The Idea of God and the Empirical Investigation of Nature in Kant’s Critique of Pure Reason

Abstract This article aims to justify the positive role in the empirical investigation of nature that Kant attributes to the idea of God in the Critique of Pure Reason. In particular, I propose to read the Transcendental Ideal section and the Appendix to the Transcendental Dialectic together to see whether they can reciprocally illuminate each other. I argue that it is only by looking at the transcendental deduction of the ideas of reason and the resulting analogical conception of God (which Kant provides in the Appendix) that a fully legitimate positive use of the idea of God can be vindicated.


Introduction
In Section Two of the Ideal of Pure Reason (The Transcendental Ideal), Kant reconstructs the steps that lead human reason to postulate the idea of the most real being, or the ens realissimum. This idea plays a central role in Kant's negative critique of rationalist theology. For Kant, the ens realissimum is the philosophical basis of the idea of God and the concept underlying the traditional arguments for God's existence. 1 As is well known, Kant argues that the ontological, cosmological and physico-theological arguments are fallacious and that we cannot theoretically demonstrate the existence of God. This is not, however, the end of the story. Kant insists that the idea of God has also a positive role to play, not only in the practical, but also in the theoretical realm. In particular, the idea of God is presented as a necessary regulative principle for the systematization of empirical cognition. Indeed, as Kant argues in the second part of the Appendix to the Transcendental Dialectic, we 'must presuppose' this idea 'in relation to the systematic and purposive order of the world's structure' (A698/B726). 2 It is far from clear, however, whether Kant is thereby rehabilitating some aspects of the ens realissimum and, if this is the case, how this rehabilitation can be critically legitimate. The literature has been divided on this issue. As noted by Wood, the rationalist background of the arguments Kant presents in the Transcendental Ideal has made it not particularly appreciated among his readers, particularly his English-speaking ones (Wood 1978: 27). Kemp Smith, Strawson and Bennett, for example, all consider Kant's derivation of the ens realissimum at odds with the critical project. 3 After Wood's ground-breaking study, however, several attempts at critically interpreting the ideal in positive terms have been made (e.g. , Allison 2004, Longuenesse 2005. In this article, I will argue that such attempts are promising and grounded in the text, but they all miss what I take to be the essential element that explains the critical legitimacy of the ens realissimum. This element is the transcendental deduction of the idea of reason Kant provides in the second part of the Appendix to the Transcendental Dialectic. The transcendental deduction of the ideas has not been particularly studied in the literaturenor has it been discussed in relation to the transcendental ideal. 4 This is an unfortunate gap in the literature since the deduction is supposed to explain how the ideas of reason, including the idea of God, can obtain objective validity and become critically legitimate with respect to the systematization of empirical cognition. In this article, I will show that the second part of the Appendix gives us precise instructions on how to critically understand the postulation of the idea of God and its role in the investigation of nature. In particular, I will argue (i) that ideas must be postulated as schemata rather than concepts of objects; and that (ii) the content of ideas must be understood in analogical rather than descriptive terms. The proposed reading of the deduction will provide a template for understanding the fundamental characterization of the idea of God as the ens realissimum.
The plan of the article is as follows. I will first reconstruct Kant's derivation of the transcendental ideal in the Ideal of Pure Reason and discuss its critical legitimacy (section 2). I will then take a close look at the transcendental deduction of ideas in the second part of the Appendix (section 3). In section 4, I will apply the deduction to the derivation of the ideal of pure reason and derive its critical version. I will conclude in section 5.

The transcendental ideal: the argument and its critical legitimacy 2.1 Reconstruction of the argument
In the first section of the Ideal of Pure Reason, Kant introduces the general notion of ideal and distinguishes it from both categories and ideas on the basis of their 'distances', as it were, from 'objective reality'. Objective reality, according to Kant, is a property that representations have when they are 'related to an object' and 'have significance and sense in that object' (A155/B194). 5 Categories are mere forms of thought, but they can obtain objective reality when related to appearances through transcendental schemata. Ideas are 'more remote' from objective reality because no empirical representations can be found that correspond to them (A567/B595). Indeed, ideas are presented as 'transcendent concepts': concepts that go beyond possible experience (see A320/B377, A327/B384). Since, for Kant, knowledge of objects is limited to possible experience, it seems to follow that ideas cannot obtain objective reality from a theoretical point of view. 6 They still maintain some validity and an indispensable function though, namely that of serving as 'rules' for the systematic unity of cognition (A568/B596).
An ideal seems even 'further removed' from objective reality than an idea. Kant uses the term in the specific sense of indicating an idea 'in individuo, i.e., an individual thing which is determinable, or even determined, through the idea alone' (A568/ B596). Whilst a mere idea is a general concept, the ideal is a fully determinable, or determined, representation of an individual being. To this specific definition corresponds a particular function. If ideas give us general 'rules' for the systematic unity of empirical cognition, the ideal provides 'the original image for the thoroughgoing determination of the copy' (A569/B597).
They provide an indispensable standard for reason, which needs the concept of that which is entirely complete in its kind, in order to assess and measure the degree and the defects of what is incomplete. (A569-70/B597-8) The definition of ideal here introduced is highly general and sketchily anticipates arguments that will be fullyyet puzzlingly, as several commentators have noted developed in the course of the chapter. Let me, however, already highlight the point that will represent the main concern of the present article. Note that Kant places great emphasis on the problem of objective reality of the ideal and ideas more generally understood. Note also that the use of this term is ambiguous. Although Kant talks of different 'distances' from objective reality, it would seem that ideas and ideals, given their transcendent status, are simply unable to become objectively real. But if ideas and the ideal cannot have objective reality, how can it be possible for them to maintain some validity in relation to cognition? Indeed, it may seem illegitimate to use representations that go beyond possible experience and have no relation to objects as 'rules' and 'standards' for systematizing empirical cognition. In this article, I will try to shed light on these ambiguities. In particular, I contend that Kant is here employing a particular understanding of 'objective reality' (or 'objective validity') 7 that will be fully clarified only in the second part of the Appendix to the Transcendental Dialectic, with the transcendental deduction of the ideas. This deduction, although not particularly investigated in the literature, will be key to understanding the positive use of the idea of God.
After introducing ideals in general and using particular examples such as that of the Stoic sage, Kant's subsequent discussion focuses on the concept of ens realissimum. This is not a matter of choice. The concept of ens realissimum corresponds to the 'transcendental ideal': an ideal which is necessarily required by the use of our reason (see A576/B604). Accordingly, what follows in Section Two of the chapter is the much debated and highly complicated derivation of the transcendental ideal from the rational sources of our mind. The function of the argument Kant presents in this section as well as its reconstruction constitute interpretative problems themselves. For the purposes of this article, I will follow the widely accepted assumption that this section is part of a long and uninterrupted story regarding the rational origin of the idea of God. 8 I will give only a rough sketch of the main line of argument presented.
Several reconstructions of Kant's derivation of the transcendental ideal have been proposed. Allison proposes a three-step argument, Grier has four steps in her reconstruction, and finally Willaschek has recently proposed a five-step derivation. 9 I will follow the latter one for it includes all the elements of the principal line of reasoning. The argument starts with a contrast between two principles: a logical principle and a transcendental principle which in turn contains a transcendental presupposition. These represent the first three steps of the argument. The first principle is the 'principle of determinability' (PD) which applies to concepts only. The principle says that: (1) PD: 'of every two contradictorily opposed predicates only one can apply to it'. (A571/B599) This is a merely logical principle for, as Kant explains, it rests on the principle of contradiction and abstracts from the 'content of cognition' (A571/B599). It says that for every concept and any predicate P, if P is added to the concept then non-P cannot also be added to its content. Suppose that the concept 'human being' is indeterminate as to whether a human being is 'mortal'. I can only add the predicate 'mortal' (P) or 'non-mortal' (non-P) to it.
The second, transcendental principle is 'the principle of thoroughgoing determination (durchgängige Bestimmung)' (PTD) and specifically applies to objects. It says: (2) PTD: 'among all possible predicates of things, insofar as they are compared with their opposites, one must apply to it'. (A571-2/B599-600) This principle goes beyond logic for 'it deals with the content and not merely the logical form' (A572/B600). In other words, it is a synthetic principle that provides us not merely with the analytic determination of a concept through given predicates, but with 'the complete concept of a thing' (A572/B600). It tells us that for every object and every possible predicate P, either P or non-P must apply to it. Here Kant seems to rehash the Leibnizian idea that only a 'complete concept'that is, a concept determined with respect to all pairs of possible predicatesallows us to represent one individual thing. 10 This principle, in turn, contains a transcendental presupposition. By contrast with PD, PTD does not simply consider a thing in relation to two opposite predicates. The complete concept of a thing requires instead the comparison of the thing with the 'sum total of all predicates in general (Inbegriff aller möglichen Prädikate überhaupt)' (A573/B601). PTD therefore presupposes the following: (3) SUM: 'the material of all possibility, which is supposed to contain a priori the data for the particular possibility of everything'. (A573/B601) The presupposition of this materialthe 'storehouse', as it were, 'from which all possible predicates of things can be taken' (A575/B603)is of the utmost importance for it constitutes the transcendental basis for the derivation of the rationalist idea of God.
Before turning to the remaining two steps of the argument, let us briefly pause on these three steps which already pose a number of interpretative riddles. First, Kant does not really explain the move from PD to PTD. It is plausible to think, however, that PD presupposes PTD when applied to objects. 11 The general thought seems to be that, in order for us to conceptually determine a single object, we need to presupposeat least hypotheticallythat the object is completely determined. This reading, however, does not settle whether it is legitimate for us to make such a presupposition. Is this move transcendentally valid? Or is it a deceiving illusion affecting the dialectician?
From a critical point of view, the second step, that is, the very attempt at completely determining objects through conceptstherefore independently from sensibilityseems prima facie illegitimate: the dialectical residue of Leibnizian 'intellectualism' (see A275-6/B331-2), rather than a positive part of the critical system. In Kant's transcendental philosophy, objects are never conceptually given, but always given to us under the conditions of sensibility as appearances. 12 The third step poses additional problems. Again, from a critical point of view, possibility is the agreement with the formal conditions of the understanding (see e.g. A218/B265), not the 'storehouse' of data that provides the content of objects. Leech convincingly argues that the presupposition of a sum total of possibility completes the formal conditions provided by the understanding as regards the content of phenomena (Leech 2017). But even granted such a completion, the sum total remains an ideasomething 'which has its seat solely in reason' (A573/B601). How could we meaningfully apply this idea to objects? This would again require some kind of objective validity attached to our ideas.
To make things worse, the last two steps of the argument seem even less plausible. The sum total of all possibility, Kant says, is still an indeterminate concept: 'on closer investigation', however, we find that this idea 'excludes a multiplicity of predicates, which, as derived through others, are already given, or cannot coexist with one another' (A573-4/B601-2). Simply put, we do not need to include in the presupposed sum total more than is strictly necessary for the reality of beings. A negation is not properly a reality, but a mere lack thereof (A574/B602). Properly speaking, therefore, the presupposed sum total contains only primitive, positive predicates (an 'All of reality', omnitudo realitatis). The fourth step is therefore: (4) OMNITUDO: the transcendental substratum of determination is 'nothing other than the idea of an All of reality (omnitudo realitatis)', of which 'all true negations are nothing other but limits'. (A575-6/B603-4) The complete determination of this idea itself (the properly called ideal) is finally obtained only through the final step. The idea of an 'All of reality' is itself a concept of an individual being (the ens realissimum) for the simple reason that we can completely determine it with the idea of reality: as a being which is only positively determined and therefore possesses all positive realities. The final step therefore amounts to: This last part of the derivation has attracted considerable criticism for at least two reasons. First, it seems to ignore the possibility of 'real repugnance (Realrepugnanz)' among positive predicates, thus failing to show that the ens realissimum is really possible. 13 Following   and Willaschek 2018), however, I think that this does not pose a serious threat to the idea of ens realissimum. 14 First, in the Ideal chapter Kant does not seem to discuss real repugnance in any significant way. Second, the most real being is only a rationally presupposed idea. As such, we are not required to prove its real possibility as an object. Indeed, as I will further argue, the validity of such an idea will not be based on any determination of objects at all.
More problematically, the hypostatization in an individual being seems to blatantly presuppose the possibility of conceptually determining a being without appealing to sensibility. Kant himself seems to dismiss this step (A580/B608). Reason, Kant explains, grounds the complete determination of things only on the idea of all reality, 'without demanding that this reality should be given objectively, and itself constitute a thing' (A580/B608). This stepspecifically understood as the positing of a real thingseems therefore to be unwarranted in the natural progression of reason.

The critical legitimacy of the ideal
As should already be evident from the above reconstruction, the question of the legitimacy of the rational progression that leads to the transcendental ideal is a thorny issue to disentangle. On the one hand, as several commentators suggest, Kant seems to merely reconstruct the fallacious reasoning of the metaphysician. Indeed, the principle of complete determination together with its presupposition of the material of all possibility seems at odds with the critical framework. On the other hand, Kant clearly admits some permissibility of the ideal as a mere idea 'in order to cognize a thing completely' and for prescribing to the understanding the 'rule of its complete use' (A573/B601). It is, however, highly difficult to understand, first, how an idea can be applied to our concepts of objects, and second, where exactly to draw a line between a legitimate and an illegitimate use of reason.
Following the clues Kant offers, several interpreters have tried to propose a critical reading of this section. In fact, after Wood's study, there has been much work on the positive interpretation of the ideal: most notably Longuenesse (2005), Grier (2001), Allison (2004) and Leech (2017). In the rest of this article, I will contend that such attempts are promising and grounded in the text. However, they all miss an essential element, without which the rehabilitation of the ideal cannot be made fully compatible with the positive use Kant attributes to the idea of God. This element is the crucial question of the objective validity of ideas that Kant clarifies only in the second part of the Appendix to the Transcendental Dialectic. 15 For clarity and convenience, I will build my analysis on Longuenesse's account of the transcendental ideal, which has generally been taken as a landmark in the recent literature. 16 It is particularly helpful to discuss her position for, although I share the same purpose of critically interpreting the Ideal chapter, my reading will substantially diverge from her proposal and hopefully solve the problems connected with it.
Longuenesse has argued that there is a 'perfectly legitimate, critical reading for the move from the principle of complete determination to the supposition of a sum total of all possibilities' (Longuenesse 2005: 220). On her reading, the principle of thoroughgoing determination (PTD) is a critical principle if restricted in its application to the objects of sense only. Crucially, she employs such a restriction by reading the principle as following from the Transcendental Analytic. From the standpoint of the Analytic, she argues, the principle of complete determination is not even a new principle. Any singular object of experience is completely determined because it can be compared to every other possible object of experience, as a result of its belonging in the same concept 'object of experience' (p. 218). This reading finds textual support in the last paragraphs of the section where Kant seems to limit PTD to empirical predicates (A581/ B609) and SUM to 'all empirical reality' (A582/B610).
If PTD, SUM and presumably also OMNITUDO are legitimate steps (since they follow from the Analytic; see Longuenesse 2005: 220), where does the dialectical error come from? According to Longuenesse, the error would consist in transforming a unity of the understanding into a unity of reason. The textual evidence for this reading would be contained in the last paragraph of the section: That we subsequently hypostatize this idea of the sum total of all reality, however, comes about because we dialectically transform the distributive unity of the use of the understanding in experience, into the collective unity of a whole of experience; and from this whole of appearance we think up an individual thing containing in itself all empirical reality, which thenby means of the transcendental subreption we have already thoughtis confused with the concept of a thing that stands at the summit of the possibility of all things, providing the real conditions for their thoroughgoing determination. (A582-3/ B610-11) The dialectical transformation, on her reading, is the transformation of the distributive unity of the understanding (that is, the logical unity that results from comparing an object of sense with all possible predicates) into the collective unity of a 'whole of experience' (the unity of the totality of empirical reality), which is then hypostatized. Therefore, Longuenesse argues for the legitimacy of SUM and OMNITUDO only as principles generated by the logical use of the understanding. The hypostatization into an individual being, which is grounded on the collective whole, turns out to be an illegitimate move. Thereby her reading does not license a positive use of the ens realissimum as such (ENS).
While this may seem convincing at first glance, there are a number of discrepancies between the text and the offered reading that undermine the plausibility of the overall picture. Let us focus on the crux of the argument. First, as noted by Verburgt, it is surprising that Longuenesse reads the principle of thoroughgoing determination as a principle of the understandingwhereas Kant is clear that such a principle 'is grounded on an idea which has its seat solely in reason, which prescribes to the understanding the rule of its complete use' (A573/B601; Verburgt 2011: 252). As a result, she reads the transition from distributive unity to collective unity as an illegitimate move. But this clearly fails to consider that collective unity (the unity of the totality of empirical reality) can have a positive meaning from the standpoint of reasonwhen it is legitimately used for the sake of the thoroughgoing determination of concepts of empirical objects.
There is no lack of evidence for this more plausible reading. First, in the passage quoted above the transformation of the distributive unity into the collective unity of reason is only the first step and, as it were, a precondition of the dialectical hypostatization. 17 The dialectical hypostatization only happens with what Kant calls 'transcendental subreption': the mistaking of an empirical principle for a principle that applies to things in general (A583/B661). We should therefore carefully distinguish between the transformation into the collective unity of reason and the hypostatization, which is a misuse of reason when combined with the subreption. In the important footnote to this paragraph, Kant identifies the former with the step of 'realization', that is, of transformation of a representation into an object, and the latter with a separate, second step: This ideal of the supremely real being, even though it is a mere representation, is first realized, i.e., made into an object, then hypostatized. (A583/B611 fn.) That Kant leaves room for a positive meaning of collective unity and realization is then confirmed in a number of passages throughout the corpus. Most importantly, it is confirmed at the beginning of the Appendix, where Kant clearly recognizes a positive, regulative meaning of reason and its collective unity. 18 Thus reason really has as object only the understanding and its purposive application, and just as the understanding unites the manifold into an object through concepts, so reason on its side unites the manifold of concepts through ideas by positing a certain collective unity as the goal of the understanding's actions, which are otherwise concerned only with distributive unity. (A643-4/B671-2) As we will see, the second part of the Appendix not only openly admits a positive use of the collective unity of reason, but it also explains how exactly we are critically allowed toindeed, we mustuse it. This explanation will provide an important missing element for fully vindicating PTD as a transcendental principle of reason. In fact, if PTD is recognized as a principle of reasonnot of the understanding as suggested by Longuenesseits objective validity becomes in itself a problem. How can we legitimately realize the ideal and apply it to objects of sense?
The second major problem with Longuenesse's account is more evident and points towards the same direction of inquiry. According to her reading, the natural progression of reason is legitimate up until the 'All of empirical reality'. But if this is the case, why does Kant insist so much that the ideal itselfthe ens realissimumhas a necessary and indispensable use? Longuenesse asks herself this question and answers that this move is only motivated by the need to maintain a role for God in the realm of practical philosophy (Longuenesse 2005: 228). As noted by many, this cannot be a satisfactory answer. 19 Kant not only advocates for a regulative use of the idea of God, he also explicitly specifies that the idea of God is necessary from a purely speculative point of view. To quote the phrase with which I opened the article: 'we must presuppose' the idea of God in the investigation of nature. From which it is clear that the idea of God (and not merely the omnitudo realitatis) has a theoretical, not only practical function.

The transcendental deduction of the ideas 3.1 Why a transcendental deduction of ideas?
In the previous section we saw that the legitimacy of the transcendental ideal hinges upon its 'realization', namely its transformation into some kind of 'object'. The correct understanding of this move is still highly unclear at the end of Section Two of the Ideal of Pure Reason. It is true that Kant states that the transcendental ideal can be legitimate as a necessary idea for the thoroughgoing determination of concepts (e.g. A573/B601), but no clear explanation is offered of how an idea can be critically realized. Indeed, one might be tempted to simply equate this realization with the illegitimate step of treating a mere idea as a thing given objectively. As already suggested, a way out from this dialectical quagmire is only given in the second part of the Appendix where Kant presents the much-neglected transcendental deduction of ideas. In this section, I contend that the transcendental deduction of ideas reveals a positive, critically legitimate way of realizing an idea of reason from the theoretical perspective.
Despite being presented as 'the completion of the critical business of pure reason' (A670/B698), the transcendental deduction of the ideas of reason has not been particularly studied in the secondary literature. One reason behind this interpretative dismissal is that the deduction does not fit well with a common reading of the ideas of reason. According to this interpretation (which we may call the 'methodological interpretation'), 20 ideas are methodological tools or useful guidelines that we may use in order to extend the system of our cognitions. 21 Since ideas have a merely logical function, it is not necessary to show that they have a legitimate application to objects. As a result, the transcendental deduction of the ideas is a negligible if not misleading part of the Dialectic. This reading, however, cannot be textually satisfactory. Kant simply does offer a highly sophisticated transcendental deduction of the ideas of reason. And such deduction is meant to show that ideas are not just useful methodological guidelines, but 'indispensably necessary' principles that guide the understanding and assure its complete use (A644/B672).
There is, however, a second, more subtle reason why the deduction has not attracted particular attention. It presents a notion of objective validity (and of realization of the idea) that is not fully compatible even with a more charitable reading of the objectivity of ideas (what we may call the 'descriptive interpretation'). This interpretation makes the following plausible distinction. Ideas of reason seem to describe objects that go beyond the possibility of experiencenoumenal objects or things in themselves. Since our knowledge is limited to the field of experience, we cannot know whether our ideas actually correspond to those objects. For example, we cannot know whether there is an existing being the corresponds to our idea of God. However, we can still grant our ideas of reason a weaker epistemic status than knowledge. Since, as Kant says, ideas are necessary to regulate the understanding and promote the investigation of nature, we are merely required to assume that they determine things in themselves. 22 Various ways have been proposed to understand such weak assumptions (e.g. as hypotheses or as necessary illusions). 23 Although I cannot here discuss these proposals in detail, let me point out that they all agree that ideas are objective inasmuch as they potentially describe objects.
Taking my cue from a recent normative approach to the ideas of reason (Massimi 2017 and Kraus 2020), 24 I will argue that Kant's view on the objectivity of ideas is more radical than generally assumed by the descriptive reading. The objectivity of ideas does not consist in their actual or potential characterization of noumenal objects. Rather, their objectivity consists in the relational function they afford. As we will see, ideas are legitimately realized as 'objects in the idea'. An object in the idea is not an object in any common understanding of the term. It is rather a 'schema' that allows us to progressively systematize objects of sense. Crucially, however, Kant does not simply deduce ideas as schemata, he also specifies how we should understand the content of ideas in non-descriptive terms, namely as analogies. In the next sub-section, I will elucidate these points by looking at the text more closely. I will first reconstruct the two steps of the deduction and the analogical nature of ideas. Finally, I will explain what this entails for the idea of God. 25

The realization of the idea
Ideas are deduced in two steps. The first step revolves around the distinction between presupposing an 'object absolutely (Gegenstand schlechthin)' and an 'object in the idea (Gegenstand in der Idee)' (A670/B698). Kant is finally spelling out how to critically realize an idea (transform it into an object)a realization that was only dialectically presented in the Ideal chapter. An object given absolutely is an object that can be determined through concepts. Objects of sense are of this kind: I can use the concepts of the understanding (causality, reality, etc.) to determine them regardless of whether they exist or not. On the other hand, an object in the idea is an object only in a highly specific sense of the term. As Kant says, an object in the idea is, strictly speaking, a 'schema': [An object in the idea] is only a schema for which no object is given, not even hypothetically, but which serves only to represent other objects to us, in accordance with their systematic unity, by means of the relation to this idea, hence to represent these objects indirectly. (A670/B698) Let us try to unpack this brief but dense passage. First, an object in the idea is not a hypothetical object that might or might not exist. An object in the idea is rather a 'schema' or an 'imagined object (eingebildeter Gegenstand)' (A670/B698) that is not meant to represent anything out there, as it wereinstead, its function is to indirectly represent 'other objects to us'. As Kant continues, if we relate an idea 'straightway to an object', we simply 'would not be able to justify its objective validity' (A670/ B698). But why is this the case? After all, some of our ideas are free of logical contradictions and can be used to think entities that transcend our experience. 26 Kant, however, argues that logical consistency is not a sufficient condition for assuming ideas as objectively valid representations. As he puts it: Nevertheless, in order to assume something it is not enough that there is no positive hindrance to doing so, and we cannot be allowed to introduce mere thought entities that transcend all our concepts, though they contradict none of them, as real and determinate objects merely on credit, just so that speculative reason can complete its business as it likes. (A673-4/B701-2) I take Kant to mean that, although it is possible to use ideas to think entities that transcend our experience, this is not how ideas obtain objective validity. The objective validity of ideas cannot rest, as it were, on a mere wishful assumption of reason. Since we cannot know whether the object of the idea is more than a merely logically possible 'thought entity', we also do not know whether the idea is objectively valid. This is an important insight for it casts serious doubts on interpretations that read the objectivity of ideas of reason in terms of descriptive assumptions about noumenal objects. As Kant makes clear: One mistakes the significance of this idea right away if one takes it to be the assertion, or even only the presupposition, of an actual thing to which one would think of ascribing the ground for the systematic constitution of the world. (A681/B709) Ideas should not be taken even as mere presuppositions of objects. As such, taking them as descriptive of objects even if granting them weaker epistemic status than knowledge cannot explain their objectivity. Now, if objects in the ideas are not object in any standard meaning of the word, what are they? Kant's use of the word 'schema' should help us understand its meaning. In the Analytic, a schema is a third thing that links pure concepts with objects of sense (A138/B177). Here, objects in the ideas seem to play a different, yet similarly relational role. They are 'imagined objects' that act as the 'ground or cause (Grund oder Ursache)' from which we can derive objects of sense (A670/B698). They do not represent the actual or potential grounds of the objects of experience. Rather, they are mental representations that allow us to progressively represent those objects as systematically organized. As a schema, therefore, the object in the idea is a third thing which neither coincides with the objects of experience nor with their systematic unity 27it is instead the relational object that mediates between the two and allows our empirical investigation to converge towards systematic unity.
Accordingly, ideas are not, as Kant says, 'ostensive' concepts that show us how a noumenal object is or might be constituted (A671/B699). They are rather rules that tell us how we ought to systematize objects of experience. As Kant puts it, they 'should not be assumed in themselves', but 'their reality should hold only as that of a schema of the regulative principle for the systematic unity of all cognitions of nature' (A674/ B702). To sum up, the objective validity of ideas does not consist in an actual or potential relation to objects, but in the relational function they afford. This function consists in the progressive systematization of objects of experience they make possible.
The second, final step of the transcendental deduction of ideas consists in arguing that, if the three kinds of transcendental ideas (psychological, cosmological and theological) meet the above illustrated requirements and are realized as relational objects in the idea that lead to systematic unity without 'going contrary to experience', then it is a 'necessary maxim of reason to proceed in accordance with such ideas' (A671/ B699). This is how ideas are transcendentally deduced. As noted by Kant, this indirect and relational objective validity is quite different from that of the categories, but this does not mean that ideas are not properly transcendental. It only means, as Kant clearly says, that the deduction proves ideas as regulative, non-constitutive principles (A671/B699). They do not constitute experience, but they are necessary principles for attaining systematic unity of empirical cognition.
Let me conclude this analysis with some critical remarks. While accepting the deduction as sound, one may still doubt its usefulnesswhat do ideas of reason add to the thought that we must attain systematicity in empirical investigation? 28 I submit that ideas of reason make the notion of systematicity (i) meaningful and (ii) applicable to objects. (i) First, as we saw, ideas are what allow us to think objects of experience as systematically unified. I take this to mean that ideas spell out the meaning of systematicity with respect to different objects of experience or different aspects of them. Reason demands objects of experience to be systematized, but systematicity is a general notion. What does it mean for inner appearances to be systematized? What does it mean for nature to be systematized? Ideas are the imaginary grounds that specify how to think of systematic unity in different contexts. The analysis of the idea of God below will provide an example of such specification. (ii) Second, by spelling out, as it were, the rules of its thinkability, ideas of reason make systematicity applicable to objects of experience. By acquiring objective validity, ideas allow us to apply the general concept of systematicity to objects of naturesomething we would not be warranted to do without the ideal schemata acting as third elements between objects of experience and their systematic unity. The transcendental deduction of ideas of reason is the culmination of the critical project because it shows that the highest concepts of reason find legitimate application in the realm of possible experience.
Finally, it is important to briefly remark on the limits of the deduction of the ideas. While this deduction shows that ideas of reason are necessary to realize systematic unity, it does not independently establish that systematic unity is in itself necessary. Rather, it presupposes that human reason constitutively demands systematic unity. As Kant puts it in the Appendix, 'the systematic in cognition' is 'what reason quite uniquely prescribes and seeks to bring about' (A645/B673) and similarly that 'the unity of reason is the unity of a system' (A680/B708). Given the nature of our reason, we are compelled to proceed according to what progressively realizes systematicity, namely ideas of reason. 29

Analogies, not descriptions
The above relational reading of the deduction of the ideas should have partly clarified the meaning of the 'realization' of an idea into an object. There is, however, an important aspect of the idea that we still need to specify. If ideas are mere schemata that do not correspond to any objects out there, how can we still positively characterize their content? In the Appendix, Kant not only deduces the objective validity of ideas as schemata, but he also specifies how we are allowed to qualify the content of an idea in non-descriptive terms.
Recall that the object in the idea acts as the imaginary 'ground or cause' of sensible objects. In order to think these imaginary grounds or causes we cannot but rely on concepts of the understanding. These concepts lose descriptive power when not applied to objects of sense so that, as Kant frequently remarks, objects in the idea should not be assumed 'in themselves' or as 'things in themselves' (A674/B702). The noumenal ground of sensible objects remains beyond our conceptual determination. Objects in the idea should be assumed, instead, as 'analogues of real things (Analoga von wirklichen Dingen)' (A674/B702). 'Analogy' is a technical term for Kant that fits particularly well with the relational reading of ideas suggested in this article.
As Kant explains in the Analytic, philosophical analogies do not give us the 'identity of two quantitative but of two qualitative relations' (A180-1/B222-3). In the Prolegomena, Kant specifies that analogical thinking 'does not signify, as the word is usually taken, an imperfect similarity between two things, but rather a perfect similarity between two relations in wholly dissimilar things' (P, 4: 357-8). 30 I take Kant to mean that, in philosophy, analogies do not give us real or tentative descriptions of a to-be-determined object, but rather qualify the relation to an object that remains unknown to us. For example, a philosophical analogy of the form 'a : x = b : c', where only a, b and c are known to us, does not allow us to attempt a derivation of x, but only establishes a relation between a and x. 31 This understanding of analogies finds confirmation in the Appendix. By acting as the imaginary ground of the systematic unity of objects of sense, the object in the idea does not in any way attempt to establish a similarity with (or a 'description of') the noumenal ground of appearances (the unknown x). Rather: We are thinking of a Something about which we have no concept at all of how it is in itself, but about which we think a relation to the sum total of appearances, which is analogous to the relation that appearances have to one another. (A674/B702) The object in the idea is a mere 'Something (Etwas)' that leaves the ground of appearances completely undetermined with respect to its attributes -'how it is in itself', or its 'inner property' (A675/B703). Thinking such a thing qualifies, instead, the relation between appearances and their unknown ground (a : x). This relation can be thought as analogous to the relations existing among appearances, namely as an empirical relation (b : c). In other words, we can use concepts of the understanding (that have their proper use only within the world of sense) to positively characterize the type of relation an unknown ground has to objects of sense. This positive characterization is legitimate because it avoids establishing a similarity between our ideas and noumenal objects. 32 These points can be made clearer if we take a closer look at the specific idea which concerns us in this article: the idea of God. In accordance with the general account given above, the idea of God is 'the idea of something on which all empirical reality grounds its highest and necessary unity' (A675/B703). If we assume such an idea, we do not attempt a description of the inner properties of the noumenal ground of empirical reality, but we 'deal satisfactorily with all other questions concerning the contingent' and 'consider the objects in one complete whole' (A676/B704). As Kant puts it, we are presupposing a ground 'relatively'. That is, in relation to the world of senseas an object in the idea or a schema (cf. P, 4: 359). Indeed, since this idea is 'unavoidably necessary for approximating to the highest possible degree of empirical unity' (A677/B705), we must presuppose and realize this idea: I am not only warranted, but even compelled to realize this idea, i.e., to posit for it an actual object, but only as a Something in general with which I am not acquainted at all and to which, as a ground of that systematic unity and in relation to that, I give such properties as are analogous to the concepts of the understanding in its empirical use. (A677-8/B705-6) Here the realization of the idea is strictly conducted for the sake of the 'greatest possible empirical use of my reason' (A677-8/B705-6). Since this use is necessarily based on the idea of 'complete systematic unity', then I can and indeed must posit something that grounds such complete systematic unitynamely, the idea of God. I can thereby apply concepts of the understanding to this something and think it 'according to the analogy of realities in the world, of substances, causality, and necessity': as a 'being that possesses all of these in their highest perfection' (A678/B706). As the imaginary ground of 'complete systematic unity', the idea of God contributes to systematicity in the twofold way I described in section 3.2. First, it spells out the meaning of systematicity by allowing us to think nature as grounded in the idea of God, and therefore as systematically organized in terms of realities, substances, causal connections, etc. Second, the idea of God makes systematicity applicable to empirical objects since it allows us to systematize nature according to its analogical characterizations.
As I showed in this section, we can think the idea of God only by analogically applying our concepts, including that of reality, to it. Now, to think God as the being that specifically possesses reality in the highest perfection is to think God as the most real being. But what does it mean to analogically think God as the ens realissimum?

The analogical Ens Realissimum
In section 2, I reconstructed the natural progression of reason according to which the transcendental principle of thoroughgoing determination presupposes the material of all possibility, as the sum total of all predicates of things in general. This whole of possibility is then refined to its subset of positive predicates and then hypostatized in one individual being, the ens realissimum: Kant is there reconstructing the dialectical steps that lead the metaphysician astray. But, as we saw, he also gives important clues on how to critically interpret this transcendental principle and its presupposition. Most notably, Kant suggests that, with the latter, we are only presupposing an idea which can prescribe to the understanding the rule of its complete use. In the final paragraphs of the section, he also suggests that the principle could be legitimately applied if restricted to the objects of sense. At the same time, Kant also gives opposite indications: it seems that the hypostatization itself is an illegitimate move and that the whole process can be classified as dialectical. These ambiguities have led to interpretative difficulties. There was in fact an important element missing and that only the completion of the critical business finally provides: the transcendental deduction of the ideas, and particularly of the idea of God. Without this element, it is indeed highly dubious how an idea can regulate concepts and be transcendental in the sense of applying to objects of sense at all. In this section, I contend that the transcendental deduction finally warrants a positive use of the ens realissimum as it is described at the end of Section Two of the Ideal.
As I argued, the key step in the natural progression of reason consists in the 'realization' of the idea: that is, in transforming the idea of the sum total of all possibility presupposed by the transcendental principle of complete determination into a kind of 'object', which is then hypostatized. We now know how to distinguish the dialectical from the correct realization of the idea. In the former case, the idea is transformed into the concept of an object and the ideal is confused with a condition of possibility of things in general. This is the 'transcendental subreption' Kant talks about at the end of Section Two of the Ideal chapter. By realizing the idea in this way, we illegitimately end up using PTD in constitutive terms. But the second kind of realization licenses instead a perfectly legitimate, regulative use of the same idea and of the resulting principle. This realization consists in transforming the idea of the sum total (the basis of the ideal) into an object in the idea (or schema): that is, a something which in itself remains unknown to us, and yet we can analogically think in accordance with the concepts of our understanding, in particular with the concept of reality. We are allowed to do this not in order to determine the idea as an object, but in order to ground the complete empirical use of the understandinghere specifically understood as the complete determination of our concepts of objects of sense.
The relational, analogical reading of ideas finally allows us to understand the positive remarks included in the reconstruction of the dialectical illusion that make the interpretation of the ideal so difficult to discern. At the end of the derivation, Kant says: It is self-evident that with this aimnamely, solely that of representing the necessary thoroughgoing determination of thingsreason does not presuppose the existence of a being conforming to the ideal, but only the idea of such a being, in order to derive from an unconditioned totality of thoroughgoing determination the conditioned totality, i.e., that of the limited. (A577-8/ B605-6) The thought here clearly anticipates the deduction given only later in the second part of the Appendix. For the idea has objective reality only inasmuch as it grounds the thoroughgoing determination of the 'conditioned'. 'Conditioned', however, is still an ambiguous term: it may refer both to empirical and to non-empirical objects. Kant restricts the application to empirical objects at the end of the section. Since we can now separate the dialectical from the proper use of reason, we can also positively interpret this restriction without implausibly reading PTD as a principle of the understanding. The new version of PTD reads as follows: PTD*: 'now an object of sense can be thoroughly determined only if it is compared with all the predicates of appearance, and is represented through them either affirmatively or negatively'. (A581/B609; emphases added) The principle now states that for every empirical object and every possible empirical predicate P, either P or non-P must apply to it. With this restriction Kant gives the Leibnizian ideal of complete determination a critical twist. As noted by Wood, Kant does maintain the Leibnizian ideal of knowledge of objects as complete determination, but the latter is not grounded in conceptual analysis anymore. It is now a regulative task of synthesis which is grounded on an idea of reason. 33 PTD* is not, therefore, as argued by Longuenesse, a principle of the understanding. It is instead a principle of reason for the complete use of the understanding. The idea on which the regulative task of synthesis is grounded is that of a sum total of realities in appearance. SUM*: 'nothing is an object for us unless it presupposes the sum total of all empirical reality (Inbegriff aller empirischen Realität) as condition of its possibility'. (A582/B660) This idea can be critically realized as an object in the ideathat is, as a schema for the complete determination of empirical objects. As we saw in the previous section, we are compelled to think the relation between objects of sense and the ground of their systematic unity in analogical terms. In this case, we analogically think what grounds the complete determination of objects of sense as the sum total of empirical reality. 34 From this SUM*, we can further derive an analogical OMNITUDO* as the subset of positive empirical reality. Do we need to stop here in the derivation as suggested by Longuenesse? Or can we also proceed with a non-dialectical hypostatization? I contend that, if grounded in a critical, legitimate realization, the omnitudo realitatis can also be further hypostatized as an individual ideal being, namely as an analogically thought ens realissimum (ENS*): as Kant puts it, 'an individual thing containing in itself all empirical reality' (A582/B610). By doing this, we are not determining an individual being, but only thinking it as a schema for the complete use of the understanding. This is not only compatible with the admission of a regulative function of the idea of God in the theoretical realm, but also specifically confirmed by passages in which Kant explicitly assumes the ideal itself as a regulative principle. For instance, he says that 'the ideal of the highest being is, according to these considerations, nothing other than a regulative principle of reason' and that 'systematic unity of nature cannot be set up as a principle of the empirical use of reason except on the basis of the idea of a most real being as the supreme cause' (A619/B647).
To sum up, the non-dialectical derivation of the ens realissimum amounts to: PD → PTD* → SUM* → OMNITUDO* → ENS* We start from a merely logical principle of determinability that applies to concepts (PD). We then apply PD to empirical objects, thus inferring PTD*. By doing so, we presuppose the regulative idea of a sum total of empirical realities (SUM*), which reason further refines into its positive subset OMNITUDO* and finally hypostatizes as an ideal individual ENS*. If instead we end up with the corresponding illegitimate sequence, this is due to the fact that we mistake an object in the idea (SUM*) for the concept of an object (SUM), and thereby we transform a regulative, empirical principle (PTD*) into a constitutive principle that determines things in general (PTD). 35 From this principle, we then derive the entire dialectical, metaphysical progression that we saw in section 2.

Conclusion
In this article, I suggested that the transcendental deduction of the ideas licenses a positive use of the idea of God as the ens realissimum (transcendental ideal) and that such use is a key component for thinking the whole of empirical nature as systematic.
Although the ideal cannot be directly related to an object, it can be critically realized and obtain indirect objective reality. Ideas are critically realized when they are presupposed as 'objects in the idea' for the systematization of empirical cognition. Realizing the idea of God means to presuppose an imagined ground of the systematic unity of the whole of nature. Since such a ground is necessary for promoting the empirical investigation of nature, we are compelled to think it in analogical terms. Analogical characterizations do not attempt to describe objects, but rather give us indispensable rules to investigate nature. In particular, the analogical ens realissimum prescribes to the understanding the task of the complete determination of objects of experience. This analogical conception finally explains how the transcendental ideal, despite being 'removed' from the objects of sense, must indirectly guide empirical investigation.
I did not suggest, however, that this is the only source that explains the relation between the idea of God and systematicity. As we saw in section 3, the concept of reality is only one of the concepts that can be analogically applied to the idea of God in order to promote the systematic unity of our empirical cognition. It would be instructive and beneficial for our understanding of the role of the idea of God in science to investigate whether and how other conceptions of God, such as 'necessity in existence' (A607/B635) and 'highest intelligence' (A695/B723) can be analogically characterized, and what their significance for the empirical investigation of nature amounts to. Unfortunately, a proper study of the other characterizations of the idea of God goes beyond the remit of this article and should be pursued elsewhere. 36 Notes