1. Kant’s architectonic and Ypi’s schematism of reason

The Architectonic of Reason (Ypi Reference Ypi2021; cited throughout by page number) follows a series of volumes dedicated to the concepts of systematicity, organicism, architectonic unity and the teleology of reason (e.g. Nuzzo Reference Nuzzo2005; Mensch Reference Mensch2013; Fugate Reference Fugate2014; Ferrarin Reference Ferrarin2015; Gava Reference Gava2023). Its fundamental claim is that, though in the first Critique ‘the unity of reason is achieved through the purposive function of the ideas of reason’, Kant’s project ultimately fails because ‘practical reason has no distinctive domain for its own legislation, and no necessary connection to transcendental freedom’ (p. 11).

Key to this demonstrandum is Ypi’s account of the schematism of reason. In chapter 2, we read that the schematism of reason plays a role that is analogous to the schematism in the Analytic: mediating between two different faculties in order to account for their lawful connection (p. 47). However, unlike the schematism in the Analytic – built on the deduction of the categories – in the case of the schematism of pure reason in the Architectonic there is no preceding deduction of the ideas.

Further details follow in chapter 4, where we get back to the Appendix to the Transcendental Dialectic in order to deal with the only available deduction of the ideas, and the connection between the ideas ‘and the ideal of pure reason that Kant suggests as their schema’ (p. 82).

When addressing the issue, Ypi seems to move straightforwardly from the schematism in the Appendix to the schematism in the Architectonic (pp. 45–9).Footnote ¹ The move from the Architectonic back to the Appendix confirms this: since the Architectonic contains no deduction of the ideas preceding the schematism, we should get back to the argument in the Appendix (pp. 50–2, 81–2). Finally, when appealing to the transcendental ideal, Ypi seemingly takes for granted that its schematic role in the Appendix somehow reappears in the Architectonic (pp. 112–13). It thus seems that Ypi assumes a continuity between what I take instead to be two different but complementary kinds of schematism.Footnote ²

The schematism of pure reason of the Architectonic is not – I argue – the same as the schematism of the ideas and the ideal in the Appendix, for four main reasons. (1) In the Appendix the ideas and the ideal work analogously to the cognitive schemata between sensibility and understanding in the Analytic of Principles, while in the Architectonic it is the idea of reason’s whole that is to be schematized. (2) In the Appendix the schematism of the ideas and the ideal is meant to systematically arrange the whole of the understanding’s cognitions, while in the Architectonic what is at stake is the systematic unity of reason in the most general sense. (3) The schematism of the ideas and the ideal concerns only the theoretical use of reason, while the schematism of pure reason requires the practical standpoint as well – which Kant introduces in the Canon because he needs it in the Architectonic. (4) Only the schematism in the Appendix entails a mediation between two different faculties, while in the Architectonic the schema of systematic unity follows from reason’s articulation from within itself.

The schematism of pure reason in the Architectonic encompasses the schematism of the ideas and the ideal in the Appendix: the systematic arrangement of the understanding’s cognitions is an epiphenomenon of reason’s general quest for its own self-consistency and systematic unity (see p. 138). The issue is the relation between the practical and the theoretical use of reason, ‘and indeed the systematic connection between the two’ in the context of the justification of the role of systematization for the general methodology of philosophical inquiry (p. 51).

Yet this does not mean that we are dealing with the same schematism, nor should we make the boundaries between the Doctrine of Elements and the Doctrine of Method disappear. Only the latter is responsible for the guidelines of reason’s internal organization and the overall arrangement of its constitutive elements.Footnote ³ These two sections should be distinguished in order not to conflate the idea of systematicity at stake in the Appendix with Kant’s account of reason’s most general systematic unity in the Architectonic.

Let me recall the fundamental tenets of Ypi’s interpretation. One claim (pp. 45–52) is that (A) the schematism of reason is key to understanding the positive role and the methodological import of the ideas in framing the unity of reason. The view is that there is a close connection between the pure concepts and the ends of reason. The extent of this connection also works by contrast: in the end, the first Critique lacks the means to account for transcendental freedom and the practical ends – thereby compromising the project of unification. This is further strengthened by the view that (B) Kant’s systematic efforts in scientific cognition are part of a broader account of systematicity involving both the theoretical and the practical standpoint (p. 81). Ypi also points out that the schematism of reason leads us to the transcendental ideal and an account of purposive-systematic unity deeply influenced by the fact that (C), in the first Critique ‘there is nothing to suggest that practical reason has a distinctive causality based on freedom’ (pp. 116, 176). The result is that we are compelled to understand reason’s purposiveness in terms of design, and not normatively (as it will instead be in the third Critique). The last claim is that (D) while the Dialectic

I agree that the methodological import of the ideas should be more explicitly acknowledged (A) and that Kant’s account of scientific systematicity is part of a broader view which also includes the practical standpoint (B). However, I do not think there is ‘nothing’ in the first Critique pointing to the distinctively practical employment of reason (C), nor do I think that the Architectonic develops the account of the Appendix (D). Finally, I think that Kant does explain the nature of the schema in the Architectonic (unlike Ypi, p. 135). We should then reverse the interpretative direction of the thread connecting the schematism of the ideas and the ideal in the Appendix and the schematism of pure reason in the Architectonic. The latter has logical and methodological priority over the former.

The schematism of the ideas and the ideal has a more limited – though not less relevant – scope: it accounts for the systematic arrangement of the understanding’s cognitions up to the prototypon of the transcendental ideal. In these terms, this schematism does represent a whole, yet it cannot account for reason’s idea of the whole as Kant presents it in the Architectonic. The latter idea is indeed the ‘rational concept of the form of a whole’ (KrV, A832/B860):Footnote ⁴ it must take logical precedence because we cannot reach the idea by assembling and putting together its parts – including the system of the understanding’s cognitions. It must also take methodological precedence, as it is the drive underlying the regulative function of the ideas. In projecting its own unity, reason is moved and driven from within itself to achieve its goal (see Ferrarin Reference Ferrarin2015: 33–4, 57).

In the Architectonic we are dealing with reason’s most general unity. We are not schematizing the understanding upwards towards higher-order concepts; rather, reason itself is schematizing the form of its whole and articulating it in the form of the most comprehensive systematic unity. Systematic unity is the shape the whole takes on by means of the schematism of pure reason.

This articulation does not involve any mediation with the understanding, for reason is drawing the form of systematic unity from within itself. Kant’s employment of the metaphor of the organism is due to this.Footnote ⁵ We also have to acknowledge the specific role of the practical employment of reason Kant introduces in the CanonFootnote ⁶ – otherwise we would be quite paradoxically compelled to account for reason’s unity ignoring one of its two lawful employments. The Appendix leaves the practical standpoint aside (see pp. 135–8), while we cannot dispense with it in the Architectonic: in the former section the task is the systematic arrangement of the understanding’s cognitions; in the latter section the task is the systematic unity of pure reason in the most general sense.

Moving from this background, in section 2 I point out the relevant features of the schematism between reason and the understanding. In section 3 I show that Kant’s concern in the Appendix is to account for a specific sense of systematic unity that concerns the understanding alone. Obviously, this is part of reason’s quest for its overall systematic unity. However, as such – as a part – it cannot exhaustively account for the latter.

In section 4 I compare the picture sketched in sections 2 and 3 with Kant’s argument in the Architectonic. Here we find that it is the idea of reason’s whole in the most comprehensive and general sense that is to be schematized. There is no mediation between reason (in the narrow sense) and the understanding, for instead reason (in the most general sense) is internally articulating the form of its whole by declining it into the general structure of a system. Systematic unity is the schematic shape of reason’s idea of the whole: systematicity is the schema of reason’s idea of unity.

The Architectonic brings the practical employment of reason into the picture – for the all-encompassing systematic unity reason is seeking would not be conceivable without one of the two lawful employments of reason itself. The Architectonic draws the outline of reason’s systematic development, the schema for the execution of the idea, the monogram and general framework for its domains.

While one may say that the first Critique lacks the means to establish the practical domain of freedom, it still succeeds in grounding the practical employment of reason and accounting for its unity with the theoretical.Footnote ⁷ In turn, this is the fundamental condition for the system to be actually established. The Architectonic leaves us with a plan which cannot be separated from its execution.

2. Schematism without time: reason and the understanding

When comparing the cognitive schematism in the Analytic with the schematism between the understanding and reason, Ypi writes that, unlike sensibility, ‘both understanding and reason are superior cognitive faculties characterized by spontaneity’ ordering a manifold.

Unlike the schematism in the Analytic, the mediation here at stake concerns the two superior faculties: reason and the understanding. There is indeed no reference either to sensibility or the imagination in this case. This requires us to expand on the schematism of the ideas and the ideal and make it explicit that this schematic mediation has no direct reference to the form of time. The fact that the schematism of the ideas is non-temporal has significant consequences for the outcome of the schematic procedure itself: no third representation or element follows from the schematism between the understanding and reason. This is why the ideas’ role is merely regulative.

Another important point is the meaning of manifold in this context. The manifold of intuition is given because of space and time. It is a mere manifold because its elements lack the internal connection that only the categories provide. Manifold here means a kind of logical unrelatedness between the Merkmale of sensible representations. This cannot be the meaning of the manifold of the rules of the understanding. Ypi is not pointing to the fact that there is a plurality of categories, for pure reason does not aim at unifying the categories (pp. 89–90, 110). After all, the pure concepts of the understanding already articulate the synthetic unity of apperception. Thus, in a sense, they are utterly unified from the outset. More likely, Ypi is here referring to the several cognitions the understanding achieves in the domain of nature. Yet in this case as well it is important to make it explicit that these cognitions are not given, but rather produced by means of a determining synthesis. They do not lack the internal connection and synthetic unification of their constitutive elements.

The key target of reason’s unifying drive is the very function of the understanding, not just its corpus of particular cognitions. The schematism of the ideas and the ideal properly entails a mediation between two faculties, not between two different kinds of representation (as it does in the cognitive case).

As for the non-temporal status of the schematism of the ideas, the relevant point is that the connection between the faculties does not bring about any third outcome. To schematize between the understanding and reason does not mean to bring about a different kind of representation. What we get instead is, by no means less importantly, an encompassing systematic framework for the whole of the understanding’s cognitions. The schematism of the ideas and the ideal is meant to articulate the a priori function – not the empirical achievements – of the understanding, precisely by means of a regulative expansion of its scope (p. 114).

As for the second issue, the understanding as reason’s target, it must be pointed out how the parallelism between cognitive schematism and the schematism of pure reason reaches its boundaries at this point, and cannot hold further.Footnote ⁸ The synthetic unity that the understanding provides is necessary for us to be able, in general, to have cognitions. The unity that the ideas of reason seek for these cognitions is necessary for their systematic arrangement, yet it is not the first constitutive ground of cognition itself. This is not to diminish the positive import of the ideas or to undermine their necessity (see Rauscher Reference Rauscher and Guyer2010) but, rather, to point out again that reason’s key target is the faculty of the understanding in general, not just its corpus of cognitions. The task of the ideas is to schematize the understanding: the result is the systematic arrangement of the understanding’s cognitions.

The schematism of the ideas is meant to provide the understanding with the only thing it cannot achieve by relying exclusively on itself: the systematic arrangement of the cognitions at stake (which, in turn, is undoubtedly necessary for the completeness of our cognition in general and the result of reason’s unification of the faculty of the understanding; see Mudd Reference Mudd2017).

While Ypi actually recognizes this latter point (pp. 109–11), it seems that she also relies on the schematism of the ideas and the ideal (the schematism between the understanding and reason in the Appendix) when accounting for what I call the schematism of pure reason in the Architectonic.

Before moving to this topic in section 4, we have to highlight Kant’s key statements on the schematism of the ideas and the ideal in the Appendix.

3. The schematism of the ideas and the ideal in the Appendix

After having clarified that the understanding ‘constitutes an object for reason, just as sensibility does for the understanding’, Kant points out that the ‘idea of the maximum of division and unification of the understanding’s cognition in one principle’ plays the role of the analogue of the schema (A665/B693). Each of the transcendental ideas – the soul, the world, God – represents a maximum working as a prism: the articulation of the understanding according to the ideas displays to the understanding itself the systematic connection of the whole of its own cognitions.

A further qualification of this schematism is to be found at A670/B698, where Kant states that the ‘object in the idea’ serves as a schema in order to represent, indirectly, other objects to us ‘in accordance with their systematic unity’, namely ‘the greatest unity of reason’ in its empirical use. Kant is here proceeding by means of analogical thinking: the point is to consider all objects ‘as if they had gotten their existence from a highest intelligence’ (A671/B699). The ascending series of systematization – from the understanding, through the ideas, up to the transcendental ideal – relies on this analogy (see Caimi Reference Caimi1996). The ideas and the ideal have the reality ‘of a schema of the regulative principle for the systematic unity of all cognitions of nature; hence they should be grounded only as analogues of real things’ (A674/B702). The ideas and the ideal as schemata are key to the systematicity of the understanding’s cognitions, namely for the ‘greatest possible empirical use of reason’ (A679/B707). By means of the transcendental ideal reason ‘extends systematic unity over all experience’ (A682/B710).

Kant binds in a peculiar fashion the schematism of the ideas and the ideal, the systematic arrangement of the understanding’s cognitions and the theoretical employment of reason. The ideas and the ideal are understood as the summit of the theoretical employment of reason in accordance with the lawful boundaries of the possibility of experience. They work as schemata in that they allow the understanding to outline the systematic interconnection of all cognitions.

Kant’s concern in the Appendix is very specific and limited to an account of systematic unity related to the understanding alone. Nowhere had we read of the systematic unity of reason in the most general sense. The reason is that the topic here is not the practical standpoint of reason – which must however play a role in reason’s systematic unity in the most general sense.

This requires us to leave the interpretative lens of the Doctrine of Elements and attune ourselves to the Doctrine of Method (see Mensch Reference Mensch2013: 139–43). By switching section, we also take on a different task and have to account for the systematic unity of reason per se, far beyond the necessity to systematize the understanding’s cognitions. The task of the Architectonic, to which we now turn, is to outline the schema of the overall system of reason’s lawful employments (the theoretical and the practical).

4. The schematism of pure reason in the Architectonic

The schematism of pure reason in the Architectonic is meant to articulate the form of reason’s whole in terms of the systematic unity between its two lawful employments – the theoretical and the practical. No doubt the schematism of the ideas and the ideal in the Appendix is part of this broader picture, but there Kant’s aim is to account for the systematic arrangement of the understanding’s cognitions – thereby also accounting for the regulative role of the ideas, i.e. the elements of reason in the narrow sense. Kant’s aim in the Architectonic is to account for the systematic unity of reason as a whole – not only for the systematic unity of its theoretical employment.

The schematism of pure reason proceeds organically – i.e. from within reason itself – in order to let reason outline the general framework of its own domains. It is only by means of this articulation that the form of reason’s whole can be genuinely qualified in terms of systematic unity. Accordingly, it is only by means of the very same articulation that we get acquainted with the need to unify and let systematically coexist the two lawful employments of reason and their respective domains. It is by no means by chance – quite the opposite, for systematic reasons – that the Canon introduces the practical standpoint right before the Architectonic.

It is important to begin by pointing out clearly what kind of idea is going to be schematized in the Architectonic. In the Appendix the ideas and the ideal work analogously to the schemata between sensibility and understanding in that they unify the scope of the understanding. Through the ideas the understanding is provided with a general systematic framework for the whole of its cognitions. Instead of being restricted to the conditions of sensibility, the understanding faces a regulative expansion towards systematic unity.

The picture is quite different in the Architectonic. The idea here at stake is not this or that pure concept of reason: the soul, the world, God. It is, instead, the very ‘rational concept of the form of a whole’ which contains ‘the unity of the end’ (A832/B860). The execution (Ausführung) of the idea

In every science ‘the schema contains the outline (monogramma) and the division of the whole into members in conformity with the idea, i.e., a priori’, namely in conformity with the end ‘which first makes possible the whole’ (A833–4/B861–2). Since the idea and the end of a science constitute its first ground, we are left with the issue of the elaboration and execution of the idea: systematic unity is the schematic articulation of the idea of reason’s whole. Now Kant’s concern is not just the systematic arrangement of the understanding’s cognitions but reason’s most internal self-consistency, namely the systematic unity between its two lawful employments – the theoretical, for which the whole Critique exhaustively accounted, and the practical, which must be introduced.

The very possibility of establishing a science – even in the case of metaphysics – relies on an idea as its ground. The idea, in turn, needs a schema: the outline of its execution. It is at this point that Kant calls this schema ‘the original seed’ in the context of the ‘mere self-development of reason’ (A835/B863). Here Kant means reason in the most general sense, not in the narrower sense of the faculty of the ideas. Accordingly, there is no need of a mediation between two self-standing faculties. Reason organically articulates from within itself the idea of its own whole in the concept of systematic unity. Reason’s legislations – nature and freedom – are systems to be ultimately unified ‘in a single philosophical system’ (A840/B868). Accordingly, metaphysics ‘is divided into the metaphysics of the speculative and the practical use of pure reason’ (A841/B869).Footnote ⁹

Kant’s concern in the Architectonic is to draw the general outline of metaphysics as a science, and this cannot be done without the practical employment of reason. If we are to understand – and also establish – metaphysics as a science, we are required to account for the systematic unity of the whole of its principles (see Euler Reference Euler2018: 27–8). Metaphysics has two domains because reason has two employments: it is impossible to account for the unity of the former without the unity of the latter as a condition. In some way one may argue that in the first Critique Kant fails to properly and exhaustively establish (1) the practical domain of freedom and (2) the unity between nature and freedom. However, I think it is hard to deny that Kant does not fail to ground the unity between the two employments of reasons – the theoretical and the practical.

It is the schematism of pure reason that will orientFootnote ¹⁰ Kant towards the proper establishment of the domain of freedom and the individuation of the transcendental principle of the Urteilskraft, namely the faculty meant to bridge between nature and freedom by way of the principle of purposiveness.

Ypi assigns a relevant role to what she calls the schematism of reason in the context of the individuation of the idea of the whole – which is, in turn, key to understanding the Architectonic – and in order to account for the positive role of the ideas in the Appendix and their practical development in the Canon. While I am sympathetic with this picture, I also think that three main differences emerge from the distinction between the two kinds of schematism.

The first difference is that the ideas and the ideal in the Appendix are only analogous to the schemata between sensibility and understanding. Moreover, there is a mediation between reason and the understanding. The Architectonic instead is about reason’s non-mediated self-schematism, from the form of the whole to the idea of systematic unity.

The second difference is that, while the Appendix aims to account for the systematic arrangement of the understanding’s cognitions, the Architectonic aims to account for the systematic unity of reason in the most general sense. The two tasks are connected, but not identical. More importantly, it is the Architectonic that makes it necessary to schematize the understanding by means of the ideas – by no means the other way around. The methodological drive of the Architectonic is prior to – and the condition of – the regulative employment of the ideas in the Appendix.

The third difference is that the schematism in the Appendix only concerns the theoretical use of reason, while the schematism in the Architectonic also relies on the introduction of the practical standpoint in the Canon.

What consequences are to be drown from this?Footnote ¹¹ As for Ypi’s claims (A), regarding the positive role of the ideas, and (B), regarding systematicity as a speculative-practical issue (see section 1 above), I think my reconstruction strengthens them: the Appendix confirms that the ideas are reason’s tools for the systematic arrangement of the understanding’s cognitions (see Ferrarin Reference Ferrarin2015: 42–55). From another point of view, the primacy of the schematism of pure reason in the Architectonic enables the view that the regulative role of the ideas for the understanding is part of a broader picture pointing towards the systematic unity between the theoretical and the practical employment of reason. However, as for claims (C), regarding the lack of the practical domain, and (D), regarding the architectonic development of the outcomes of the Appendix, the Appendix/Architectonic distinction allows us, in response to (C), to better understand the relevance of Kant’s argument in the Canon, thereby making it clear that – while the practical domain of freedom finds no authentic foundation in the first Critique, its key condition – the practical employment of reason is not only grounded on, but also systematically connected to the theoretical one. In response to (D), we see that all attempts at systematization are specific applications of reason’s most general drive as Kant presents it in the Architectonic, whereby systematicity is the schematic shape of reason’s idea of the form of the whole.

Finally, this also makes it clear that there is no need for a deduction of the ideas in the Architectonic: here we are not dealing with the justification of their employment as schemata for the understanding, nor are we schematizing the ideas of the Appendix. The idea at stake in the Architectonic is reason’s form of its own whole in the most general sense, namely the most fundamental regulative idea in the execution of reason’s architectonic-systematic drive (see Nuzzo Reference Nuzzo, Fricke, König and Petersen1995: 101). This idea does not need a deduction, but only the practical employment of reason itself.Footnote ¹²