parents alone on this topic.

IMO, the existence of such arguments is one of the best arguments for God not existing.

If there were any better arguments, we'd be using them instead.

Nobody needed an ontological argument for platypuses, because we had actual material evidence.

That's an interesting example to pick since there was a brief period when educated people doubted the existence of the platypus, too.

It would be silly to request material things as proof for immaterial things. Similar to math or ethics, it doesn't make sense to ask for material evidence that the square root of 2 is irrational or that torturing babies is evil.

The person you're responding to isn't asking for a material proof.

They're pointing out that ontological arguments are typically seen as an "argument of last resort" in a philosophical setting, and are making an (abductive) argument that the use of an ontological argument indicates a weaker position than the importance of the proof (the existence of a god) would otherwise suggest.

I can conceive of a greater God which does have a material existence, so I think it's valid to request material proof.

In which case you have no claims

The only claims possible are material

Please demonstrate to me a non-materialist claim that has no impact on the materialist world, and still complies with a conception of an omnipresent God

the claim (sqrt(2) being irrational) needing material evidence can be reduced even further to the number two needing material evidence. I'm not posing this either for/against your argument, just saying at some point you can doubt the existence of 2 itself. (handing me 2 items doesn't count, what is ... two?)

The truth of these arguments also seemingly removes any degree of faith from Christianity, because it's been proven that God now exists. Have always been puzzled why they want to prove this given the circumstances of needing faith.

> many philosophers find it intriguing

Citation needed.

1. It's possible to conceive of the greatest possible teapot-shaped 7-foot-tall spaghetti-descended invisible alien orbiting Jupiter. Even teapot-spaghetti-alien skeptics agree on this.

2. Existing in reality makes something greater than existing only in someone's head (proof: seems reasonable).

3. But we're talking about the greatest possible one of those things (see 1).

4. Therefore such a thing exists.

The article covers this -- it's Gaunilo's Island -- but it's very odd that this keeps coming up as a philosophical puzzler.

> many philosophers find it intriguing

Citation needed.

Other (great) philosophers discussing it are very clearly linked in the article.

Spaghetti/teapot stuff

Considering the tradition of genuinely great minds taking the argument seriously (including Russell in spite of his facetious teapot), dismissals derived from internet atheist memes look emotional or knee-jerk in comparison, which is possibly why you missed the links.

It's unsurprising that "genuinely great minds" raised in a religious tradition would try to apply the tools of their trade to justify what would otherwise surely appear to them to be a very strange and illogical set of beliefs, but that doesn't mean that "many philosophers find it intriguing", and certainly not currently.

Russell's ultimate view of it, as I'm sure you know, was to summarise it as "cases of bad grammar", which is also how it appears to this (I happily admit) non-genuinely-great mind: all it is demonstrating is that English is not a formal language.

I find ontological arguments interesting because so many smart people took them seriously (Leibniz and Godel being two, but there are many more). Even if these kinds of arguments are wrong, their popularity seems to suggest something interesting about human psychology and pitfalls that even geniuses can't always avoid.

Ontological arguments are also interesting because of the cricisms they provoked. Hume, Kant, and others famously criticized ontological arguments.

Is it possible they took it seriously due to the social and political conditions of the time?

You can't rule it out but I'm skeptical. Godel was alive in the 20th century. Spinoza was another philosopher who found the ontological argument convincing and he was such a radical that he was kicked out of the Jewish community he was raised in (i.e. not someone who would have yielded to social pressure).

"That than which no greater can be conceived" feels a little like "that number than which no greater can be conceived." No matter what number I conceive of, I can in fact conceive of a greater one, and if I couldn't, that's likely because I filled up my brain's limited working memory. Even conceptions of infinity exist on a ladder of progressively larger infinities.

One also can't actually conceive of such a thing, you're correct. We can have the idea that such a being might possibly be conceivable, like a linguistic positing of a perfect being, but as you say, actually conceiving the being will take you your whole life and still not even get close to a conception of the actual being. One of the many places the argument falls apart for me. Anselm is also the fool for considering that such a thing can exist in the mind of a fool.

Maybe god is just another name for set theory’s e, the set of everything.

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