This article aims to explain and comment on Kant’s refutation of The Ontological Argument (OA). The sections quoted below are from page 500-507 under the heading “The Impossibility of an Ontological Proof of the Existence of God” in Norman Kemp Smith’s translation of A Critique of Pure Reason (CPR) by Immanuel Kant.
Why explain Kant’s refutation? There are no more than seven very good reasons to do so. One good reason is that many philosophers today take this to be the best refutation of the OA in all of the history of philosophy. If you use the OA on a philosopher, no doubt he’ll snag his barely-worn copy of CPR, turn to page 500, hand it to you, and watch you suffer. Secondly, it is worth explaining this section because it is difficult to understand. Once the advocate of the OA is directed here, he might just get lost in the noumenal maze – or whatever. Even worse, he might misunderstand Kant and provide a poor refutation of him. Consequently, and as an aside, it is entirely possible that I, myself, will misunderstand parts of it, and I hope someone will take the time to correct me if I’ve erred. Thirdly, Kant uses many useful philosophical arguments and distinctions from which we can learn. Fourthly, CPR deserves explaining, even if only in part, because it is a classic philosophical work. Fifthly, many others refute the OA in ways inferior to Kant’s refutation, so it is good to realize that there is a more respectable refutation out there. Sixth, it is good to explain it because it helps the explainer understand it better. Seventh, there are many other good reasons, not yet named, for explaining this section of CPR.
The Ontological Argument
Descartes version of the OA may be summarized as follows:
P1: God is a being who possesses all perfections
P2: Existence is a perfection
Therefore God possesses existence.
Since P1 is simply part of the definition of God, God’s existence must be inferred by definition. As a side note, Kant calls judgements inferred by definition analytic judgements, and judgements that cannot be inferred by definition synthetic judgements. Anyway, if God is defined as the being than which none more perfect can be conceived, and if existence would make God more perfect, then he must exist. So, one is a fool if he denies that God exists because it is absurd to assert the imperfection of a perfect being. So goes Descartes’ version of the ontological argument.
It is evident, from what has been said, that the concept of an absolutely necessary being is a concept of pure reason, that is, a mere idea the objective reality of which is very far from being proved by the fact that reason requires it. For the idea instructs us only in regard to a certain unattainable completeness, and so serves rather to limit the understanding than to extend it to new objects. But we are here faced by what is indeed strange and perplexing, namely, that while the inference from a given existence in general to some absolutely necessary being seems to be both imperative and legitimate, all those conditions under which alone the understanding can form a concept of such a necessity are so many obstacles in the way of our doing so. In all ages men have spoken of an absolutely necessary being, and in so doing have endeavoured, not so much to understand whether and how a thing of this kind allows even of being thought, but rather to prove its existence. There is, of course, no difficulty in giving a verbal definition of the concept, namely, that it is something the non-existence of which is impossible. But this yields no insight into the conditions which make it necessary to regard the non-existence of a thing as absolutely unthinkable. It is precisely these conditions that we desire to know, in order that we may determine whether or not, in resorting to this concept, we are thinking anything at all. The expedient of removing all those conditions which the understanding indispensably requires in order to regard something as necessary, simply through the introduction of the word unconditioned, is very far from sufficing to show whether I am still thinking anything in the concept of the unconditionally necessary, or perhaps rather nothing at all.
In the beginning of CPR, and all throughout it, Kant argues for the importance of determining the capabilities and limitations of reason. After all, the human mind has limitations and we don’t want to be claiming knowledge in areas in which we simply have no way of having any. Because an idea is necessary in though, does it have to exist in the real world? How could we show such a thing?
For Kant, there is a distinction between the world as we perceive it with our minds, and the world as it really is. This is Kant’s famous distinction between the phenomenal and noumenal worlds; where things as we perceive them are phenomena, and things as they actually are in and of themselves are noumena.
On this distinction, the concept of a necessary being resides in our minds, in the phenomenal world. Kant is not arguing that we can’t make up some concept which must exist. We can define a snark as a Klingon which exists. Then, it would be unthinkable to deny that a snark exists. Kant begs us to give criteria to show that the non-existence of snarks and God is unthinkable, or to be able to distinguish between necessary beings and non-existent concepts like snarks.
Nay more, this concept, at first ventured upon blindly, and now become so completely familiar, has been supposed to have its meaning exhibited in a number of examples; and on this account all further enquiry into its intelligibility has seemed to be quite needless. Thus the fact that every geometrical proposition, as, for instance, that a triangle has three angles, is absolutely necessary, has been taken as justifying us in speaking of an object which lies entirely outside the sphere of our understanding as if we understood perfectly what it is that we intend to convey by the concept of that object.
All the alleged examples are, without exception, taken from judgments, not from things and their existence. But the unconditioned necessity of judgments is not the same as an absolute necessity of things. The absolute necessity of the judgment is only a conditioned necessity of the thing, or of the predicate in the judgment. The above proposition does not declare that three angles are absolutely necessary, but that, under the condition that there is a triangle (that is, that a triangle is given), three angles will necessarily be found in it. So great, indeed, is the deluding influence exercised by this logical necessity that, by the simple device of forming an a priori concept of a thing in such a manner as to include existence within the scope of its meaning, we have supposed ourselves to have justified the conclusion that because existence necessarily belongs to the object of this concept always under the condition that we posit the thing as given (as existing) we are also of necessity, in accordance with the law of identity, required to posit the existence of its object, and that this being is therefore itself absolutely necessary and this, to repeat, for the reason that the existence of this being has already been thought in a concept which is assumed arbitrarily and on condition that we posit its object.
Many have provided examples of necessary judgements in geometry, but these judgements are not like the OA because they do not extend beyond the phenomenal realm, to real existence. The OA, however, is a necessary judgement whose implications extend beyond the phenomenal world. It claims to prove the existence of God in the noumenal world, not just in the phenomenal world. Kant complains that the examples that most people use when explaining the concept of necessity do not show that any real beings are necessary. When a person defines a triangle as having three angles, he is not, by conceiving the triangle, able to show that three angles really and noumenally exist. Rather, a triangle may possibly exist and, if it does, it will necessarily have three angles. However, if there is no triangle, there needn’t necessarily be three angles. In the same way, if God is defined as possessing all perfections including existence, if there is no God, there isn’t necessarily a being which possesses all perfections.
A word of criticism here. I do not think Kant’s analogy holds. The analogy is drawn between two propositions: (a) Triangles have three angles and (b) God has existence. Let us grant that when one denies the triangle, he isn’t contradicting himself if he denies the three angles. But when one denies God, is he then free to deny existence itself? If Kant were to adhere to the analogy, he ought to argue this. Instead, he seems to argue that if God can be denied, then his existence can also be denied to him. A miserable tautology. Kant continues along this line:
If, in an identical proposition, I reject the predicate while retaining the subject, contradiction results; and I therefore say that the former belongs necessarily to the latter. But if we reject subject and predicate alike, there is no contradiction; for nothing is then left that can be contradicted, To posit a triangle, and yet to reject its three angles, is self-contradictory; but there is no contradiction in rejecting the triangle together with its three angles. The same holds true of the concept of an absolutely necessary being. If its existence is rejected, we reject the thing itself with all its predicates; and no question of contradiction can then arise. There is nothing outside it that would then be contradicted, since the necessity of the thing is not supposed to be derived from anything external; nor is there anything internal that would be contradicted, since in rejecting the thing itself we have at the same time rejected all its internal properties. ‘God is omnipotent’ is a necessary judgment. The omnipotence cannot be rejected if we posit a Deity, that is, an infinite being; for the two concepts are identical. But if we say, There is no God’, neither the omnipotence nor any other of its predicates is given; they are one and all rejected together with the subject, and there is therefore not the least contradiction in such a judgment.
The criticism given above seems to hold strong. Kant is not arguing that no contradiction is produced when God is denied and existence with him. Instead he is argueing that when God is denied and “his” existence is denied, no contradiction is produced. Therefore, the analogy is equivocal. If the analogy were modified to say there is no contradiction in rejecting the triangle together with “a triangle’s” three angles, it would fit, but it would lose its force.
Now, you might ask Kant whether or not the subject, God, even can be denied in thought.
We have thus seen that if the predicate of a judgment is rejected together with the subject, no internal contradiction can result, and that this holds no matter what the predicate may be. The only way of evading this conclusion is to argue that there are subjects which cannot be removed, and must always remain. That, however, would only be another way of saying that there are absolutely necessary subjects; and that is the very assumption which I have called in question, and the possibility of which the above argument professes to establish.
For I cannot form the least concept of a thing which, should it be rejected with all its predicates, leaves behind a contradiction; and in the absence of contradiction I have, through pure a priori concepts alone, no criterion of impossibility.
Kant points out the circularity in asserting that there are subjects which cannot be annihilated in thought. On Kant’s part, he can’t think of any subject at all which leaves a contradiction if it is denied. One might suggest, and some have, that the concept of truth cannot be denied in thought. For, in denying it, one assumes it. One might also suggest that the law of contradiction cannot be denied in thought. To this, Kant might say that to deny such concepts would do away with the criterion of possibility and would, therefore, not provide contradiction at all. However, it is still not at all clear that it is possible to deny truth in thought. For Kant to show that an ontological proof is impossible, it seems that he is required to prove that God actually can be denied in thought.
Moreover, it is not at all clear what Kant means by rejecting or removing a subject from thought. The vagueness of the argument makes it difficult to refute with clarity.
Notwithstanding all these general considerations, in which every one must concur, we may be challenged with a case which is brought forward as proof that in actual fact the contrary holds, namely, that there is one concept, and indeed only one, in reference to which the not-being or rejection of its object is in itself contradictory, namely, the concept of the ensrealissimum. It is declared that it possesses all reality, and that we are justified in assuming that such a being is possible the fact that a concept does not contradict itself by no means proves the possibility of its object: but the contrary assertion I am for the moment willing to allow. [footnote begin] A concept is always possible if it is not self-contradictory. This is the logical criterion of possibility, and by it the object of the concept is distinguishable from the nihil negativum. But it may none the less be an empty concept, unless the objective reality of the synthesis through which the concept is generated has been specifically proved; and such proof, as we have shown above, rests on principles of possible experience, and not on the principle of analysis (the law of contradiction). This is a warning against arguing directly from the logical possibility of concepts to the real possibility of things. [footnote end]
Now [the argument proceeds] ‘all reality’ includes existence; existence is therefore contained in the concept of a thing that is possible. If, then, this thing is rejected, the internal possibility of the thing is rejected which is self-contradictory.
My answer is as follows. There is already a contradiction in introducing the concept of existence no matter under what title it may be disguised into the concept of a thing which we profess to be thinking solely in reference to its possibility.
All brackets are Kant’s except the two about the footnote. Now, Kant argues that there is a contradiction produced when one asserts the actual existence of something on the basis of logic not experience. This is because any judgement of the existence of anything is a synthetic judgement (recall the distinction between synthetic and analytic judgements explained earlier). Since existence, by definition, cannot be judged from the definition of something, it follows that one can’t include existence in his definition of a concept without contradicting himself. To make existence part of the definition of a concept is to say that existence judgements are all synthetic and not all synthetic.
But, why can’t we just reject the idea that a thing’s existence must be judged synthetically? Kant makes a fascinating reply.
If that be allowed as legitimate, a seeming victory has been won; but in actual fact nothing at all is said: the assertion is a mere tautology. We must ask: Is the proposition that this or that thing (which, whatever it may be, is allowed as possible) exists, an analytic or a synthetic proposition? If it is analytic, the assertion of the existence of the thing adds nothing to the thought of the thing; but in that case either the thought, which is in us, is the thing itself, or we have presupposed an existence as belonging to the realm of the possible, and have then, on that pretext, inferred its existence from its internal possibility which is nothing but a miserable tautology.
The word ‘reality’, which in the concept of the thing sounds other than the word ‘existence’ in the concept of the predicate, is of no avail in meeting this objection. For if all positing (no matter what it may be that is posited) is entitled reality, the thing with all its predicates is already posited in the concept of the subject, and is assumed as actual; and in the predicate this is merely repeated. But if, on the other hand, we admit, as every reasonable person must, that all existential propositions are synthetic, how can we profess to maintain that the predicate of existence cannot be rejected without contradiction? This is a feature which is found only in analytic propositions, and is indeed precisely what constitutes their analytic character.
For arguments sake, Kant concedes that a thing’s existence can be an analytic judgement. Given this, Kant argues, existence is a meaningless predicate. The predication of existence on a thing would add nothing to the subject. To assert that something exists in the phenomenal realm is to assert that something exists as a conception. But what would this even mean? I can conceive of the Abominable Snowman and then assert that he exists as a conception, but he obviously existed as a conception by virtue of the fact that I conceived him in the first place, so nothing extra is said in claiming that the phenomenal world houses the Abominable Snowman. This is a “miserable tautology.” Existence, for it to be meaningful (or for it to add to the subject), must be an assertion concerning the noumenal world and must be a synthetic judgement. Kant continues to press the point by a comparison between the logical copula and the word exist.
I should have hoped to put an end to these idle and fruitless disputations in a direct manner, by an accurate determination of the concept of existence, had I not found that the illusion which is caused by the confusion of a logical with a real predicate (that is, with a predicate which determines a thing) is almost beyond correction. Anything we please can be made to serve as a logical predicate; the subject can even be predicated of itself; for logic abstracts from all content. But a determining predicate is a predicate which is added to the concept of the subject and enlarges it. Consequently, it must not be already contained in the concept. ‘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. It is merely the positing of a thing, or of certain determinations, as existing in themselves. Logically, it is merely the copula of a judgment. The proposition, ‘God is omnipotent’, contains two concepts, each of which has its object God and omnipotence. The small word ‘is’ adds no new predicate, but only serves to posit the predicate in its relation to the subject. If, now, we take the subject (God) with all its predicates (among which is omnipotence), and say ‘God is’, or ‘There is a God’, we attach no new predicate to the concept of God, but only posit the subject in itself with all its predicates, and indeed posit it as being an object that stands in relation to my concept. The content of both must be one and the same; nothing can have been added to the concept, which expresses merely what is possible, by my thinking its object (through the expression ‘it is’) as given absolutely. Otherwise stated, the real contains no more than the merely possible.
Kant makes a distinction between real and logical predicates. Logical predicates can be anything that can be conceived to function as the predicate of a proposition. Real predicates, which are the same as determining predicates, must add something to the concept of a subject. Consequently, real predicates can’t be already contained in the subject. “Being” isn’t a real predicate. It is merely the copula of a judgement. To use a similar example to Kant’s, ‘The Abominable Snowman is white’ contains two concepts, whiteness and the Abominable Snowman. The word “is” is not an extra concept or predicate. So, to say “there is an Abominable Snowman” is to add nothing to the subject. It is the same as the incomplete assertion “the Abominable Snowman is”. An assertion must contain subject, copula, and predicate, but this example only contains subject and copula.
One might argue for a distinction between a concept’s “being” and a concept’s “existence as a concept”. Kant might reply that since existence can be predicated of all possible concepts (real or not), and no possible existing concepts can’t be predicated, existence is one and the same with predicability. The same is true of “being.” Hence, for a concept to “exist” means that a concept “is”.
Kant showed that if we want to allow for the predicate “exist” to apply in the phenomenal realm, it means nothing. If, however, we take existence to apply to the noumenal world only, and, thus, make the existence of a thing a synthetic judgement, then we deny the possibility of a necessary being by definition.
Kant prefers the latter option. Therefore, the most a concept can provide is possible existence. Real existence must be determined by experience. Now we come to the famous example:
A hundred real thalers do not contain the least coin more than a hundred possible thalers. For as the latter signify the concept, and the former the object and the positing of the object, should the former contain more than the latter, my concept would not, in that case, express the whole object, and would not therefore be an adequate concept of it. My financial position is, however, affected very differently by a hundred real thalers than it is by the mere concept of them (that is, of their possibility). For the object, as it actually exists, is not analytically contained in my concept, but is added to my concept (which is a determination of my state) synthetically; and yet the conceived hundred thalers are not themselves in the least increased through thus acquiring existence outside my concept.
By whatever and by however many predicates we may think a thing even if we completely determine it we do not make the least addition to the thing when we further declare that this thing is. Otherwise, it would not be exactly the same thing that exists, but something more than we had thought in the concept; and we could not, therefore, say that the exact object of my concept exists. If we think in a thing every feature of reality except one, the missing reality is not added by my saying that this defective thing exists. On the contrary, it exists with the same defect with which I have thought it, since otherwise what exists would be something different from what I thought. When, therefore, I think a being as the supreme reality, without any defect, the question still remains whether it exists or not. For though, in my concept, nothing may be lacking of the possible real content of a thing in general, something is still lacking in its relation to my whole state of thought, namely, [in so far as I am unable to assert] that knowledge of this object is also possible a posteriori. And here we find the source of our present difficulty. Were we dealing with an object of the senses, we could not confound the existence of the thing with the mere concept of it. For through the concept the object is thought only as conforming to the universal conditions of possible empirical knowledge in general, whereas though its existence it is thought as belonging to the context of experience as a whole. In being thus connected with the content of experience as a whole, the concept of the object is not, however, in the least enlarged; all that has happened is that our thought has thereby obtained an additional possible perception. It is not, therefore, surprising that, if we attempt to think existence through the pure category alone, we cannot specify a single mark distinguishing it from mere possibility.
Whatever, therefore, and however much, our concept of an object may contain, we must go outside it, if we are to ascribe existence to the object. In the case of objects of the senses, this takes place through their connection with some one of our perceptions, in accordance with empirical laws. But in dealing with objects of pure thought, we have no means whatsoever of knowing their existence, since it would have to be known in a completely a priori manner. Our consciousness of all existence (whether immediately through perception, or mediately through inferences which connect something with perception) belongs exclusively to the unity of experience; any [alleged] existence outside this field, while not indeed such as we can declare to be absolutely impossible, is of the nature of an assumption which we can never be in a position to justify.
The difference between having eaten a real bratwurst and the concept of having eaten one is not a difference in concept. The concept is the same. However, your noumenal stomach is filled by the real eating of the brat, and not by the concept. Even if we posit the concept of having eaten a bratwurst and add to it the predicate “exists,” our stomach gets no satisfaction. For Kant, it is always a contradiction to include “real,” “exists,” or other predicates meant to convey being in the noumenal world in the concept of a thing.
Interestingly, Kant says: “It is not, therefore, surprising that, if we attempt to think existence through the pure category alone, we cannot specify a single mark distinguishing it from mere possibility.” This reinforces the point that if we try to add “existence” to a concept, we empty it of its meaning and, so, add nothing to the concept. Therefore, it is impossible to distinguish a real dollar from its concept in thought.
Since Kant has been engaged in conceptually explaining existence to us, one wonders if he hasn’t shot himself in the foot; providing to us all the arguments we need to organize a mutiny. What is the difference between the meaningless concept of existence and the existence which Kant has been describing? For Kant, “we cannot specify a single [difference]…”
To continue summarizing the argument, once a concept is thought of, a posteriori methods are required to determine whether or not our concept relates to a reality. Since the only methods available for a posteriori knowledge must deal with objects of the senses, only sensible objects can be known to exist. Kant is quick to point out that this does not mean that only sensible objects can exist. However, since God is not usually conceived to be a sensible object, he cannot be known a posteriori.
The concept of a supreme being is in many respects a very useful idea; but just because it is a mere idea, it is altogether incapable, by itself alone, of enlarging our knowledge in regard to what exists. It is not even competent to enlighten us as to the possibility of any existence beyond that which is known in and through experience. The analytic criterion of possibility, as consisting in the principle that bare positives (realities) give rise to no contradiction, cannot be denied to it. But since the realities are not given to us in their specific characters; since even if they were, we should still not be in a position to pass judgment; since the criterion of the possibility of synthetic knowledge is never to be looked for save in experience, to which the object of an idea cannot belong, the connection of all real properties in a thing is a synthesis, the possibility of which we are unable to determine a priori. And thus the celebrated Leibniz is far from having succeeded in what he plumed himself on achieving the comprehension a priori of the possibility of this sublime ideal being.
The attempt to establish the existence of a supreme being by means of the famous ontological argument of Descartes is therefore merely so much labour and effort lost; we can no more extend our stock of [theoretical] insight by mere ideas, than a merchant can better his position by adding a few noughts to his cash account.
Knowledge of existence is synthetic knowledge and, therefore, it must be obtained through experience. Therefore, an ontological argument is excluded by definition.
Kant has argued that necessary concepts cannot prove the existence of real beings. He has contended that we contradict ourselves if we add real existence to a concept. Therefore, if we ascribe existence to the concept of God, we contradict ourselves. If Kant grants that existence can be ascribed to concepts, then, he shows us, that existence is a meaningless concept. To exist must mean to reside outside the mind in the noumenal world or it means nothing. Since all existing objects are not mental concepts, it is self-contradictory to ascribe existence to any concepts including the concept of God.
It seems to the author that Kant has said more than his system allows him to say. Kant does not allow existence to be predicated of concepts, but he allows it to be predicated of real things. This seems like a contradiction because, as Kant admits, the “real thing” of which he predicates “existence” is really just a concept itself. It would be more consistent for Kant to follow his own reasoning and simply refrain from predicating existence of anything.
In fact, the unknowability of the noumenal world is a problem for which many people have criticized Kant’s system. It seems that Kant knows a lot more about what exists than he allows others to know. How does Kant get away with predicating existence of the noumenal world at all? Kant has much to say about this, but the objection remains that the noumenal world of which Kant predicates existence is, itself, a concept.
Assuming this criticism is valid, what if we followed Kant’s argument consistently? It might seem, then, that nothing would exist. This is not quite right. Kant’s discussion of “existence” as a logical predicate makes the important point that if we make existence a logical predicate, we make it mean the same as the copula “to be.” Logically, the phrase “God is” is meaningless because it is an incomplete assertion. For a logical assertion to be meaningful in formal logic, it must contain subject, copula, and predicate. To say “God is omnipotent” is meaningful because it relates two concepts, but to say “God is” or “God exists” is to say nothing more than “God.”
In this author’s opinion, Kant’s argument for the impossibility of an ontological proof for the existence of God fails. Kant has not showed that such an argument is impossible. However, Kant has showed that the predicate “exist” is meaningless if it is applied to concepts. Therefore, the conclusion of the classic ontological argument as understood by Kant is meaningless. However, since Kant has not proven the impossibility of necessary concepts, some necessary beings (as long as they are not supposed to exist in some unknowable world of things in themselves) can slip past the epistemological gavel. Perhaps the Biblical idea that God is truth could sidestep the Kantian arguments, if only it be shown that truth is necessary. This would require that we grapple with questions of “being” and “reality,” and decide what it is that we actually mean when we conclude that God exists, or decide what it is that we actually want to prove.
 Descartes version of the ontological argument is not the first version. Anselm is credited with the first formulation of the ontological argument and similar arguments can be found in Augustine. Alvin Plantinga and others have argued that Kant’s refutation of the OA does not really apply to Anselm’s version of the OA. Plantinga’s understanding of the OA is different than Kant’s understanding of it. Since this article is more about getting the gist of Kant’s refutation, we will not dispute Kant’s interpretation of the OA.
 I can’t see why necessary subjects in thought would be a problem for Kant, since he can still argue that necessary subjects in thought don’t have to correspond to the noumenal world. Perhaps I’ve misunderstood him somewhere.
 Kant rightly takes it to be given that “am,” “are,” and “is” are included under the same analysis since they are conjugates of the verb “to be.”
 Kant means to contrast “a posteriori” with “a priori”. What is known a priori are known by reason alone without the help of experience. What is known by experience or with the help of experience is known a posteriori.