‘Existence is not a predicate.’ Anyone familiar with philosophy will have come across this oft-repeated phrase numerous times. Many believe it is true, perhaps at least in part because they do not want to accept the ontological argument. Others are not even entirely sure what it means.
A predicate, according to the dictionary definition, is: ‘The part of a sentence or clause containing a verb and stating something about the subject’. It could be considered a quality or characteristic of the subject, such as ‘white’, ‘intelligent’, ‘tall’, etc. In categorical logic, the predicate is often treated as just another class of objects. ‘All cats are mammals’ affirms something about the subject class of cats, namely, that they are mammals, or that all members of the class have the predicate of being mammalian. ‘No cats are fish’ denies that any member of the category has being a fish as one of its predicates, so there is no overlap of the two categories.
If Kant is right, then existence, or ‘things that exist’ could never be predicated of any subject; it would be incorrect to say ‘Cats exist’ because that treats existence as though it were a predicate. This would mean that it must be impossible for some reason to consider ‘things that exist’ as a class of objects the way that we do with fish and mammals, though I do not see why. Now perhaps Kant, or some practitioner of predicate logic, would say that a categorical proposition such as ‘Some cats exist’ is just ill-formed, like a sentence that is grammatically incorrect. Existence is not a property or attribute of the subject, it is an affirmation or denial that there is a subject. They might tell you that it would be more correct to say something like ‘There are cats’. But it seems to me that this is really just another way of saying that cats are included in the category of ‘things that exist’, which in turn would mean that existence is a predicate of at least some cats. In fact, it would be a predicate of everything in that category, including you and I.
There is no reason why one could not categorize things that are actual, or ‘things that exist’ as a class. Another category would be for subjects that are merely hypothetical, or ‘things that are imaginary’. Both would be predicated of any subject that has membership in the category. ‘Some birds are existing things’ is a perfectly legitimate categorical proposition.
So why did Kant make such a strange claim? The part of the ontological argument that he was objecting to was Anselm’s assertion that ‘that than which nothing greater can be conceived’ would be greater if it existed in reality rather than if it was merely imagined. Kant’s point seems to be that existence should not be thought of as some additional property or characteristic that an object has which would make it greater than its corresponding idea. The content of the concept must have predicates that match exactly with those of the actual object or the concept would not be a true representation of that thing. He uses thalers, a kind of currency, to demonstrate. If a hundred real thalers were somehow greater than the concept of one hundred thalers, then the concept would not adequately represent the object, and it would not really be a concept of that thing. Kant thinks that the concept and the object would be identical in terms of greatness, which means that ‘that than which nothing greater can be conceived’ would not necessarily have to exist in reality, as ‘The real contains no more than the possible’. (See Critique of Pure Reason, A599-600/B627-628.)
Kant is right that the predicates of the concept must match the predicates of the object, but what this actually means is that the concept of an imaginary one hundred thalers is different than the concept of an actual one hundred thalers. The concept of an imaginary one hundred thalers would have, as one of its predicates, hypothetical existence. This could not be the concept which represents the object in reality, as their predicates would differ in at least this one respect. The concept of an actual one hundred thalers would have predicates that correspond exactly with the predicates of the object that it represents, including that it exists in reality.
There is one thing that I agree with Kant about concerning this issue. A necessary being – which he defines as something for which nonexistence is impossible – is thought to be a subject that would have a necessary predicate of existence. Some have concluded from this that the existence of such a being is known a priori. But Kant points out that necessity is only between subject and predicate. If we were to ‘annihilate’ or ‘cancel’ the subject in thought, or in other words, if we were to suppose that there is no subject, then the predicate would automatically be eliminated as well. Kant uses the example of a triangle to demonstrate. ‘A triangle has three angles’ is necessarily true. We could not retain the subject and eliminate the predicate without it creating a contradiction. However, if both are eliminated there is nothing at all, and therefore no means of creating a contradiction (A593-598/B621-626). ‘All unicorns are one-horned creatures’ is true by definition, but if there is no subject then there is no predicate either. I doubt that anyone would claim otherwise. But some have claimed that it is different when existence is the predicate.
We must not conflate the question of what predicates the subject would have, if there is one, with the question of whether there is one. Existence is no different than any other predicate. If there is a necessary being then it must have the predicate of existence, but there is not necessity that there is a subject.
Kant’s thinking seems to be that if existence is not a genuine predicate, and the only necessity in a proposition is between subject and predicate, then it follows that the claim that there is a subject cannot be necessary; that would be a synthetic rather than an analytic judgement. I agree with him on that part, but existence has to be a predicate of everything that is. If there is a necessary being, it would have the predicate of existence, and it would be a necessary predicate at that. Nevertheless, its predicates are only actual if the subject is, and that is the true question. One cannot legitimately reason from the necessity of the predicate if there is a subject to say there is necessity that there is a subject. Pure analytic proofs for the existence of God fail because without some external a posteriori evidence that there is a real subject, the claim can only be stated conditionally: if there is such a thing as a necessary being then existence would be one of its necessary predicates. This does not mean that existence is not a predicate, it simply indicates that it is unknown whether there is a subject.
David Johnson
2016
Addendum
A friend of mine asked how I would respond to the apparent paradoxes that come from treating existence as a property, as discussed by Bertrand Russell, and sent this link:
http://plato.stanford.edu/entries/existence/#FreRusExiNotProInd
Here is what I understand the main objections to be:
1) Existence would not add anything to the object. It is conceptually prior to predication. The thought seems to be that instantiating any property whatsoever presupposes existence and so existence is not a further property over and above a thing’s genuine properties.
Response:
Existence does not add anything to an object, that is true, but it does add something conceptually to a subject in a categorical proposition. Otherwise, what would be the difference between a subject that exists and one that does not? If it is the same subject, with identical properties in all other ways, but one of them exists and the other does not, then they are not identical. Something must make them different, and it has to be existence, because all other properties are exactly the same.
I think it is just plain wrong to say that instantiating any property of a subject presupposes the existence of that subject. If that were true, then fictional subjects could not be said to have any properties at all. We do not have to presuppose the actual existence of unicorns simply to say that by definition they are or would be one-horned creatures; that would be a property of unicorns whether they really exist or not. A fictional subject would not have actual properties, of course, but it could have hypothetical properties. I reject the notion that actual existence is conceptually prior to predication, or a required assumption for predication.
2) Another consideration mentioned concerns the puzzle of negative singular existentials. The example used in the article is ‘Ronald McDonald does not exist’. Russell thinks of existence as meaning instantiation. So if ‘nonexistence’ is the predicate then reality must include an entity designated by the term ‘Ronald McDonald’ that is instantiated in the real world and has the property of not existing. He thinks this is absurd. The problem is not just finding some entity in reality to serve as the designation of ‘Ronald McDonald’ (though that is problematic enough) it is that this leads to paradoxes. If existence stands for instantiation, then this means that something must be instantiated whose predicate says that it is not instantiated. Not only that, but if there were such a thing then it would be part of reality, and therefore existent. That means that ‘Ronald McDonald exists’ would have to be considered true, and its negation false, but this of course contradicts the content of the original expression. We arrive at the self-contradictory conclusion that ‘Ronald McDonald does not exist’ is true and ‘Ronald McDonald exists’ is also true. So, we should reject the claim that existence is a property of the designation of subject terms in existential sentences. Russell thinks that ‘Ronald McDonald’ is not a genuine referring term or expression that designates anything except (I would assume) an empty description.
Response:
I do not think that one is necessarily committed to saying that nonexistence or ‘not existence’ is a predicate if existence is. Maybe he thinks that you would be because of logical operations like contraposition, where ‘All As are Bs’ is considered logically equivalent to ‘All non-Bs are non-As’, or obversion, in which ‘All A are B’ is equivalent to ‘No A are non-B’.
Are ‘non-dogs’ and ‘non-mammals’ genuine predicates? I guess they are categories, but I would not think of them as properties or attributes of a subject. The category is formed by grouping things according to the absence of a property rather than the presence of one. The absence of a property is not itself a property, it simply remains the absence of a property. That is more of an antipredicate. ‘Short’ would be an attribute of the subject, but ‘non-tall’ is just the absence of that attribute. These are often treated as being equivalent, but they are not (not totally anyway) because ‘non-tall’ would include things of medium height in addition to short things. ‘Non-tall’ is an antipredicate that indicates the absence of the characteristic or attribute, and is equivalent to ‘not tall’. ‘Some people are non-tall’ and ‘Some people are not tall’ mean the same thing; they would not if ‘non-tall’ was a predicate, for in one instance the claim would be that some people have a predicate and in the other it would be that some people do not have a predicate. In reality, both claims actually mean that some members of the subject class lack the characteristic, property, or attribute of being tall. This is not the same as ‘Some people are short’ which is a positive affirmation that some members of the subject class have the characteristic or attribute of being short, and this may or may not refer to the same members as the prior claim.
If we are going to count antipredicates as predicates then most subjects would have billions of predicates. ‘Dogs’, for example, would have ‘not being a cat’ as a predicate, along with ‘non-building’, ‘non-human’, ‘non-fish’, ‘non-plant’, etc. If these are genuine properties of the subject why don’t we ever refer to them as distinguishing features of dogs? It would make far more sense to say that ‘All dogs are non-buildings’ just means that ‘buildings’ is not a property or attribute of dogs, or is a property that all dogs lack, rather than to say that ‘non-buildings’ is a property. So, in sum, I do not think that nonexistence would be a predicate even though existence is. No negatively expressed class complements would be predicates, they simply indicate the absence of a predicate. That resolves the paradox.
Furthermore, I believe that the whole way that Russell approaches this issue is wrong. Of the things that are possible there are two main categories that all subjects would fall into, those that are actual and those that are hypothetical. If a subject, whatever it is, does not have membership in the category of actual things, but is possible, then it would be in the category of hypothetical or merely possible things. When you say ‘Ronald McDonald does not exist’ what it means is that this subject is not instantiated in the category of actually existing things. But of course it is instantiated in the category of fictional things, which is a subset within the ‘hypothetical’ category. So it is instantiated, just not in the category of ‘actual things’; that is why it is true to say that the subject lacks the predicate of existence, because it is not a member of that category; but it does have the predicate of hypothetical existence because it is a member of that category. ‘Ronald McDonald exists as a fictional character’ is true.