Very famously, St Anselm (1078/Reference Anselm1903, 8) said:
… if that, than which nothing greater can be conceived, exists in the understanding alone, the very being, than which nothing greater can be conceived, is one, than which a greater can be conceived. But obviously this is impossible. Hence there is no doubt that there exists a being, than which nothing greater can be conceived, and it exists both in the understanding and in reality.
Kant said some equally famous things on the topic. Most celebrated is his remark that:
‘Being’ is obviously not a real predicate; that is, it is not a concept of something which could be added to the concept of a thing. … . By whatever and however many predicates we may think a thing … we do not make the least addition to the thing when we further declare that the thing is. (Kant (1781/Reference Kant1929), A598/B626–A600/B628.)
What does what Kant said have to do what Anselm said? Is it even relevant?
Several writers claim that it is not. They contend that Kant's claim that existence is not a real predicate [henceforth, Kant's dictum], the most famous objection to the ontological argument, does not even bear on Anselm's version. Alvin Plantinga (Reference Plantinga1974a, 97) writes:
But is it [Kant's dictum] relevant to the ontological argument? Couldn't Anselm thank Kant for this interesting point and proceed merrily on his way? Where did he try to define God into being by adding existence to a list of properties that defined some concept? … . If this were Anselm's procedure – if he had simply added existence to a concept that has application contingently if at all – then indeed his argument would be subject to the Kantian criticism. But he didn't, and it isn't.Footnote 1
More recently, Gareth Matthews (Reference Matthews and Mann2004, 90) writes that Kant's criticism
… does not exactly fit Anselm's statement of his argument. He [Anselm] does not speak of adding the concept of existence … to the concept of God … . What he does instead is ask us to compare something existing merely in the understanding with something existing in reality as well.
Peter Millican (Reference Millican2004, 437–438) writes of ‘the Kantian doctrine that “existence is not a predicate”’ that:
… this most popular objection to the argument has not stood up entirely convincing under critical scrutiny, partly because it has never been fully satisfactorily elucidated and defended, but also partly because its implications for the argument are anyway rather obscure: suppose we accept that ‘exists’ is not ‘logically’ a predicate – how exactly does this undermine Anselm's reasoning: which particular step in it fails to go through … ?
I believe that under at least one plausible elucidation of Kant's dictum, we can say exactly how it undermines Anselm's reasoning.
As further evidence of the popularity of the view that Kant's dictum is irrelevant to Anselm's argument, let me quote three more philosophers. E. J. Lowe (Reference Lowe, Meister and Copan2007, 337) contends that ‘nothing in … the ontological argument implies that … existence … must be a divine attribute or property, in the way that omniscience or omnipotence are. … . [T]he Kantian objection … is just a red herring with no real bearing on the soundness of the ontological argument.’ James Harris (Reference Harris2002, 108) maintains that ‘the claim that existence is not a predicate … leaves[s] untouched Anselm's more interesting version of the argument’. And Brian Davies (Reference Davies, Davies and Leftow2004, 171) writes,
… philosophers have often attacked the Proslogion while echoing Kant's assertion that ‘Being is obviously not a real predicate.’ And perhaps there is much to be said for this assertion … . In the Proslogion, however, Anselm does not seem to be arguing that ‘— exists’ is or is not a first-level predicate.
The idea that Kant's dictum may be true, yet Anselm nowhere presupposes or commits himself to anything in opposition to it, is thus rather popular.
But I believe it is mistaken. In this paper, I explain the way in which Anselm's argument is committed to the falsity of Kant's dictum. It is interesting and relevant to note that, in claiming that existence is not a real predicate, Kant was not in fact responding to Anselm's version of the ontological argument but to Descartes'. Kant was aware that Anselm had offered proofs for God's existence, but Kant did not write on them (Byrne (Reference Byrne2007), 23). Jerome Sobel (Reference Sobel2004, 68–69) suggests that Plantinga is thus unfair to Kant, for Plantinga is criticizing Kant's objection for being irrelevant to an argument to which the objection was not directed. This is a fair point. Nevertheless, many philosophers, such as all of those above, have naturally wondered whether Kant's objection applies to Anselm's version. Those who have answered in the negative, I hope to show, are mistaken.
Anselm's argument
I will understand Anselm's ontological argument as Plantinga and many others do: as a reductio ad absurdum of atheism that draws a comparison between two beings, one that exists merely in the understanding and another just like it that also exists in reality. It will be helpful to quote Plantinga's (Reference Plantinga1974a, 95) interpretation of Anselm at length:
Anselm's argument can be seen as an attempt to deduce an absurdity from the proposition that there is no God. If we use the term ‘God’ as an abbreviation for Anselm's phrase ‘the being than which nothing greater can be conceived’, then the argument seems to go approximately as follows: Suppose
(1) God exists in the understanding but not in reality.
(2) Existence in reality is greater than existence in the understanding alone. [premise]
(3) God's existence in reality is conceivable. [premise]
(4) If God did exist in reality, then He would be greater than He is. [from (1) and (2)]
(5) It is conceivable that there is a being greater than God is. [(3) and (4)]
(6) It is conceivable that there be a being greater than the being than which nothing greater can be conceived. [(5) by the definition of ‘God’]
But surely (6) is absurd and self-contradictory; how could we conceive of a being greater than the being than which none greater can be conceived? So we may conclude that:
(7) It is false that God exists in the understanding but not in reality.
It follows that if God exists in the understanding, He also exists in reality; but clearly enough He does exist in the understanding, as even the fool will testify; therefore, He exists in reality as well.
Other philosophers offer essentially the same interpretation. Matthews, who, as noted earlier, denies that Kant's dictum presents a problem for Anselm's argument, agrees that ‘the argument [Anselm] presents is, in form, a reductio ad absurdum’, that ‘ask[s] us to compare something existing merely in the understanding with something existing in reality as well’ (Matthews (Reference Matthews and Mann2004), 87, 90). Thus, in aiming to show, contrary to Matthews, that Kant's criticism does fit Anselm's argument, I will thus be interpreting Anselm just as Matthews does. Graham Oppy (Reference Oppy1995, 9) also interprets Anselm's argument as a reductio of the belief that ‘A being than which no greater can be conceived does not exist in reality’, and one that has us compare entities that exist in these two different ways.
Simplifying somewhat, we begin with an idea that Anselm's atheist opponent will admit: that God exists in the understanding but not in reality. We note that a being that exists in reality as well as in the understanding seems greater than an otherwise similar one that exists just in the understanding.Footnote 2 These two claims imply the contradictory thought that we can imagine a being greater than the greatest imaginable being. Thus, the original atheist supposition must be rejected.
Naturally, other philosophers interpret Anselm differently. Oppy (Reference Oppy and Edward2009) contains helpful extractions of interpretations by Lewis (Reference Lewis1970), Adams (Reference Adams1971), Barnes (Reference Barnes1972), and Oppenheimer & Zalta (Reference Oppenheimer, Zalta and Tomberlin1991). Oppy goes on to criticize these as interpretations of Anselm. Since it is beyond my scope to argue that the interpretation of Plantinga et al. is the correct interpretation of Anselm, we can understand my thesis as the claim that Kant's criticism is relevant to at least one popular and defensible interpretation of Anselm's argument – and indeed one that some who deny the relevance of Kant's criticism accept.
Kant's dictum
What does it mean to say that existence is not a real predicate? I will also follow Plantinga's (Reference Plantinga1974a, 95–97) understanding of this idea, which is equivalent to a proposal offered by James Van Cleve (Reference Van Cleve1999, 188). Plantinga takes as his lead, among other things, Kant's remarks that ‘“Being” is obviously not a real predicate; that is, it is not a concept of something which could be added to the concept of a thing’ (Kant (1781/Reference Kant1929), A598/B626), and that ‘By whatever and however many predicates we may think a thing … we do not make the least addition to the thing when we further declare that the thing is’ (Kant (1781/Reference Kant1929), A600/B628).
Call property F and property G equivalent iff it is impossible for there to exist an object to which one of F or G, but not the other, applies (Plantinga (Reference Plantinga1974a), 97). Examples of equivalent properties (if they are indeed distinct properties – we can ignore this question here) are triangularity and trilaterality, and being the smallest even number and being the smallest prime number. Two properties – or concepts (I use the terms as mere stylistic variants in this context) – are inequivalent iff it is possible for something to have one of them without also having the other. Plantinga then explains what it is for a property to be real as follows: a property P is real just in case the result of adding P to some lists of properties defines a concept inequivalent to that defined by the original list.Footnote 3
Thus, if we want to establish that some property P is real, we must first produce a certain list of properties. This list will define a concept, in the sense that it will contain those properties that are individually necessary and jointly sufficient for something to instantiate the concept. Call that concept ‘C’. Then we add P to the list. The resulting list also defines a concept, which we can call ‘C+’. Then we ask, Are C and C+ equivalent? If they are, and if this would happen for any list to which we add P, then P is not real. If, on the other hand, it is possible for there to be an object to which C but not C+ applies, then the concepts are inequivalent, and P is real.Footnote 4
To illustrate, consider this list of properties:
is round
is ripe
This list defines a concept – namely, the concept of being round and ripe. Suppose we want to know whether the property is red is real. We can see that is red is real because if we add it to the list above, the new list defines a concept inequivalent to the concept of being round and ripe. The old list applies to the green apple on my desk, but the new list,
is round
is ripe
is red
does not. Since by adding redness to some list we define an inequivalent concept, redness is real.
Now consider the property either is a rhinoceros or is not a rhinoceros. Adding either is a rhinoceros or is not a rhinoceros to the list above yields:
is round
is ripe
is red
either is a rhinoceros or is not a rhinoceros
It is impossible for there to be an object that has the first three members of the list but fails to have the fourth member. The second, four-membered list fails to define a concept inequivalent to that defined by the original three-membered list. This follows from the fact that either is a rhinoceros or is not a rhinoceros is a ‘trivial’ property: it is not possible for something to lack it (ignoring issues of vagueness).
Since, necessarily, everything either is or is not a rhinoceros, it should be clear that the result of adding either is a rhinoceros or is not a rhinoceros to any list of properties will likewise fail to define a new concept. It follows that either is a rhinoceros or is not a rhinoceros is not a real property. As Kant might say, by whatever and however many predicates we may think a thing, we do not make the least addition to the thing when we further declare that the thing either is a rhinoceros or is not a rhinoceros.
What about existence? For similar reasons, it is at least intuitively appealing that existence is not a real property either. Consider the result of adding existence to the earlier list:
is round
is ripe
is red
exists
It is not implausible to suppose that, necessarily, all those things that are round, ripe, and red are also round, ripe, red, and existent. How could something be round, ripe, and red without also existing? Since the point generalizes – no list is such that adding existence to it defines an inequivalent concept – existence, it seems, is not a real property.
This might be contested. Meinong famously held that some things lack existence while having all sorts of other properties. We won't settle this dispute here. My aim instead is to show how Anselm's ontological argument is, like Meinong, committed to the idea that existence is a real property, a property that some things might have and others might lack, a property that does ‘make an addition’ to a thing.
James Van Cleve's equivalent interpretation of Kant's dictum is derived from Kant's remark that ‘a determining predicate is a predicate which is added to the concept of the subject and enlarges it’ (Kant (1781/Reference Kant1929), A598/B626). (Kant uses ‘determining predicate’ and ‘real predicate’ interchangeably.) Van Cleve (Reference Van Cleve1999, 188) offers the following definition of ‘enlarges’: a property P enlarges a concept C just in case it is possible for something to have C and lack P. Note that enlarging a concept by adding a property to it narrows its extension. Van Cleve then explains what it is for a property to be real as follows: a property P is real just in case P enlarges at least one concept. As before, redness is real because redness enlarges some concepts, such as the concept of being round and ripe. And as before, it is at least intuitively plausible that existence is not real, since it does not seem possible for something to have some features without also existing.
Naturally, other philosophers interpret Kant differently. One popular interpretation holds that Kant's dictum is the thesis, often associated with Frege, that existence is a second-order property of concepts: the property of having instances.Footnote 5Everitt (Reference Everitt1995) offers another interesting interpretation.Footnote 6 Since it is beyond my scope to argue that the interpretation of Plantinga and Van Cleve is the correct one, we can understand my thesis as the claim that at least one popular and defensible interpretation of Kant's dictum is relevant to at least one popular and defensible interpretation of Anselm's argument – and, furthermore, that at least one philosopher (Plantinga) who denies the relevance of Kant's criticism to Anselm's argument accepts both interpretations.
The relevance of Kant's dictum to Anselm's argument
Recall the first part of Anselm's argument, as Plantinga and we are interpreting it:
(1) God exists in the understanding but not in reality. [assume for reductio]
(2) Existence in reality is greater than existence in the understanding. [premise]
(3) God's existence in reality is conceivable. [premise]
(2) and (3) are the argument's only premises, and thus seem to be the only parts of the argument to which one can object (assuming, as I will, that the subsequent inferences are valid). I certainly wouldn't want to contest (3); in any case, that cannot be the target of Kant's famous objection.
What about (2), Anselm's infamous great-making assumption? Some commentators believe that this is where Kant's dictum is relevant. The idea would be that (2) implies, contrary to the dictum, that existence is a real predicate. However, it is interesting to note, as Plantinga does, that there are interpretations of (2), which is a claim Anselm never elucidates, that can serve Anselm's purposes but do not imply that existence is a real predicate. A person could affirm (2) while denying that adding existence to a list ever defines an inequivalent concept. She could do this if she interprets (2) as,
(2*) If something does not exist in some possible world, then it does not have maximal greatness at that world,
where maximal greatness is had by a thing just in case it is not possible for something to be greater than it.Footnote 7 (The being than which none greater can be conceived, if it exists, has maximal greatness.)
(2*) is a rather weak understanding of what it means for existence to be a perfection, but it is strong enough to do the work it needs to do in the argument. And it is consistent with existence not being a real property. For it could be held that, if an object lacks existence at a world, the object has no other properties there as well – the object simply fails to exist there. So the object would have no greatness there either. Then (2) could be true without it being possible that an object has some properties (such as omniscience and omnipotence) while lacking existence.
I want instead to focus on (1), the assumption that God exists in the understanding but not in reality. Now, (1) is just Anselm's assumption for reductio. Are we therefore allowed to object to it? If we do object to it, aren't we then just agreeing with Anselm, since it is his whole point to show that (1) is false?
I think we can see Kant's dictum as an objection to (1), in a sense. More exactly, it is an objection to the idea that the fool must accept (1) if he is to deny God's existence. The fool, Kant might say, should never have admitted that when he rejects God's existence, he thereby accepts (1). The fool is committed to accepting the following:
(0) God does not exist.
It is Anselm who puts in the fool's mouth that therefore it must be that:
(1) God exists in the understanding but not in reality.
I believe that assuming that (1) is what any atheist fool must affirm when he denies God's existence is what leads one to the mistaken conclusion that Kant's dictum is irrelevant to Anselm's argument. Kant's dictum is arguably irrelevant to Anselm's argument understood as Plantinga's (1)–(7). But it is precisely in the step that Plantinga and others take for granted – the step from (0) to (1) – that Kant's point is relevant. To see how, let's understand a possible motive for believing that (0) commits the fool to (1).
The problem of negative existentials
The fool says:
(0) God does not exist.
This is a so-called negative existential. Negative existentials raise an interesting puzzle in the philosophy of language: How could any of them be both meaningful and true? It seems that for some negative existential to be meaningful, its subject must refer. If its subject refers, then the object referred to exists. But the statement itself says that that object doesn't exist. So, if the statement is meaningful, it must be false.
We might see Anselm's move from (0) to (1) as supported by a certain solution to the problem of negative existentials, which we can anachronistically call Meinongianism.Footnote 8 Meinongianism is an ontological thesis, or set of theses:
(i) There are two kinds of existence: existence in reality and existence in the understanding;
(ii) Some things exist in the understanding without existing in reality; other things exist both in reality and in the understanding.Footnote 9
A distinction between kinds of existence is intuitive enough. Santa Claus, the Fountain of Youth, and Vulcan have one kind of existence: they exist only in the understanding; they are imaginary. You, I, the Eiffel Tower, and the Milky Way have another kind of existence: we exist in reality; we are real.
Given the Meinongian ontology, we have available the following semantic thesis:
The Meinongian solution to the problem of negative existentials: A statement of the form ‘x does not exist’ is true iff x exists in the understanding but does not exist in reality.
Thus, ‘Santa does not exist’ is true just in case Santa exists in the understanding but not in reality. Given Meinongianism, this sentence's being meaningful does not preclude its being true. ‘Santa’ does refer, but it refers to something that exists only in the understanding. So when we say of that thing that it fails to exist, we speak truly, because our sentence picks the thing out and says of it that it fails to exist in reality, which indeed it fails to do.
Some students of the ontological argument may be inclined, at least tentatively, to give Anselm the Meinongian solution to the problem of negative existentials. We are doing theology, after all, and Meinongianism underwrites a solution to a problem in the philosophy of language. And it is one that is endorsed independently by ontologists and philosophers of language without the least interest in philosophical theology. Should philosophers of religion be prepared to give Anselm whatever philosophy of language he wants, at least if that philosophy of language is a going concern among philosophers of language?
The relevance of Kant's objection
Perhaps, but this is precisely where Kant's point bears on Anselm's argument. Kant's dictum says that existence is not a real property. Now that Meinongianism is on the table, we have to interpret Kant's dictum. Presumably Kant's dictum means that existence in reality is not a real property.Footnote 10 How precisely is the dictum so interpreted relevant to the inference from (0) to (1)?
It is relevant as follows. The fool asserts
(0) God does not exist.
In order for Anselm to deduce
(1) God exists in the understanding but not in reality
from this, he assumes that there are two kinds of existence and that (0)'s being true requires its subject term to refer to something that has one of these kinds of existence (existence in the understanding) but not the other (existence in reality). That is, he assumes some theory like Meinongianism along with its solution to the problem of negative existentials. But if a theory like Meinongianism is true, then existence in reality is a real predicate, and Kant's dictum is contradicted. Existence in reality is a real predicate, given Meinongianism, because it does enlarge some concepts. There are some lists of properties that have the following feature: we can define a concept inequivalent to that defined by the list by adding exists in reality to the list. This can be done because, given Meinongianism, some things exist in the understanding without existing in reality. Existence in reality is not a trivial property.
Consider the following list:
is jolly
lives at the North Pole
delivers gifts on Christmas Eve
exists in the understanding
Call this list ‘S’. Now consider the list S+:
is jolly
lives at the North Pole
delivers gifts on Christmas Eve
exists in the understanding
exists in reality
Given Meinongianism, the concept defined by S is not equivalent to the concept defined by S+. It is possible for there to be an object that has all the members of S without having all the members of S+. Santa Claus, that imaginary person who exists only in the understanding, is just such an object. On the Meinongian picture, we can have an object that has all sorts of characteristics without having the additional characteristic of existing in reality. We do make an addition to a thing when we further declare that the thing is.
Here, then, is how I understand Kant's objection to Anselm's argument:
Kant's objection to Anselm's ontological argument:
P1 If Anselm's ontological argument is sound, then Meinongianism (or some theory relevantly like it) is true.
P2 If Meinongianism (or some theory relevantly like it) is true, then existence in reality is a real property.
P3 But existence in reality is not a real property.
C Therefore, Anselm's ontological argument is not sound.
P1 is justified by the fact that Anselm needs Meinongianism – or some theory relevantly like it – for the inference from (0) to (1) above to work.Footnote 11 The Santa example above and the preceding discussion illustrates why P2 is true. P3 is Kant's dictum. If I am right about P1 and P2, then Kant's dictum is at least relevant to Anselm's argument, interpreted as lines (0) through (7) above. If Kant's dictum is true, then Anselm's ontological argument is unsound.Footnote 12,Footnote 13
Appendix: Two alternative interpretations of Kant's dictum
I said above that presumably Kant's dictum means that existence in reality is not a real property. I presume this because anti-Meinongians like Kant believe in only one kind of existence, and it corresponds, arguably, to Meinongian existence in reality. But it is interesting to consider two alternative interpretations of Kant's dictum.
One says that existence in the understanding is not a real property. Does Meinongianism contradict this interpretation of Kant's dictum? At first blush, it seems there is a way for Anselm to say ‘No’ (and so to affirm the irrelevance of Kant's criticism, at least under this interpretation). Anselm the Meinongian could plausibly agree with Kant that existence in the understanding is not a real property if a case can be made that necessarily, everything that exists at all exists also in the understanding. Ironically, whether such a case can be made might depend on the very conclusion Anselm's argument is meant to establish. For everything that exists at all exists also in the understanding if there is an all-knowing being – a being like God! But of course Anselm cannot appeal to God to deflect the Kantian objection (so interpreted) as irrelevant. For this is what the argument itself is meant to establish.
Under a third interpretation, Kant's dictum maintains that just-plain-existence is not a real property. Just-plain-existence is what corresponds to the existential quantifier; what all the things there are (speaking unrestrictedly) have in common is that they just plain exist. (Given Meinongianism, of course, many – perhaps even all – of these things also exist in the understanding, and some – though certainly not all – exist in reality.) One advantage of interpreting Kant's dictum in this third way is that it is certainly true. Even a Meinongian should admit that the following is a contradiction: some things fail to just-plain-exist. It follows that, necessarily, everything just-plain-exists. Just-plain-existence therefore enlarges no concepts and is not a real property. But the disadvantage of interpreting Kant's dictum in this third way is that it is indeed irrelevant to Anselm's argument. That just-plain-existence is not a real property is compatible with Meinongianism.
How, then, to interpret Kant? Charitableness with respect to the likelihood of Kant's dictum being true suggests the third interpretation. But I think the first interpretation (the one discussed in the body of the paper) is best. The third interpretation does make the dictum true, but only trivially so; and it makes the dictum irrelevant to the argument. That is less charitable to Kant. The first interpretation makes the dictum clearly relevant to the argument and, furthermore, makes it a substantive and interesting thesis. It is a thesis for which Kant has arguments; its rival, Meinongianism, also enjoys argumentative support. This is where the debate should take us: to a contest between the substantive and contradictory theses of Kant's dictum and Meinongianism.
