Three Interpretations

I begin by presenting the three accounts that dominate the literature.

2.1 The INTUITIONS INTERPRETATION

According to the first account, schemata are intuitions. This view is defended by Moltke Gram (1968, pp. 83–129), Henry Allison (1981, 1983, pp. 179–85, 2004, pp. 210–8) and Sarah Gibbons (1994, pp. 53–78), and endorsed by Konstantin Pollok (2017, pp. 235–8). These interpreters differ over the scope of the INTUITIONS INTERPRETATION: Gram and

Allison claim only that the schemata of the categories (i.e. the “transcendental schemata”) are intuitions, whereas Gibbons and Pollok seem to hold that all schemata are intuitions.

On this reading, a schema represents a certain pattern or set of features that typifies the objects falling under the relevant concept. Since an intuition is a representation of a particular not a general feature, a schema so construed would present a token-instance of this pattern or feature. For example, the schema of the concept <fox> would be a “singular intuitive representation” of the distinctive features of foxes.5

Perhaps this intuition would present the brownish-redness, the pointed ears and the ambling movements that make foxes so recognizable. (As I argue in Section 5.1, I suspect that this proposal collapses into the idea that the schema is a mental image of some paradigm fox—a view which Kant clearly rejects.) In the case of a category, the schema would be an “intuitive exhibition” of a certain temporal structure, e.g. something continuing to exist while its properties change in the case of the concept <substance>.

The rationale for thinking of schemata in this way comes from a mixture of structural and textual considerations. Gram (1968) and Gibbons (1994) argue that this is the only available way to render Kant’s account of judgment coherent (mainly by giving arguments against the SUBSUMPTION-RULES INTERPRETATION); Gram (1968) and Allison (1981, 1983,

5 _{Cf. Gibbons (1994, pp. 61, 74).}

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2004) emphasise Kant’s remarks about some of the categories’ schemata (discussed below in Section 4.2), and some asides relating to schemata from the 2nd and 3rd Critiques (discussed below in Sections 4.3–4).

2.2 The SUBSUMPTION-RULES INTERPRETATION

According to the second account, schemata are rules for subsuming intuited objects under concepts. The SUBSUMPTION-RULES INTERPRETATION is defended by Harold A. Prichard

(1909, pp. 246–55), Jonathan Bennett (1966, pp. 151f.), Paul Guyer (1987, pp. 162–81) and Rolf-Peter Horstmann (2018, pp. 58, 64, 86–96).

On this reading, a schema is a rule specifying the features that typify the objects falling under the relevant concept. For example, the schema of the concept <fox> would be a rule stating that things with reddish-brown fur, pointed ears, ambling movements, etc. are to be subsumed under the concept <fox>. In the case of a category, the schema would specify that objects with a certain temporal structure are to be subsumed under a certain category, e.g. that things which continue to exist while their properties change are instances of the concept <substance>. A schema qua subsumption rule would be a representation of a mental act, i.e. the act of “subsuming” or classifying an object under a concept, which Kant attributes to the power of judgment (A132/B171). However, it would represent this act by specifying features that objects must exemplify in order to fall under the relevant concept: as well as representing a mental act, it would represent features of objects. Unlike an intuition, such a rule would be general in content, so a schema thus construed would represent a kind of mental act (and general features of objects).

Many commentators think that, for Kant, concepts are rules for subsuming objects, and contain marks specifying the features exhibited by the objects that fall under them (e.g. Allison, 2004, p. 79; Guyer, 1987, p. 164; Longuenesse, 1998, p. 50; cf. A68/B93, A106). For this reason, proponents of the SUBSUMPTION-RULES INTERPRETATION often explicitly equate schemata with a kind of concept (Bennett, 1966, p. 151; Horstmann, 2018, pp. 58, 89; Prichard, 1909, p. 248). This further illustrates the fact that a subsumption-rule is

simultaneously a representation of a mental procedure and a representation of a type of object. In the case of the categories, the schema takes the merely logical content of the category and adds further temporal content, resulting in a concept which falls under the category, but also has sensible objects falling under it. In the case of sensible concepts (i.e. empirical and mathematical concepts), the schema is really just the same representation as the

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concept it schematizes (Bennett, 1966, p. 151; Guyer, 1987, pp. 163–5). Insofar as Kant differentiates sensible concepts from their schemata, he is just “half-heartedly generalis[ing] in order not to look excessively ad hoc” (Chipman, 1972, p. 42).

The motivation for thinking that schemata are rules of subsumption is mainly contextual. In the short section preceding the Schematism, Kant raises the issue of how agents are capable of subsuming particular objects under concepts. Then the Schematism chapter opens with a discussion of subsumption. Kant even refers to this part of the Critique as ‘The Transcendental Doctrine of the Power of Judgment’—the power of judgment being “the capacity to subsume under rules, i.e. to decide whether something stands under a given rule” (A132/B171, Kant’s emphasis). So, by the time we reach Kant’s characterizations of schemata, it is natural to expect him to be focusing on the power of judgment’s activity of subsuming intuited objects under concepts. And indeed some of Kant’s remarks are compatible with such a reading: to say that a schema is a “representation of a general

procedure […] for providing a concept with its image” (A140/B179f.) might well be read as meaning that it is a representation of how to find or identify an image that falls under a given concept. In what follows, I will argue that other ways of reading such passages are ultimately more satisfying. Nevertheless, the view is not without its prima facie appeal.

2.3 The SYNTHESIS-RULES INTERPRETATION

According to the third account, schemata are rules for synthesis of imagination. On this view, schemata are neither intuitions nor concepts, but rules for producing intuitions that fall under concepts. This view is espoused by Martin Heidegger (1929, pp. 88–113), J. Michael Young (1984, 1988), Michael Pendlebury (1995), Béatrice Longuenesse (1998) and Samantha Matherne (2015).6

What would it mean for a schema to be a rule for synthesis of imagination? In this context, a rule is simply a general representation of a repeatable activity. Certain token- activities fall into kinds; there can be mental representations of these activity-types; such representations can be called “rules”. (I intend the term “rule” to be neutral regarding the role these representations play, e.g. whether they merely describe an activity-type or whether they

6 _{Longuenesse’s position seems rather equivocal: many of her remarks favour the SYNTHESIS-RULES}

INTERPRETATION (pp. 13, 50, 116, 39) but other remarks seem to conflict with it (pp. 245, 250, 273, 332, 369, 371). Note also that Allison (2004) endorses the SYNTHESIS-RULES INTERPRETATION for empirical and mathematical schemata (but the INTUITIONS INTERPRETATION for transcendental schemata).

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play some role in bringing the activity about.) Kant’s notion of synthesis of the imagination is a large topic, but here is a brief (and hopefully relatively unpartisan) characterization.

Synthesis of the imagination can be understood in functional terms as the mental operation that “bring[s] the manifold of intuition into an image” (A120). We can represent this functional structure with a flowchart (fig. 1).

By the “manifold of intuition”, Kant means the plurality of states (“sensations”,

“impressions”) that arise when the faculty of sensibility is affected by objects (A120f.). These can be equated with the physiological changes that our sense-organs undergo when

stimulated by objects.7 Kant holds that we can also produce images of numbers and geometrical objects without drawing on sensations, in which case the structural features of the mind’s receptive capacities serve as a “pure” manifold of intuition (cf. A99f., B137). So the input of synthesis of imagination is a plurality of non-representational8 sensory states.

The output of synthesis of imagination is an “image”, i.e. a complex intuition.9 An intuition is a singular representation of a particular object, a representation with spatial and temporal structure. Kant gives the examples of perceiving a house (B162) and “drawing”

7 _{Kant talks about “impressions” in physiological terms in his Anthropology (7:176). Cf. Horstmann (2018, pp.}

18f.).

8 _{Note that some interpreters hold that these sensations jointly constitute a representation of an object, even prior}

to synthesis. See below.

9 _{“Image (which means an intuition that contains a manifold in certain relations, consequently a figure)” (ÜE}

8:201f.). N.b. we shouldn’t assume that by “image”, Kant means an internal mental intermediary, rather than a mental state directed at the outer world. For example, Heidegger (1929, pp. 90f.) argues that Kant uses the term “image [Bild] ” in the sense of “view” or “sight” (“Anblick”). Cf. Matherne’s (2015).

synthesis of imagination i i i i image manifold of intuition

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lines and groups of dots in the mind’s eye (A102, B137f., A140/B179). In each case, the resulting intuition is complex in the sense of having components, which each represent different features of the object. This complex structure can be mereological, as when the different parts of an intuition of a line each represent a different part of the line; and it can also be non-mereological, as when the visual and tactile sensations that make up my intuition of a lump of cinnabar jointly represent the lump as red and as heavy (cf. A100f.).

Let me flag up a disagreement in contemporary Kant-scholarship that bears on this discussion. It is controversial whether Kant thinks that all of our intuitions depend on synthesis of imagination, or whether we possess some intuitions prior to synthesizing. Some “Nonconceptualist” interpreters hold that the “manifold of intuition” constitutes an intuition even prior to synthesis (despite the fact that the individual “sensations” making it up are non- representational).10 Nevertheless, these interpreters agree that synthesis is required in order for us to reach certain kinds of complex intuitions, and certainly the kinds of representation that Kant calls “images”.11

They also agree that synthesis is required in order to reach intuitions that present objects in a way that allows them to be subsumed under concepts.12 The (alleged) intuitions that precede synthesis have a kind of “sensible unity”, but they do not present us with things exhibiting the kinds of unity needed for us to be able to take them up into thought. In effect, all parties agree that “images”—the kinds of intuition that can be subsumed under concepts—are products of synthesis. For the purposes of this essay I will therefore remain neutral on the issue of whether all intuitions presuppose synthesis, and simply rely on the consensus view that synthesis is needed to get us from passively received “sensations” to unified “images” of objects.

We can now sum up the import of the SYNTHESIS-RULES INTERPRETATION. To claim

that a schema is a rule for synthesis of imagination is to claim that it is a general representation of a procedure for converting sensory stimulations (“sensations”) into a unified, complex perceptual representation of an object (an “image”). Returning to our example of seeing a fox, the “manifold of intuition” consists of the many firings of

photoreceptors caused by light reflected from the animal; “synthesis of imagination” denotes the sequences of processing that convert these neural signals into a complex perceptual representation (i.e. an image); and the schema of the concept <fox> is a representation of the

10 _{Nonconceptualists with this view include Tolley (2013, pp. 122f.), Matherne (2015:32f.), McLear (2015, pp.}

100f.) and Allais (2017, pp. 32f.).

11 _{See Tolley (2013, pp. 122f.) and Matherne (2015, pp. 755f.).} 12 _{See McLear (2015, pp. 98–106) and Allais (2017, pp. 37–44).}

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process of synthesis of imagination required to produce an image matching that concept, i.e. one that presents its object as having reddish-brown fur, pointed ears, ambling movements, etc.