1. Introduction
In the section of Critique of Pure Reason titled Anticipations of Perception, Kant attempts to prove what we can call the ‘principle of intensive magnitudes’ (PIM).Footnote 1 According to the PIM, every possible object of experience will, as a matter of a priori and transcendental necessity, display some determinate ‘degree’ (Grad) of ‘continuous’ or ‘intensive magnitude’ (intensive Gröβe) of ‘reality’ (Realität). An intensive magnitude is a measure of how an object ‘fills’ (erfüllt) space or time. Kant's official formulation of the principle reads, ‘In all appearances, the real, which is an object of the sensation, has intensive magnitude’ (B207).Footnote 2
Intensive magnitudes quantify the matter in an object and vary independently of ‘extensive magnitudes’, which quantify spatiotemporal form. The principle of extensive magnitudes (the ‘PEM’, defended in the Axioms of Intuition: see A162/B202ff.) and the PIM are ‘mathematical’ principles dealing with how an intuited object is constituted and quantified.Footnote 3 By articulating the PIM as distinct from the PEM, Kant is claiming that one cannot give an exhaustive mathematical description of an object by appeal to its size and shape alone. The thesis that one could give an exhaustive description of an object through size and shape alone was held by Kant's mechanist predecessors (both the atomists and the Cartesian plenumists) and it was in opposition to these theories that Kant developed his own ‘dynamical’ theory of matter in the Metaphysical Foundations of Natural Science (MFNS) of 1786.Footnote 4 According to the dynamical theory, two bodies can have the exact same size and shape (i.e. have identical extensive magnitude) and yet still differ in their density, and hence contain different quantities of matter. If Kant's argument for the PIM is successful, then this aspect of Kant's physical theory would have a transcendental basis in the doctrine of the Critique.Footnote 5 This fact alone makes the task of interpreting Kant's argument in the Anticipations an important one.
Yet it cannot be denied that the argument for the PIM is somewhat peculiar. Its central premise is a psychological claim about sensations: sensations are intensive magnitudes. From this premise, Kant infers that the reality in the objects of experience must also be intensive magnitudes. This conclusion is the PIM itself, which is a metaphysical thesis about objects. In short, from a psychological premise about sensations, Kant infers a metaphysical thesis about objects.
Perhaps unsurprisingly, this argument has met with a great deal of scepticism in the literature. Most commentators pass it over in silence, and the few who do say anything typically dismiss it as unsalvageably flawed and they conclude that the PIM is not a legitimate part of the transcendental system. For instance, Guyer concludes that, ‘the principle of intensive magnitudes seems to lack any a priori basis, let alone a clear place in Kant's theory of time-determination or even in the official schematism of the categories’ (Guyer Reference Guyer1987: 204). Warren suggests that, ‘it seems very possible that, at the time of the writing of the Critique, Kant had not fully worked out his views about how [the claims of] the Anticipations are possible as a priori knowledge, i.e., about what he would call its “transcendental” ground’ (Warren Reference Warren2001: 16). Wolff (Reference Wolff1973: 238) and Bennett (Reference Bennett1966: §§42–3) make similarly pessimistic appraisals.
The purpose of this article is to show that these pessimistic appraisals of the argument are unwarranted. I will attempt to show what would be necessary to read the argument for the PIM as sound within Kant's system, and thereby show how the PIM can be rehabilitated back into the transcendental theory of experience. What most stands in need of clarification is Kant's inference from the intensive magnitudes of sensations to the intensive magnitudes of objects. While most commentators have interpreted Kant to mean that the intensive magnitudes of sensations causally depend on, and hence are evidence for, intensive magnitudes in objects, I will argue that Kant sees things the other way around: realities in objects have intensive magnitudes because sensations do, and it is this dependency relation that grounds Kant's inference. That is, Kant is arguing that certain of the basic metaphysical determinations that we must represent in empirical objects (namely, their intensive magnitudes) depend on basic psychological facts about the sensory data out of which the representations of these objects are constructed (namely, their intensive magnitudes). Interpreting the Anticipations along the lines I propose provides a way of situating that chapter within Kant's broader transcendental project, and it fills in an important part of the story regarding what the sensory matter of our representations contributes to the cognition of physical objects.
I will proceed as follows. In section 2 I explain how Kant understands the concept of reality and give a rough taxonomy of the kinds of things we can judge as realities. This will give a clearer picture of what Kant takes himself to be proving in the Anticipations. In section 3 I lay out Kant's argument for the PIM as articulated in the B-edition of the Critique, showing where interpretative work needs to be done if sense is to be made of the argument. In section 4 I offer a defence of Kant's premise that sensations have intensive magnitudes. This will put us in a position to analyse the relationship between sensation and the real in appearance that corresponds to it. In section 5 I reject an interpretation of the argument according to which the argument is based on an inference about the cause of sensation. I will show that this interpretation lacks an adequate textual basis and imputes an obviously bad argument to Kant. In section 6 I present my preferred interpretation, according to which Kant is arguing that all objects of experience must be represented as intensive magnitudes because the sensory matter out of which their representations are constituted are intensive magnitudes. Unlike the causal interpretation, this interpretation of the argument takes into account the full range of Kant's remarks about the relation between sensation and the real in appearance, and each of its premises can be defended with resources from Kant's broader transcendental theory. In section 7, I respond to objections and draw out several important consequences of the interpretation.
2. The Category of Reality
The concept of reality (Realität) is the first category under the heading of quality (A80/B106) and it corresponds to the affirmative form of judgement (A70/B95). The closestFootnote 6 we get to a definition of reality comes in the Schematism chapter, where Kant says that ‘Reality is in the pure concept of the understanding that to which a sensation in general corresponds, that, therefore, the concept of which in itself indicates a being (in time)’ (A143/B182, cf. A175/B217). The correspondence between reality and sensation will be addressed at length later. Regarding the category's representation of a ‘being’, Kant means simply that any particular concept will fall under the category of reality if it is a representation of a positive determination of the existence of an object, as opposed to a representation of what is absent or lacking in the object (e.g. weight or redness, as opposed to weightlessness or colourlessness, which would fall under the category of negation).Footnote 7 Just as a judgement is affirmative when it makes a positive predication (or ‘affirmation’) of a subject concept (see Vienna Logic, 24: 929 and Jäsche Logic, 9: 103), a conceptualization represents an object's reality when it represents a positive determination of the object.Footnote 8 In general, we can say that a concept expresses a kind of reality when it explains how an object has being, or that in virtue of which it is.Footnote 9
Kant insists that concepts of reality are not all or nothing affairs. A full characterization of the reality of an object will not simply involve specifying whether a given reality is instantiated by the object, but also to what extent. As Kant attempts to demonstrate in the Anticipations, the quantification of reality is given in terms of ‘intensive magnitude’ or ‘degree’. Intensive magnitudes are capable of continuous variation, such that between any two intensive magnitudes, there will be a third. Extensive magnitudes (distances and durations) are specified in terms of the successive addition of homogeneous units (cf. A161/B202ff.), and thus ‘the representation of the parts makes possible the representation of the whole (and therefore precedes the latter)’ (A162/B203). Intensive magnitudes, by contrast, are those ‘which can only be apprehended as a unity, and in which multiplicity can only be represented through approximation to negation = 0’ (A168/B210). Because they can only be grasped ‘as a unity’, they are grasped as wholes first, and any multiplicity or ‘parts’ within these magnitudes can be thought only abstractly through the imagined possibility of a continuous change from one degree of intensity to another. This epistemological point about the priority of the apprehension of the whole is meant to indicate something about realities themselves, namely that (unlike extensive magnitudes) they are entirely and wholly present at a point. Hence the intensity of a reality cannot be made smaller or greater through division or composition, but only through continuous diminution or increase.
Thus far we have seen that the concept of reality describes an object insofar as it (a) possesses a positive determination and (b) to a certain (intensive, continuous) degree. Given this general characterization, what sort of ‘positive determinations’ does Kant typically have in mind when he refers to realities in objects? The examples he gives are few but varied, and their range is instructive. First, sensations (Empfindungen) are said to possess reality. Kant refers to the ‘real of sensation’ (B207), arguing that ‘every sensation has a degree or magnitude, through which it can more or less fill the same time’ (A143/B182). The ‘real’ of sensation that possesses intensive magnitude is simply the quality displayed by the sensation, i.e. its sensory ‘feel’ (whether chromatic, haptic, gustatory, etc.).
Kant also lists the sensible qualities of objects as examples of realities: ‘Every color, e.g., red, has a degree, which, however small it may be, is never the smallest, and it is the same with warmth, with the moment of gravity, etc.’ (A169/B211). These basic perceptible features of objects mark positive determinations of the objects, which can be instantiated across a continuum of possible degrees.
In addition to sensations and the sensible properties of bodies, Kant also indicates that the very material of physical bodies is a kind of reality and hence possesses an intensive magnitude.Footnote 10 This is implicit in his treating of ‘the matter of appearance’ and ‘the real of appearance’ as synonymous: both are said to ‘correspond to sensation’ (see A20/B34, A165, B207, A175/B217, A581/B609, A723/B751) and both are said to be that in virtue of which an object fills space (see B18, A174/B216, A413/B440, MFNS 4: 496).
As indicated in section 1, this claim about physical matter marks a sharp break with most of Kant's predecessors. According to the Cartesian mechanists, matter is to be identified with extension, and consequently the quantity of matter in an object will be a direct function of its extensive magnitude only. As Descartes put it: ‘The nature of body consists not in weight, hardness, color, or the like, but simply in extension’ (Descartes Reference Descartes1985: §4). The atomists (e.g. Gassendi and Boyle), by contrast, rejected the identification of matter and extension, insisting instead on an atomism that reduced all bodies to absolutely solid atoms interspersed with empty void. What both of these schools shared was the claim that density, strictly speaking, is an absolute feature of matter and not something that could come in degrees. The appearance of differences in density between two bodies (rarefaction) was explained by appeal to the porosity of the bodies in question.
Against these theories, Kant argues that the mechanists falsely ‘assume that the real in appearance is always equal in degree and differs only in aggregation and its extensive magnitude’ (A173/B215). He thinks they are especially wrong if they pretend to assume this ‘on the basis of a principle of understanding a priori’ (A175/B216). Kant elaborates his own physical theory in MFNS, tying it to the categories of quality discussed in the Anticipations:
First the real in space (otherwise called the solid), is the filling of space through repulsive force; second, that which, in relation to the first … is negative, namely, attractive force … ; third, the limitation of the first force by the second, and the determination of the degree of filling of a space that rests on this. (MFNS 4: 523)
Elsewhere, Kant argues that these forces are intensive magnitudes that can come in continuum-many degrees (MFNS 4: 499, 525). According to Kant's ‘dynamical’ theory of matter, solid bodies result from the interaction of these two forces, and physical density is subsequently determined by the interaction of attractive and repulsive forces. Since the degrees of the two forces can vary continuously, the density of matter can also vary continuously.
Or so at least Kant would have us believe. That the reality in the objects of experience (whether their sensible qualities or the matter itself) can be known a priori to possess intensive as well as extensive magnitude is the conclusion of the argument for the PIM. In order to see why Kant thinks this metaphysical theory about objects has a basis in transcendental philosophy, we will need to give a careful reconstruction of the argument of the Anticipations.
3. The Argument
In this section I will lay out the argument as Kant presents it in order clarify its basic structure and determine where interpretative work needs to be done if sense is to be made of the argument. I focus on the B-edition reformulation of the argument that Kant added to the beginning of the chapter because this is his clearest and most focused statement of the argument. I quote the argument in its entirety, and then explain how it should be carved up.
[1] Perception is empirical consciousness, i.e., one in which there is at the same time sensation. [2] Appearances, as objects of perception, are not pure (merely formal) intuitions, like space and time (for these cannot be perceived in themselves). [3] They therefore contain in addition to the intuition the materials for some object in general (through which something existing in space or time is represented), i.e., the real of the sensation, as merely subjective representation, by which one can only be conscious that the subject is affected, and which one relates to an object in general. [4] Now from the empirical consciousness to the pure consciousness a gradual alteration is possible, where the real in the former entirely disappears, and a merely formal (a priori) consciousness of the manifold in space and time remains; thus there is also possible a synthesis of the generation of the magnitude of a sensation from its beginning, the pure intuition = 0, to any arbitrary magnitude. [5.1] Now since sensation in itself is not an objective representation, and in it neither the intuition of space nor that of time is to be encountered, it has, to be sure, no extensive magnitude, but yet it still has a magnitude (and indeed through its apprehension, in which the empirical consciousness can grow in a certain time from nothing = 0 to its given measure), thus it has an intensive magnitude, [5.2] corresponding to which all objects of perception, insofar as they contain sensation, must be ascribed an intensive magnitude, i.e., a degree of influence on sense. (B207–208; numerical markers added)
Sentences 1–3 assert that perceptions, as well as the objects of these perceptions (appearances), possess a matter in addition to a form; the matter is associated with sensation and the form with space and time. Sentence 4 makes an observation about the possible continuous diminution and vanishing of any given sensation, and 5.1 asserts that sensations must therefore be intensive magnitudes. Lastly, 5.2 makes the inference from sensations having intensive magnitudes to the objects corresponding to them having intensive magnitudes.
We can simplify the argument as follows:
(A1) Sensation corresponds to the real (i.e. the matterFootnote 11) in appearance. [1–3]
(A2) Sensation has intensive magnitude. [4–5.1]
Therefore, (PIM) the real in appearance has intensive magnitude. [5.2]
This simplified version of the argument is plainly invalid. Its form is: A corresponds to B, A is F, therefore B is F. If any good sense is to be made of this argument we will need to determine what sort of correspondence Kant had in mind in A1 such that the inference to the PIM is licensed. In section 5, I will discuss one of the only interpretations of this correspondence in the literature; after rejecting it, I will be in a position to present a different, better interpretation (sections 6–7). However, before addressing the correspondence described in A1, a remark is in order about A2 and the claim that sensations are intensive magnitudes (since this premise is common to both of the interpretations to follow).
4. Sensations as Intensive Magnitudes
In the fourth sentence of the argument, Kant asserts that any sensation can diminish in a continuous decrease to nothing (or in a continuous increase from nothing to something). I will refer to this as the continuity thesis. From the continuity thesis, he concludes that sensations are intensive magnitudes (which claim I have labelled A2). The continuity thesis is an assertion of a psychological fact, and Kant does not give any indication that he took the claim to be controversial or open to debate. Likewise, he does not seem to think that the inference to A2 is controversial either. Not everyone has been willing to go along with him so easily though.
Jonathan Bennett disputes the apriority of the continuity thesis on the grounds that the claim does not express a necessary fact. He writes,
[the continuity thesis] merely says that our sensations are like that: it states an empirical fact, and has no place in Kant's apparatus of a priori principles. He provides no arguments for the impossibility of a world in which nothing is ever dim or in-between, in which there is only one level of pain, say, and only three degrees of saturation for each color. (Bennett Reference Bennett1966: 172)
If the continuity thesis is contingent, then A2 is also contingent, and Bennett takes this to undermine the transcendental necessity of the argument.
It is true that Kant provides no argument against the alternative scenario described by Bennett, but it is a mistake to think that he needs to. Although Kant claims that it is an a priori fact that sensations (for us) come in continuous degrees, he is not saying, nor does he need to say, that this is an absolutely necessary fact. Although the continuity of sensation is a priori, this fact may very well be contingent, and no argument can be given for it other than to point out that it is true (for us).
It may sound strange to assert of a fact that it is both contingent yet a priori, and in most cases Kant will treat the necessary and the a priori as coextensive. However, this would not be the only place in the Critique where such an assertion is made: that space and time are the forms of human intuition is both a priori yet contingent. Space and time happen to be the forms of human sensibility, but it did not have to be this way, and Kant acknowledges the possibility of other creatures with different forms of intuition.Footnote 12 If we are not bothered by the contingent status of this a priori fact about the (human) forms of intuition, then we need not be bothered when certain facts about the structure of sensation have the same status. Another way to put the point is that, although for us humans it is necessary that space and time be the forms of intuition and that sensations come in continuously variable degrees, this necessity does not hold for all possible cognizers.Footnote 13 Thus the appropriate question to ask about the continuity thesis is not whether the claim is absolutely necessary, but simply whether it is a priori true.
Daniel Warren worries about this latter question because he thinks Kant owes us a better argument (Warren Reference Warren2001: 15–16). He notes that the only support for A2 given in the Anticipations is the continuity thesis. But elsewhere Kant seems to argue in the opposite direction, i.e. from A2 to the continuity thesis.Footnote 14 Warren thus sees a circularity in the justifications for the continuity thesis and for A2 and he is not optimistic that a satisfactory (non-circular) justification for either claim can be found.
Fortunately, we do not need to follow Warren's pessimism. The conclusion we should reach instead is that the move from the continuity thesis to A2 should not be read as an inference at all. Rather these two claims should be understood as equivalent: A2 is not proved by the continuity thesis, but is rather a specification of what the continuity thesis means. To be continuously variable in intensity is to be an intensive magnitude, and to be an intensive magnitude is to be continuously variable in intensity. Further, neither claim stands in need of proof, because Kant thought their truth to be self-evident. In his introductory remarks to the System of Principles, Kant distinguishes the epistemic status of the ‘mathematical’ principles (the Axioms and the Anticipations) from that of the ‘dynamical’ principles (the Analogies and the Postulates). He argues that the first two ‘are capable of an intuitive certainty’ while the other two ‘are capable only of a discursive certainty’ (A162/B201). Unlike the dynamical principles, the mathematical principles rest on the self-evident structure of intuition (which includes the form of space and time as well as the ‘anticipated’ continuity of ‘sensation in general’: A167/B209), which is given immediately and a priori and which need not be inferred.
In short then, the continuity thesis and the claim that sensations are intensive magnitudes (A2) should be taken together as a single a priori fact about the structure of sensation: whatever specific empirical qualities sensations happen to instantiate, they are known a priori (‘anticipated’) to be capable of continuous variation in intensity, i.e. they possess intensive magnitude.
5. The Causal Interpretation
We are now in a position to address the most puzzling aspect of Kant's argument: the claim that sensations somehow correspond to the real in appearance, and that this correspondence justifies the inference to the PIM. According to one of the only worked out interpretations of the argument for the PIM in the literature, the argument turns on an inference regarding the cause of sensations. I will refer to this reading as the ‘causal interpretation’. This interpretation is inspired by Kant's repeated characterization of sensation as the effect of an object on the senses (e.g. A20/B34 and A50/B74). In the Anticipations itself, Kant seems to equate an object having an intensive magnitude with it being ‘ascribed … a degree of influence on sense’ (B208) and he says that, through sensation, ‘one can only be conscious that the subject is affected’ (B207). Given these remarks about realities as causes and sensations as effects, proponents of the causal interpretation take the relevant correspondence between sensation and the real in appearance to be a causal relation.
Guyer endorses a version of this interpretation when he claims that according to ‘the inference of the Critique … if a degree of intensity is assigned to a sensation, only a degree of efficacy can be assigned to the reality which produces it’ (Guyer Reference Guyer1987: 200). On this view, the inference from the continuity of sensation to the continuity in the matter of appearance is an evidential one (this is my term, not Guyer's). Similarly, Falkenstein argues that:
The real of appearance is a ‘consequence’ of the real of sensation in the sense that we ascribe a certain degree of reality (a certain attractive force or impenetrability) to the appearance corresponding to the degree of reality (the intensity of sensible quality) evidenced by the sensation. We make this ascription because we take the reality of the appearance to be the cause of the reality of the sensation, so that, in ascribing reality to the appearance as a consequence of the reality of sensation, we are reasoning back from effect to cause. (Falkenstein Reference Falkenstein1995: 117)
This suggestion that we ‘reason back from effect to cause’ is what is essential to the causal interpretation. This interpretation of the argument can be expressed as follows:
(C1) Sensation has intensive magnitude.
(C2) The intensive magnitudes of sensation could only be caused by other intensive magnitudes.
(C3) The real in appearance is the cause of sensation.
Therefore, (PIM) the real in appearance has intensive magnitude.
C1 is identical to A2 and was discussed in section 4. C3 asserts that the correspondence relation between sensation and the real in appearance (initially stated as A1 above) is to be understood as a causal relation. Later (section 7) I will give reason to think that C3 is, strictly speaking, false. For now, however, I will argue that problems with C2 are fatal for the causal interpretation of the argument, and that C3, whether true or not, does not seem to do any real work in the argument as Kant presents it.
Kant himself never asserts anything like C2, and there is good reason to think he would have rejected it. The problem with this premise (as Guyer himself notes, 1987: 199–200) is that intensive magnitudes in objects are not the only possible explanations of the intensive magnitudes in sensations. As Guyer points out, Kant will often explain the difference between the intensities of two sensations of the same type by appeal to facts about the extensive magnitudes of their causes.Footnote 15 For instance, it is possible that the continuous change in the intensity of my sensation of a light-source is due only to continuous change in the visible surface area of the light-source (a change merely in extensive magnitude). Or perhaps the intensity of my sensation of the light-source is a function only of my distance (an extensive magnitude) from the light-source (in accordance with the inverse-square law). In general, there are possible explanations of the continuity of sensation that are independent of any variation in the intensity of the reality causing the sensation, and thus C2 is false.Footnote 16
Another problem with this interpretation is that C3, whether true or not, does not seem to do any real work in the argument. Between the two editions of the Anticipations, there are only three references to sensation as effect or reality as cause. At A168/B210, Kant says the real in appearance can be ‘regarded’ (betrachtet) as the cause of sensation, but he immediately remarks that this issue is tangential to the task at hand – ‘I touch on this here only in passing’ (A169/B210) – because causality is not to be discussed until the Analogies chapter. In the B-edition argument, he remarks that sensations are ‘merely subjective representations, by which one can only be conscious that the subject is affected’ (B207, emphasis added). Sensations tell us that the subject is affected, but not by what, and hence Kant seems to be ruling out the suggestion that we could infer anything about the causes of sensations on the basis of the fact that something caused them (which is also further evidence against C2).Footnote 17 Lastly, when Kant remarks at the end of the B-edition argument that ‘all objects of perception … must be ascribed (beigelegt) an intensive magnitude, i.e., a degree of influence on sense’ (B208), he seems only to be specifying what it means to understand an object as having an intensive magnitude. Part of the content of my representation of an object's reality is that this reality exerted an influence on me. Or, to put it in other terms, if I represent a sensed object as an intensive magnitude, then I may represent it as having a causal influence on sense. However, the fact that I may ‘ascribe’ causal efficacy to the real in appearance does not seem to do any heavy lifting in the argument as Kant presents it.
So C2 is false and C3 does not seem to do any work in Kant's argument. A final problem with the causal interpretation is that it would entail that the PIM rests on an empirical premise, and hence could not have a proper place in Kant's transcendental theory. For if the PIM is proved on the basis of the empirical effects of objects on us, then we cannot have knowledge of the principle prior to our actually having sensations. The sense in which the argument is based on an a priori ‘anticipation’ would be lost. The PIM would thus be an empirical principle, not a transcendental one as Kant thinks it must be.
Thus the causal interpretation fails to make good sense of Kant's argument for the PIM. The basic assumption of this interpretation was that the correspondence between sensation and the real in appearance was to be understood in terms of a (causal) dependency of the intensive magnitude of sensation on the intensive magnitude of the real in appearance. In the next section, I will argue that, if we invert the dependency relation, we can understand why Kant took the inference to the PIM to be justified. I will argue, that is, that Kant thinks that the intensive magnitude of the real in appearance depends on the intensive magnitude of sensation (and not the other way around).
6. The Sensory Constitution Interpretation
In order to give a proper analysis of Kant's argument for the PIM, we are going to need a better understanding of the correspondence between sensation and the real in appearance, so let us look more closely at what Kant actually says about this correspondence in the Anticipations. In the formulation of the PIM itself, Kant states that, ‘the real’ in the appearance is ‘an object of sensation’ (B207).Footnote 18 And when establishing the correspondence between sensation and the real in appearance, he writes, ‘appearances, as objects of perception, … contain … the materials for some object in general (through which something existing in space or time is represented), i.e., the real of sensation’ (B207). So the relation between sensation and the real in appearance has to do with the real in appearances being the ‘objects’ of sensation and of perception, and with these objects somehow containing ‘the real of sensation’, which materially constitutes appearances.Footnote 19 On their own, the meaning of these claims is far from transparent. However, I propose that if we import what we know about Kant's theory of empirical intuition, we can make good sense of these remarks.Footnote 20
In the Transcendental Aesthetic, Kant claims that intuitions are ‘empirical’ when they refer to their objects ‘through sensation’; these objects are ‘undetermined’ and are identified with appearances (A20/B34). Further, ‘that in the appearance which corresponds to sensation [is] its matter’ (ibid.). Lastly, Kant indicates that intuitions are analysable into their form (space and time) and their matter, which is ‘everything that belongs to sensation’ (A22/B36).Footnote 21
So sensations constitute intuitions as their matter, they are necessary for an intuition's reference to appearance and they correspond to the matter of appearance. These claims about sensation, appearance and intuition in the Aesthetic directly parallel what Kant says about sensation, appearance and perception in the Anticipations. In both cases, sensations materially constitute the representation, they enable the representation's reference to the appearance, and the matter of the appearance is defined in terms of sensation. Thus I argue that, where Kant refers to ‘perception’ in the Anticipations, ‘empirical intuition’ can be read in its place.Footnote 22
Reading ‘empirical intuition’ in place of ‘perception’ allows us to import what we know about empirical intuitions and their representational content as we attempt to make sense of Kant's argument. In what follows, I will show that, on a proper understanding of Kant's theory of how sensations constitute empirical intuitions, the objects of empirical intuitions (‘undetermined’ appearances in space and time) are themselves constituted by the sensory qualities initially presented in sensation. This interpretation will allow us to make sense of the otherwise mysterious claim that appearances ‘contain sensation’ (B208). As the crucial elements of this interpretation depend on, first, the constitution of intuitions by sensations, and, second, the constitution of the objects of intuition by the qualities given in sensations, I will refer to this interpretation of the argument as the ‘sensory constitution interpretation’.
I will here present the argument as I understand it and then give a detailed discussion of each step.
(SC1) Sensations (specifically, the qualities thereof) have intensive magnitudes.
(SC2) The qualities of the sensations constituting an intuition are identical to the qualities represented by the intuition.
(SC3) The qualities represented by the intuition are identical to the real in the appearance.
Therefore, (PIM) the real of appearance has intensive magnitude.
The basic idea here is that, if the entities that come to be conceptualized as physical realities in space are identified with something which, prior to and independently of being conceptualized as such, are continuous intensive magnitudes, then when those objects are conceptualized in judgement, conceptual determinations of intensive magnitude can be made with objective validity. SC1 is effectively equivalent to A2 (discussed in sections 3–4); I add the remark that it is the qualities of sensations that display intensive magnitudes because this fact will be important for my reading of the argument, but this caveat was already implicit in the claim that sensations are intensive magnitudes.Footnote 23 SC2 and SC3 each require substantial elaboration.
SC2 asserts an identity between the qualities of the sensations constituting an intuition and the qualities represented by that intuition. I base this identification on Kant's account of the representational content of empirical intuitions. An empirical intuition is a representation that refers non-conceptuallyFootnote 24 to a manifold of sensible qualities arrayed in space (A20/B34). Kant elucidates the function of sensation in constituting the representational content of intuition when he remarks that sensations are ‘ordered and placed’ (A20/B34) within the a priori representation of space, and that they are thereby represented ‘outside and next to one another’ (A23/B38). In making these claims, Kant can't mean that sensations are literally in space: this would be absurd, for sensations are mental and mental entities cannot be in space. He also cannot mean that sensations are represented as sensations in space: representing something as both mental entity and in space is conceptually impossible.Footnote 25 Rather, Kant must mean that the qualities of sensations are projected into and thereby represented in the representation of space. In other words, in an empirical intuition, sensory matter is synthesized with the form of space to yield a representation of a manifold of sensory qualities in space.
We can express this model of empirical intuition more precisely. Say a given intuition is constituted by a manifold of sensations, s1,…,sn. Each of s1,…,sn will possess a sensory quality to some intensive degree, which can be described with the ordered pairs: <q1,i1>,…,<qn,in>. In the intuition, <q1,i1>,…,<qn,in> will be assigned or ‘mapped’ onto some volume (‘represented outside and next to one another’), which is a range of spatiotemporal coordinates l1,…,ln. The content of the intuition is exhausted by the representation of those qualities at these coordinates, for example, <q1,i1> at l1, <q2,i2> at l2, and so on.Footnote 26 Since the <q1,i1>,…,<qn,in> represented at l1,…,ln are the very same <q1,i1>,…,<qn,in> possessed by s1,…,sn, it follows that the qualities of the sensations constituting an intuition are identical to the qualities represented by the intuition, which is what SC2 asserts.
At this point, a brief disambiguation is in order.Footnote 27 For there are different ways one could understand the identification made in SC2 (namely, the identification of the <q1,i1>,…,<qn,in> possessed by s1,…,sn with the <q1,i1>,…,<qn,in> represented at l1,…,ln by the intuition), and although I wish to remain officially uncommitted to any particular interpretation of transcendental idealism in my presentation of the sensory constitution interpretation, how one understands transcendental idealism will determine how one understands this identification. Specifically, one could take the identification as a token identity or a type identity. If the identification is taken as a token identity, then the very same (i.e. numerically identical) qualitative sensory states constituting the intuition also constitute the object intuited. This reading of SC2 would take very literally Kant's claims that ‘the objects of perception … contain sensation’ (B208) and that ‘every outer perception … is itself the real [in space]’ (A375). Such a reading would fit best with a phenomenalist interpretation of transcendental idealism according to which Kant would share with Berkeley the thesis that the objects of experience are constructions of sensory states.Footnote 28 If, on the other hand, one were uncomfortable with phenomenalist readings of transcendental idealism, one could take the identification in SC2 as a type identity. On such a reading, the qualities constituting the intuition would be qualitatively but not numerically identical to the matter of the object intuited. Nevertheless, the qualities of the matter of the intuited object would still depend on the qualities of the sensations constituting the intuition. In this case, the sensations would ‘inform’ (as it were) the intuition, determining its representational content: the reason the intuition represents this specific object (and not another) is because the intuition is composed of these specific sensations (and not others). I suspect that most of Kant's readers would be inclined to read the identification in SC2 in terms of type identity, but, again, I take no stand on this question here.Footnote 29
SC3 says that the sensible qualities represented in empirical intuitions are identical to the real in appearance. In a certain respect, this claim was already implicit in the account I gave of SC2. For the appearance, considered just as object of intuition, is nothing more than a manifold of sensible qualities represented in a volume. Thus, combined with SC1, we could say already that the matter of the intuited appearance has intensive magnitude. However, this is not sufficient to establish the PIM as Kant intends it. For the PIM, as a pure principle of understanding, is a thesis about the conceptual representations through which we judge objects, not simply a thesis about the intuitions through which we sense them. The PIM will only be established once it is shown that the objects of experience are necessarily conceptualized as intensive magnitudes, and so ‘the real of appearance’ described in SC3 must be understood in terms of the appearance's conceptual determination in judgement. Fortunately, given the setup thus far, this will not be difficult to establish. For the object (or ‘target’, if you will) of a judgement about an object's reality is just the matter of the appearance presented in intuition, which is what SC3 asserts. Although intuitions and judgements of reality represent their objects through radically different contents, their objects are the same: they both represent, in their own ways, the <q1,i1>,…,<qn,in> ‘ordered and placed’ in l1,…,ln. Where the intuition presents these qualities immediately and indeterminately to consciousness, the understanding specifies in judgement how these qualities should be understood as determinate realities in the object.Footnote 30
Once the identifications in SC2 and SC3Footnote 31 are established, the final inference to the PIM comes easily. Since it has already been established (by SC2 with SC1) that the matter of appearance in fact possesses intensive magnitude (irrespective of it being represented as such), it follows that the understanding must apply determinations of intensive magnitudes to the matter of appearance if it is to conceptualize it with objective validity.
The sensory constitution interpretation is valid (its form is: a = b, b = c, a is F, therefore c is F), and I have shown how each of its premises is grounded in Kant's broader theory of experience. I thus claim that this reading of the argument is the best way to make sense of everything Kant says about the justification of the PIM. Before concluding I will consider three objections that might be raised against this interpretation. Addressing these objections will provide an opportunity to flesh out in greater detail the relation between sensations and the realities we judge to be in objects. It will also instruct us on how we should understand the consequences of the PIM for Kant's physical theory.
7. Objections and Clarifications
The cause of sensation
It might be argued that the model I have presented here cannot make sense of the causal relation between realities in objects and sensations. If a perceived object's realities depend on the qualities of the sensations constituting the intuition of the object, then it cannot also be the case that those realities caused the sensations. For this would imply that realities in the object depend on sensations while sensations simultaneously depend on realities in the object.Footnote 32 These two claims are incompatible, and it might be argued that, since Kant refers to a causal relation between reality and sensation in the Anticipations, the sensory constitution interpretation must be rejected.
In response, I claim that it must simply be denied that sensations are caused by realities in appearances. A careful look at what Kant says in the Anticipations reveals that he never explicitly states that realities in objects are the cause of sensations. Rather, he says that ‘all objects of perception, insofar as they contain sensation, must be ascribed (beigelegt) an intensive reality, i.e., a degree of influence on sense’ (B208, emphasis added). And later he says only that one can ‘regard’ (betrachtet) reality as a cause of sensation (A168/B210).Footnote 33 Kant is not claiming that realities in appearances cause sensations, but that these realities may (in some cases, perhaps, must) be represented as the causes of sensation. The represented causal relation between reality and sensation is a necessary feature of the content of our representations of objects insofar as we represent these objects in relation to our perceptions of them. It is perfectly consistent to claim both that (i) the real in appearance depends on sensation and hence cannot, strictly speaking, cause it, and that (ii) I nevertheless represent the real in appearance as though it exerts an influence on my senses.Footnote 34
Sensory determination of judgements of reality
Another objection to the sensory constitution interpretation could arise from a misunderstanding of my characterization of the correspondence between sensation and the real in appearance. If, it might be argued, the sensible qualities of the sensations constituting an intuition are identical to the object judged in applications of concepts of realities, then the reality judged in an object will be determined by the qualities and intensities of the sensations constituting the intuition. For instance, if an intuition non-conceptually represents <q1,i1> at l1, <q2,i2> at l2, and so on, then the judgement of the reality of this object will apply conceptual articulations of these specific qualities (namely, by forming the concepts ‘<q1,i1>’, ‘l1’, ‘<q2,i2>’, ‘l2’,Footnote 35 etc., into the judgements ‘<q1,i1> is at l1’ and so on). The claim that the contents of judgements of realities are determined directly by the qualities of sensations is, however, surely false. For instance, when I make a judgement about the colour of something, I take myself to be judging a relatively permanent feature of the object. If I see a blank sheet of paper in daylight I experience sensations very different from those I experience when seeing it under a dim lamp at night. In the one case I would have sensations of a very intense light grey, and in the other I would have sensations of a much less intense orange. Nevertheless, in both cases I apply the same concept – ‘white’ – to the object.
What this sort of example shows is that our conceptual representations of the realities in objects involve a great deal of interpretation of the sensory data, and that these judgements are not simple ‘readings off’ of the qualities displayed by the sensations. However, nothing in the interpretation I have given should preclude this distinction between the quality represented in intuition and the conceptualization made of it in judgement.
Part of the reason why this distinction is possible is the non-conceptuality of intuitions. Since an intuition represents its object indeterminately, there is nothing in the content of the intuition to constrain the judgement such that the only possible judgement is one that matches the reality of the sensation itself. The ‘spontaneous’ understanding still has room to do work as a rational faculty aimed at conceptualizing the objective world of publically available objects. Such objective conceptualizations generally require treating objects as relatively stable in their properties. For example, the surfaces of objects generally remain physically stable through changes in illumination, and the understanding takes this sort of stability into account when ‘deciding’ (so to speak) how best to conceptualize the colour of the object. Such interpretations are typically unconscious and unnoticeably fast, but we can infer that they must take place because of a phenomenology that presents a relatively stable objective world that nevertheless appears to us through a wildly varying and variegated sensory stream. Generalizing, we can say that, if an intuition represents the qualities <q1,i1>,…,<qn,in> in some spatiotemporal array, the reality-concepts applied in judgement will be some ‘<q1*,i1*>’,…,‘<qn*,in*>’ which are more or less correlated with, but by no means necessarily identical to <q1,i1>,…,<qn,in> themselves.Footnote 36
Transcendental necessity undermined?
So judgements made in applications of reality-concepts to intuited objects are not fully constrained by the specific qualities and intensities presented in the intuition. The understanding has interpretative work to do in determining which reality-concept is the most appropriate and ‘objective’ in any given case, and so the quality and intensity specified in the concept need not match exactly the quality and intensity presented in intuition. This might seem to open the door to a further objection. It might be argued that the ever-present difference between the quality in the intuited appearance and the conceptualization of it undermines the transcendental necessity of the PIM.
Here is how this problem might be thought to arise. If the continuous variability of the intensity of sensation does not necessitate conceptualizing the object's realities as continuous, it would seem always to be an open possibility that the most objective determination of these qualities will appeal only to discrete, non-continuous reality-values. Perhaps, as the Cartesians or atomists would have it, there is only one such value that the density of bodies instantiates. For they could grant that Kant's ‘real of sensation’ has continuous intensive magnitudes, but then deny that the understanding must interpret these intensities as corresponding to continuous intensities in objects. If this possibility remains open, then it would seem that the PIM loses its necessity.Footnote 37
Kant himself makes some remarks that might seem to indicate that he was willing to retreat somewhat on the necessity of the PIM. In the Anticipation's critique of atomism (A173/B215ff.), he does not attempt to show that the theory of absolute (i.e. non-continuous) density was impossible or even false, but simply that it is not necessary:
Against [the atomists’] presupposition [of absolute density], for which they can have no ground in experience and which is therefore merely metaphysical, I oppose a transcendental proof, which, to be sure, will not explain the variation in the filling of space, but which will entirely obviate the alleged necessity of the presupposition that the difference in question cannot be explained except by the assumption of empty spaces. (A174/B215)
This ‘metaphysical presupposition’ is unjustified because the perceived differences in density could equally well be explained by differences in the intensive magnitudes of matter filling space entirely (with no empty spaces). Kant seems to be suggesting that, considered a priori, the atomistic explanation and his own dynamic explanation are both metaphysically possible. He goes on to concede that,
My aim here is by no means to assert that this is how it really is concerning the specific gravity of the variety of matters, but only to establish, on the basis of a principle of pure understanding, that the nature of our perceptions makes an explanation of this sort possible. (A174–5/B216)
These passages might be taken as a concession that the PIM does not express a transcendental necessity but a mere transcendental possibility. But this is not how the passages ought to be taken. Although Kant is claiming here that his dynamic conception of matter is merely contingent (at least with the resources only of the Critique), he is not conceding that the PIM itself expresses a mere possibility. For one thing, such a retreat would contradict the rest of the claims of the Anticipations, which assert the principle as an a priori and necessary law of all objects generally (A165, B207, A170/B212). More to the point, if we pay attention to what exactly the PIM actually says, we see that it is consistent with both the empirical contingency of the dynamic theory of matter and the possibility that a form of atomism or Cartesian mechanism be true. The PIM states that every reality has a determinate intensive degree. This does not entail that every reality is physically capable of varying through a continuum of other such degrees. A reality with a given degree is an intensive magnitude even if this reality happens never to increase nor decrease in intensity for the entire duration of its existence. If every piece of matter in the universe turned out (because of some empirical physical law) to possess the exact same degree of density, then the world would effectively be as the atomists describe it, and differences in perceived density would only be explained by appeal to a body's porosity. But this would not change the fact that the uniform density possessed by all matter was still a determinate intensive magnitude.Footnote 38
The objection under consideration said, in effect, that,
(i) Even though the qualities of sensations have intensive magnitude, there is no guarantee that the most objective interpretation of the physical world will involve judgements of intensive magnitudes.
We see now that all the objector is really entitled to is
(ii) Even though the qualities of sensations vary continuously in intensity, there is no guarantee that the most objective interpretation of the physical world will involve judgements of magnitudes which vary continuously in intensity.
(i) is false; (ii) is innocuous. (i) is false because even if the only reality-concept that can be applied is not a magnitude which ever actually varies, there will still be a determinate value that can be applied to the density of the object; hence the object will have a determinate, continuous (albeit not continuously varying), intensive magnitude. (ii) is innocuous because it asserts only that Kant's dynamical theory of matter (as opposed to the transcendental theory of possible objects of experience) is not completely a priori. But Kant never claimed that this theory was entirely a priori, for it rests on the empirical concepts of matter and motion. The only entirely a priori theory is the general transcendental theory of experience, of which the PIM is a component.
8. Conclusion
The sensory constitution interpretation provides the best way to rehabilitate the argument for the PIM back into Kant's transcendental theory of experience. This interpretation describes a valid argument, and each of its premises are firmly grounded in central elements of the doctrine of the first Critique. Hence, we do not need to conclude (e.g. with Bennett, Wolff, Guyer or WarrenFootnote 39) that the Anticipations have no legitimate place within Kant's transcendental theory of experience.
The most important upshot of this interpretation is that it entails that the realities we judge in objects are metaphysically dependent on the sensations that correspond to them (rather than the other way around). Such a dependency relation would not be available to traditional ‘realist’ accounts of the relation between representations and objects. But Kant is of course no traditional realist, arguing instead for a transcendental idealism according to which the appearances we cognize as objects depend for their existence on being represented, and are nothing apart from this. Many different writers have understood Kant's transcendental idealism in many different senses, and I have intentionally avoided presupposing any one interpretation of transcendental idealism in my reconstruction of the argument for the PIM. But it is worth pointing out that one of the virtues of my reconstruction of the argument is that it shows how to situate this section of the Critique within Kant's transcendental project of reconceptualizing ‘being an object’ in terms of ‘being an object of representation’. Kant's claims about the intensive realities in objects is seen to be another instance of his more general thesis that basic metaphysical facts about the empirical objects we experience in the world depend on the cognitive structures and mechanisms by which we come to represent them.
