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 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).
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.
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.
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.
> 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.
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).
[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”.
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.
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.
> 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.
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.
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.
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)"
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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.
RTFA before replying. Paging Emanuel Lasker...
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.
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.
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.
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!
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
Deleted Comment
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/
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.
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
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”.
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.
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.
Dead Comment
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.
* 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 suppose you could argue for anything with this reasoning.
Yes. It's the divide-by-zero error of philosophy.
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)"