1.1 Reason As Faculty for Inference and Hypothesis Formation

In the Critique of Pure Reason, Kant discusses the peculiar fate of reason mainly in the Transcendental Dialectic: there, he introduces reason primarily as the faculty of inferring, before setting out to raise a fundamental critique of the illicit use of reason in dialectical inferences leading to transcendental illusions.Footnote ¹⁰ According to this definition, reason’s most common employment is in drawing syllogistic inferences. Such inferences of reason connect two judgements (a major premise and a conclusion) through the mediation of a third one (the minor premise) (see A309/B366). Typically, such inferences proceed deductively: they start from a given, general rule (i.e., the major premise) and descend towards a specific application of that rule (i.e., the conclusion).Footnote ¹¹ To adapt a classic example:

In this deductive function, reason builds on the workings of the understanding (Verstand) – in its function of combining concepts (and ultimately intuitions) into judgements – and also on the deliverances of sensibility (Sinnlichkeit) – in terms of its sensory intuitions. Reason depends on the understanding for supplying general cognitions that can be used as major premises, and on the power of judgement (Urteilskraft) for subsuming a more specific cognition under a general one in the minor premise.Footnote ¹² Reason thus assists the understanding in gaining cognition through its ‘derivation … from principles’ (A300/B357) and preserves the objective validity of the premises for the conclusion.

As such, reason appears to be ‘merely subordinate’ to the understanding (A305/B362): by subsuming the condition of a given cognition (in the minor premise) under a universal rule (the major premise), reason reveals a more general condition of that cognition and thereby promotes the aim of the understanding to determine an object through cognition. The example syllogism above reveals mortality as a more general condition of Xanthippe than the already known condition of being human.

Kant distinguishes three logical forms of syllogisms dependent on three forms the major premise can take: Following the three forms of relational judgements, the categorical syllogism has a categorical judgement as its major premise (‘A is p’), the hypothetical syllogism has a hypothetical judgement as its major premise (‘If A is p, then B is q’), and the disjunctive syllogism has a disjunctive judgement as its major premise (‘A is p or A is q’) (where A and B are subject terms, and p and q are predicates).Footnote ¹³

Yet this deductive function also raises the question of how we can find general rules in the first place. In order to recognize a generalization, we must be provided with a set of experiences and by comparing and contrasting these experiences find observational patterns. To explain these patterns, we posit a hypothesis as the general rule that governs the observed objects. For example, if we observe the falling of several material objects, such as the dropping of an apple from a tree and the sliding of a feather to the ground, we can find a common pattern in these observations despite noticeable differences and eventually identify a general causal rule, such as Newton’s law of gravitation.

Kant does not explicitly provide us with an account of inductive reasoning, through which one can derive a universal rule from individual cases. Nonetheless, he is familiar with the work of Francis Bacon, who first defined the method of induction as the fundamental knowledge-generating principle of the empirical sciences, as well as with David Hume’s sceptical doubts regarding induction.Footnote ¹⁴ Kant occasionally addresses related issues in his account of laws of nature, especially with respect to the search for particular empirical laws.Footnote ¹⁵ In the Critique of the Power of Judgment, Kant introduces the reflecting power of judgement to explain how to find a universal rule under which given particulars can be subsumed.Footnote ¹⁶

In the first Critique, Kant still sees a fundamental role of reason in the search for general rules, namely in its hypothetical use, which he introduces only in the Appendix to the Dialectic. The hypothetical use is ‘not such that if one judges in all strictness the truth of the universal rule assumed as a hypothesis thereby follows’, but rather such use is ‘only regulative, bringing unity into particular cognitions as far as possible and thereby approximating the rule to universality’ (A647/B675). Reason in its hypothetical use generates hypotheses that generalize over what is given in experience, but it cannot guarantee the universal validity of the hypothesis as it does in the case of derivative inferences. Even though reason goes beyond immediate inferences from actual experience, it still operates within the realm of possible experience. A hypothesis can be tested in light of particular empirical cognitions and is confirmed (or at least corroborated) as a general rule, if (or as long as) no counterexample is found.Footnote ¹⁷ We may, for example, hypothesize that animals are mortal, and this hypothesis has been corroborated as a general rule, since so far no immortal animal has ever been discovered.Footnote ¹⁸

By assigning the function of generating hypotheses to reason, Kant reverses the direction in which reason operates in inferences, as well as the dependence relation between reason and the understanding. Reason no longer descends from the universal validity of a rule established by the understanding to a more specific application of that rule in the conclusion, as is the case in deductive inferences. Rather, reason now ascends towards a more general universality than that hitherto cognized through the understanding. Reason now directs the understanding ‘by opening up new paths into the infinite (the undetermined) with which the understanding is not acquainted, yet without ever being the least bit contrary to the laws of its empirical use’ (A680/B708).

Even though reason, in its hypothetical use, ‘prepares the field for the understanding’ (A657/B685), it does not yet leave the ‘field of possible empirical cognition’ in an illegitimate way (A644/B672). To observe these boundaries of experience, the hypothetical use should not be exercised randomly, but in some sense purposively, namely with the purpose of enhancing the faculty of cognition by maximizing its scope and explanatory power. Kant argues that ‘the hypothetical use of reason is therefore directed at the systematic unity of the understanding’s cognitions’ (A647/B675). This systematic unity is necessary to prove (or at least corroborate) that a hypothesis ‘approximat[es] the rule to universality’, that is, can be assumed as universally valid (as far as we know) (A647/B675).Footnote ¹⁹

Kant always conceives of reason as the ‘supreme faculty of cognition’, which aims to pursue the ‘highest unity of thinking’ (A299/B355). This highest ‘unity of reason’ (A302/B359) is superior to the ‘unity of the understanding’ (A307/B363): the latter can be fully realized in experience and is reflected in the form of unity that an empirical judgement exhibits, whereas the former goes by definition beyond any experiential grasp. Let me explain with an example.

The understanding defines kinds of unities, expressed in its pure concepts, that we can find in experiential episodes, despite the fragmentary nature of our sensible intuitions. For example, when I observe a red apple rolling off my kitchen table, I have a multitude of sensible intuitions. These intuitions present the apple to me only from a particular visual perspective. They show the front, but not the back, of the apple. They might not show every infinitesimal unit of the apple’s motion either. Nonetheless, by applying the understanding’s pure concepts such as substance and causality – as categories – to my sensible intuitions, I can cognize the apple as a unified object, as a substance with changing accidents and persisting through a course of motions in accordance with a causal law. This leads to empirical judgements such as <The apple is red> and <The apple is rolling off the table>.Footnote ²⁰ Hence, the understanding’s categories, such as substance and causality, give rules for synthesizing intuitions into specific kinds of unities. The resulting cognitions exhibit these unities defined by the understanding.

Reason, however, is not satisfied with singular cognitions. By its nature, reason keeps asking for further and further conditions of the apple. It asks, for example, about the condition of why the apple rolled off my kitchen table, but also why the apple ended up on my kitchen table in the first place, why it came into being, which biochemical processes led to its existence, and perhaps also why it has become an object of my culinary preferences. This quest of reason seems to come to an end only when reason has completely determined the apple. But in this quest for completeness, reason seeks a kind of unity ‘that can never come forth in experience’ (A765/B793). Reason, therefore, runs the risk of transcending the bounds of sense. Most of the Transcendental Dialectic is therefore devoted to uncovering these transgressions of reason. But why does reason pursue this ‘unity of reason in appearances’ (A326/B383) at all, although we cannot experience such unity? Can such a pursuit serve a constructive purpose?

1.2 The Totality of Conditions and the Unconditioned

Reason has a natural tendency to seek completeness, namely the totality of conditions to a given conditioned.Footnote ²¹ This tendency is already implied in its basic function in inferential reasoning, since the central point of an inference is to reveal a more general condition, for example, the governing law, of a given cognition and its object. Already in its harmless use in hypothesis generation, reason seeks to move beyond the rules established by the understanding. But reason strives towards the totality of conditions. The complete set of conditions, if available, would fully determine an individual thing. Reason thus seeks a complete and thoroughgoing determination of things in all their properties, including possible ones (A571/B579).

Kant explains the striving for completeness in terms of an iteration of syllogisms in an ‘ascending series’, that is, a series of so-called ‘prosyllogisms’ (A331/B388, also A307/B364). Each prosyllogism reveals a yet more general condition for the premise of the preceding syllogism.Footnote ²² In our classic example (concerning Xanthippe), the next prosyllogism would have the previous major premise that all human beings are mortal as its conclusion and reveal a yet more general condition. It could, for example, run as follows:

The whole series of prosyllogisms results not in another conditioned cognition, but in the totality of premises, that is, the totality of conditions for a given conditioned cognition. In light of any given cognition, reason is ‘necessitated to regard the series of conditions in an ascending line as completed and given in their totality’ (A332/B388). Why is reason so necessitated? To answer this question, we have to turn to the intrinsic principles of reason itself and hence to pure reason, that is, reason in its pure use in abstraction from any (sensible or logical) content supplied by subordinated faculties (A305/B362ff.).

The first principle that reason intrinsically follows is the logical maxim ‘to find the unconditioned for conditioned cognitions of the understanding, with which its unity will be completed’ (A307/B364). This maxim is a subjectively valid ‘logical prescript’ that guides reason’s regressive employment in an ascending series of inferences (A309/B365).Footnote ²³ Yet this logical maxim raises the concern that it may only be properly applicable under the assumption that something unconditioned must exist that stops the regressive inquiry. This could be, for example, an initial unconditioned condition that started the series (e.g., the beginning of the universe in time) or something unconditioned that underlies the whole series (e.g., the noumenal character that grounds the whole series of a person’s actions). Searching for the totality of conditions and ultimately for the unconditioned would be reasonable only if we assumed that these actually existed.Footnote ²⁴

The logical maxim therefore seems to imply a second principle, the supreme principle of pure reason: It appears that if the logical maxim is to be meaningful and instructive for human reason at all, then one must also ‘assume that when the conditioned is given, then so is the whole series of conditions subordinated one to the other, which is itself unconditioned, also given’ (A307-8/B364).Footnote ²⁵ This supreme principle would be the candidate for the first synthetic principle of pure reason. It is synthetic since it reaches beyond the analytic relations between cognitions given through the understanding to something unconditioned.

Yet this supreme principle raises an even more serious concern: since the totality of conditions and hence something unconditioned can never be encountered in experience, the supreme principle and all principles derived from it can only ever be ‘transcendent’ in respect of appearances (A308/B365). Does the application of the supreme principle lead to the assumption of a given unconditioned?Footnote ²⁶ Yet in the Transcendental Dialectic, Kant exposes the assumption of something unconditioned that exists ‘in itself and absolutely’ as a transcendental illusion. Such an illusion consists in the assumption that something unconditioned is given independently of the human mind but can nonetheless be determined by our categories. Kant rejects this assumption as deceptive and fallacious.Footnote ²⁷

1.3 The Transcendental Ideas of Reason

In its quest for completeness, pure reason becomes ‘a genuine source of concepts and judgments’ (A305/B362, see also A299/B355), namely of the pure concepts of reason or simply of transcendental ideas (e.g., A311/B368, A321/B378). These are ‘necessary concept[s] of reason’ that can be derived from reason’s own iterative inferential procedure (A327/B383). These concepts are formed by ‘ascending in the series of conditions’ until one reaches the totality of conditions (A336/B394): ‘So the transcendental concept of reason is none other than that of the totality of conditions to a given conditioned thing’ (A322/B379). This totality is then ‘explained through the concept of the unconditioned’: the concept of the unconditioned represents the ‘ground of synthesis for what is conditioned’ and hence the ground of the entire series of conditions (A322/B379).

Corresponding to the three types of syllogisms – the categorical, the hypothetical, and the disjunctive syllogism – Kant distinguishes three kinds of relations that these ascending series of conditions can express: ‘1) the relation to the subject, 2) the relation to objects, and indeed either as appearances, or [3)] as objects of thinking in general’ (A333/B390‒391). These three kinds of relations lead to three classes of transcendental ideas: (1) the concept of the ‘absolute (unconditioned) unity of the thinking subject’ (A334/B391), that is, the idea of the soul or, more generally, the psychological ideas; (2) the concept of ‘the absolute unity of the series of conditions of appearance’ (A334/B391), that is, the idea of the world-whole or, more generally, the cosmological ideas; and (3) the concept of ‘the absolute unity of the condition of all objects of thought in general’ (A334/B391) or ‘the idea of an All of reality (omnitudo realitatis)’ (A575/B603), which culminates in the ‘highest rational concept of a being of all beings’ (ens entium) (A336/B393), that is, the theological idea of God.Footnote ²⁸ Let me say a word about each.

The idea of the soul is obtained through a series of categorical syllogisms that are applied to one’s representations. For each representation R_i, the thinking of R_i is predicated of a subject S_i in a categorical judgement of the form ‘S thinks R’. The whole series then results in the ‘unconditioned … for the categorical synthesis in a [single] subject’ (A323/B379). The idea is thus the concept of ‘the absolute (unconditioned) unity of the thinking subject’ (A334/B391). It can be further specified by sub-concepts such as <simple thinking substance> (see A673/B701), <being endowed with a fundamental power>, and <being entirely distinct from a body> (see A682/B710). The idea, if it refers to something real, would represent a thinking substance in which all one’s representations inhere.

An idea concerning the world-whole (in the broad sense) starts from a given appearance, runs through an infinite regression of hypothetical conditions (‘If A is p, then B is q’), and finally completes the ‘hypothetical synthesis of the members of a series’ of appearances (A323/B379). This infinite regression results in the concept of ‘the absolute unity of the series of conditions of appearance’ (A334/B391). This absolute unity can be explicated in a variety of ways, for example, as the absolute unity of space or of time in the mathematical ideas of the world (in the narrow sense) (see A418/B446 ff.). This absolute unity can also mean the ‘sum total [Inbegriff] of appearances’ that are interconnected by causal laws, or simply nature (see A418/B446 n ff., also B163 and A328/B384).Footnote ²⁹

The idea of God is derived from the ‘disjunctive synthesis of the parts in a system‘ (A323/B379), which leads to the concept of ’the absolute unity of the condition of all objects of thought in general’ (A334/B391). The derivation procedure in this case is more complicated. It starts from the principle of thoroughgoing determination (PTD), according to which for each possible predicate either it or its negation applies to a thing (see A571/B579ff.). This can be expressed in a series of disjunctive judgements of the form ‘A is p or A is non-p’. Using this principle iteratively leads to ‘the idea of an All of reality (omnitudo realitatis)’ (A575/B603), that is, a reality in which all things are completely determined. This idea is then explained through the ‘concept of a being of all beings’ (ens entium) (A336/B393), or the concept of the highest being (i.e., ‘ens realissimum’) (A576/B604), or simply the idea of God.

These three classes of transcendental ideas should not be confused with other ideas of reason such as ‘pure earth, pure water, pure air’ (A646/B674). Like the transcendental ideas, these ideas are concepts of the ‘form of a whole of cognition’ (A645/B673). But they cannot be derived from the nature of reason itself, that is, from its forms of syllogisms. Rather, they arise by considering some empirical results in a particular area of nature and they serve to ‘question nature’ to find more lawful connections in that area (A645/B673). They function like idealized models in science. For example: ‘one reduces all materials to earths (mere weight, as it were), to salts and combustibles (as force), and finally to water and air as vehicles (machines, as it were, by means of which the aforementioned operate), in order to explain the chemical effects of materials in accordance with the idea of a mechanism’ (A646/B674).Footnote ³⁰

In sum, reason’s characteristic inferential procedures give rise to transcendental ideas. These ideas express the totality of conditions for a given conditioned cognition. In turn, these totalities are ‘explained’ by concepts of something unconditioned (A322/B379). For example, the totality of conditions of a representation is explained by the concept of the absolute subject; the totality of conditions of a spatial entity is explained by the concept of absolute space. As concepts of absolute wholes, ideas cannot have ‘congruent object[s] … given in the senses’ (A327/B383), so that their use naturally leads beyond the boundaries of experience. But what legitimate use could these ideas still have, and in what sense could they have a transcendental status with respect to empirical cognition?Footnote ³¹ Before considering the answers that noumenalist and fictionalist interpretations give to these questions (in 1.5 and 1.6, respectively), I introduce the regulative use of transcendental ideas.

1.4 Is the Regulative Use of Ideas a Real Use of Reason?

A central question is whether reason itself can provide insight into objects of cognition or even into things-in-themselves. That is, does reason have a real use? Kant distinguishes between a logical and a real use for both the understanding and reason. Logical use is the mind-to-mind application of a faculty relating mental or representational items to one another (from Greek logos, meaning word, thought, or principle). Real use is a mind-to-world application relating mental or representational items to objects or things in the world (from Latin res, meaning thing). For example, in its logical use, the understanding relates different concepts in a judgement, whereas in its real use, it applies concepts to sensible intuitions and hence makes judgments about objects of experience. In the Transcendental Analytic, Kant offers complex arguments that (and how) the real use of the understanding provides a priori transcendental principles of experience. But he is far more hesitant about reason: in fact, the Transcendental Dialectic deconstructs the rationalist attempts to derive insights about the reality of things from reason. But is there really no legitimate real use of reason over and above its logical use in formal syllogisms that abstract from all content?

Let us refine the taxonomy of uses of reason in comparison with the understanding. So far, reason, as the faculty of inferring has two kinds of uses, the derivational (or deductive) use and the hypothetical (or inductive) use. In these uses, reason relates directly to cognitions provided by the understanding. In other passages, reason is introduced as the faculty of principles or, more precisely, as the ‘faculty of the unity of the rules of understanding under principles’ (A302/B359). In this definition, reason is considered in its pure use, in abstraction from any content given through the understanding. Nonetheless, the understanding itself now constitutes an ‘object for reason’ (A664/B692): ‘pure reason is never related directly to objects, but instead to concepts of them given by the understanding’ (A335/B392). How does reason apply to ‘concepts’ or ‘rules’ of the understanding?

Three distinctions apply to both faculties, the understanding and reason: the distinctions (1) between a logical and a real use, (2) between an immanent and a transcendent use, and (3) between a constitutive and a regulative use.

1. (1) The distinction between logical and real use depends on the kind of mental item the faculty is applied to. A faculty operates on representations either in abstraction from their relation to objects or under explicit consideration of their reference to objects or things (see A299/B355). The logical use concerns only the logical relations among representations ‘abstract[ing] from all content of cognition’ (A299/B355). The logical use of the understanding combines concepts within a judgement in accordance with the forms of judgement (i.e., the ‘logical functions’ of the understanding, see A69ff./B94ff.). The logical use of reason combines judgements within a syllogism, in accordance with the three forms of inferences (i.e., the categorical, the hypothetical, and the disjunctive, see A299/B355 and A303ff./B359ff.). The real use, by contrast, considers the relation the representations have to their objects.

2. (2) Within this real use we can distinguish different kinds of objects or kinds of reality that a faculty aims at. An immanent use concerns only objects within the ‘boundaries of experience’ (Erfahrungsgrenze) (Bxxiv, A296/B352‒353, A637/B665), that is, appearances. A transcendent use is not limited by experience, but transcends the bounds of sense and potentially aims at things-in-themselves (see A296/B352, A637/B665, A643/B671). Kant accepts only the immanent use of the categories of the understanding for appearances as legitimate. But if the categories are taken to determine real things beyond the bounds of experience, we engage in an illegitimate ‘misuse’ (A296/B352) of them.Footnote ³² His critique of rationalist metaphysics rejects such transcendent use.

3. (3) A use can come with different kinds of necessity (or validity). A constitutive use defines conditions that are strictly necessary (and therefore universally valid) for a representation to be of a particular type. A merely regulative use specifies conditions for a type of representation that are not strictly necessary for the type, but conducive to approximating universal validity. These are conditions we should seek to satisfy, though we may never be able to do so completely.Footnote ³³

The categories of the understanding have a constitutive use with regard to experience because they establish strictly necessary conditions for a representation to count as experience, or empirical cognition. For example, the relational categories, such as substantiality and causality, are strictly necessary for the experience of a substance with causal powers. However, the relational categories are only regulative regarding the intuitions involved: they are not strictly necessary for us to have an intuition, but they give rules for synthesizing intuitions, if we aim for cognition (see A664/B692 and A180/B222‒223). The category of substance gives us a rule for how to combine a manifold of intuition such that a persisting substance can be distinguished from its changing accidents. Importantly, the constitutive use of the categories generates a priori real contents of empirical cognition and thus determines the most general features of objects of possible experience, such as persistence in time.

For reason, Kant rejects a constitutive use but admits a regulative use. In the Appendix to the Dialectic, Kant identifies the ‘good and consequently immanent use’ of reason as the regulative use of its ideas (A643/B671). Recall that pure reason is the origin of transcendental ideas, as the pure understanding is the source of pure concepts, namely the categories. The regulative use of ideas consists in ‘directing the understanding to a certain goal’ (A644/B672). This goal has earlier been defined as the ‘unity of reason in appearances’ (A326/B383) and is now described as ‘the greatest unity alongside the greatest extension’ of our cognitions (A644/B672), or as ‘systematic unity … of the understanding’s cognition’ (A648/B676, also A647/B675). The regulative use of reason thus aims to bring systematic unity to the cognitions of the understanding. Can we construe this regulative use as a real use like that of the categories? In what sense could ideas refer to something real?

Like the understanding, the real use of reason would aim at objects or things. It would reveal not only logical entailment relations among judgements, as in its logical use, but real conditioning relations of cognitions. These are the relations that feature in the explanation of appearances and that correspond to relations among and within objects. Corresponding to the three forms of syllogisms – categorical, hypothetical, and disjunctive – we can distinguish three types of real conditioning relations that obtain between a cognition and its condition(s): subsistence, dependence (or causality), and community (or reciprocity).Footnote ³⁴

The real use of ideas, as concepts of absolute wholes, is often understood as the real determination of things-in-themselves (as noumena).Footnote ³⁵ On this reading, it involves assumptions such as these: that an appearance must be grounded in the existence of an unconditioned subsistent thing, or that it must ultimately follow from an unconditioned causal power. But since, in contrast to the pure concepts of the understanding, nothing can be given to the senses that would correspond to these ideas, it is often concluded that their real use can only be transcendent and thus illegitimate. It leads precisely to the transcendental illusions Kant exposes in the Dialectic.

The question of whether or not the regulative use of ideas is a real use, and if so, to which reality it relates, divides the interpretations offered in the literature. According to what I called noumenalism, ideas relate to something unconditioned, and their regulative use requires a commitment to the existence of this unconditioned reality. According to fictionalism, by contrast, ideas provide heuristically useful fictions, which, however, are empty, that is, without denoting anything real. I now discuss each interpretive tendency in turn and indicate potential shortcomings.

1.5 Noumenalism: Ideas As Concepts of Real Things

Noumenalism treats ideas as ‘concepts of real things’ (e.g., A643/B671) and assumes that they relate to what Kant calls ‘noumena’ or ‘beings of understanding’ (B306).Footnote ³⁶ According to its strong version, any legitimate use of ideas must involve a commitment to the existence of such real things, although we cannot have cognition of those things, since ideas cannot have corresponding intuitions. This strong version is rarely stated in the literature, and there may be good reasons for this. However, there is a growing number of views on which Kant’s account of reason involves a commitment to the existence of something unconditioned.Footnote ³⁷ This commitment, if it is explicitly discussed at all, is sometimes understood as what Kant calls ‘doctrinal beliefs’ (A825/B853), a special case of the epistemic attitude of taking-to-be-true (or assent). In contrast to knowledge, belief requires only subjectively sufficient reasons but lacks objectively sufficient reasons.Footnote ³⁸ Can these interpretations, though not dealing directly with ideas, offer a plausible account of the regulative use of ideas?

In a recent proposal, Schafer (Reference Schafer2023) develops a noumenalist reading of the supreme principle of reason (see 2.2). According to Schafer, Kant defends a version of the supreme principle that ‘does commit us to the bare existence of the “whole series of conditions” and so to the unconditioned’, even though ‘that commitment leaves the nature of the thing or things we are committed to almost wholly indeterminate’ (Schafer Reference Schafer2023:175). Schafer construes this commitment as doctrinal belief or ‘assent’ that is ‘necessary for theoretical reason to successfully engage in its essential activities’ (Schafer Reference Schafer2023:173). So, Schafer allows for assent to the existence of something unconditioned but concedes that the content of what is assented to must remain ‘almost wholly’ indeterminate. In this way, Schafer’s view can avoid the transcendental fallacies that arise from the determination of the unconditioned by our categories. Any determination would transform the regulative use into a constitutive use of reason. Can we take this view to develop an account of the regulative use of ideas?Footnote ³⁹

At first glance, the proposal offers a natural explanation for the legitimacy and the normative bindingness of ideas: their regulative use is legitimate and binding because it is backed by a commitment to the existence of something unconditioned. The unconditioned is assumed to ground (in some sense) what the ideas demand us to realize, that is, it grounds the systematic unity of cognitions that reason demands us to seek. But this proposal also raises some worries.

First, a worry regarding the indeterminacy of doctrinal belief. Ideas of reason are concepts that complete a particular ‘whole series of condition’ and contain specific predicates such as <simple substance> or <fundamental power>. If the regulative use of any idea involves the same commitment to the bare, but entirely indeterminate existence of something unconditioned, then the view cannot explain the differences between ideas. It appears that regardless of the kind of idea we use, in all cases we are committed only to the ‘bare existence of the unconditioned in a highly abstract form’ (Schafer Reference Schafer2023:174). This might be unsatisfactory as an account of ideas. If the commitment is entirely indeterminate, we may lack a sufficient justification for why we ought to use these ideas rather than others.

Second, a worry regarding a potential objectification. If we instead assume that each idea presupposes a different belief, then it might be difficult to defend the claim of the indeterminacy of these beliefs. The regulative use of the idea of the soul may presuppose a belief in the existence of thinking substances, while the idea of God may presuppose a belief in an author of a purposively ordered world. This suggests that the beliefs differ in content depending on the idea they ground. However, it might be difficult to spell out these differences in content without allowing a determinative use of the categories. We may run the risk of slipping from a regulative into a constitutive use and determine the unconditioned as an object for us according to our categories.Footnote ⁴⁰ But then we do exactly what Kant warns against in the Dialectic: we ‘hypostatize’ ideas, that is, ‘mak[e] thoughts into things’ (A395; see also A384, B402, A615/B643), instead of regarding ideas as ‘imagined object[s]’ (A670/B698) or ‘analogues of real things’ (A674/B702). Indeed, the significance of ideas is ‘misunderstood’ if they are taken ‘for concepts of real things’ (A643/B671) or for things ‘assumed in themselves’ (A674/B702). Thus, if the regulative use of ideas requires doctrinal beliefs, these should not be understood as positing the existence of metaphysically robust objects that correspond exactly to these ideas, as this would lead to transcendental fallacies (see A327/B383, A643/B671).Footnote ⁴¹

Third, there is a worry regarding the subjectivity of doctrinal beliefs. Doctrinal belief requires only subjectively sufficient reasons, which Schafer construes as ‘sufficiency with regard to reason’s purposes’ (Schafer Reference Schafer2023:171). Drawing on doctrinal belief only explains why ideas are justified subjectively with regard to reason’s own inferential procedures. But it does not explain why their regulative use gives rise to principles of systematic unity that have ‘objective but indeterminate validity’ (A663/B691), ‘as pertaining to the object itself’ (A650/B678). These principles are often characterized as ‘transcendental’ presuppositions. For example, we must presuppose that nature itself is systematically unified (e.g., A321/B378ff., A327/B383‒384, A681/B709ff.). Conceding a mere belief may be too weak to justify the transcendental status of ideas. For a belief, while subjectively warranted, could still turn out to be objectively false. That is, the unconditioned that the belief postulates could after all not exist. Appealing to doctrinal belief might thus not be effective in justifying the objective validity of regulative ideas.Footnote ⁴²

1.6 Fictionalism: Ideas As Non-Referring Fictions

A fictionalist view implies that ideas provide empty or nonreferring fictions. Their legitimate use requires the rejection of any existential commitment to what these fictions describe. Fictionalism finds its most explicit support in passages that describe the regulative use of ideas in terms of ‘heuristic’ (rather than ostensive) principles (A663/B691, A671/B699) or ‘heuristic fictions’ (A771/B799). Such heuristic fictions are subjectively necessary guidelines to pursue the ‘demands’ (e.g., A656/B684, A699/B727) and ‘interests’ of reason (e.g., A666‒678/B694‒696, A686/B704, A704/B732) rather than truthful descriptions of a mind-independent reality.Footnote ⁴³

Fictionalism takes seriously that ideas should not simply be understood as ‘concepts of real things’ (A643/B671). By renouncing any relation that ideas might have to an underlying reality, it avoids sliding into a constitutive use of ideas that illegitimately determines non-sensible objects. Many commentators therefore consider the regulative use as a species of the logical use of reason. They identify the regulative use of reason with the application of the logical principle to seek systematic unity in cognition through logical inference. They grant that this subjective principle presupposes – in some sense – the transcendental principle that nature really is systematically unified.Footnote ⁴⁴ Yet this transcendental principle is considered to be only a ‘self-serving delusion’ (Guyer Reference Guyer1979:42), an ‘inevitable illusion’ or ‘illusory postulation of reason’ (Grier Reference Grier2001:263, 276). The regulative use is thus necessarily based on a natural and unavoidable transcendental illusion, that is, the ‘transcendental and illusory postulation that nature … is already given as a complete whole’ (Grier Reference Grier2001:275). Such use still involves the ‘hypostatization’ of the idea as the ‘object of … [scientific] knowledge’ (Grier Reference Grier2001:279), and hence as the ‘intelligible ground’ of all appearances in nature (Grier Reference Grier2001:297, 301; see A384, A395, B402, A615/B643). Yet in order not to fall prey to this illusion and commit a metaphysical fallacy, it is assumed that this object, the referent of the idea, does not exist.

A major worry is that fictionalism fails to offer a suitable explanation for why ideas – employed as regulative principles – are normatively binding at all. The fictionalist is faced with the following situation: on the one hand, ideas facilitate, or even enable, the activities of the understanding in seeking systematic cognition of nature; on the other hand, ideas lead to illusory postulations that do not even have a referent. Yet the emptiness of ideas undermines the normative bindingness of the principle of systematicity. For how can an illusory assumption generate a prescriptive force for our epistemic activities that aim at the truth-apt cognition of empirical objects?Footnote ⁴⁵

In reply to this worry, the regulative use of ideas is often modelled on hypothesis formation in science. Ideas are assumed to be primarily involved in higher-order scientific theorizing, specifically in the discovery and articulation of empirical laws of nature.Footnote ⁴⁶ An idea’s regulative use consists then in the assumption of a certain hypothesis about a non-sensible object (e.g., that an appearance must be grounded in the existence of an unconditioned subsistent thing). This hypothesis serves as the highest premise in an ascending series of empirical conditions, without, however, being asserted as true. This hypothesis-formation view can apparently construe the regulative use as a real use.Footnote ⁴⁷ To avoid the transcendental illusions that may follow from a real use, the hypothesis is only accepted problematically in order to bring more ‘unity into particular cognitions as far as possible’ (A647/B675), without assuming a reference to something real.Footnote ⁴⁸

The hypothesis-formation view also raises both textual difficulties and philosophical worries. For Kant argues that the hypothetical use is possible only if it is itself ‘directed’ at the ‘systematic unity of the understanding’s cognitions’ (A647/B675). The hypothetical use, therefore, presupposes the more basic ‘indispensably necessary regulative use’ of an idea, which first defines a systematic unity (A644/B672). Moreover, Kant explicitly denies that ideas can be used to form hypotheses, at least according to Kant’s conception of a hypothesis, which requires the relation to what is ‘actually given’ in appearance (A770/B798). But ideas of reason precisely lack this relation to given appearances and therefore, if used in a ‘transcendental hypothesis … for the explanation of things in nature, would thus be no explanation at all’ (A772/B800).Footnote ⁴⁹ The hypothesis-formation view thus cannot offer a satisfying answer to the problem of normative bindingness either.

Can we nonetheless understand the regulative function of ideas in analogy with scientific idealizations? Even if a scientific hypothesis is false or empty and therefore no longer a candidate for a law of nature, it might be an idealization that, while not strictly true, can be pragmatically useful as a scientific model. For example, Newton’s laws of motion provide an adequate model for the motions of bodies at sufficiently low velocities in many contexts, although strictly speaking they are invalidated by Einstein’s theory of relativity. The assumption of certain fundamental particles of matter can be a useful mathematical idealization, even though we do not (yet) have experiments that prove the existence of these particles. Similarly, ideas may fulfil the role of idealizations rather than true descriptions of an underlying reality. In this sense, ideas may define what Philip Kitcher calls the ‘ideal limit of inquiry’ (Kitcher Reference Kitcher and Butts1986:214). For Kitcher, what counts as a causal law can be understood only against the background of a system that would result from an ideally extended inquiry. Ideas provide only the framing conditions for our minds to recognize general patterns and explain the observed real dependencies between different appearances.

This view, however, raises the question of how to evaluate the progress of our scientific inquiries to make sure we are approaching the ideal limit. If the ideal limit is defined only in terms of a system-internal standard, such as the increase in internal systematicity, then the view faces similar challenges as a coherence theory of truth: it cannot assess progress by objective criteria or in terms of a reality that exists independently of human minds as the ultimate target of human cognition. In other words, if one denies ideas any relation to a mind-independent reality, one may also have to give up on a mind-independent standard by which to measure the adequacy of our scientific endeavours. That is, by denying that ideas even indeterminately point us to the existence of something absolutely unconditioned that grounds our cognition, fictionalism may be forced to dispense with objective criteria of truth or even with a non-relativist account of truth altogether.Footnote ⁵⁰

These discussions of noumenalism and fictionalism suggest that an adequate interpretation of ideas of reason should preserve the true core of each view: the productive aspects of ideas as heuristic fictions of the human mind that promote the systematization of cognitions and the realist aspects of ideas that allow a relation to a mind-independent reality but refrain from postulating metaphysically robust objects of ideas.

2.1 The Incompleteness of the Understanding

Section 1 has shown that reason and the understanding are closely related. The understanding is an ‘object for reason’, as the senses are an object for the understanding (A664/B692). Reason does not relate directly to objects of experience, but to the concepts and cognitions of the understanding (e.g., A335/B392), or to the ‘actions of the understanding’ (e.g., A321/B378, A327/B383). But why does the understanding need a higher authority to direct it at all? There are two important aspects in which the understanding is incomplete: determining conceptual content and tracking truth.

The understanding is essentially the ‘capacity to judge’, and its central task is to make judgements with objective content, that is, theoretical cognitions (A81/B106). Such cognitions are judgements that are taken to be about an object and to have objective validity, that is, validity for everyone.Footnote ⁵² In order for a judgement to be about an empirical object, the object itself must be given (or at least able to be given) to the senses. The understanding thus relies on sensibility for an immediate representation of something particular in intuition. For example, the cognition that this rose is red requires me to have an empirical intuition of a spatio-temporal particular, such as my visual impression of the flower on my windowsill. This intuited particular is then reflected under the concept <rose> and specified by the predicate <red>.Footnote ⁵³

Kant spills much ink in the first Critique explaining how the understanding and sensibility interact with one another such that they can produce empirical cognition. The Transcendental Analytic analyses how the understanding imprints its a priori forms on sensibility, which are then transcendental conditions of experience: the logical forms of judgement not only define how concepts can be unified in a judgement, but – employed as categories – they also provide rules for the sensible synthesis by which a manifold of intuition is unified (see A79/B104‒105). Only if this sensible synthesis is carried out in accordance with these categories can it provide the appropriate kind of empirical matter for the cognition of an object of experience. The resulting cognition not only displays the logical forms, but also reflects real dependence relations in the object. For example, <The rose is red> not only displays the logical form of a categorical judgement <S is P>, but also, if appropriately related to intuition, reflects the dependence relation between a substance (e.g., the particular rose I see) and its accidents (e.g., redness). Far into the first Critique, it looks as if the understanding and sensibility together are quite capable of generating cognition with objective content. There is no significant mention of reason in this part of the book. Yet the understanding faces challenges of underdetermination, for which sensibility by itself cannot provide succour.

2.2 The Assessment of Empirical Truth

In the Appendix, reason’s demand for systematic unity is understood to provide criteria of truth (see A647/B675–A651/B679). Kant elaborates on an argument that, starting from the logical principle of reason to seek systematic unity, shows the necessity of a ‘transcendental principle of reason’ concerning the systematic unity of nature itself (A648/B676). The central passage reads as follows:

This passage implies that reason’s demand for systematic unity is not only essential for reason, but also necessary for a ‘coherent use of the understanding’ and thus for obtaining a ‘sufficient mark of empirical truth’. The argument can be reconstructed as a reductio ad absurdum:Footnote ⁵⁹

The remarkable result of this argument is that nature itself must be assumed to be systematic. The demand for systematic unity is not only a subjective principle, but a ‘transcendental principle of reason’ that must be assumed as objectively valid (A648/B676).

In an explicit application of this transcendental principle, reason serves as the arbiter of empirical truth: reason generates a working hypothesis to test whether particular cognitions are ‘coherently connected’ (A647/B675) in a chain of syllogistic reasoning. This is the hypothetical use of reason, which – as a special case of the regulative use – supplies so-called ‘touchstones’ of truth for assessing cognitions (A647/B675). The criterion of epistemic coherence, in the simplest sense, consists in logical consistency: a set of cognitions should not mutually contradict each other; a working hypothesis should not contradict any other already accepted cognition in a relevant set.Footnote ⁶⁰ In an advanced sense, it perhaps requires the derivability of cognitions from a fundamental law. A cognition that does not pass the coherence test within a set of already accepted cognitions has to be rejected as false or at least as rationally unfounded.Footnote ⁶¹

Hence, in addition to his correspondence theory of truth, Kant advocates a coherence theory (or, perhaps better, a systematicity theory) of epistemic justification.Footnote ⁶² By guiding the understanding to the systematic unity of all its cognitions, reason provides a formal method for evaluating truth that can apply both to the cognitions of a single subject and to cognitions across different subjects. What remains open at this point, however, is why this method requires a ‘transcendental presupposition’ regarding the systematic unity of nature itself (A651/B679, A678/B706). In my critique of noumenalism in Subsection 1.5, I argued that this presupposition should be understood neither as a determinative judgement about nature as a whole nor as a determinative judgement about something unconditioned that grounds appearances, since this would involve a transcendental fallacy. Section 4 will show that the formal criterion of systematicity can only be successfully applied if an idea of reason provides a sketch or blueprint of the whole system within which the criterion is applicable.

2.3 The Determination of Empirical Content

Since the dependence relations we track in cognition are directly related to the empirical concepts we use, the demand for systematicity is relevant not only for truth-evaluation, but also for the formation of empirical concepts. To avoid discrepancies and incoherencies among our cognitions as much as possible and to advance towards a more systematic description of nature, the more basic conceptualizing activities should also be guided by this demand.

In the next few paragraphs, Kant develops a similar argument for the formation of empirical concepts (A651/B679–A664/B692). The logical principle to seek systematic relations among concepts is primarily a subjective interest of reason. Yet a corresponding transcendental principle must be presupposed with ‘objective but indeterminate validity’ (A663/B691), ‘because without it no empirical concepts and hence no experience would be possible’ (A654/B682). More specifically, Kant distinguishes three logical principles of systematicity: the principles of homogeneity, specification, and continuity.Footnote ⁶³ The principle of homogeneity is defined as the principle ‘of the sameness of kind in the manifold under higher genera’ (A657/B685), guiding us in seeking, for every pair of concepts, a genus-concept with a larger ‘domain’ such that both concepts can be subsumed under it (A654/B682). The principle of specification is defined as the principle ‘of the variety of what is same in kind under lower species’ (A657/B685), guiding us in seeking for every given concept further sub-concepts (or species-concepts) that are richer in ‘content ([i.e.,] determinacy)’ (A654/B682). By assuming continuity between different concepts, according to the principle ‘of the affinity of all concepts’ (A657/B685), we arrive at an interconnected hierarchical system that proceeds, not only vertically from elementary genus-concepts to fine-grained species-concepts, but also horizontally between neighbouring concepts.Footnote ⁶⁴

As with the argument about truth-criteria above (2.2), this argument aims to show that these logical principles each presuppose a corresponding ‘transcendental principle’ (A650/B678, A663/B691). These transcendental principles guarantee a priori that if the formation of each new concept (e.g., <tree>) is guided by the logical principles, then the conceptual containment relations between all empirical concepts (e.g., <plant>, <leaves>, <stem>, <roots>, <tulip>, <orchid>, etc.) can constitute an inferential system.

Whether these conceptual containment relations, however, adequately correspond to the real dependence relations between the appearances described by these concepts can be assessed only a posteriori in light of ongoing experience. This assessment requires criteria of truth, as discussed. Moreover, whether our empirical concepts will eventually lead to a complete system of cognitions also remains an open question.Footnote ⁶⁵ The acquisition of empirical concepts must be understood as an ongoing complex activity of systematization according to the principles of generalization, specification, and continuity. In light of ongoing experience, our system of empirical concepts is continuously assessed and refined as to its adequacy by adding (or revising) increasingly comprehensive genus-concepts, increasingly determinate species-concepts, and further intermediary concepts. In turn, newly acquired concepts inform the ongoing activity of acquiring empirical cognition, which aims at a system of cognitions.Footnote ⁶⁶

What, again, remains open at this point is the transcendental status of these three principles. As with the principle of systematicity in truth-evaluation, the principles of homogeneity, specification, and continuity are by themselves topic-neutral: Like the pure categories of the understanding, they can be applied to any subject matter. But in their topic-neutral form, I contend, they cannot provide the kind of guidance and direction that the understanding seeks to obtain from reason. Reason must offer more: it must outline domains in which these formal principles can take a foothold in reality and become applicable to a particular subject matter. This, I will argue in Section 4, is the regulative use of its ideas.

3.1 The Standpoint and Horizon of Human Experience

The visual metaphors of standpoint and horizon were a common theme in eighteenth-century German philosophy. Gottfried W. Leibniz and Georg F. Meier, for example, use them to explore epistemological questions about the scope of human knowledge, often in comparison with divine knowledge.Footnote ⁶⁸

In their literal meaning, these metaphors describe aspects of human vision. A standpoint is the specific spatio-temporal location, or vantage point, from which a spectator observes an object or scene. From this vantage point, the viewer can observe a certain ‘field of view (Gesichtsfeld)’ (or visual field) (A658/B686). Only objects within this visual field can be observed from that vantage point. Objects outside of it are not visible for the observer. If one moves to a different standpoint, the visual field changes accordingly: further phenomena may become available, while others may disappear. The ‘horizon’ denotes, strictly speaking, the border line of the visual field: the line that demarcates what can be seen from a certain standpoint from that which cannot be seen from it.Footnote ⁶⁹ If you imagine yourself standing by the shores of the sea or on the top of a mountain, then the horizon is the line between the sea and the sky or, respectively, between the landscape and the sky. It is usually blurry, vague, and hard to discern. Figure 1 shows schematically the standpoint, the visual field, and the horizon of an observer.

Figure 1 Schematic representation of the standpoint, the horizon, and the visual field of an observer.

Kant himself often characterizes his transcendental philosophy as the study of the ‘human standpoint’ (e.g., A26/B42), distinguishing himself from Leibniz’s focus on divine knowledge.Footnote ⁷⁰ For Kant, a main characteristic of the human standpoint is its spatiotemporality. All human subjects are located in space and time and have a distinctive spatiotemporal standpoint from which they intuit objects. While human beings differ in their distinctive spatio-temporal standpoints, none of them can ever escape the limitations of space and time.Footnote ⁷¹ Despite their individual differences, they share a common ‘human standpoint’ from which they collectively explore the world and aim to accomplish an objective (or at least intersubjectively valid) description of nature.

In the Appendix, Kant uses the metaphors of standpoint and horizon specifically to illustrate the three general principles of concept-formation – the principles of homogeneity, specification, and continuity (see 2.3). He now considers a ‘concept … as a standpoint’ and analyses the ‘logical horizon’ that it opens up (A658/B686). In general, a horizon is ‘a multiplicity of things that can be represented and surveyed, as it were, from [the concept]’ (A658/B686). This prima facie suggests a real definition of horizon: the real horizon of a concept is its extension, ‘sphere’ (e.g., A576/B604, A655/B683) or ‘domain’ (e.g., A71/B96, A654/B682). This is the set of objects that fall under the concept or that can be adequately reflected under it. For example, the real horizon of the concept <flower> is the set of items that can be correctly described as flowers. Kant uses the notion of a horizon vaguely here, so as to include the entire domain of things, rather than only the ‘circle line’ demarcating such a domain.Footnote ⁷²

But, in the Appendix, Kant specifies the logical horizon as follows:

A logical horizon does not contain things under it (i.e., individuals objects), but sub-horizons: these are the logical horizons of subspecies, that is, more specific concepts with smaller domains but more content. The principle of specification requires that each logical horizon encompasses further smaller horizons, but no complete individual concepts that fully determine an individual.Footnote ⁷³

In turn, the principle of homogeneity requires that each logical horizon can be enveloped in a further, more general horizon, the horizon of a higher genus-concept, until one reaches the highest genus and hence the ‘universal and true horizon’:

With the metaphor of a logical horizon, Kant explores a new way of illustrating the relation of concepts to one another: genus-concepts and species-concepts are now understood as relating to one another as more or less encompassing horizons. The extent of the horizon’s domain and the richness of its content are inversely proportional to each other: the larger the horizon of a concept, the poorer the concept’s content but the larger its domain. The smaller the horizon of a concept, the richer its content but the smaller its domain.

For instance, the concept <plant> has a smaller, more specific horizon than the genus-concept <living being> and is therefore contained within the latter’s horizon. But it has a larger, more general horizon than the species-concepts <rose>, <tulip>, and <orchid>. Its logical horizon encompasses the smaller horizons of the species-concepts <rose>, <tulip>, and <orchid>, but it is itself encompassed within the still wider logical horizon of the genus-concept <living being>. Figure 2 illustrates these examples. Searching for a more general genus-concept can now be understood in analogy with climbing up a mountain to enlarge one’s visual field: in climbing up to a higher vantage point, one’s visual field grows through merging multiple, more limited visual fields of lower vantage points at the foot of the mountain or in the valley.

Figure 2 Schematic representation of the metaphorical notions of a logical standpoint and a logical horizon for the example of the concept <plant>.

Kant applies this analogy to illustrate the function of ideas of reason: the law of homogeneity leads us to the ‘highest standpoint’ of the most general genus-concept (A659/B687). This highest concept spans the ‘universal and true horizon’, which contains all other, more specific horizons (A659/B687). It thus defines the entire domain of human cognition, and this is precisely the function of ideas of reason, or so I will argue in Section 4.

The task of transcendental philosophy is, for Kant, to explore the boundaries of human understanding.Footnote ⁷⁴ In the Jäsche-Logic, Kant describes this task as the ‘determination of the horizon’ of human cognition (JL 9:40). This task requires us to assess ‘the congruence [Angemessenheit] of the quantity [Größe] of all cognitions with the capabilities [Fähigkeiten] and ends [Zwecke] of the subject’ (JL 9:40).Footnote ⁷⁵ The horizon of human cognition is thus defined in relation to human capabilities: it concerns the adequacy relation between the domain of human cognition, on the one hand, and the faculties (and ends) of the human mind, on the other. The domain within which we can gain cognition at all must be adequate to our mental faculties. The Dialectic teaches us what errors we fall into if we ignore the limits of our cognition set by our capacities. The horizon of all human cognition thus characterizes the boundaries of human ‘comprehensibility’ (Log-Bl 24:120) or intelligibility, as I will call it. But how can we possibly know our own horizon of understanding?

It seems that we are always caught in limited subjective horizons. The historical horizon of our time is constrained by historically contingent facts, such as language, culture, and the state of the art of the empirical sciences in a historical period (see JL 9:41). Moreover, each and every one of us has a ‘private horizon’: a horizon that ‘depends upon various empirical conditions and special considerations, e.g., age, sex, station, mode of life, etc.’ (JL 9:41). Philosophy, by contrast, should aim to explore the rational and universal horizon. A rational horizon is conditioned solely by the a priori insights gained through human reason that are universally valid for everyone, at all times and places (see JL 9:41). The ‘absolute and universal horizon’ is ‘the congruence (Congruenz) of the limits of human cognitions with the limits of the whole of human perfection in general’ (JL 9:41).

Now, we can understand Kant’s theory of reason as offering some guidance for exploring the ‘absolute and universal horizon’ of the human standpoint in general. In the Doctrine of Method, Kant illustrates reason’s task in determining the human horizon as follows:

Here Kant appeals to the metaphor of a horizon, too: reason defines ‘the curvature of an arc on [the] surface’ of a ‘sphere’, and this sphere is identified with the ‘field of experience’. Reason’s task is precisely to ‘ascertain[] with certainty’ the boundaries of this field, within which we can make out objects and ‘outside [of which] … nothing is an object for [human reason]’.

From this discussion, the following account emerges: human understanding is in principle limited by the universal horizon of the human standpoint. This horizon demarcates the domain within which humans can have cognition at all. It must primarily be adequate to our mental faculties and their distinctive forms (or formal conditions). The task of transcendental philosophy, and in particular of a critique of human reason, is to examine the a priori boundaries of this domain. These boundaries are a priori because they are not due to a mind-independent reality, but exclusively due to the limitations of our mental faculties themselves. The perspectivalist interpretation, as developed in Section 4, will suggest that ideas of reason serve as the highest genus-concepts opening up the universal horizon of human understanding.

3.2 The Focus Imaginarius and the World without Perspective

In the Appendix to the Dialectic, Kant borrows a further metaphor from optics: the focus imaginarius (A644/B672).Footnote ⁷⁶ Kant has already introduced this metaphor in the Dreams of a Spirit-Seer Elucidated by Dreams of Metaphysics (1766) in order to dismantle the false pretensions of certain metaphysicians. There, he describes the visual metaphor as follows:

In the case of a visual reflection in a concave mirror, the focus imaginarius is the imaginary focal point that we assume behind the surface of the mirror and from which the mirror image seemingly proceeds. Looking at the mirror gives us the illusion that an object is located at this focal point. Yet whatever is represented to exist at the point is only a ‘figment of my imagination’ (DSS 2:245). If one assumes that there really is an object behind the mirror, then one falls prey to this optical illusion. In the Dreams, Kant uses this metaphor to illustrate his criticism of spirit-seers or dreamers of reason: even when fully awake, they ‘transpose the illusion of their imagination and locate it outside themselves’ and assume it to be an existing external thing ‘in relation to their body’ (DSS 2:343–344). Figure 3 shows the schematic account of Kant’s metaphor of the focus imaginarius.

Figure 3 Schematic representation of Kant’s visual metaphors of standpoint, visual field, horizon, and focus imaginarius.

In the Appendix to the Dialectic, Kant uses the same metaphor to describe the use of ideas of reason. The regulative use of an idea consists in directing the understanding to a goal. This goal is, however, only a focus imaginarius, an imaginary focal point ‘from which the concepts of the understanding do not really proceed’ (A644/B672). We assume this point as the real ground from which our representations of reality seemingly proceed, ‘as if these lines of direction were shot out from an object lying outside the field of possible empirical cognition (just as objects are seen behind the surface of a mirror)’ (A644/B672). Unlike the horizon, the focus imaginarius is assumed to lie outside of the field of possible experience. Like the visual illusions in the case of the mirror image, the focus imaginarius leads to transcendental illusions that arise from our ideas of reason as ‘natural’ and ‘unavoidable’ (A298/B354, A422/B449‒450, A462/B490).Footnote ⁷⁷ But such an imaginary focal point is also ‘indispensably necessary’, since it ‘serves to obtain … the greatest unity alongside the greatest extension’ of the understanding (A644/B672) and ‘to take the measure of its greatest possible and uttermost extension’ (A645/B673).

The metaphor of the focus imaginarius indicates a second function of ideas: ideas also project a goal for the understanding beyond the universal human horizon. From our finite perspective, it must remain imaginary, and that is precisely why it leads to transcendental illusions. Nonetheless, I will argue, in Section 5, that ideas – by projecting the world without perspective as a focus imaginarius – define normative ideals that are indispensable for our intelligibility of nature through cognition.

4.1 Guiding the Empirical Use of the Understanding

The perspectivalist interpretation offers an account of the distinctive role of the ideas of reason in complementing the cognitive activities of the understanding. How exactly does reason guide the understanding by means of its ideas? Recall that ideas of reason result from an iterative procedure, whereby reason seeks the totality of conditions. It does this in accordance with a particular form of inference that corresponds to a dependence relation, such as substantiality, causality, or interdependence. An idea is then the concept of an absolute whole that would complete the whole series of conditions or bring the series to a stop (see 2.3). It is also characterized as the ‘concept of a maximum’ (A327/B384) that cannot itself be given in experience and, more precisely, as the ‘idea of the maximum of division and unification of the understanding’s cognition’ (A665/B693).Footnote ⁸⁰ But why is such a maximum needed to advance the empirical use of the understanding? Why should it not suffice to apply the general principles of systematicity locally, find local systematic connections in small areas of empirical reality, and expand these local systematizations step by step? Why do we need an idea of a totality to direct the understanding to ‘the greatest unity alongside the greatest extension’ of its concepts and cognitions (A644/B672)?Footnote ⁸¹

First, I argue that an idea outlines the maximal field of reality that we can hope to conceptualize and cognize in a systematic way at all. More specifically, a transcendental idea defines a totality, or maximum, that reason prescribes to the understanding as an aim of perfection for its empirical use. As such, the idea provides an a priori sketch or map of the context, as I will call it, in which the understanding can ‘be brought into thoroughgoing agreement with itself’ (A665/B693‒A666/B694).

To begin, we must note a fundamental difference from the categories of the understanding. Like the categories, the pure concepts of reason have an a priori origin (in this case, in the faculty of reason) and a transcendental status with respect to empirical cognition. They are therefore called transcendental ideas. But their transcendental status differs from that of the categories in that ideas relate not only to a single act of cognition, but ‘to the entire use of the understanding’ (A327/B384).

Before introducing the specific ideas of the soul, the world-whole, and God in the Transcendental Dialectic, Kant describes their general function as follows:

Ideas thus relate not to single tokens of cognition or particular uses of the understanding, but rather ‘to the entire use of the understanding’ (A327/B384), ‘the use … in the whole of an entire experience’ (A321/B378), or ‘all the actions of the understanding in respect of every object’ (A326‒327/B383, emphasis added). Ideas are not strictly necessary for a single use of the understanding, but they regulate the entire range of uses, including all past and future ones.

This difference can also be understood in terms of the distinction between constitutive and regulative use (see 1.4). The categories have a constitutive use regarding experience: they define strictly necessary conditions that must be instantiated in every single act of empirical cognition; otherwise, the resulting representation would not count as an instance of cognition. By contrast, transcendental ideas are ‘never of constitutive use, … however, they have an excellent and indispensably necessary regulative use, namely that of directing the understanding to a certain goal’ (A644/B672, emphasis added). A regulative use defines conditions or goals to be aspired towards in all possible uses of the understanding.

Ideas as concepts of a maximum or absolute whole are needed to ‘prescribe the direction’ and a goal to the understanding (A326/B383). Reason directs the understanding to areas of the world in search of further objects of cognition, further conditions of an object, and eventually empirical laws of nature. But it is unclear why ideas can prescribe goals to the understanding at all.

Somewhat confusingly, Kant sometimes presents the relation between ideas and the understanding as one of determination: ideas ‘determine the use of the understanding according to principles’ (A321/B378) or ideas ‘consider all experiential cognition as determined through an absolute totality of conditions’ (A327/B384, emphasis added). But this kind of determination should not be understood in a constitutive sense as the determination of nature as a real thing. (This is the mistake of some versions of noumenalism, as discussed in 1.5). Rather, the phrase ‘considering … as determined’ indicates the hypothetical nature of this determination.Footnote ⁸² At the level of cognitions, ideas define an absolute totality of conditions in which, if the totality existed, all cognitions would be fully determined.

This hypothetical formulation has led some commentators to construe the regulative use of ideas as the formation of hypotheses without asserting them. The cognizer, thus, remains neutral regarding their truth.Footnote ⁸³ Despite this epistemic neutrality, these hypotheses must be assumed to derive cognitions and principles that can be taken to be true with regard to empirical objects. The regulative use of the idea of the soul would, for instance, include the hypothetical assumption that I am a simple substance and that I have a fundamental mental power. From these hypotheses, we can derive, according to this hypothesis-formation view, psychological laws and empirical cognitions of ourselves: for example, we can derive the cognition of a character trait from a temporal series of mental states, or infer a general law about human behaviour. Since we lack a corresponding intuition, the hypotheses based on ideas cannot be descriptions of empirical objects, but only of non-sensible objects.Footnote ⁸⁴ Now, it is unclear how cognitions about me as an empirical person with diverse mental capacities, contingent behavioural patterns, and temporally distributed mental states could ever be derived from, or inferentially connected to, the a priori hypotheses that I am a simple substance and that I have a fundamental mental power. After all, as an empirical person I am never a simple substance and my empirical character always falls short of a complete systematic description. Moreover, as far as we know, there can be no simple soul-substances with a single fundamental power in nature. It is hard to see how idea-based hypotheses could serve as the most general description of the psychological beings we encounter empirically.Footnote ⁸⁵

Thus, ideas do not direct the understanding by providing the most general descriptions of empirical reality as non-assertible hypotheses. An idea in principle does not function like the determining concepts of the understanding or, as Kant puts it, an idea is not ‘the concept of an object’ in the proper sense (A645/B673). Rather, reason operates on a meta-level: its ideas define the conditions under which the understanding can approach a completion and perfection of its empirical use, even though this completion and perfection can never be reached in experience itself. Ideas are ‘concepts … of the thoroughgoing unity of [the] concepts’ of the understanding (A645/B673).Footnote ⁸⁶ I take this to mean that ideas define an entire system of concepts that the understanding is demanded to fill in with appropriate empirical concepts.

Following his metaphor of the logical standpoint, Kant describes the regulative use as ‘posit[ing] an idea only as a unique standpoint from which alone one can extend the unity that is so essential to reason and so salutary to the understanding’ (A682/B710, emphasis added).Footnote ⁸⁷ As a logical standpoint, an idea defines a systematic unity as the maximal extension of a system (of concepts or cognitions). This systematic unity is ‘salutary’ to the understanding because it prescribes how the understanding can come to perfection and completion. It prescribes the ‘aim of a perfect systematic unity in our cognition’(A675/B703; also A681/B709) and thus enables the understanding to strive for ‘a certain possible perfection of the cognition of [the] object’ (A666/B694).Footnote ⁸⁸ By orienting itself towards this aim, the understanding can approach ‘the greatest unity alongside the greatest extension’ of its cognitions (A644/B672) and ‘the greatest possible unity of experience’ (A678/B706). These notions of perfection and completion are indicated in the frequent use of superlatives in these and other passages:

Hence, transcendental ideas direct the understanding by defining a maximum towards which the understanding ‘ought to proceed’ (A685/B713), but of which it itself cannot have a concept. Prescribing a maxim is necessary for the understanding to come into a ‘thoroughgoing agreement with itself’ (A665/B693‒A666/B694) and approximate a ‘systematically coherent use of experience’ (A786/B814, also A651/B679). It is precisely this normative dimension of reason as a meta-faculty of cognition that the hypothesis-formation view sketched above cannot capture. On the perspectivalist view, a full justification of this normativity is, however, only provided by the second role of ideas in projecting normative ideals (see 5.3).

Now, the maximum an idea prescribes cannot be given determinately. It is necessarily indeterminate and unattainable from the standpoint of experience.Footnote ⁸⁹ The understanding can venture ever further in the direction of the goal without ever reaching it. It is radically open which empirical objects the understanding finds, which empirical concepts it forms, and which general laws of nature it determines in the course of its inquiry. Still, this openness might seem to raise the question with added force: how can ideas prescribe an indeterminate and unattainable goal to all uses of the understanding?

4.2 Ideas As Rules for the Understanding

In many places, Kant explains this prescriptive force by claiming that ideas serve as rules for the understanding. So, I argue next that a transcendental idea prescribes rules for the systematic extension of the use of the understanding in a specific domain of empirical reality. In other words, ideas define meta-rules for how to apply the categories of the understanding in a certain domain. For example, Kant writes in his discussion of the Antinomies of Reason:

In the Appendix to the Dialectic, Kant specifies:

Ideas thus give prescriptive rules for the understanding to proceed towards the ‘greatest possible continuation and extension of experience’ (A508/B536).Footnote ⁹⁰ This greatest extension involves both the maximal extension of a system of empirical concepts and the maximal extension of a system of empirical cognitions (including laws of nature). Extending our cognition can include exploring further areas of space and time, finding more distant objects, or enlarging the scope of reality we can describe by laws. Extending our concepts can include – according to the three principles of concept-formation – homogeneity, specification, and continuity – defining a common genus-concept of a yet larger scope (e.g., organism), defining more fine-grained species-concepts (e.g., a subspecies of rose), or differentiating a concept from further neighbouring concepts (e.g., concepts of other flowers such as tulip and orchid).Footnote ⁹¹

Kant frequently describes the extension of the understanding’s use in terms of a ‘continuous progression of the empirical synthesis’ (A462/B490) by which the understanding combines sensible intuition according to its categories.Footnote ⁹² This extension can be ‘a regress to the [higher, more general] conditions’ of an appearance (A499/B527), the progression ‘to a higher (more remote) member’ (A518/B546) of the series, or the successive composition of spaces and times (see A500/B528). It can also be the ‘decomposition [into] an unconditioned (indivisible) member of this series of conditions’ such that ‘the division goes to infinity’ (A513/B541).Footnote ⁹³

The general account is, then, that the understanding must follow the guidance of reason, if it is to extend its use. Ideas provide rules for this systematic extension. The general rule is that ideas demand us to ‘initiat[e] and continu[e] … in the series of conditions for a given conditioned’ (A508/B536).Footnote ⁹⁴ The twist here is that the transcendental ideas supplement the three general formal principles of concept-formation: they specify how these formal principles are to be applied in a specific domain and thus how the empirical synthesis of the understanding is to be extended in that domain.

Let me explain with the example of the idea of the soul. The idea of a simple substance calls us to extend the empirical synthesis of our inner intuitions towards the sum total of inner appearances. We will never find this totality in experience, regardless of how far we extend the empirical synthesis. Nonetheless, this idea supplies a rule for how to make progress: we ought to cognize inner appearances as if they were mental states inhering in a mental substance, even though we cannot intuit such a substance. The idea of the soul gives rise to domain-specific rules for applying the categories of the understanding to the domain of psychological beings. In general, how a category of the understanding is applied in empirical cognition depends on the kind of whole that we aim to explore with it.Footnote ⁹⁵

Hence, there is a sense in which the presupposition of the whole precedes the prescription of the rules for the use of the understanding. The kind of whole presupposed specifies the kind of rules that can be derived. Ideas give rise to domain-specific rules by outlining the domain, or what I will call a context of intelligibility. This is the context in which a systematic use of the understanding is at all possible for us.

4.3 Ideas As Contexts of Intelligibility

Finally, I argue that ideas of reason provide a priori mental maps of the domains of reality in which the understanding can extend its use systematically. More specifically, the regulative use of transcendental ideas outlines the context of intelligibility within which the understanding can make systematic progress by an indeterminately continued empirical synthesis.

The following problem still lurks in the background: an idea prescribes a whole as the goal for the understanding’s empirical syntheses – a goal, however, that must remain indeterminate from the standpoint of experience. There cannot be a determinate concept of this goal, nor can there be an actual ‘empirical boundary’ for the determining activities of the understanding that ‘would hold as an absolute boundary’ (A509/B537), as ‘no experience is bounded absolutely’ (A515/B543).Footnote ⁹⁶ Rather, reason prescribes only ‘a progress of indeterminate length (progressus in indefinitum)’ (A511/B539) or ‘a regress extending indeterminately far (in indefinitum)’ (A512/B540).Footnote ⁹⁷ But how can we derive rules for the determining activities of the understanding from an indeterminate goal?

The central point of the perspectivalist interpretation is this: ideas of reason provide the understanding with an a priori mapping or structuring of a domain of empirical reality, even though the boundary of this domain is indeterminate. Only by presupposing such an a priori mapping can the understanding ‘locate’ an object of a particular experience on the map and then determine it in relation to this mapping. For example, by presupposing the idea of absolute space, the understanding can place a material object on a spatial map and determine its motion in relation to this map. By presupposing the idea of the soul, the understanding can position a mental state within the temporal development of a psychological being and determine its causal effects within this development. This anchoring of an object within a map, spanned by an idea, must in a logical sense precede the determining activities of the understanding. Otherwise, no systematically coherent and inferentially connected cognition of the object can be achieved. The regulative use of an idea thus provides the understanding with what I call a context of intelligibility: an a priori map, outline, or sketch of a domain of empirical reality. An object can only become intelligible (or comprehensible) for us if an appropriate context of intelligibility is presupposed.Footnote ⁹⁸ This requires that the experience of the object must be reflected under an appropriate idea. This idea generates a context within which the object can be cognized in relation to other objects within a systematic web of dependence relations. Without such a context, the cognition of the object would remain rhapsodic or fragmentary.

Let me provide textual and philosophical support for this reading. That reason provides something like a context of intelligibility is indicated in phrases such as that reason ‘prepares the field for the understanding’ (A657/B685), ‘points the way toward systematic unity’ (A668/B696), and ‘open[s] up new paths into the infinite (the undetermined)’ (A680/B708).

A key aspect of Kant’s account, on my view, is that ideas specify an a priori structure of the field, even though they cannot determine its boundaries in an absolute or determinate way. The a priori structure concerns the kind of dependence relations in which the objects belonging to this context must stand (e.g., material causation vs. mental causation). That ideas give an a priori structure to a field of the understanding is, for example, indicated in the following passage:

According to this passage, an idea provides the ‘form of a whole of cognition’ from which explanations for a given appearance can be derived. For example, the idea of absolute space gives the ‘form of a whole’ to the system of physics, so that an explanation of the trajectory of a material object can be obtained in terms of mechanical laws. An idea also defines the ‘form of a whole’ at the level of concepts: rather than being itself the ‘concept of an object’, it gives such concepts a ‘thoroughgoing unity’ by means of an a priori form (A645/B673).

Further evidence for the claim that ideas define an a priori structure comes from Kant’s characterization of ideas as schemata, in analogy with the schemata of the understanding.Footnote ⁹⁹ Without going into detail, I propose that this analogy can help us to understand how ideas – by defining a structured whole – provide rules for the understanding. As Kant writes:

In other places, Kant argues that the execution of any idea requires a schema that provides not only ‘the outline (monogramma)’ of the system the idea spans, but also ‘the division of [its] members’ and the ‘order of [its] parts’ (A833/B861, see also A682ff./B710ff.). This analogy between the schemata of the understanding and those of reason can be understood as follows: a schema of the understanding gives ‘a rule for the determination of [the unity of] our intuition in accordance with a [category]’ (A141/B180). Similarly, a ‘schema of reason’ gives ‘a rule or principle of the systematic unity of all use of the understanding’ in accordance with an idea (A665/B693). Both define procedural rules to attain some unity: in the former case, a rule to attain the unity of a manifold of intuition in accordance with a category; in the latter case, a rule to attain the systematic unity of manifold cognitions in accordance with an idea.

This analogy is difficult to work out, because it is controversial what exactly a schema is in the first instance.Footnote ¹⁰⁰ In Kraus (Reference Kraus2020:194–206), I offer a detailed discussion, highlighting the following point: the essential role of a schema is to make a concept sensible, that is, to provide an a priori presentation of a concept to the mind in a sensible form.Footnote ¹⁰¹ The schemata of the understanding are the sensible presentations of the conceptual unities defined by the categories and thus explicate the categories in sensible form (e.g., the category of substance is schematized as persistence in time). Likewise, the regulative use of an idea results in the presentation of the ‘form of a whole’ defined by the idea. Since, however, such a whole can never be fully sensibly instantiated, it can only be a symbolic presentation.Footnote ¹⁰² We can now understand the presupposition of a whole involved in the regulative use of ideas in terms of an a priori act of presentation to the mind.

This presentation of a whole is what I mean by generating a context of intelligibility. The mind produces an internal map, as it were, of empirical reality for the guidance and orientation of the understanding. The context of intelligibility is thus a mental presentation of empirical reality as a structured whole, or simply of nature as the ‘sum total of appearances’ (e.g., B163, A257/B312, A418‒419/B446n, A674/B702). This mental presentation outlines the maximal domain in which the understanding can systematically operate to determine given appearances. In presenting this domain to the mind a priori, reason produces procedural rules for how to approach systematic unity within this domain.

So, we can now understand the rules defined by an idea as rules for the relational determination of objects of cognition against the a priori mapping that the idea provides. Several passages indicate this relational significance of ideas:Footnote ¹⁰³

An idea defines the relational structure between a whole and its parts: primarily between a system of concepts and individual concepts, but also between a system of cognitions and the individual cognitions contained in it. If our cognitive activities are successful, then this relational structure should also be reflected in the domain of reality captured by a system of cognitions and give order to the appearances that belong to this domain. The significance of ideas is thus only relational and concerns the ordering of empirical concepts and cognitions (and their corresponding appearances) according to dependence relations within a whole. With this relational significance ideas contribute to determining conceptual content: the relational structures they define ‘make it possible for us to be able to have a determinate concept of any thing’ in the first place (A674/B702).

This can perhaps be made plausible by comparing the context of intelligibility with the linguistic conception of a context of use, which inspired my terminology. A context of use, in which a certain linguistic expression is used, has a content-determining function. For example, the indexicals ‘I’, ‘here’, or ‘now’ have a definite content only in a context of use (i.e., the relevant set of states of affairs) in which these indexicals refer to something particular, namely the speaker, place, or time of the context, respectively.Footnote ¹⁰⁴ Similarly, I suggest, the context of intelligibility has a content-enabling function: the empirical content of a concept is only sufficiently defined against the background of a whole system of concepts, which can be mapped onto a domain of reality. To have a sufficient grasp of what a concept means (i.e., sufficient for a particular purpose) requires a sufficient insight into the conceptual entailment relations it has to other concepts within a system.Footnote ¹⁰⁵ Similarly, the content of a cognition is understood in terms of inferential relations it has to other cognitions within a system. These relations are supposed to capture the real conditioning relations in nature, or the sum total of appearances.

Let me illustrate this with an example. The idea of natural purposiveness can now be understood to outline the context of intelligibility for the study of living nature. It defines the form of the system of biological concepts with the highest genus-concept <organism>, as schematically shown in Figure 4. This system is supposed to map onto the domain of reality in which we can at all hope to identify organic beings, that is, the ‘living world’.Footnote ¹⁰⁶ The idea moreover supplies the rules for identifying the parts of an organism (e.g., its organs) in relation to the whole.Footnote ¹⁰⁷ Without presupposing this idea, I would not be able to interpret the rose I intuit as an organic whole and identify its parts as contributing to its organic life (e.g., its stem, petals, thorns, etc.).

Figure 4 Schematic account of the conceptual system of biological terms, spanned by the genus-concept <organism>.

To sum up, I have argued that the regulative use of ideas can be understood as outlining or sketching the contexts of intelligibility within which the understanding can be extended in a systematic way, in the hope of finding a systematic conceptualization of the empirical world and a system of inferential cognitions. A context of intelligibility is the mental presentation of empirical reality as a structured whole, which is assumed to correspond to the sum total of appearances, or simply to nature. This presentation must be presupposed a priori in any specific determination of an empirical object. It is a mental map for the understanding to advance to the greatest extension and the greatest specification of its concepts and thus approach the most detailed description of nature according to general laws. Ideas do not outline the domain of the understanding by determining its boundaries in an absolute or even only hypothetical way. Rather, ideas give an a priori inner structure to a domain, from which domain-specific rules for the continued empirical synthesis of the understanding follow. Without presupposing this a priori structured whole, objects would remain unintelligible for us. The perspectivalist view thus accounts for the fact that ideas set a priori limits to what is empirically cognizable in certain domains.Footnote ¹⁰⁸ But the view also allows for an infinite process of revision and expansion of empirical concepts and cognitions.Footnote ¹⁰⁹

Since the transcendental ideas of reason are due to the nature of human reason, they are shared among all humans and open up common contexts of intelligibility. These ideas delineate the empirical reality to be cognized from the human perspective. The perspectivalist interpretation thus offers a natural reading of the visual metaphors discussed in Subsection 3.1: an idea, as the highest standpoint of the human perspective, opens up the universal human horizon (see A659/B687). This universal horizon encompasses all commonly shared contexts of intelligibility.

4.4 Ideas Set Topics for the Understanding: Natural Kinds

In many places, reason is described as setting a task or problem for the understanding to be completed.Footnote ¹¹⁰ The perspectivalist interpretation gives this description a further twist by suggesting that reason sets topics for the understanding to explore. Ideas not only outline the a priori structures of domains of reality, but also define the kinds of objects that the understanding can hope to find in these domains. These are the natural kinds that can at all be intelligible for us. In particular, I argue that the transcendental ideas of the soul and the world-whole define the most general natural kinds that the understanding is demanded to explore in nature. I focus on the idea of the soul and the idea of absolute space.

Consider Kant’s specification of the idea of the soul: it contains the predicates (or sub-ideas) of ‘a simple substance, unchangeable in itself (identical in personality), standing in community with other real things outside it’ (A682/B710). I must presuppose this idea to derive ‘principles of the systematic unity in explaining the appearances of the soul’ (A682/B710) (or what Kant also calls inner appearances). The predicates of the soul give rise to such principles by

On the perspectivalist view, the idea of the soul generates a context of intelligibility for a particular kind of experience (i.e., inner experience) and defines the object that can be determined within this context (i.e., inner appearances). For various reasons, we cannot cognize ourselves as mental substances, since the principle of substantiality applies primarily to material objects.Footnote ¹¹¹ The idea of the soul nonetheless provides the appropriate context for explaining inner appearances in a systematic way and gives regulative rules for applying the principles of the understanding specifically to inner appearances. The principles require us to determine inner appearances as the mental states of a substance that persists through time, as states caused by mental faculties that are all grounded in a single fundamental power, and as states that are correlated with a body (without, however, determining a mental substance as a whole). These principles define the a priori structure of the context in which inner appearances can be explained: they can be explained only in relation to the sum total that makes up a person’s mental life. The idea of the soul thus sets a topic for us: we ought to explore psychological beings through the inner relation of their inner appearances to an assumed substantial whole.Footnote ¹¹²

Another example is the idea of the world in space, which is a sub-idea of the world-whole. It plays a central role in Kant’s account of mechanics: only if we presuppose an idea of absolute space can we define a frame of reference in relation to which mechanical motion can be cognized in accordance with Newton’s laws of motion.Footnote ¹¹³ Following the perspectivalist interpretation, the regulative function of this idea is then to define the domain of physics within which Newton’s laws are valid for material objects. But the Dialectic has taught us that the idea of the world in space involves an antinomy: we must think of the spatial world as both an infinite whole without boundaries and a finite whole with boundaries.Footnote ¹¹⁴ So if we try to determine the spatial world as an unconditioned object, we cannot avoid this contradiction. We cannot even think of space as an object in the idea, that is, as a substance that logically precedes its accidents (see A673/B702). Rather, the context opened by the idea of absolute space is structured as a composition of subspaces, whereby the subspaces logically precede the whole they compose.Footnote ¹¹⁵ The idea of absolute space thus sets a different topic for us: we ought to explore material beings through their external relations to one another in an assumed compositional whole.

From these two examples, I draw broader conclusions: the two classes of ideas – the ideas of the soul and of the world-whole – define the two fundamental kinds of context-structures (substantial vs. compositional whole) and the two corresponding most general natural kinds that we can hope to find in nature at all.Footnote ¹¹⁶ Any object we seek to cognize falls under one of the two kinds. From the two kinds of systematic unities (soul-like substantial wholes or world-like compositional wholes), we can derive two natural kinds: soul-like (or animate) objects and material objects. Soul-like objects are defined by their inner unity, which precedes their parts, and by the internal relations that their parts have to the whole.Footnote ¹¹⁷ For example, a mental state is determined in relation to the whole person, and mental causation is understood to be exercised by the person as a whole. Material objects, by contrast, are defined by their external relations to other objects, which together form a compositional spatial whole. A material part is primarily defined by its relation to other material parts. Mechanical forces are exerted by mass particles on each other, not by space as a whole. Biological organisms are a hybrid case because they fall under both types: organic parts are understood as functions of the whole organism, and yet we seek mechanical explanations for them in terms of their parts.Footnote ¹¹⁸

The perspectivalist interpretation suggests that reason sets topics for the understanding to explore in nature. An idea of reason defines a ‘sketch of a science’, which is given as a ‘problem’ (A335/B392). The ideas of the soul and the world-whole, in particular, are indispensable for exploring the domains of animate and of inanimate nature.Footnote ¹¹⁹

5.1 Assessing the Empirical Use of the Understanding

How can we make sure that our efforts for a systematic conceptualization and cognition of appearances are really successful?Footnote ¹²² How can we assess whether we make progress towards systematic, complete, and indeed true descriptions and explanations of objects in nature? We must grant that empirical concepts and empirical laws are ever revisable and extendable. But how then can we judge whether an empirical law of nature that we have discovered is actually true, or at least approximates universal validity? How can we judge whether a cognition in fact tracks real dependence relations between (or within) the object(s) it describes?Footnote ¹²³

In Subsection 2.2, we saw that reason’s demand for systematic unity provides a ‘touchstone’ (A647/B675) or ‘mark of empirical truth’ (A651/B679). Since we cannot judge independently of our representations whether a cognition really corresponds to an object of experience, as Kant’s correspondence theory of truth requires, we have to use criteria of systematicity to evaluate the truth of empirical cognitions. So, I argued that Kant advocates a systematicity theory of truth-criteria:Footnote ¹²⁴ The truth of a cognition is judged in terms of its systematic relations to other cognitions already accepted as true.Footnote ¹²⁵ The fit of a cognition within a system of cognitions entails that it does not contradict any cognitions already accepted as true; it arguably also entails its derivability from higher-order principles. Does this systematic fit provide objectively sufficient grounds for assenting the cognition, that is, grounds that are valid in light of the object?Footnote ¹²⁶

This raises a fundamental worry: if the demands of reason for systematicity guide the way we form empirical concepts and gain systematically connected cognition, then nature will simply present itself to us according to the systematic conceptualization we have put into the cognition of nature. But if we in turn use systematicity as a measure of the progress we have made in approaching a complete and true description of nature, we might only ever measure the subjective systematizing efforts we have put into that description, following our formal principles of reason, rather than the objective progress we have really made in light of nature itself. So, we lack an objective standard for judging progress that is independent of our own subjective demands for systematization. Put differently, there may be a problem of circularity if we use reason’s own principles of systematicity both to extend the use of the understanding and to assess the correctness of that use. Let me explore this worry further before turning to Kant’s solution based on the idea of God.

Consider the formal and the material definition of nature in the Antinomies chapter:

According to its formal definition, nature is necessarily structured according to an ‘inner principle of causality’. The Transcendental Analytic has shown that the principle of causality is applicable to all appearances. As a transcendental principle, it gives rise to a formal order in which appearances must be formally related to each other to be cognizable at all. Yet if we consider nature in terms of its matter according to its material definition, it could still turn out to be ‘a raw chaotic aggregate’ of appearances without showing ‘the least trace of a system’ (FI 20:209). We have no guarantee a priori that, if we apply the formal principle of causality to all appearances, they will constitute a systematic whole in which all appearances are really in a ‘thoroughgoing [causal] connection’ with each other. That is, the real thoroughgoing determination of appearances is not guaranteed, as we will see in 5.2.

Kant considers the extreme case that nature simply does not display systematic connections and therefore does not lend itself to the kind of systematic description that reason demands. Kant entertains the possibility that there could be ‘such a great variety … of content, i.e., regarding the manifoldness of existing beings … that even the most acute human understanding … could not detect the least similarity’ (A653/B681). However, if this were the case, then not only could there be ‘no concept of a genus, nor any other universal concept’, but also ‘indeed no understanding at all’; that is, ‘no empirical concepts and hence no experience would be possible’ for us (A654/B682). This argument from the possibility of infinite variety leads Kant to conclude that the principle of homogeneity must have a transcendental status and is thus objectively valid with regard to nature itself.Footnote ¹²⁸

If we are guided by the transcendental, albeit regulative principles of systematicity, they guarantee a priori that we form empirical concepts to reflect systematic conditioning relations of genus and species, at least to some degree. On this basis we then acquire empirical cognitions that stand in systematic conditioning relations to one another so that we can draw further inferences from them. Hence, nature – if viewed only regarding its form – presents itself to us in such a way that it satisfies reason’s demand for systematicity. But since these transcendental principles are not constitutive of nature as a whole, we do not have an a priori guarantee that we empirically succeed in finding highest genus-concepts or lower, more specific species-concepts, or that there is always another concept between two neighbouring concepts. For example, we might see more hues of a colour than we can distinguish conceptually.

The same applies with regard to completeness. Formally speaking, the transcendental deduction shows that all appearances necessarily stand under the categories of the understanding. It follows that all appearances that make up nature as their sum total are objects of possible experience and thus cognizable. If we systematically extend the empirical use of the understanding, it is a priori guaranteed that no appearance in principle eludes our capacity for cognition, even if we fail to access many appearances, lack actual intuitions, or fail to grasp certain aspects of nature under systematic laws. However, nature taken in its material completeness might not be an actually infinite totality or representable as a systematic whole.Footnote ¹²⁹

Back to the problem of truth-evaluation. Again, if we follow reason’s principles of concept-formation, we are guaranteed a priori that the empirical concepts we use in cognition stand in logical conditioning relations. But it can only be assessed a posteriori in light of actual experience whether these conceptual relations correspond to real dependence relations in the objects of experience to be described.Footnote ¹³⁰ For example, we can only examine empirically whether objects that fall under the concept <rose> also instantiate predicates such as <have five petals> or <have a stem with thorns>, which are not analytically contained in <rose>. But how do we decide whether an exception we find, for example a rose that has no thorns or only three petals, is in fact a misapplication of <rose> or a counterexample to the systematic connection we established between <rose> and <have a stem with thorns>, or between <rose> and <have five petals>?

Now, how can systematicity be an indicator of empirical truth at all, as Kant claims? Can we measure the degree of systematicity that a newly acquired concept (or cognition) adds to the system of concepts (or cognitions)?

Taking a cue from the convergence of infinite series in mathematics, we can distinguish between an internal and an external measure for systematicity.Footnote ¹³¹ An external measure would measure the degree of systematicity in a system by its convergence to its limit, which is an external value, similar to a mathematical series that converges to a certain number, such as ${\sum }_{n=0}^{\infty }\frac{1}{2^n}=2$ . An internal measure, by contrast, would measure systematicity not against its limit, but by comparing the elements of the system to one another. In our case, this could be in terms of an increase in the density between concepts or in the scope of a conceptual system, regardless of whether the system as a whole approaches an external limit, that is, a mind-independent reality.Footnote ¹³²

Now, if we judge the degree of systematicity internally, we run the risk of measuring only the systematization efforts we have put into the system. We might measure the systematicity among cognitions only in terms of the logical conditioning relations between concepts we stipulated but miss out on the dependence relations that really exist in nature. In other words, we might be in a frictionless spinning in the void without testing our cognitions against the resistance of reality.Footnote ¹³³ If, however, we use an external standard, we would require something like a given external value against which we can measure the convergence of the whole system. But we have no access to an external reality that is independent of the system of cognitions in the relevant sense.Footnote ¹³⁴

In what follows, I suggest that Kant offers a solution to the problem of truth-evaluation based on the idea of God. This idea must be presupposed in the empirical study of nature, since it enables the ideal of an external measure of truth.

5.2 The Idea of God As a Normative Standard

More than any other idea, Kant associates the idea of God with the notion of perfection. The idea is, for example, associated with the notion of ‘complete purposive unity’, which is identified with ‘perfection’ (A694/B722). The purpose of this idea ‘is to serve us as the standard [Richtschnur] for the empirical use of reason’ (A674‒675/B702‒703), and it is therefore ‘legislative for us’ (A695/B723). Early in his discussion of ideas of reason, Kant introduces a comparison with Plato: a Platonic idea defines ‘what is most perfect of its species’; for example, ‘the idea of humanity’ defines what is most perfect for human beings (A318/B374). So far, the ideas of the soul and the world-whole have been understood as ideas of human reason, which outline the human horizon. But following Plato, Kant now considers the ideas that a divine intellect might have, which he calls ideals. An ideal is, like the Platonic ‘idea in the divine understanding’, understood as ‘the most perfect thing of each species of possible beings’ (A568/B596). Importantly, with this shift towards the divine intellect, ideas of reason are assigned a new function: they do not only provide rules for extending and refining the understanding’s systematic use within the human horizon, but, as ideals, they also serve as an ‘indispensable standard [Richtmaß] for reason’ (A569/B597):

Hence, specifically the idea of God fulfils the function of cultivating our cognitive activities and assessing their ‘correctness [Richtigkeit]’ (A680/B708, see also A671/B699). It enables us to at least think of a normative standard that is not derived from human reason, but from the regulative idea of a divine intellect, an ‘intellectus archetypus’ (A695/B723). What a divine intellect gives, if it exists, is an archetype, that is, an ‘original image’ or ‘original ground of all its copies in appearance’ (A569/B597). It is a kind of storehouse for perfect things against which we can measure the faint empirical copies that appear to us.

While I cannot do justice to the large body of literature on this topic, I offer an interpretation of the idea of God in line with the perspectivalist interpretation. In the Appendix, Kant claims to provide a transcendental deduction for its objective validity: this deduction is supposed to show that the idea of God is a ‘regulative principle of [the] investigation of nature’ (A697/B725). Before I discuss the transcendental deduction in Subsection 5.3, I turn to the Transcendental Ideal (TI) in the Dialectic and highlight its relevance for the problem of truth-evaluation.Footnote ¹³⁵

The argument for the TI (A571/B599‒A591/B619) appeals to the principle of thoroughgoing determination (PTD). This principle is crucial for the possibility of truth and definite reference of empirical cognition: it defines the state of the world in which a thing is fully determined with regard to all its possible properties. I contend that this state is what makes a cognition true and gives it a definite reference to a completely determined individual. Without reconstructing the argument in detail, I show how the TI can offer us further insight into Kant’s solution to the problem highlighted in 5.1.Footnote ¹³⁶ Recall that the problem is to explain how systematicity, although a regulative principle of reason, can provide an objective standard for evaluating truth and assessing the real progress made in the cognition of nature.

Even though truth is not explicitly discussed in the argument, the passage defines a logical and a material condition for truth.Footnote ¹³⁷ First, a cognition has a definite truth-value only if the concepts used in it satisfy the logical principle of determinability (PD): ‘that of every two contradictorily opposed predicates only one can apply to [the concept]’ (A571/B599). For this logical principle to be applicable to empirical cognition, it requires the transcendental principle of thoroughgoing determination (PTD), ‘according to which, among all possible predicates of things, insofar as they are compared with their opposites, one must apply to it’ (A571‒572/B599‒600). Put in a more formal way:

In further steps, the argument shows that PTD requires that there is ‘the sum total of all [positive] predicates’ (A573/B601), which is thought through ‘the idea of an All of reality (omnitudo realitatis)’ (A575/B603). This idea, then, leads Kant in a last step to the concept of the ‘ens realissimum’, which is the concept of the ‘individual being’ that is ‘the ground of the thoroughgoing determination’ of all reality (A576/B604). This is simply the idea of God.Footnote ¹³⁸ As several commentators convincingly show, the ideas of the All of reality and of the ens realissimum must be restricted to a regulative use.Footnote ¹³⁹ A constitutive use would lead to transcendental illusions, in particular the ‘hypostatization’ of the ideas into really existing things (see A583/B611).

In consequence, PTD must be restricted to appearances and empirical predicates:

PTD* presupposes that there is the ‘sum total of empirical reality’ (A582/B610), that is, nature as the sum total of appearances. The existence of nature as a systematic unity can only be guaranteed if we are justified in presupposing ‘an individual thing’ that is (or contains) the determining real ground of nature (A582/B610).Footnote ¹⁴⁰ This leads Kant to define the TI as

As such ground, TI is ‘the supreme and complete material condition of [nature’s] possibility’ as a systematic whole (A576/B604, emphasis added). If it were to exist, TI would guarantee that nature – viewed materially – would be a systematic whole.Footnote ¹⁴¹ However, the argument for TI is not meant to show the ‘existence of a being conforming to the ideal’ (A577‒578/B605‒606). Rather, we can only assume TI and hence the idea of such a being, viz. God, regulatively (see A578/B606).

What does this imply for our problem of truth-evaluation? The idea of God must be assumed regulatively as the sufficient material condition for all objects in nature to be completely determinable. The assumption of a complete determination is a necessary condition for the cognition of an object to have a definite truth-value. The idea of God thus legitimizes our assumption that every cognition can be assessed against an objective standard of truth. What its regulative qualification amounts to becomes clear only in the Appendix, to which I now turn.

5.3 Ideas As Projections of a World without Perspective

Based on these considerations regarding the idea of God, I now argue that ideas of reason have their legitimacy with regard to the cognition of nature only as normative ideals. These ideals are projections of an ultimate reality beyond the human horizon. This is the reality against which we should measure the success of our cognition, if there were such a reality. But such a projection cannot itself amount to a truth-assessable assertion about such a reality. It can only ever be a focus imaginarius for us. The normative function of ideas is thus captured by this third visual metaphor (see 3.2).

Support for my argument is provided in Kant’s transcendental deduction of the three ideas – the soul, the world-whole, and God – in the Appendix. Kant concedes that ideas cannot be shown to have the same kind of objective validity as the categories, since no corresponding intuition can be given.Footnote ¹⁴² However, ideas are said to have ‘objective but indeterminate validity’ (A663/B691), or to be ‘valid, albeit only indirectly, for the object of experience’ (A665/B693). One way to understand this indirect (or indeterminate) objective validity is to accept that ideas do not establish positive claims about nature, as the categories do about objects of experience. Rather, in a negative sense, they define restrictions on nature: they project ideals without which nature could not be intelligible to us at all. If cognition were not ‘cultivated and corrected’ against these ideals, it could not be asserted as true (A671/B699; see 2.2).

In the transcendental deduction, Kant specifies that an idea has objective validity in terms of an ‘object in the idea’, rather than by being instantiated by a real thing (A670/B698, A671/B699, A697/B725). Positing an object in the idea, I argue, generates a normative ideal or standard for judging the correctness of cognition. Regarding the idea of God, Kant explicitly writes:

Together with my argument about the TI in 5.2, we can now understand the regulative use of the idea of God as the positing of an object in the idea: we posit in the idea ‘a substratum, unknown to us, of the systematic unity, order, and purposiveness of the world’s arrangement’ (A696/B724). This positing is not a conceptual determination, or an assertion, of such a substratum as an existing thing, as assumed by some noumenalists. Rather, it is the projection of an ultimate goal of our cognitive efforts.Footnote ¹⁴³ The regulative use of the idea of God enables the projection of an ultimate reality that would ground the world of appearances. An ultimate reality is what would make the cognition of appearances true, independently of the way we carve up nature by our a priori forms and our empirical concepts.

The projection must remain an ‘imagined object’ (A670/B698) and as such a focus imaginarius. Recall that ideas of reason

A visual focus imaginarius is an illusory point ‘behind the surface of a mirror’ (A644/B672) from which an object seems to emerge. Similarly, an idea is a focus imaginarius from which ‘an object lying outside the field of possible empirical cognition’ (A644/B672) seems to appear. This focal point thus stands in for a reality that lies outside the world of appearances but that is assumed to ground appearances. To project this focal point imaginatively is indispensably necessary ‘to take the measure of [the understanding’s] greatest possible and uttermost extension’ (A645/B673). That is, the focal point is required as an ideal standard for measuring our progress in finding systematic connections among appearances.

In the mirror case, we take an object behind the mirror to be the source of the image in the mirror. Similarly, we take an ultimate reality ‘behind’ the world of appearances to contain its ground. Even if we cannot prove that this ultimate reality exists ‘absolutely and in itself as something actual’ (A681/B709), we must project it. These projections are such that we can ‘consider all experiential cognition as determined through an absolute totality of conditions’ (A327/B384, emphasis added), that is, through an ultimate reality. In contrast to strong fictionalism, however, these projections are not arbitrary fictions or ‘mere figments of the brain’ (A569/B597), but placeholders for an ultimate reality.

This ultimate reality, which must be assumed not to be conditioned by the human mind, might be identified with what Kant calls things-in-themselves.Footnote ¹⁴⁴ Without taking a stance on the many thorny questions about things-in-themselves and their relation to appearances, I take an essential assumption of Kant’s transcendental idealism to be that things-in-themselves exist. In other words, there is a reality independent of the human forms of cognition, especially of time and space.Footnote ¹⁴⁵ What is at stake, however, is whether this mind-independent reality actually matches our idea-based projections of it.

With regard to the problem of truth-evaluation, this suggests that ideas used as foci imaginarii serve to project the ultimate circumstances of evaluation for our cognition. At these circumstances, the truth of our cognitions is assessed in light of the states of the world that ultimately make our cognitions true.Footnote ¹⁴⁶ These circumstances should thus be identified with the world as it is in itself, rather than the world of appearances, which is structured by the human forms of cognition and contingently carved up by empirical conceptualization (see 4.3 and 4.4). We may call this the world viewed ‘from nowhere’ or simply without perspective.Footnote ¹⁴⁷ And this is the world we should aim to know.

To sum up, the transcendental deduction, whether successful or not, is meant to show that ideas of reason are ‘legislative for us’ (A695/B723): they define the ‘indispensable standard for reason … to assess and measure the degree and the defects of what is incomplete’ in our cognition of nature (A569‒570/B597‒598). Ideas project an ultimate reality as the ideal standard of truth, which, because it is freed from the limitations of the human perspective, is normatively binding across all times and places, across all cognitive subjects and epistemic groups.Footnote ¹⁴⁸ However, there is no a priori guarantee that the actual process of human inquiry will ever approximate this ideal standard.Footnote ¹⁴⁹ It remains fundamentally open from the human standpoint what the human horizon actually converges upon, if it converges at all. We can only hope to approach a truthful description of nature by continuously refining and revising our empirical concepts and cognitions. We can only hope to reach the ultimate reality in the ideal limit of all our epistemic inquiries.Footnote ¹⁵⁰

One may object to the perspectivalist interpretation that it leaves the function of ideas fundamentally ambivalent: it seems unclear when an idea serves to outline the world of appearances as the context of intelligibility and when it serves to project ultimate reality as circumstances of evaluation. The fact, however, that one and the same idea serves both purposes is the key to resolving the impasse between fictionalism and noumenalism. The double function of ideas to delineate the human horizon and to project ideal standards of truth beyond the human horizon gives rise to our rational hope that the world of appearances, which is conditioned by human limits and contingent empirical choices, will eventually converge with the world without perspective in the ideal limit of infinite inquiry. Figure 5 illustrates this mapping.Footnote ¹⁵¹ Without presupposing ideas of reason as objectively valid ideal standards of truth, nature could not be intelligible to us at all and cognition would lose its meaning for us. Such ideals cannot themselves be asserted as theoretical truths but must be presupposed in our human practice of exploring nature.

Figure 5 Schematic mapping of the world of appearances, i.e., the universal human horizon, and ultimate reality, i.e., the world without perspective or things-in-themselves, in the ideal limit of inquiry.