Kant on the Ontological Argument for the Existence of God: Why Conceivability Does Not Entail Real Possibility

Abstract

In the ontological argument for the existence of God, Descartes famously argues that the idea of God is the idea of a perfect being. As such, the idea of God must combine all of the perfections. Now, as (necessary) existence is a perfection, God must exist. Leibniz criticized Descartes’ argument, pointing out that it rests upon the hidden assumption that God is possible. Leibniz argues, however, that God is really possible because realities cannot oppose one another, and so there could be no real opposition between the perfections. So, at least in the case of God, conceivability entails real possibility. Kant rejects this assumption and insists that the non-contradictoriness of an idea is not an adequate criterion for the real possibility of the object of the idea, for although predicates may be combined in thought to form a concept, this does not entail the properties they indicate may be so combined in reality. For this reason, Kant believes that it is impossible to prove the real possibility of God, and so the ontological argument is not sound. In this paper, I examine Kant’s reasons for reaching this conclusion. I pay particular attention to Kant’s argument in the Amphiboly, which deals with the concepts of agreement and opposition, and where Kant stresses the importance of the distinction between logical and real opposition. I will argue that this distinction plays a crucial role in Kant’s rejection of the ontological argument and rationalist Leibnizian–Wolffian metaphysics in general. I also show how Kant’s rejection of the possibility of what he calls the complete determination of a concept in the Ideal of Pure Reason, plays a role in his rejection of the conceivability entails real possibility principle.

1. Introduction

In the ontological argument for the existence of God, Descartes famously argues that the idea of God is the idea of a perfect being. As such, the idea of God must combine all of the perfections. Now, as (necessary) existence is a perfection, God must exist. Leibniz criticized Descartes’ argument, pointing out that it rests upon the hidden assumption that God is possible.1 Leibniz argues, however, that the idea of God is possible because realities cannot oppose one another, and so there could be no real opposition between the perfections. So, at least in the case of God, conceivability entails real possibility. Kant rejects this assumption and insists that the non-contradictoriness of a concept is not an adequate criterion for the real possibility of the object of the concept, for although predicates may be combined in thought to form a concept, this does not entail the properties they indicate may be so combined in reality. For this reason, Kant believes, it is impossible to prove the real possibility of God, and so the ontological argument is not sound. Thus, although his most famous argument against the ontological proof involves the claim that existence is not a real predicate, Kant also believes (like Leibniz) that the proof presupposes that we can demonstrate that God is really possible, and (unlike Leibniz) believes that this cannot be done. Thus, Kant concludes his discussion of the ontological proof in the Idea of Pure Reason of the Critique of Pure Reason by arguing that the connection of all real properties in a thing is a synthesis about whose possibility we cannot judge a priori because the realities are not given to us specifically [die Realitäten spezifisch nicht gegeben sind]2—and even if this were to happen no judgment at all could take place because the mark of possibility of synthetic cognitions always has to be sought only in experience, to which, however, the object of an idea can never belong—the famous Leibniz was far from having achieved what he flattered himself he had done, namely, gaining insight a priori into the possibility of such a sublime ideal being (A602/B630).

Kant’s arguments against the possibility of showing the real possibility of God have received far less attention than his argument that existence is not a real predicate.3 I take this to be unfortunate because Kant’s claim that existence is not a real predicate just seems to be question-begging, and there is no good reason for the proponent of the ontological argument to accept such a claim. Following Stang (2016), I believe that Kant’s claim that existence is not a real predicate is to be understood as the claim that existence is not a determinate predicate in the sense of being a predicate that may or may not apply to objects. As such, existence as a predicate is to be thought of as a shadow of the existential quantifier; for an object to exist in this sense is just for it to fall within the domain of quantification. It follows from this account that all possible objects of quantification exist, and that there is no room for merely possible objects.4 In contemporary logic, there are a large number of formal systems of quantified modal logic. Some of these logics have determinate existence predicates, some do not. So, for example, many proponents of fixed-domain possible world models propose that we need both an existential quantifier and a separate (in Kant’s sense, “determinate”) existence predicate.5 For example, Linsky and Zalta (1994, 1996) argue for a modal logic in which there are both continently concrete objects (actual existing objects) and contingently non-concrete objects (objects that do not actually exist). Many other logicians propose such logics. I find such logics very plausible, and at least the question of which sort of quantified modal logic to accept seems to be a matter of inference to the best explanation. So, insofar as Kant’s strongest argument against the ontological argument is based on the claim that existence is not a real determinate predicate, as Stang (2016) argues, Kant’s argument is quite weak.6 And Stang is not an outlier here, as there seems to be an (implicit) assumption among Kant scholars that Kant’s strongest argument against the ontological argument is the one based on the claim that existence is not a real predicate. I believe, in contrast, that the (epistemic) argument that we cannot know that God is really possible offers a much stronger argument against a defender of the ontological argument than the argument based on the (semantic) claim that existence is not a real predicate. There is no consensus amongst logicians today as to whether we should take existence to be a real predicate, and I do not see why the onus should be on the defender of the ontological argument to prove that existence is a real predicate to get their argument off the ground. In the case of this argument that we cannot know that God is really possible, I believe that a stronger case can be made that the onus is on the defender of the ontological argument to offer some reason to think that we can know that God is really possible. And I think Kant convincingly argues that finite minds like ourselves cannot know whether a most perfect being is really possible.

In this paper, I focus on examining Kant’s reasons for believing that it is impossible for us to know whether or not God is really possible. I pay particular attention to Kant’s argument in the Second Amphiboly of the Critique of Pure Reason, which deals with the concepts of agreement and opposition, and where Kant stresses the importance of the distinction between logical and real opposition. This distinction plays a crucial role in Kant’s rejection of the ontological argument and rationalist Leibnizian–Wolffian metaphysics, in general, and motivates the Kantian distinction between the faculties of understanding and intuition. I also show how Kant’s rejection of the possibility of what he calls the complete determination of a concept in the Ideal of Pure Reason section of the Critique of Pure Reason plays a central role in his rejection of the conceivability entails the real possibility principle. And I agree with Kant that it is extremely plausible to assume that we cannot make our concepts fully determinate.

Before examining their arguments, let me say a few words about terminology. Both Leibniz and Kant distinguish between predicates and properties, but they use a range of different expressions to indicate this distinction. The expressions “realities”, “perfections”, “simple forms”, “properties”, and “qualities” are all ways of talking about the (potentially) real properties corresponding to our predicates. Similarly, the expressions: “predicates”, “marks”, “concepts”, and “terms” are ways of talking about (putative) representations of such properties. Although there are obviously differences between these various expressions, I think that generally these differences are not essential to the arguments developed in this paper, and so, for the purposes of many of the arguments in this paper, members of each set of expressions are used interchangeably. This is unavoidable as these expressions are used in various of the quotations I will appeal to.7

1.1. Leibniz on the Ontological Proof and Real Possibility

In the fifth Meditation, Descartes famously argues that we can know that God exists merely by examining our idea of God. Thus, he argues that if, from the fact alone that I can produce the idea of a given thing from my thought, it follows that everything I clearly and distinctly perceive to belong to the thing does in fact belong to it, cannot I also find here a further proof of the existence of God? Certainly, I find the idea of him, that is, of a supremely perfect being, in myself, just as much as I find the idea of any shape or number. And I clearly and distinctly understand that eternal existence belongs to his nature—just as clearly and distinctly as I understand that the properties I can demonstrate of some shape or number belong in fact to the nature of that shape or number. So that, even if not all the conclusions I have come to in my meditations over the past few days were true, I would still have to ascribe the same degree of certainty to the existence of God that I up to now have ascribed to mathematical truths (Descartes 2008, p. 47).

Now Leibniz thinks that there is a missing premise in the Cartesian argument, namely that God is really possible. One might have doubts about the real possibility of God because one might think that just because the predicates that make up the concept of God can be combined in thought, this does not entail that the properties these predicates refer to can be combined in reality; I can form the concept of the highest prime number, but we know that there can be no such thing.

Thus, Leibniz argues in his Mediations on Knowledge, Truth and Ideas, which was published in 1684 (and so would have been available to Kant) that, [a]n argument for the existence of God, celebrated among the Scholastics long ago and revived by Descartes… goes: whatever follows from the idea or definition of anything can be predicated of that thing. Since the most perfect being includes all perfections, among which is existence, existence follows from the idea of God… Therefore, existence can be predicated of God. But one must realize that from this argument we can conclude only that, if God is possible, then it follows that he exists. For we cannot safely use definitions for drawing conclusions unless we know first that they are real definitions, that is, that they include no contradictions… To clarify this, I usually use the example of the fastest motion, which entails an absurdity (Leibniz 1989, p. 25—emphasis added).

So, Leibniz believes that Descartes has only established the conditional claim that if God is (really) possible, then God exists. Leibniz believes, however, that we can prove that God is really possible. Thus, for example, he argues in Paragraph 45 of the Monadology (a text that Kant is known to have read) that,

Thus, only God, or the Necessary Being, has this privilege, that he must exist if he is possible. And since nothing can prevent the possibility of that which contains no limits and no negation, and consequently no contradiction, this by itself suffices to establish the existence of God a priori.

(Leibniz 1991, p. 23)

Here, Leibniz’s argument for the possibility of God seems to be based on the assumption, made explicit in a letter to Duchess Sophia, where he discusses the same argument in more detail, that “all simple forms are compatible with one another” (Leibniz 1991, p. 154). Elsewhere, in a letter to Countess Elizabeth, he argues that “there is always a presumption on the side of possibility, that is, everything is held to be possible unless it is proven to be impossible” (Leibniz 1989, p. 238). Kant would have rejected the “presumption on the side of possibility” as an unjustified dogmatic assumption. And I believe that there is an onus on the side of the defender of the ontological argument to offer some reason to think that finite minds like ours can know that God is really possible. But what about the claim that all simple forms are compatible with one another?

Leibniz tries to provide proof of his claim that true realities cannot contradict each other in his essay ‘That the Most Perfect Being Exists’. In this essay, Leibniz argues that,

I call a perfection every simple quality which is positive and absolute, and expresses without any limits whatever it does express. Now since such quality is simple, it is also irresolvable or indefinable, for otherwise it will either not be one simple quality, but an aggregate of several, or if it is one, it will be circumscribed by limits, and will therefore be conceived by a negation of further progress, contrary to the hypothesis, for it is assumed to be purely positive. Hence it is not difficult to show that all perfections are compatible inter se, or can be in the same substance. For let there be such a proposition such as ‘A and B are incompatible’ (understood by A and B two such simple forms or perfections—the same holds if several are assumed at once), it is obvious that this cannot be proved concerning them… But it could be proved concerning them if it were true, for it is not true per se; but all necessarily true propositions are either demonstrable, or known per se.

(Leibniz 1991, p. 155)

Here, Leibniz argues that we can know that the members of a set of qualities are compatible if we can know that we cannot know that they are incompatible. The relationship of incompatibility is a type of necessity, and all necessary truths are either self-evident or provable.8 Thus, there are only two ways of knowing that the members of a set of qualities are incompatible: either it is self-evident (“known per se”) that the members of a set of qualities are incompatible, or it can be proved that they are incompatible. If it is not self-evident that two qualities are incompatible, then, if we cannot prove that two predicates are really opposed to one another, then we must assume that the combination of the corresponding qualities in one object is really possible. Leibniz, then, thinks that one can prove the consistency of a set of concepts by showing that we cannot know that they are inconsistent.9 As we shall see in Section 1.4 of this paper, Kant offers convincing arguments for the rejection of this principle.

Leibniz distinguishes between what he calls a nominal definition and a real definition. A nominal definition involves combining predicates (what Kant will call “marks”) in thought; to show one has a real definition, one has to show that the thing so defined is really possible.10 Thus, although we can combine the concepts HIGHEST and PRIME NUMBER in thought to produce the concept of THE HIGHEST PRIME NUMBER, this is only a nominal and not a real definition, and we know this as we can offer a proof of the impossibility of such a number. However, Leibniz thinks that in the absence of a possible proof of the incompatibility of the concepts that make up a nominal definition, the definition should be taken as a real definition, for the object so defined must be really possible. Now, Leibniz thinks, it is not possible to prove that God is impossible; therefore, our definition of God must be a real definition, and God must be really possible. Kant will agree with Leibniz that it is not possible (at least for us) to prove that God is really impossible, but he rejects the claim that this entails that we know that God is really possible.

In the rest of this paper, I will explain why Kant came to reject the Leibnizian claim that we can know that God is really possible, or, in other words, that we cannot know that we have a real definition of God. I will begin in Section 1.2 and Section 1.3 by examining Kant’s discussion of the distinction between real and logical opposition in the Amphiboly of the Concepts of Reflection of the Critique of Pure Reason. And then in the Section 1.4, I will reconstruct Kant’s argument as to why the fact that we (as finite discursive intellects) cannot prove that God is really impossible does not entail that (we can know that) God is really possible.

But, before turning to Kant, it is worth making a few observations about Leibniz’s understanding of possibility. As Nachtomy (2017) argues, Leibniz is not a realist or a nominalist about possibility, but a conceptualist who thinks of possibilities as thoughts in God’s intellect.11 And he is also committed to what Nachtomy aptly calls a “combinatorial approach to possibility” (p. 69). Concepts consist of terms, and although any terms can be defined to create a nominal definition, only consistent terms can be combined to form a real definition—that is, the definition of something possible. Now Leibniz believes that all complex concepts must ultimately consist of simple concepts or terms, and be, in principle, analyzable into such concepts. And these simple concepts, which are the building blocks of all complex concepts, are (representations of) what Leibniz calls “perfections” or “realities”. Thus, Leibniz (1992) explains, “I term a “perfection” every simple quality which is positive and absolute, or, which expresses without any limits whatever it does express. But since a quality of this kind is simple, it is therefore indefinable or unanalyzable” (p. 99). Now, these perfections have a different modal status than complex concepts, for as they do not have parts, there is no question as to whether their parts are consistent. So, these simple forms, which are the ultimate constituents of all real definitions, must be actual rather than (merely) possible; they are the grounds of all possibility. And Leibniz ultimately identifies these simple forms with the perfections or simple attributes of God. Thus, Leibniz thinks that God is the ground of all possibility because possibility has to do with the consistency of the combination of terms, and so presupposes the actuality of the real properties (or perfections) that simple terms represent.12

As we shall see, Kant follows Leibniz in his conceptualism and something like combinatorialism about possibility. But he will de-theologize the account, arguing that possibility has to do with the consistency of combining terms by a human finite discursive intellect rather than in a divine mind. As a result of this de-theologization, he rejects the idea that concepts can be decomposed into ultimately simple elements. Leibniz thought that the basic building blocks of (divine) thought must correspond to the simple attributes (perfections) of God. For human thought, there are no simple conceptual building blocks. All concepts contain other concepts as part of their definition;13 for Kant, every concept is a whole that is composed of marks, and (at least some of) these marks themselves are concepts.14 All concepts, for Kant, are complex. So, although a concept can be defined with reference to the terms or “marks” that compose it, we have no way of knowing whether our enumeration of the terms is complete, and no way of knowing whether our analysis of each of the terms that make up our (nominal definitions of) concepts is itself complete. In Kant’s technical vocabulary (to be discussed in the Section 1.4 of this paper), we have no way of knowing whether our definitions are exhaustive and (fully) profound, which are the two features required for any concept to be fully distinct (vol. 9, pp. 62–63). So, Kant rejects the possibility of a complete analysis of any (non-mathematical) concept.15 For all that we know, our enumeration of the marks that make up a concept may be incomplete, or our analysis of the marks that make up the concept may be incomplete. And, as I will argue, we can only show that two concepts are not-inconsistent if we know that the concepts are fully distinct; to demonstrate the real possibility (of the putative object of a concept) we would have to show that the concepts that form part of the nominal definition of the concept are consistent, and without a full analysis of these concepts, this is not possible. So, Kant thinks that the rejection of the possibility of a complete analysis of concepts entails that one cannot prove the real possibility by the analysis of concepts.

1.2. Kant’s Distinction Between Logical and Real Possibility

Kant distinguishes between logical and real possibility and argues that non-contradictoriness is merely a criterion for logical possibility (or what he calls thinkability) and not a criterion for real possibility (which he connects to what he calls cognizability). Kant explains this distinction between thinkability and cognizability in his preface to the second edition of the Critique of Pure Reason, explaining that

To cognize an object, it is required that I be able to prove its possibility (whether by the testimony of experience from its actuality or a priori through reason.) But I can think whatever I like, as long as I do not contradict myself, i.e., as long as my concept is a possible thought, even if I cannot give any assurance whether or not there is a corresponding object somewhere within the sum total of all possibilities (Bxxvi).

In other words, he believes that we can think of things without contradiction, which might actually be impossible. The ideas of pure reason, then, can be thought of as having no apparent contradiction, but this thinking does not lead to cognition because no objects corresponding to them can be given in our spatio-temporal sensible intuition. Thus, for example, in his lectures on metaphysics, he remarks that

The concept of spirit has nothing contradictory in the representation, but whether it is possible that such an immaterial being can exist, this cannot be comprehended… [For] there can nevertheless be objects impossible in themselves that are assumed as possible because their concept experiences no contradiction.

(vol. 29, p. 962—Metaphysik Vigilantius)

To claim that x is really possible is to claim that there could be an intuition corresponding to the concept x. He explains this quite clearly in the Critique of Pure Reason, where he writes that, “[T]he possibility of a thing can never be proved merely through the non-contradictoriness of a concept of it, but only by the vouching of it with an intuition corresponding to this concept” (B307).

As we shall see in the Section 1.4 of this paper, Kant thinks that because we are finite discursive intellects, it is not possible for our concepts to be fully distinct, and the move from conceivability to real possibility is only plausible (even given rationalist assumptions) if we think our concepts are fully distinct.

Now, our form of intuition is spatio-temporal, so the only criterion we have for whether something is really possible is that it can be given in space and time. But it is logically possible that there are other forms of intuition; there is no logical contradiction in the concept of a non-spatio-temporal form of intuition. So, the fact that something cannot be given in space and time does not entail that it is not really possible; this just shows that it cannot be a possible object of our intuition, not that it could not possibly be an object of intuition.16

For example, we may possess ideas of immaterial spirits or of God, and these concepts may contain no contradictions, and so are thinkable (or conceivable), but this does not imply that spirits are really possible. Thus, although the ideas of immaterial spirits and of God contain no contradiction, this gives us no ground for assuming that immaterial spirits or God are really possible. On the other hand, the fact that neither God nor immaterial spirits can be experienced in space and time gives us no reason to assume that they are not really possible. This is why Kant names such concepts, problematic concepts. For although there may be nothing obviously contradictory in the idea of a being that is both omnipotent and omniscient, there may be a de re impossibility involved in the combination of omnipotence and omniscience. The analogy Kant wishes to draw here is something like the following: we can have the concept of a triangle, but we only know that triangles are possible because a triangle can be given in intuition, that is, because we can construct a triangle corresponding to our concept in (the pure intuition of) space. We do not know, however, whether there is any form of intuition in which an actual spirit corresponding to our idea could be given.17 As a consequence, any argument that takes as a premise the claim that spirits, say, are really possible because the idea of a spirit contains no contradiction cannot be sound. This is why no reasoning from ideas can provide us with any knowledge, for any such reasoning must begin with the ungrounded assumption that the putative object of the idea is really possible.18 Working out the conceptual relationships between, say, our ideas of spirit, world, and God, however, does not involve any appeal to the real possibility of the (putative) objects of these ideas, and so is a legitimate form of inquiry, so long as we do not make the further assumption that such investigations can provide us with knowledge of objects.

Lying behind this position is a radical reconceptualisation of modal properties. For Kant, modal categories are not properties of objects, but instead concern the relationship between concepts and objects. When we claim that “unicorns are possible”, we are not asserting something about the nature of unicorns. Instead, we are making the claim that there could be an object corresponding to our concept “unicorn”. A more Kantian way of putting this would be to say that to claim that “unicorns are possible” is to claim that an object could be given in intuition corresponding to the concept “unicorn”. Such an account of modal claims rests upon distinguishing between the faculty through which concepts are thought (the understanding) and the faculty through which objects are given, and Kant calls the faculty through which objects are given the faculty of intuition. Kant’s radical reconceptualization of modality, then, lies behind the distinction he draws between understanding and intuition—although this does not entail anything about our particular form of intuition.

The distinction between the understanding and intuition, then, was not introduced primarily to explain the particular nature of actual human experience, but is necessary for more abstract reasons, having to do with his logic. Specifically, Kant believes that the distinction between a faculty of thinking and a faculty through which objects are given (intuition) is necessary to conceptualize adequately what is going on in modal judgments, and, in particular,, the distinction between the real and the logical use of modal concepts. This distinction between the real and logical use of modal concepts is a distinction that is needed when we engage in what Kant calls, in the Amphiboly, “transcendental reflection”. Kant makes this clear in the Critique of Judgment. Here, he argues that

For if two entirely heterogeneous elements were not required for the exercise of these faculties, understanding for concepts and sensible intuition for objects corresponding to them, then there would be no such distinction (between the possible and the actual)… all of our distinction between the merely possible and the actual rests on the fact that the former signifies only the position of the representation of a thing with respect to our concept and, in general, our faculty for thinking, while the latter signifies the positing of the thing in itself (apart from this concept).

(vol. 5, p. 402)19

The reason for this connection between Kant’s analysis of modal properties and his commitment to a distinction between the faculties of understanding and intuition is that if we reject the position that the non-contradictoriness of a concept is an adequate criterion of real possibility, we need to appeal to some other, non-logical criterion for real possibility. Non-contradictoriness is merely a criterion for whether a concept can be thought by us. Real possibility, Kant thinks, has to do with whether an object can be given that corresponds to the concept, and this is a question that cannot (in principle) be answered merely by analyzing the concept. Pure logic alone cannot, in principle, answer questions about real possibility, nor, as a consequence, questions about existence. Any being that can make the distinction between actual and merely (logically) possible objects must possess both a faculty through which objects are given (a faculty of intuition) and a faculty through which objects are thought (the understanding).

Let us now turn to Kant’s argument in the Second Amphiboly, which helps us understand what he thought was wrong with traditional rationalist arguments for the existence of God, the World, and the Soul, and why Kant was compelled to distinguish between the faculties of understanding and intuition.

1.3. The Second Amphiboly: Logical and Real Opposition

In the Second Amphiboly, Kant distinguishes between logical and real opposition and argues that the fact that two marks can be combined together in thought does not entail that the realities these two marks represent can actually be combined in reality.20 And he claims that Leibniz’s argument for the real possibility of God rests on a failure to make this distinction. Before examining Kant’s arguments in the Second Amphiboly, I will begin by saying a few words about the Amphiboly in general, as the Second Amphiboly needs to be understood in context.

The title of the Amphiboly of the Concepts of Reflection raises two obvious questions: (a) What is an amphiboly? And, (b) What are the concepts of reflection? Strictly speaking, an amphiboly is an ambiguous sentence in which the ambiguity does not depend upon the equivocation of any particular words, but upon its grammatical structure. Thus, for example, “I shot the elephant wearing my pajamas” is an example of an amphiboly. However, the term is often just used to mean an equivocation, and this is, I assume, how Kant is using the term.21 Thus, the amphibolies Kant discusses in the Amphiboly section of the Critique are not really cases of amphiboly in the strict sense but are actually cases of equivocation.22

In the first paragraph of the Amphiboly, Kant introduces four pairs of concepts, which he calls concepts of reflection, that we use in comparing representations: (1) identity and difference, (2) agreement and opposition, (3) the inner and the outer, and (4) the determinable and the determination (matter and form). In the introductory remarks to the Amphiboly, Kant explains that his aim is to engage in what he calls transcendental reflection. And, as he explains in his logic lectures, to reflect is to “see to which power of cognition a cognition belongs.” (vol. 9, p. 73).

Now Kant believes that representations can have their source either in the understanding (concepts and ideas) or in intuition (intuitions) or can have a mixed source (such as cognition involving schematized concepts). One type of possible equivocation, then, would be to confuse the concept of a (putative) intelligible object with a possible object of experience. And the equivocations identified in the Amphibolies involve taking principles that would govern the application of the concepts of reflection to putative intelligible objects as if they were applicable to possible objects of experience; and/or taking the principles that govern the application of the concepts of reflection to sensible objects as if they were applicable to putative intelligible objects. The first type of mistake is characteristic of rationalists who tend to intellectualize the sensible; the second type of mistake is characteristic of empiricists who tend to sensualize the intelligible. So, the equivocations identified in the Amphibolies have to do with confusing what Kant calls a (purely) logical use of the concepts of reflection and a real use of these concepts.

Kant argues, then, that we can distinguish between a purely logical and a real use or sense of the concepts of reflection, and an amphiboly occurs when we equivocate between purely logical use of the concept and a real use of the concept. Insofar as the concept of reflection is used in a purely logical sense, then the use of this concept will be governed by a principle that is appropriate for intellectual representations. Leibniz’s mistake, according to Kant, is to assume that such principles necessarily apply to things in general, including phenomena. Thus, for each of the four concepts of reflection, there is an amphiboly based upon confusing two different uses of the concept, one purely logical and one real. As a result of this confusion, Kant thinks that the Leibnizians mistakenly assume that principles that govern things taken purely intelligibly also apply to phenomenal objects; this is the sense in which he thinks they “intellectualize appearances”.23 Thus, for each amphiboly we should be able to, firstly, identify a distinction between a purely logical and at least one real use of the concept of reflection, and, secondly, identify the principle, which I will call the amphiboly principle, that Kant thinks applies to intelligible objects (if any exist) but not to phenomenal objects. Before turning to the Second Amphiboly, let me begin by illustrating the general schema of the Amphibolies by sketching the claims of the other three Amphibolies.

The First Amphiboly (A263-4/B319-20) concerns the concepts of identity and difference. And the amphiboly principle that applies to intelligibilia but not to phenomenal objects is the principle of the identity of indiscernibles. The logical sense of identity is one that is tied to the faculty of understanding, and to be identical in this sense means to fall under the same concept. The real sense of identity, in contrast, has to do with the faculty of intuition, and given the fact that our form of intuition is spatio-temporal, the only way we can individuate and re-identify objects is in terms of their spatio-temporal location. The Third Amphiboly has to do with the concepts of inner and outer, and the principle that Kant thinks legitimately applies to intelligibilia (but not to phenomena) is the principle that all substance must have some intrinsic nature.24 Kant argues that this principle is true of intelligible objects, but does not apply to phenomena because the inner (“deep” as opposed to “surface”) properties of material substances are themselves outer (“extrinsic”) in the logical sense. The Fourth Amphiboly has to do with the distinction between the concepts of matter (the determinable) and form (the determination), and the amphiboly-principle that Kant identifies is the principle that matter must be prior to form. This is true as a logical principle, for logically the genus (as determinable) is prior to the species, as one must add a specific difference (a determination) to the genus (the determinable) to logically determine a species. But this principle does not hold of phenomenal objects because for such objects the spatio-temporal form of intuition is prior to physical matter; space and time make objects of possible experience possible and not vice versa.

The plausibility of Kant’s arguments here depends upon what he means by intelligibilia. If we identify intelligibilia with things in themselves, then Kant’s arguments would seem highly implausible. For example, the principle of the identity of indiscernibles seems to be a principle that governs conceptual identity, so two concepts are the same concept if they contain the same marks. It is in this sense that the principle is a logical one. But why should we assume that the principle is one that governs the putative objects of our ideas of pure reason? I take it that the illusion involved in the dialectic is that in the case of ideas of pure reason, we take our ideas to be thoughts of their objects and so confuse the concept with the object and then take conditions for the thinkability of the concept with conditions for the being of the (putative) object. If we think there is a radical distinction between the concept of an intelligible object and the object itself, then why should we think that conditions for the concept of the object are ontological conditions for the possibility of the object of the concept?

So, on my preferred reading, intelligibilia are not really objects at all. Rather, when Kant talks about intelligibilia, he is talking about our ideas, which reason conflates with cognitions of objects. This taking of our ideas of pure reason to be intuitions of objects is what Kant calls transcendental illusion. So, Kant’s claim is not that the real principles apply to phenomena and the (merely logical) principles govern the application of the concepts of reflection to things as they are in themselves, but that the logical principles are principles that apply to concepts (understood widely to include ideas) and that we have no (theoretical) principles for applying the concepts of reflection to things as they are in themselves.

Let us now, finally, turn to Kant’s argument in the Second Amphiboly, which concerns what Kant takes to be Leibniz’s conflation of what Kant calls logical and real opposition. The amphiboly principle here is that realities cannot oppose one another. This is, Kant thinks, a correct logical principle in the sense that positive predicates cannot logically exclude one another, and so is a criterion of conceivability. But this principle does not apply to phenomenal objects in space and time, because physical forces are (phenomenally) real, but they can oppose one another and cancel each other out. Also, positive properties (such as being-red and being-green) can exclude one another in reality in the sense that a single phenomenal object cannot be both red and green at the same place and time.

Thus, in the Second Amphiboly (A264-5/B320-1) Kant discusses the concepts of agreement and opposition and introduces a distinction between what we may call logical and real opposition.25 Here is the full text of the “Second Amphiboly”:

Agreement and opposition. If reality is represented only through the pure understanding (realitas noumenon), then no opposition between realities can be thought, i.e., a relation such that when they are bound together in one subject they cancel out their consequences, is in 3 − 3 = 0. Realities in Appearance (relitas phaenomenon), on the contrary, can certainly be in opposition and with each other and, united in the same subject, one can partly or wholly destroy the consequences of the other, like two moving forces in the same straight line that either push or pull a point in opposed directions, or also like an enjoyment that balances a scale against a pain (A264-5/B320-1).

And in the second remark on the Amphibolies, he draws the conclusion that “the principle that realities (as mere affirmations) never logically oppose each other is an entirely true proposition about the relations of concepts, but signifies nothing at all either in regard to nature nor overall in regard to anything itself” (A272-3/B329) Leibniz and Wolff, however, mistook this logical principle for a real principle that applies to things in general, and this mistake plays a major role in driving the rationalist metaphysics that Kant is responding to in the First Critique. Thus, Kant explains that “[a]though Herr von Leibniz did not exactly announce this proposition with the pomp of a new principle, he nevertheless used it for new assertions, and his successors expressly incorporated it into their Leibnizian-Wolffian doctrine” (A273/B329). In particular, Kant argues that a commitment to this principle played an important role in rationalist theology, as adherents to this principle, “find it not merely possible but also natural to unite all reality in one being without any worry about opposition, since they do not recognize any opposition except that of contradiction… and do not recognize the opposition of reciprocal destruction, where one real ground cancels out the effect of another” (A274/B330). As we have seen, this is the principle that Leibniz appeals to in his attempt to prove what he took to be a missing premise in Descartes’ ontological proof, namely a proof that God is really possible. Leibniz argues that we can unite all realities in one being, God, because realities cannot oppose one another. It is Kant’s rejection of this principle, and his distinction between real and logical opposition, that fundamentally lies behind his break with rationalist metaphysics and also motivates drawing a distinction between the faculties of understanding and intuition.

Kant’s claim in the Second Amphiboly, then, is that the Leibnizians, and rationalist metaphysicians in general, fail to make a distinction between logical possibility and real possibility; that is, they assume that if a concept is thinkable, then the purported object of such a concept is really possible. Kant’s critical turn involves a rejection of this assumption. In the following section, I will attempt to reconstruct Kant’s arguments for the rejection of this principle.

1.4. Kant’s Rejection of Leibniz’s Principle

Let us return to Leibniz’s principle that we started to discuss at the end of Section 1.1. There, I argued that Kant rejects the Leibnizian principle that “all necessarily true propositions are either demonstrable, or known per se”, and I showed how Leibniz appeals to this principle in his argument for the claim that conceivability entails real possibility. We are now in a position to examine why Kant rejects this principle. His arguments have to do with the fact that we have finite discursive intellects and, as such, we can never know that the analysis of any of our concepts is complete. For, as Kant claims in a note in his edition of Meier’s logic textbook, “[i]n consciousness there are marks. But where marks are represented, there is not always consciousness.” (vol. 16, p. 296). Through analysis of our concepts, we become more fully conscious of the marks that (already) belong to our concepts. Now, even if we buy into the assumption of the rationalist logicians that concepts can only be made distinct through analysis, we can only show that two concepts can be combined without contradiction if the concepts themselves are distinct. For without this, it is possible there are inconsistencies that we are (as yet) not conscious of. So, even given the rationalist’s own assumptions, the fact that the concepts that are combined in a concept appear consistent can only prove that they are consistent if we possess a complete analysis of the concept. But analysis is not the only way that a concept can become distinct. Thus, Kant explains in his Jäsche Logic,

Logicians of the Wolffian school place the act of making cognitions distinct entirely in the mere analysis of them. But not all distinctness rests on analysis of a given concept. It arises thereby only in regard to those marks that we already thought in the concept, but not in respect to those marks that are first added to the concept as parts of the whole possible concept. // The kind of distinctness that arises not through analysis but through synthesis of marks is synthetic distinctness. And thus there is an essential difference between the two propositions: to make a distinct concept and to make a concept distinct (vol. 9, p. 63).

Unlike the case of mathematics where the mathematician is able to offer stipulative definitions of concepts, whose real possibility can be demonstrated by construction in intuition, in the case of philosophy our concepts, including our concept of God, are given to us “confusedly” or “in an insufficiently determinate fashion” (vol. 2, p. 291) and are in need of definition.26 For Kant, the definition of a concept involves listing each of the concept’s “marks” (Merkmale). At least some of these marks, however, will also be concepts, and so will also be potentially definable.27 For any concept, a full definition (or what he often calls a “complete determination”) will involve two things: Firstly, we must determine for each and every possible predicate whether it belongs to the concept or not. Secondly, each concept that forms part of the definition of the concept must itself be distinct. In the Jäsche Logic (vol. 9, pp. 62–63) Kant labels these two aspects that are required in the ideal of complete distinctness of a concept, exhaustiveness and profundity. Thus, Kant explains that, as for what concerns logical distinctness in particular, it is to be called complete distinctness insofar as all the marks which, taken together, make up the whole concept have come to clarity. A completely distinct concept can be so, again, either in regard to the totality of its coordinate marks or in respect to the totality of its subordinate marks. Extensively complete or sufficient distinctness of a concept consists in the total clarity of its coordinate marks, which is also called exhaustiveness. Total clarity of subordinate marks constitutes intensively complete distinctness, profundity (vol. 9, p. 62).

Now, we can only know that our definition is exhaustive if we know for each possible predicate whether or not the predicate belongs to the definition or not. However, for this to make sense, it presupposes that there is a complete list of all possible predicates. And Kant thinks such a list is impossible. Instead, Kant thinks that the set of all possible marks is indeterminate. So, the idea of a “complete analysis” of any given concept is impossible because we can never know whether or not the definition is exhaustive. The only exhaustive definitions are stipulative definitions, such as those we find in mathematics.

We cannot know that our definition of any concept is profound.28 Because we can never know that a definition of a given concept is exhaustive, we can never know that a definition is profound, as we cannot know whether the concepts that form part of the definition of a given concept are themselves defined exhaustively. For a definition to be profound, all the concepts that make up the concept have to be completely distinct. I assume that Kant thinks that even stipulative mathematical definitions cannot be made fully profound in this way, and so even mathematical concepts cannot be made completely distinct.29

For any analysis one has given, for all that we know, further marks may be added to the concept, or to the marks of the marks, or the marks of the marks of the marks, etc.

Absence of a proof of the incompatibility of two concepts (say OMNIPOTENCE and OMNIPRESSENCE) does not entail that there is no possible proof, for perhaps after further elucidation of the concepts, we will be able to show that the two concepts are incompatible. The only justification for moving, as Leibniz does, from the lack of a proof of real incompatibility to the real possibility of two concepts being combined is if a complete analysis of each concept is possible (in principle). If we reject the possibility of a complete analysis of a concept, then the apparent compatibility of two concepts does not entail real compatibility, as further elucidation of the concepts (which requires an appeal to intuition) might reveal incompatibility. So, even assuming, as the rationalist does, that a concept can only become distinct through analysis, we have no good reason to assume that our concept of God is, or could be made, fully distinct. And without this, we cannot know that there is some hidden contradiction in the concept.

But Kant has a further argument that goes beyond the assumptions of the rationalist. Because the concept of God not only needs to be made fully distinct, but in order to know that God is really possible, we need to make a fully distinct concept of God. And this we cannot do. Kant’s most significant claim here is the claim that we should not take the full list of all possible marks as something given, even in principle, to an ideal intellect. He thinks that, for us, new marks are discovered through empirical investigation of objects given in space and time. This is how we make a more distinct concept of an empirical object. And for any given concept, we can ask whether the new mark belongs to the concept or not. As our concepts are clarified in this way, we may discover that things that seemed compatible are not compatible. So, even from our perspective as beings with a spatio-temporal form of intuition, we may come to discover that concepts that we thought were compatible turn out to be incompatible. But things are even worse than this, as there may be marks that only beings with another form of intuition could understand, and so it is logically possible that intellects with another form of intuition may be able to prove that there is a contradiction involved in the idea of a being that is both OMNIPOTENT and OMNISCIENT. Given the fact that the concept of a non-spatio-temporal form of intuition is logically possible, it is logically possible that there could be a discursive intellect that could prove that the concept of God is really impossible. So, it is conceivable that GOD is really possible, and it is conceivable that GOD is really impossible.

Kant’s point here is that to prove logically that two concepts are really compatible would involve a complete determination of each concept. But such a complete determination of concepts is impossible. Any analysis is indefinite, and ultimately, how concepts are further determinable depends upon the nature of the possible objects of these concepts. So, it is possible that there are necessary truths about incompatibilities that are not demonstrable (at least by us). Leibniz’s assumption that all necessary truths are either self-evident or demonstrable (by us) underwrites his claim that positive realities cannot oppose one another, but this claim rests on the assumption that a complete analysis of any concept is (at least in principle) possible. But this is precisely what Kant denies when he claims that concepts are essentially general. For beings with finite discursive intellects need to make our concepts of objects distinct, and we can only do this by discovering what is and can be given in intuition. Given the finite, discursive nature of our intellects, we cannot know whether God is really possible or not.

2. Conclusions

Unlike most readers of Kant, I believe that Kant’s (epistemic) argument that we cannot know that God is really possible is a more powerful argument against the ontological argument than the one based on the (semantic) claim that existence is not a real predicate. The reason for this is that the (semantic) claim that existence should not be used as a real determinate predicate is a contested claim amongst logicians. There are clearly logical systems in which there are determinate existence predicates and logical systems in which there are not. Those systems that use a determinate existence predicate treat the so-called “existential” quantifier as not having existential import. And it seems that the decision about which logic to adopt here is a matter of inference to the best explanation.30 There are plausible arguments in favor of logics that use a real existence predicate (as well as plausible arguments for logics that do not use such a predicate). And I think the fact that a plausible case can be made for existence being a real predicate is enough to get the ontological argument started. I do not think, dialectically, that the onus is on the defender of the ontological argument here to prove that the best logical system is one in which there is a real existence predicate. So, to start an argument against the ontological argument with the claim that existence is not a real predicate is to just beg the question against the defender of the ontological argument.

In the case of the epistemic argument that we cannot know that God is really possible because this would require us to know that our concept of God were fully determinate, things are different dialectically, and that the onus is on the defender of the ontological argument to offer some reason to think that we can know that God is really possible or, what comes to the same thing that we have a real definition rather than merely nominal definition of “God”. The argument here is epistemic, and Kant has given an argument to the effect that we cannot know that we have a real definition of “God”, and I think that the onus is now on the defender of the ontological argument to show that we do have a real definition, that we can know that God is really possible. Kant has convincingly offered a prima facie plausible argument for the claim that finite intellects cannot know that God is really possible, as we can only be sure of the real possibility of non-sensible objects if we know that our ideas of them are completely distinct, and even if it were (per impossibile) possible to make our idea of God completely distinct, we would not be able to know that our idea was completely distinct.31 This argument amounts to the claim that, at least as far as we can know, we have a merely nominal definition of God and there is no way for finite minds to know whether a real definition is possible. Given that the ontological argument can only work if we have a real definition of God, I think the onus is on the defender of the ontological argument to show that we do, or can, have a real definition of God. And I do not see how they can do this. For this reason, I believe this is Kant’s most effective argument (dialectically) against the proponent of the ontological argument.