Does the ontological proof of God’s existence really contain all the probative force of the cosmological argument? The early criticisms of Kant’s thesis by Flatt, Abel and Eberhard

1 Kant’s main criticism of the cosmological proof, reduced to formal arguments, and the two chief approaches to discussing it

Kant’s main criticism of the cosmological proof can be summed up in a series of formal arguments. The first is the following compound syllogism, which takes the form of a “sorites” or “chain syllogism”:

In order to obtain as a conclusion Kant’s explicit claim concerning the cosmological proof, this inference chain has to be completed with the following:

Before considering these two arguments, a terminological remark on the logical question of the conversion of judgments or propositions is in order. The terms used by logicians may be misleading, as sometimes the original given judgment is called the judicium conversum, and at other times the same name is given to the judgment resulting from the conversion. The issue may be clarified by looking at the treatment of the conversio from two perspectives. Firstly, the logical operation of the conversion of a judgment into another can be considered. From this point of view, the original given judgment, i. e. the term a quo of the logical process, is referred to as the judicium convertendum, and the derivative judgment, the result of the immediate inference, i. e. the term ad quem of the conversion, is called the judicium conversum.

Secondly, however, it is also possible to pay attention to the logical relationship between the propositions, which are such that, when their terms are inverted (whether or not their quantity is changed) and when their quality is preserved, they nevertheless necessarily express the same truth. From this perspective, the judgment that is the term a quo of the conversion is often referred to by logicians as the judicium conversum (converse judgment, umgekehrtes Urteil), and the judgment that is the term ad quem of the conversion is referred to as the judicium convertens (converting judgment, umkehrendes Urteil), perhaps by analogy with a judgment that opposes another given judgment (the latter, in fact, is usually called the judicium oppositum and the former the judicium opponens). Georg Friedrich Meier, in his Excerpts from the Doctrine of Reason,^[9] and Kant himself, in his lectures on logic – in which Meier’s compendium was used as a textbook – adhere to this second use of the terms.^[10] As we will see, Eberhard also adheres to this terminology in his criticism of Kant’s claim about the cosmological proof.

It is worth adding that the logical doctrine of the conversion of propositions is in close connection with the theory of syllogism and the possibility of reducing the four traditionally accepted figures to the first figure.^[11] The reduction of a syllogism is then ultimately a matter of regressing, so to speak, from a premise that is considered derived to an original premise that we need to search for. It is important to note that the proposition whose truth is considered derived is the converse proposition (propositio conversa) – or, if preferred, the propositio convertendum, the given judgment to be converted – while the proposition whose truth is considered more original is the converting proposition (propositio convertens), i. e. the propositio conversa, the product of the logical operation of conversion.^[12]

These terminological clarifications, then, sufficiently explain the meaning of “Kant’s additional syllogism 1” and the aims pursued by the philosopher. To claim that the ontological proof contains all the probative force of the cosmological proof is tantamount to asserting that the proposition that expresses the nervus probandi of the cosmological argument (propositio conversa) can be reduced to a more original one, precisely that which expresses the nervus probandi of the ontological argument (propositio convertens) – or, in other terms, that the proposition on which the ontological proof rests (propositio conversa) is convertible to the proposition on which the cosmological proof is based (propositio convertendum). Use of this syllogism is intended to achieve two main aims. The first, as just stated, is to expressly point out that the cosmological proof surreptitiously resorts to the ontological, to the extent that it is basically the same argument, just that its “clothing and voice” (Anzug und Stimme) have been altered (KrV, A 606/B 634). The second is to implicitly state that the cosmological proof incurs the same logical errors that brought Kant to assert “the impossibility of an ontological proof of God’s existence” ([…] d[ie] Unmöglichkeit eines ontologischen Beweises vom Dasein Gottes) (KrV, A 592/B 620). If the probative force of both proofs of God’s existence is the same, because the cogency of one is reduced to that of the other, and if the ontological proof is invalid, then the cosmological proof will also necessarily be invalid.

As for “Kant’s sorites”, the first and third propositions merely state Kant’s conception of both the cosmological and the ontological proofs. As regards the ontological argument, it is well known that Kant views it as the “proof of the existence of a highest being from concepts” (KrV, A 602/B 630).^[13] Interpreted this way, the argument consists of the ambitious aspiration of inferring existence from the concept of the ens realissimum, i. e. from the concept of a being that has all perfections, among which existence cannot be absent. In general terms, therefore, the nerve of the argument, as the third proposition claims, is the statement “Every most real being is at the same time an absolutely necessary being.”

As regards the cosmological argument, it is also well known that Kant identifies two steps within it. The first is the transit from the ascertainment that something, whatever it may be, exists to the claim that then “an absolutely necessary being also has to exist” (KrV, A 604/B 632).^[14] The second step is the need to “determine” (bestimmen) the concept of an absolutely necessary being, i. e. to analyse which predicates correspond to such a being. Since, with regard to each possible pair of opposed predicates, an absolutely necessary being can only be determined by one of them, “it must be thoroughly determined through its concept,” i. e. a priori.^[15] But, as Kant continues, “only one single concept of a thing is possible that thoroughly determines the thing a priori, namely that of an ens realissimum” (KrV, A 605/B 633; see V-Phil-Th/Pölitz, AA 28: 1029–30).^[16] Thus, the second and decisive step of the cosmological argument for affirming the existence of God consists in the transit from the absolutely necessary being to the most real being. Kant attributes this step to Leibniz himself: “Leibniz needed the ontological proof to finalise the cosmological one” (V-Met-L2/Pölitz, AA 28: 599, my translation).^[17] It is thus easy to see that, according to Kant, the nerve of the proof lies in the general contention, expressed in the first proposition of the chain syllogism, that “Every absolutely necessary being is at the same time the most real being.”

The proof of the second proposition of the sorites is presented by Kant “in a scholastically correct way” (auf schulgerechte Art) (KrV, A 608/B 636), which Flatt quotes at length at the beginning of his essay (see EKC: 94). Kant’s reasoning runs as follows:

If the proposition is correct: “Every absolutely necessary being is at the same time the most real being” (which is the nervus probandi of the cosmological proof), then like any affirmative judgment, it must be convertible per accidens, thus: “Some most real beings are at the same time absolutely necessary beings.” But now one ens realissimum does not differ the least bit from another, and thus what holds of some beings contained under this concept holds also of all. Hence I will also be able (in this case) to convert the proposition absolutely, i. e., “Every most real being is a necessary being.” Now because this proposition is determined merely from its concepts a priori, the mere concept of the most real being must also carry with it the absolute necessity of this being – which is just what the ontological proof asserts and the cosmological proof does not want to recognize, despite the fact that it underlies its inferences, though in a covert way. (KrV, A 608–609/B 636–637).^[18]

The core of Kant’s argument, which resorts to the already mentioned logical doctrine of the conversion of propositions (see Log, AA 09: 118 – 119), can also be summarised in syllogistic form:

Just as in the case of “Kant’s additional syllogism 2,” the conclusion of both the “sorites” and the “additional syllogism 1” also follow from their premises. Certainly, any two things equal to a third thing are equal to each other. The nervus probandi of the cosmological proof expresses the same truth as the nervus probandi of the ontological proof. Therefore, the cosmological argument is reduced to the ontological one, or, more accurately, the ontological proof in fact contains all the probative force of the cosmological one.^[19]

Quite clearly, the rejection of the conclusion of the “sorites” (and, consequently, of the subsequent “additional syllogism 1” as a whole), which has such disastrous consequences for the cosmological argument, can only be based on the refutation of the first and the third propositions, or of the second proposition, or of all three propositions together. There will then be objections based on the denial of the first and the third propositions. In this first challenge to Kant’s claim, objections focused on the description of the cosmological argument contained therein can be expected. For, in principle, it can be argued that the transit from the absolutely necessary being to the most real being does not occur in other possible versions of the cosmological argument. Thus, Kant’s criticism, even if it were correct, would not affect all versions of the proof. But objections that, in addition, consider the characterisation of the ontological proof can also be foreseen. For it is possible to cast doubt on whether the concept of an “absolutely necessary being” has the same meaning in the ontological and the cosmological proof.

There will also naturally be objections grounded in the refutation of the second proposition of the chain syllogism and, consequently, in the rejection of the “additional syllogism 2”. In this second opposition to Kant’s criticism of the cosmological proof, objections of three kinds are to be expected. Some of them will point out certain assumptions invalidating the inference. Other criticisms will try to show that the conversion of the propositions in question, even if legitimate, in no way affects the validity of the cosmological proof. Lastly, some other criticisms will claim that the reasons invoked in no way demonstrate the reciprocity of the concepts of a “most real being” and an “absolutely necessary being”.

These two chief approaches to discussing Kant’s main criticism of the cosmological proof, and almost all of the possibilities opening up before them, were employed by the early critics of Kant’s claim. Thus, the first objection proposed by Flatt in his essay in the Philosophisches Magazin (preceded by that posed by Abel in his 1787 book) attacks the first proposition of the “sorites”, in order to show the irrelevance of Kant’s criticism to other possible versions of the cosmological argument. Flatt’s second objection focuses on the second proposition of the chain syllogism and, consequently, on the “additional syllogism 2”. It tries to highlight a misunderstanding that invalidates the pure or absolute conversion of the nervus probandi of the cosmological argument into that of the ontological argument. On the other hand, Eberhard’s two objections also examine the second proposition of the “sorites” and, therefore, the “additional syllogism 2”, but also the soundness of the “additional syllogism 1”, in order to show the unacceptability of Kant’s claim concerning the dependence of the cosmological proof on the ontological one. Let us, then, consider these four objections separately.

2 Flatt’s (and Abel’s) first objection: objection based on the different possible versions of the cosmological proof

Flatt’s first objection is directed at the Kantian characterisation of the cosmological argument. Certainly, in the first proposition of the above “sorites”, Kant considers one possible version of the proof, which some thinkers have undoubtedly defended. But it is not in every possible or historically given version of the argument that “the highest reality of the original being” is inferred “merely from the absolute necessity of its existence” (EKC: 95). Hence Flatt’s claim regarding Kant’s conclusion: “Even if this conclusion were perfectly compelling, the objection based on it would only concern one, not all the variants that can be given, and have really been given, of the cosmological proof” (EKC: 94).

As previously stated, to illustrate the possibility and actuality of other versions of the argument, Flatt invokes Abel’s teachings in his 1787 An Attempt on the Nature of Speculative Reason. Confronting the narrow and partial Kantian conception of the cosmological proof, Abel teaches, as Flatt recalls, that, strictly speaking, if in the proof “the highest reality were to be inferred merely from the necessity of existence, it would indeed be quite the same case [as in the ontological proof], because then one could convert the proposition according to the rule, and infer the necessity of existence from the highest reality” (VNsV: 262). But this is not the case at all, because the cosmological proof infers the supreme reality of God “from the fact that in it we search for the source of all possible realities and of spirits in particular, which does not happen in the same way in the mere ontological argument” (VNsV: 262).

Flatt goes one step further. He tries to show that Kant himself, if he does not want to incur a manifest inconsistency, would have to accept at least the possibility of the version of the cosmological argument indicated by Abel, perhaps the first to propose such an objection to Kant’s famous contention regarding the cosmological argument. According to Flatt, on the one hand, Kant “admitted that the existence of limited beings is demonstrable by theoretical reason.” On the other hand, he “did not deny to this [i. e. theoretical reason] the right to transfer subjectively necessary principles to the objective” (EKC: 95). In this regard, Flatt cites the essay published by Kant in the Berlinische Monatsschrift, October 1786. In “What does it mean to orient oneself in thinking?” Kant indeed claims that “not only does our reason already feel a need to take the concept of the unlimited as the ground of the concepts of all limited beings”, “but this need even goes as far as the presupposition of its existence, without which one can provide no satisfactory ground at all for the contingency of the existence of things in the world.” (WDO, AA 08: 137 f).^[20]

Thus, Kant seems to admit that in the cosmological proof, God’s highest reality is inferred not merely from the absolute necessity of its existence, but above all from the fact that the unlimited being is the ground and source of all limited realities encountered in the world. Therefore, Kant would have to recognise – such seems to be the result of Flatt’s considerations – the restricted scope of his critique of the argument a contingentia mundi. At best, then, Kant’s criticism would not concern all possible versions of the cosmological proof.^[21]

Kant undoubtedly knew the obvious historical fact pointed out by Flatt and Abel, namely, that there are forms of the cosmological argument in which the supreme reality of God is not inferred merely from the contingency of the world. As Flatt illustrates, Kant knew the cosmological argument to which Abel refers in his criticism, i. e., the one based on the finitude or limitation of the beings in the world. In his lectures on rational theology, Kant also mentions the celebrated de primo motore proof, devised by the ancients, founded on motion in the corporeal world. Why does Kant not consider these and other possible variants of the argument as genuine cosmological proofs?

This question reveals the different, indeed opposite, assumption underlying Flatt’s and Abel’s objection and Kant’s conception of the cosmological proof. For Kant’s critics, the cosmological proof may have its starting point in any “universal fact of experience”, so to speak, of the world’s beings, whether it be their contingency or their finitude or the movement to which they are subject. Instead, according to Kant, “although the cosmological proof is grounded on an experience in general, it is not carried out on the basis of any particular constitution of experience, but on pure principles of reason in relation to an existence given through empirical consciousness in general” (KrV, A 614/B 642).^[22] “Experience in general” (Erfahrung überhaupt) is by no means equivalent to “a universal fact of experience”. The term is synonymous with “possible experience” or “formal conditions of experience,” according to the other names used by Kant. These subjective and formal conditions are only known a priori, and they alone make experience possible, as Kant states (see KrV, A 230/B 283). The formal conditions of experience include agreement with the concept of contingency, a pure concept of understanding. Any genuine cosmological proof can therefore only be based on contingency. For this reason, the “important difference between the two proofs” (VNsV: 262), the ontological and the cosmological, asserted by Abel, is not significant at all for Kant. Both proofs, Kant claims, “were attempted transcendentally, i. e., independently of empirical principles” (KrV, A 614/B 642).^[23]

Thus, while a fundamental tenet of transcendental idealism is the difference between the form and the matter of experience, this distinction is completely alien to the proponents of the a contingentia mundi argument. Beyond the obvious claim that Kant does not take into account other versions of the cosmological proof, Flatt’s (and Abel’s) first objection seriously calls into question the success of Kant’s criticism: is the distinction between the matter and the form of experience a truth that is proven as a consequence of the “impossibility of a cosmological proof of God’s existence” (d[ie] Unmöglichkeit eines kosmologischen Beweises vom Dasein Gottes) (KrV, A 603/B 631), or is it rather an assumption that precedes the criticism of such a proof?

3 Flatt’s second objection: objection based on the four possible meanings of the proposition enunciating the nervus probandi of the cosmological proof

Flatt’s second objection concerns the absolute conversion of the proposition that recaps the nervus probandi of the cosmological argument. This new criticism tries to show that the validity of the cosmological proof is in no way affected, either by the logical possibility or by the impossibility, of the simple or absolute conversion of such a proposition.

Flatt’s reasoning is intricate and frankly not too clear. But perhaps it can be reconstructed in a free and self-standing way, although true to its original purpose, as follows:

Indeed, Flatt discovers an ambiguity in the proposition that expresses the nervus probandi of the cosmological proof. To avoid it, he appeals to two distinctions. On the one hand, the “absolutely necessary being” and the “most real being” can be understood either “out of my representation (außer meiner Vorstellung)” or “in my idea (in meiner Idee)” (see EKC: 96).^[24] On the other hand, both “out of my representation” and “in my idea” can be understood either “as a determination of the predicate: the most real being, or as a determination of the concept of being” (EKC: 96), i. e. either as one of the real predicates of the concept of an ens realissimum or as a (non-real) predicate expressing the mode of being of the most real being. Flatt does not address the question of whether any of the possible meanings of the proposition faithfully reflect the genuine core of the cosmological proof. He only wants to show that, in none of the four possible cases in which the nervus probandi of the cosmological proof can tentatively be understood, does “the conclusion that Kant tries to prove” come about (EKC: 96).

Certainly, the converting proposition under consideration – “Every being that possesses the highest reality out of our representation also has an absolutely necessary existence out of our representation” – “can be considered true”, Flatt states, “without the need to recognise the Cartesian proof as valid” (EKC: 96). Flatt does not even consider it necessary to point out that the ontological proof, in Kant’s own view, consists of affirming a very different proposition, namely that a being that possesses the real predicate of the highest reality in our idea also possesses the (allegedly) real predicate of the absolutely necessary existence out of our representation. Indeed, it is not in vain that Kant characterises the ontological argument as the proof of the existence of a highest being from concepts (see KrV, A 602/B 630). Therefore, even if the simple conversion of the central proposition of the cosmological proof is legitimate, nothing obliges the defender of the cosmological argument also to admit the validity of the ontological proof.

Flatt recalls that Kant defends, “with Gassendi, Göden, Dryfhoud and others,” the thesis that “existence and the mode of existence is not a special reality, is not a real predicate of something” (EKC: 97; see KrV, A 598/B 626 ff.).^[25] The absolute conversion of the proposition “Every absolutely necessary being is at the same time the most real being,” understood as asserting the actual necessary existence, would have to rely on a reasoning the logical incorrectness of which is obvious. Flatt sets it out “in scholastic form” in a way that could indeed be considered as an explicit criticism of the minor premise of “Kant’s additional syllogism 2”:

If one most real being does not differ from another in anything (neither regarding a real predicate nor concerning any other predicate), then one also has precisely the same mode of existence as the other. Now, one most real being does not differ from another with regard to any real predicate; consequently, there can also be no difference between one and the other regarding the mode of existence. (EKC: 97)

“But who does not see at first glance that this conclusion contains more than the premises?” Flatt rhetorically asks. Certainly, Kant has proven that one most real being does not differ in the least from another regarding any real predicate. But it does not follow that they cannot differ concerning the mode of existence, which is attributed by means of a non-real predicate. Therefore, “we are not authorized,” Flatt claims, “to transform the proposition ‘Every absolutely necessary being out of our representation is out of our representation a highest real being’ into this: ‘Every highest real being is absolutely necessary out of my representation’” (EKC: 97–98). It is therefore possible to accept the claim that invalidates the ontological proof and at the same time to defend the cosmological argument as valid.^[26] As Flatt himself recognises, “one can also, as far as I can see, assert at least without detriment to the cosmological proof” that “existence and the mode of existence is not a special reality, is not a real predicate of something” (EKC: 97).

Concerning the proposition “Every absolutely necessary being in my idea is also in my idea a highest perfect being”, Flatt points out that it is possible to admit “with Sam Werenfels and others” that the proposition in question, absolutely converted, is true “without needing to acknowledge the validity of the Cartesian proof.” Relying on Werenfels’s understanding of the Cartesian proof, Flatt states that “we can then always doubt whether Descartes has not merely admitted beggingly (bittweise) the assumption that some object out of our mind corresponds to the idea of the supremely perfect being” (EKC: 98).^[27] But, obviously, if the ontological argument does really try to state that “some object out of our mind corresponds to the idea of the supremely perfect being,” then the converting proposition at issue, “Every supremely perfect being in our mind has in our mind an absolutely necessary existence,” does not express in any way the central claim of the ontological argument.

Flatt states that if we admit Kant’s thesis that existence is not a real predicate of the highest real being, then we incur “a logical error if the previous proposition [“Every absolutely necessary being in my idea is also in my idea a highest perfect being”] is converted.” For, in that case, “we could think of some highest real being without connecting to its concept the concept of an absolutely necessary existence” (EKC: 98–9).

Flatt’s reasoning can therefore be summarised in the form of a dilemma.

Flatt’s dilemma:

Either the proposition that states the core of the cosmological proof can simply be converted (first and third cases) or it cannot simply be converted (second and fourth cases).

If it can simply be converted, then the converting proposition does not state the core of the ontological proof (and, therefore, the cosmological proof does not rest on the probative force of the ontological proof).

If it cannot simply be converted, then the core of the ontological proof is revealed to be false (and, therefore, the cosmological proof does not rest on the probative force of the ontological proof).

Therefore, in none of the possible cases does the cosmological argument rest on the probative force of the ontological proof.

But again, Flatt takes a step beyond this reasoning. He is indeed not content with showing “without presumption” that Kant’s criticism “cannot be counted among the valid ones.” He also declares, “I am even tempted to suspect that Kant himself does not put as much weight on it as it might seem at first sight” (EKC: 99).

To prove this last assertion, Flatt invokes two passages from Kant’s works. By adducing them, he seems to want to show that, as a matter of fact, Kant defends the primacy of the cosmological argument over the ontological. The first passage adduced is taken from the Critique of Pure Reason. In it, Kant claims that “the natural course of human reason” (der natürliche Gang der menschlichen Vernunft) does not consist in moving from the concept of the highest real being to the concept of an absolutely necessary being. The course is exactly the opposite: first reason “convinces itself of the existence of some necessary being”; it then finds that the concept of a highest real being corresponds to the concept of such a necessary being; “and thus reason infers that the highest being, as the original ground of all things, exists in an absolutely necessary way” (KrV, A 586 f/B 614 f).^[28] The second passage is found in a footnote to the Critique of Practical Reason. In it, Kant recognises that the concept “of an absolutely necessary being” (der eines schlechterdings nothwendigen Wesens) is “a need of reason (ein Bedürfniß der Vernunft)”, but it is also “the objective ground of a need of speculative reason, namely, to determine more closely the concept of a necessary being that is to serve as the original ground of others” (KpV, AA 05: 143).^[29]

Thus, Flatt concludes, “in this way, however, according to their own judgments, the proposition that the highest reality corresponds to the absolutely necessary being seems to be objectively founded and, correspondingly, also objectively valid” (EKC: 100). Therefore, if the central proposition of the cosmological proof is objectively valid and more original than the proposition summarising the ontological proof, then the ontological proof cannot contain the probative force of the cosmological argument.

Flatt’s considerations on the possibility or impossibility of conversion of the proposition stating the nervus probandi of the cosmological proof and his additional remarks have the virtue of bringing to light two assumptions concerning Kant’s critique of the a contingentia mundi argument. The first assumption is that, in trying to reduce the probative force of the cosmological proof to that of the ontological one, Kant cannot but attribute to the former the same error that, according to him, definitively undermines the validity of the latter, namely, the consideration of existence as a real predicate. But this supposition is in no way accepted by the proponents of the argument, who maintain that the claim that the necessary being exists is not based on the mere concept of the supreme being, but rather on the experience of the existence of contingent beings in the world.

Kant’s second assumption is that the argumentative process followed by reason in the ontological proof is more original or primitive than the reasoning behind the cosmological proof. Not only is this supposition not shared by defenders of the cosmological argument, many of whom reject the validity of the ontological proof, but it seems to contradict Kant’s express statements. As we have seen, Kant claims that, in its “natural course”, reason is first convinced of the existence of a necessary being and only later attributes to that being all perfections as the source of the limited perfections of contingent beings.

Thus, Flatt’s second objection once again raises two questions that cast doubt on the validity of Kant’s criticism of the cosmological proof. The first question is: is the claim that the cosmological proof is based on “an existence given through empirical consciousness in general” (KrV, A 614/B 642)^[30] compatible with the claim that the probative force of this argument depends on the ontological proof, which seeks to infer an existence from mere concepts (see KrV, A 602/B 630)? The second question is: is the assertion that reason, in its “natural course”, arrives first at the ens necessarium and then determines it as the ens realissimum compatible with the assertion that, in its demonstrative procedure, it happens in reverse, i. e. reason begins with the most real being and then affirms its necessary existence?

4 Eberhard’s first objection: objection based on the need for a proof of the reciprocity of the concepts of a most real being and an absolutely necessary being

Eberhard’s two objections are aimed at showing that Kant transgressed certain elementary logical laws by trying to prove his thesis that the ontological proof contains all the force of the proof of the cosmological argument. In both objections, the logical operation of the conversion of the proposition enunciating the nervus probandi of the cosmological proof (propositio conversa) into the proposition expressing the nervus probandi of the ontological proof (propositio convertens) is therefore taken into consideration. In the first objection, however, the conversio is taken in a broad sense, while in the second it is understood in a strict sense. Or, put differently, in the first objection the additional proof required for the absolute or simple conversion of the propositions in question is critically examined, and in the second the validity of the proof is not questioned, or, in other words, the proof is deemed valid or unnecessary. In both cases, however, Eberhard thinks that Kant has not demonstrated what he intended. Let us now consider the first objection.

Eberhard begins his criticism by stating the following fact: “But in order to bring the cosmological proof back to the ontological, he [Kant] has to make by reciprocation (durch Reciprokation) from the proposition: ‘The necessary being is the most real being,’ the proposition: ‘The most real being is the necessary being’” (ZdH: 107). “Reciprocation” is also the term used by logicians for the conversion of propositions. Certainly, Kant expressly claims that the former proposition is the latter converted simply, or, in other words, that both propositions are reciprocal. How does he prove it?

The logical doctrine of conversion teaches, as Eberhard recalls, “that singular propositions are to be regarded as universal propositions” (ZdH: 107). Thus, it is legitimate to maintain, as Kant does, that the singular affirmative proposition “The necessary being is the most real being” expresses the same truth as the universal affirmative proposition “Every necessary being is a most real being.” Also part of the doctrine of conversion is the claim that, strictly speaking, a universal affirmative proposition may only be converted per accidens into a particular affirmative proposition. The reason is adduced by Kant himself: in every universal affirmative proposition, the predicate has a broader extension than that of the subject (see Log, AA 09: 118). It is then a conversion sensu stricto because both propositions, the universal and the particular, express the same truth. Thus, the same truth formulated by the previous universal proposition can also be expressed by this particular proposition: “Some most real beings are necessary beings,” as Kant himself expressly recognises (see KrV, A 608/B 636).^[31]

But the conversio simplex of an affirmative universal proposition, i. e. the inversion of its extremes without changing their quantity, can also be called “conversion,” though in a broad meaning, not in the proper sense. It is indeed a conversion sensu lato because, even if both propositions are true, the converting proposition (propositio convertens) expresses another truth than the converse proposition (propositio conversa). In the case at hand, the proposition constituting the nervus probandi of the cosmological argument is converted simply into the proposition “Every most real being is a necessary being.” But this new proposition expresses a different truth from that expressed in the original proposition, and the truth of the new proposition requires a separate proof.

The required additional proof must show, indeed, that the concepts of the subject and the predicate of the converse proposition do not differ regarding their quantity. Eberhard expressly says so: “If a universal proposition is to be converted simply, so its main concepts must be reciprocal concepts (Wechselbegriffe), i. e. they must have the same extension” (ZdH: 108). Certainly, the proof will be unnecessary if it is obvious that both concepts are identical, because they will then have the same extension, as Eberhard recognises (see ZdH: 108). But if the concepts are not identical, then a specific proof is required for the claim that “a main concept is a proper attribute (attributum proprium) of the other”, since only in that “single case” do two different concepts have the same extension (ZdH: 108). Does Kant really prove that the different concepts “most real being” and “necessary being” are reciprocal?

Kant’s argument is already well known: “But now one ens realissimum does not differ the least bit from another, and thus what holds of some beings contained under this concept holds also of all” (KrV, A 608/B 636).^[32] Eberhard, in addition to literally reproducing these words, formulates the proof in general terms as follows: “[T]he abstract subject of the converting proposition does not differ the least bit from the same abstract subject, and what holds of some of those contained under it holds also of all” (ZdH: 107). Is this moving from the conversion per accidens to the conversion simpliciter really a proof that one concept is a proprium of another?

Certainly not, Eberhard claims. But the only reason he gives is the example of mathematicians: “With this method (Art zu schließen), mathematicians could save themselves a lot of effort, for in this case of no affirmative universal proposition they would have to specifically prove its simple converting” (ZdH: 107). Theodosius of Bithynia, Eberhard illustrates, proposed the conversio simplex of the famous theorem stated in Proposition 6 of Book I of his Sphaerica: “All circles passing through the centre of a sphere are the largest circles of the same sphere.” However, he was not content to argue that all the largest circles of the same sphere do not differ in the least in abstracto, “so if it holds for some of them that they pass through the centre of the sphere, then it should hold for all”; rather, the Greek astronomer and mathematician of antiquity specifically demonstrated the converting proposition (see ZdH: 107–108).

Eberhard uses the example to illuminate the main reason for the insufficiency of Kant’s proof. Eberhard does not expressly state this reason. His objection to Kant’s criticism, however, can be supplemented as follows. A propium is, according to Porphyry’s definition, a predicate that holds of a certain subject-concept “alone”, of “all” its inferiors, and “always”, i. e. necessarily.^[33] Therefore, Eberhard might have said that Kant, by invoking the abstract subject of the converting proposition, did not properly prove that the concepts of a “most real being” and of a “necessary being” convert. The abstract consideration of the concept of a “most real being” does not even allow it to be proved rigorously that ratione materiae, i. e. by reason of the matter or content of the concept, all most real beings are necessary beings, much less that they alone and always are. Certainly, in Kant’s argument, the matter of the judgment, i. e. “the given representations that are combined in the unity of consciousness in the judgment” (Log, AA 09; 101),^[34] is in no way attended to. But in his Logic, Kant himself recognises that the ground for why some universal affirmative judgments may be converted simpliciter “lies not in their form but in the particular character of their matter” (Log, AA 09: 119).^[35] The conclusion of Eberhard’s first objection is, then, that Kant has not demonstrated what he needed to prove in order to justify his claim that the ontological proof contains all the probative force of the cosmological proof.

Curiously enough, the need for a proof of the reciprocity of the concepts of the most real being and the absolutely necessary being, claimed by Eberhard, in his first objection, as a requirement for a conversio sensu lato, seems to have been recognised by Kant as well. Kant expressly states, thereby implicitly doing justice to Eberhard’s reproach, that “the transcendental proof of the existence of God […] depends solely on the reciprocality of the concepts of the most real being and the necessary being, and cannot be sought anywhere else” (KrV, A 788 f/B 816 f).^[36] So new doubt is cast on the effective achievement of Kant’s criticism of the cosmological proof: why does Kant not give a rigorous proof of the reciprocality of the concepts of the ens realissimum and the ens necessarium?

5 Eberhard’s second objection: objection based on non-compliance with certain logical rules of conversion of propositions

Eberhard’s first objection sought to demonstrate that Kant’s argument is based on a purely abstract consideration of the subject of the converting proposition. For this reason, it cannot be considered a genuine separate proof, valid for showing the reciprocity of the concepts “most real being” and “necessary being.” Ultimately, according to Eberhard, Kant was attempting the logical impossibility of deriving, by mere immediate inference, the truth of the converting proposition “Every most real being is a necessary being” from the converse proposition. However, for the sake of argument, Eberhard now concedes, by introducing his second objection, the truth of the converting proposition. That is, he concedes to Kant that a simple conversion sensu stricto of the propositions in question is possible. Despite this, he believes that Kant has not proved his claim that the cosmological argument depends on the ontological. Indeed, Eberhard writes: “But if now, by mere conversion, without a specific proof (ohne einen eigenen Beweis), the truth of the converting proposition could be proved, then it would not yet follow that the cosmological proof takes its cogency from the ontological one” (ZdH: 109).

Eberhard substantiates this new criticism with three reasons, based on the claim that there is a breach of certain logical rules of the conversion of propositions.^[37] The first of these reasons is built upon two complementary logical rules, which occur, Eberhard writes, “even in accordance with Mr Kant’s deduction.” The first rule says that from the truth of the converse judgment the truth of the converting judgment is legitimately inferred, and the second says that this inference does not occur in reverse, i. e. that from the truth of the converting judgment it is logically impossible to conclude the truth of the converse.^[38] Thus, the truth of the proposition “Every absolutely necessary being is at the same time the most real being” cannot be guaranteed by the truth of the proposition “Every most real being is an absolutely necessary being”, since, Eherhard writes, “the truth and certainty of the former must already be presupposed if the converting is to arise from it by means of a conversion according to rules” (ZdH: 109). Eberhard’s conclusion is that if the truth of the nervus probandi of the ontological proof is to be rightly inferred from the truth of the nervus probandi of the cosmological proof, then the latter truth must already be presupposed. Therefore, the cogency of the cosmological proof cannot depend on that of the ontological one.

The second reason is stated somewhat cryptically by Eberhard, but perhaps its meaning can be explained as follows: If the converting proposition we are concerned with is true by simple conversion, then this immediate inference “depends only on the extension of the main concepts of the premise, but not in the least on the content of these concepts” (ZdH: 110). In this case, the logical rule saying that if two concepts are reciprocal concepts with respect to a third then they are also reciprocal concepts with each other^[39] would not apply. Certainly, this rule implies a consideration of the matter of the concepts in question. Thus, the proof of the convertibility of the ens necesarium and the ens realissimum by philosophers of the Wolffian school cannot be used in the simple conversion at issue. This proof (which Kant refutes in his 1763 book The Only Possible Argument) is indeed based on the reciprocity of the concepts of “necessity” and “infinity”.^[40]

Additionally, if it is evident that the concepts have the same extension, then from the truth of one of the propositions the truth of the other can be immediately inferred, or, as Eberhard himself says, “then whatever proposition one may want may be taken as a premise, with just that it be otherwise certain” (ZdH: 110). Certainly, the logic teaches that if two concepts a and b are reciprocal, then all a must be b, and all b must be a, i. e., one concept can be put in the place of the other.^[41] If the truth of one proposition is known, then the truth of the other can be immediately inferred, without further addition.

Applying this line of reasoning to the case in question, Eberhard claims that if the converting proposition “Every most real being is an absolutely necessary being” “should be made certain by mere conversion, then it would no longer be necessary to develop the infinity from the necessity, but even less the necessity from the infinity”. The reason is obvious: the truth of the converse proposition “must already be accepted as certain if the converting proposition is to be true and certain” (ZdH: 110).

Consequently, Eberhard’s conclusion is that, in this assumption, the nervus probandi of the ontological proof can be made certain by mere conversion of the nervus probandi of the cosmological proof. Thus, the former proof cannot in any way contain the probative force of the latter.

Eberhard’s third reason can be stated very simply. In the cosmological proof, the proposition “The necessary being is actual (wirklich)” has been proven “from the contingency and from the causality” of the world. It therefore does not need a proof taken from the “concept of the most real being.” Whatever the strength of the cosmological proof, Eberhard’s conclusion can only be that “the cosmological proof is completely independent of the ontological one”. Certainly, if the cosmological proof is convincing, “then it does not need the force of the ontological”. But if the cosmological proof is not convincing, “then no other proposition can be derived from the not certain proposition through logical conversion, by means of which it could obtain its certainty” (ZdH: 110).

Eberhard’s first and second objection, taken as a whole, give rise to the following dilemma.

Eberhard’s dilemma:

Either the converting proposition stating the core of the ontological proof needs an additional proof or it does not need an additional proof.

If it needs an additional proof, this can only be based on the reciprocity of the concepts of an ens realissimum and an ens necessarium (and then the cosmological proof does not rest on the probative force of the ontological proof).

If it does not need an additional proof, then the truth of the converting proposition is only guaranteed by the truth of the converse proposition (and then the cosmological proof does not rest on the probative force of the ontological proof).

Therefore, in neither case does the cosmological argument rest on the probative force of the ontological proof.

But let us add a few brief comments to Eberhard’s second objection. Undoubtedly, the logical laws of the conversio sensu stricto, so clearly recalled by Eberhard, are entirely shared by Kant himself. In particular, Kiesewetter’s Kant-inspired logic textbook testifies that Kant admitted the rule, as applied in the present case, according to which the truth of the converting proposition is only assured by the truth of the converse proposition, and not in reverse. This fact cannot but call into question the success of Kant’s criticism of the cosmological proof. For, if the logical rule is accepted, it does not seem possible to also admit the validity of what we have called “Kant’s additional syllogism 1”. Certainly, if the laws of logic do not allow us to assert that the truth of the proposition that expresses the core of the ontological proof is more original or primitive than the truth of the proposition stating the core of the cosmological proof, why does Kant grant exclusive probative force precisely to the ontological proof and not, rather, to the cosmological proof? And why does he deny the independence of the latter from the former? Moreover, Kant seems to agree with the third reason given by Eberhard, namely that the cosmological argument, in its first step, concludes that there is an absolutely necessary being (see KrV, A 604/B 632). Why then does this argument need the “probative force” of the ontological proof?

6 Concluding remarks: the early discussion on Kant’s main criticism of the cosmological proof

The claim that the cosmological proof depends for its probative force on that of the ontological proof is a central thesis of transcendental philosophy. Kant’s fundamental conviction, expressed as early as 1763, that there is only one “argument in support of a demonstration of the existence of God” does not disappear in his critical philosophy but undergoes a radical transformation. Kant’s famous “Copernican revolution” imposes a twofold task: to reduce all possible proofs of God’s existence to one, namely, the ontological, and to show the “impossibility” of this unique proof. Whereas for Anselm his unum argumentum does not need to rely on any other proof to be probative, for Kant only the “ontological argument” contains the probative force to which all other proofs of God’s existence must resort. The reduction of the Leibnizian proof a contingentia mundi to the Cartesian argument is a decisive step in Kant’s project, the final goal of which is the “critique of all theology from speculative principles of reason” (Kritik aller Theologie aus speculativen Principien der Vernunft; KrV, A 631/B 659) as an indirect confirmation of the truth of transcendental idealism.

It is therefore not surprising that a panoply of objections was raised in Kant’s time to this reduction of one proof of God’s existence to the other. Thus, two main results can be drawn from the collection of criticisms studied in the preceding pages. The first refers to the complete, exhaustive (we might say) nature of the proposed objections – to the fact that, taken as a whole and in their general features, they seem to form a system. The second concerns the soundness of the objections studied. Certainly, certain assumptions typical of the dogmatic philosophy underlie these reproaches. But, apart from that, all of them succeed in pointing out certain obscurities and flaws in the reasons given by Kant in support of his main criticism of the cosmological proof.

Indeed, the above considerations show that the objections by Kant’s early opponents seem to exhaust all possibilities of criticism, at least from a logical standpoint. If the objections considered above are correct, then Kant will have failed to prove in any of the possible cases that the ontological proof really contains all the probative force of the cosmological proof. He will have failed even if it is admitted that the reasons he gives to account for the reduction of the cosmological proof to the ontological proof are correct in the case of some formulation of the cosmological proof, as stated in Flatt’s (and Abel’s) first objection. Moreover, he will have failed to accomplish his goal, irrespective of the validity or invalidity of the reasoning offered for the conversion of the respective propositions expressing the probative core of both proofs, according to the results of Flatt’s second objection. And finally, he will have failed precisely because, according to Eberhard’s two objections, Kant’s argument in support of the dependence of the cosmological proof on the ontological proof is not valid according to the laws of logic. As expected, the two chief ways of challenging Kant’s statement on the cosmological proof followed by these early critics (i. e. the refutation of either the first and the third propositions or the second proposition of “Kant’s sorites”) are still currently being explored, in one way or another.^[42]

It must be recognised that, by highlighting certain obscurities and inaccuracies in Kant’s argument, these objections by the early critics cast doubt from a logical point of view on the success of Kant’s main criticism of the cosmological proof. The first doubt concerns the characterisation of the cosmological argument. Flatt’s (and Abel’s) first objection leads to the following question. As we know, Kant characterises the cosmological argument as a transcendental proof based “on pure principles of reason”. Is this description of the proof the result to which Kant’s criticism necessarily leads, or is it rather the assumption from which the critique is undertaken?

The remaining doubts refer to the relationship between the cosmological proof and the ontological proof. Flatt’s second objection raises two questions. Why does Kant claim that the cosmological proof depends on the ontological proof if the former in no way commits the error (according to Kant) made by the latter, namely treating existence as a real predicate? How is it that the cosmological proof depends on the ontological proof if the former is an expression of the “natural course” of human reason, while the latter represents the complete inversion of such a course? Eberhard’s first objection also raises a new question. If the concepts of the ens realissimum and the ens necessarium on which the two transcendental proofs are founded are reciprocal concepts, why does the ontological argument have primacy over the cosmological argument? Finally, Eberhard’s second objection leads to two questions. If the logical rules assert that the truth of the proposition resulting from conversion is only assured by the truth of the given, starting proposition, is it not more in keeping with the rules of correct thinking to hold that it is the cosmological argument that underpins the validity of the ontological argument? Apart from that, is the fact, affirmed by Kant himself, that the cosmological argument succeeds in proving, in its first step, the existence of a necessary being not sufficient evidence of the independence of this proof from the ontological proof?

To sum up, an examination of the early objections against Kant’s main criticism of the cosmological proof presents us with a quandary. Has Kant really identified a flaw in the cosmological proof that leads this argument to rely on the ontological proof? Or has Kant shown, rather, the incompatibility of the basic tenets of transcendental idealism with the possibility of proving God’s existence from the contingency of beings in the world? The very discussion that emerged in the aetas kantiana also seems to suggest, however, a response in relation to the claim about the dependence of the cosmological argument on the ontological proof. In Kant’s justification of this criticism, his conception of both experience and the indeterminate and “abysmal” nature of the concept of an ens necessarium (see KrV, A 613/B 641) ultimately plays a more important role than the questions posed by the logical conversion of judgments.