Intensive Magnitudes and the Normativity of Taste 
In Aesthetics and Cognition in Kant’s Critical Philosophy, ed. Rebecca Kukla (Cambridge: Cambridge Univrsity Press, 2006)

What is it that distinguishes a judgment of taste from a cognitive judgment?  According to Kant, both forms of judgment are normative and both rely upon the transcendental faculties of imagination and understanding for their normativity.  Yet one refers to a subjective feeling of pleasure while the other refers to an object.  In Kant's account, it is the role of the imagination that differs in aesthetic judgments and cognitive judgments.  In cognition, the imagination is subject to the rules of the understanding to which it has an "objective" relation (20: 223).  In a judgment of taste, the imagination's relation to the understanding is "subjective" (20: 223).  This is because it is not referred to a concept of the understanding, but to the subject and his or her feeling of pleasure or displeasure (5: 204).  Kant describes this as a relation of "free lawfulness" (5: 240).  
But what is the reason why the imagination is subject to the understanding in one instance and not in the other?  Many commentators have attempted to explain the freedom of the imagination from concepts in judgments of taste by finding places in Kant's theoretical philosophy that indicate that there could be a form of synthesis without a concept.  They point to Kant's discussion of the "threefold synthesis" in the first edition of the Critique of Pure Reason where it is only by the last of these syntheses, "the synthesis of recognition in the concept," that the manifold is unified by a concept.  This allows for the possibility that there can be a synthesis of the imagination prior to that which is achieved by concepts and that judgments of taste represent this arrested stage of a threefold process toward cognition.  Or commentators refer to the "judgments of perception" in the Prolegomena, which "require no pure concept of the understanding, but only the logical connection of perception in the thinking subject" (4: 298).  Still, merely to show that it is possible for there to be a form of synthesis that is not determined by concepts is not to give a reason for why such a synthesis occurs. Any account of Kant's argument for a principle of judgments of taste must be able to provide a reason for why, in these judgments, the imagination is not restricted by a concept.  Such an account will thus also be one that explains why aesthetic judgments are "merely reflecting" judgments rather than determining judgments (20:223), since these judgments do not involve concepts. 
In what follows, I argue that the reason why the imagination is not restricted to a particular rule of cognition in judgments of taste is because the form of intuition by which it apprehends the manifold is different.  In cognitive judgments, the determination of the manifold by a concept requires that this manifold be apprehended in an extensive form of intuition.  However, in judgments of taste, it is because the manifold is apprehended by the imagination in an intensive form that it cannot be subsumed under any determinate concept.  I will thus argue that the ontology of the Critique of the Aesthetic Power of Judgment is different from that of the Critique of Pure Reason in that what is judged in a judgment of taste is an intensive magnitude, whereas what is judged in a cognitive judgment is an extensive magnitude.  This is why it is possible for judgments of taste to attribute a value to an object, namely the value of beauty, whereas determinative, cognitive, judgments do not attribute a value to the object at all.
I will also argue that what gives us the norm for judgments of taste is the sensus communis, "a faculty for judging that in its reflection takes account (a priori) of everyone else's way of representing in thought" (5: 293).  On my view, the sensus communis is itself an a priori intensive form of sense that makes possible the sensing of an intensive magnitude.  Kant explains that the sensus communis is the sense of the feeling of pleasure that is the "effect of mere reflection on the mind" (5:295).  By understanding judgments of taste as involving what is apprehended in an intensive form of intuition, and by understanding the sensus communis as an a priori form of sensibility, it will be possible to account for three of the most important (and problematic) distinctive features of judgments of taste: (1) they are not determined by a concept, (2) they give rise to a feeling of pleasure and (3) they make a subjective claim to universal validity. 
In section 1, I review the distinction between intensive and extensive magnitudes in the first Critique.  Section 2 argues that, for Kant, concepts can only be applied to what is apprehended in an extensive form of time and thus that the determinative judgments that are the subject of Kant's first Critique require an extensive from of time.  Section 3 focuses on the Critique of the Power of Judgment and shows that there the imagination "in its freedom" is the imagination that apprehends the manifold in an intensive form and is thus "free" from determination by concepts. Section 4 argues that the sensus communis is the a priori form of intensive magnitudes and is therefore the basis for the subjective form of universal agreement that is distinctive of claims of taste.

1.	Intensive and Extensive Magnitudes
In this section, I will review Kant's distinction between intensive and extensive magnitudes.  My account will focus primarily on the Critique of Pure Reason, since my aim is ultimately to compare the presentation of intensive magnitudes in the first Critique with that in the third.  As we have seen, for Kant, an intensive magnitude is the measure of a quality. Quantitative distinctions among qualities that are the same, such as distinctions between different shades of the same color blue, are measured in terms of degrees of intensity.  This is in contrast to an extensive magnitude, which is measured in terms of the addition of homogeneous units.  Because intensive magnitudes are qualities, Kant refers to them primarily in his discussion of the categories of quality, their schematism, and the principle of the "Anticipations of Perception."  Although, as we have seen, Kant's discussion of intensive magnitudes in the Critique of Pure Reason seems to rely upon the presupposition that they have an a priori ground, he does not make this explicit.  This is because, in that work, Kant is primarily interested in the possibility of synthetic a priori judgments of objects that appear in the extensive forms of space and time.   It is my view that the loose strands of argument in the first Critique that have to do with intensive magnitudes ultimately come together in the third Critique where what is judged is what has an intensive magnitude rather than an extensive one.

1.1 Extensive Magnitudes
An extensive magnitude is one "in which the representation of the parts makes possible the representation of the whole (and therefore necessarily precedes the latter)" (A162).  In the "Transcendental Aesthetic" of the Critique of Pure Reason, Kant describes both space and time as extensive magnitudes and thus as having the essential characteristics of extensivity: homogeneity and additivity.  Homogeneity is the property of being of uniform quality throughout, and additivity is the property by which something can be measured in terms of the addition of units that are its parts.  The length of something, for example, is the sum of the length of its parts.  By contrast, an intensive magnitude such as density is not the sum of the densities of its parts.  
	Because Kant views space and time as extensive, he argues that the pure schema of magnitude, or quantity, is number.  The schema of magnitude is that by which the categories of quantity can be applied to the intuition of time, and hence to objects of experience. Since time and space are extensive, that is, homogeneous and additive, their quantity, and, indeed, the quantity of anything that is spatial or temporal, thus ends up being measured in terms of numerical units.  Kant writes, 
The pure image of all magnitudes (quantorum) for outer sense is space; for all the objects of the senses in general, it is time.  The pure schema of magnitude (quantitas), however, as a concept of the understanding, is number that is a representation that summarizes (zusammenfaßt) the successive addition of one (homogeneous) unit to another.  This number is nothing other than the unity of the synthesis of the manifold of a homogeneous intuition in general, because I generate time itself in the apprehension of the intuition. (A142-143/B182) 
Discursive or conceptual thought applied to the pure image of magnitude (time or space) thus yields a metric in which one unit thought after a preceding homogeneous unit will yield two units, etc.  As Charles Parsons points out, unlike other views of addition in which "we have a timeless relation, for example, that one set is the union of two others...and in reference to which any talk of successive addition is on the face of it entirely metaphorical," in Kant's view, addition has to be successive, because it is literally the placing of one unit after another in thought.   It is this succession that creates the order of units that is called number.  Consequently, number is the measure of extensive magnitudes.

1.2 Intensive Magnitudes
In contrast to extensive magnitudes, which are measured by homogeneous unitary parts that succeed one another, intensive magnitudes are measured by the degrees contained within them.  Kant writes of intensive magnitudes, "I call that magnitude (Größe) which can only be apprehended as a unity (Einheit), and in which amount (Vielheit) can only be represented through approximation to negation = o, intensive magnitude" (A168/B210).  Kant's description of intensive magnitudes as what can "only be apprehended as a unity" contrasts them to extensive magnitudes "in which the representation of the parts makes possible the representation of the whole (and therefore necessarily precedes the latter)" (A162).  The difference between intensive and extensive magnitudes thus involves how each of these forms of unity relates to their "quantity" (Vielheit), the multiplicity of which they are the unities.  Unities of extensive magnitude are the sums of their parts.  For example, one yard is made up of thirty-six inches. Intensive magnitudes, on the other hand, are measured as wholes from which "parts" (or degrees) can be derived, or which can gradually be diminished to zero. In the Metaphysik Vigilantus (1794-95), Kant thus describes an intensive magnitude as one 
whereby the parts are not cognized previously in order to determine the magnitude, rather (it) must be cognized as a unity, and the parts drawn from the unity.  Thus e.g., a line, which must be composed, differs from an extinguishing light: with the latter there is only a unity of sensation, but in each following state a different degree of this.  (29: 999)
Intensive magnitudes can thus be called the "ground" from which a range of values can be derived.  By contrast, an extensive magnitude is not the "ground" of the quantities it posits, but merely a collection of units.  Intensive magnitudes are thus those things whose standard of measurement pertains to them alone.  Extensive magnitudes on the other hand, such as "space (or) the size of an army" are all measured by the same system of counting. 
Kant calls the different forms of unity that result from the synthesis of extensive and intensive magnitudes aggregates and coalitions, respectively (B201n).  In the Anticipations of Perception, he uses the example of money to illustrate this difference between extensive and intensive magnitudes.  This example is noteworthy, since it makes explicit the fact that intensive magnitudes are the measure of worth.  Kant writes, 
If I call thirteen dollars a quantum of money, I do so correctly insofar as I mean an amount of a mark of fine silver, which is to be sure a continuous magnitude, in which no part is the smallest but each part could constitute a coin that would always contain material for smaller ones.  But if by the term "thirteen round dollars" I mean so many coins (whatever their amount of silver might be), then it would not be suitable to call this a quantum of dollars, but it must instead be called an aggregate, i.e. a number of coins. (A170/B212)

Here a continuous magnitude, which is the unity of a coalition, is the value of the silver.  No matter how many units thirteen dollars can be broken up into, it will still have the same value. Such a continuous magnitude cannot be measured additively, by the counting of its units.  When thirteen dollars is understood as "thirteen round dollars," Kant even seems to suggest that they have no value at all.  They are just so many physical objects, a number of coins; "so many coins (whatever their amount of silver might be)." A continuous magnitude is thus the measure of the value of an indivisible whole.  If there is no complete whole, then there is nothing to which an intensive measure can be attributed.  This is the meaning of Kant's statement that "if the synthesis of the manifold of appearance is interrupted, then it is the aggregate of many appearances (and not really appearance as quantum)" (A170/B212).  If a degree is without reference to an original unity, it loses its value.  For example, only once something, such a lump of silver, is designated as having a value of thirteen dollars, can the value of the parts into which it is divided be determined.  If the lump has no designated worth, then the worth of its parts, as parts, cannot be determined.  The quality, or value, of a thing is thus a measure that is made with regard to a standard of the completeness or fullness of the kind of value of the thing that is measured.
 Kant's description in the Anticipations of Perception of intensive magnitudes as "flowing" is also related to the fact that they are unities from which "parts (or values) are drawn."  He writes, 
between any reality and negation there is a continuous nexus of possible realities, and of possible smaller perceptions.  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. The property of magnitudes on account of which no part of them is the smallest (no part is simple) is called their continuity…magnitudes of this sort can be called flowing, since the synthesis (of the productive imagination) in their generation is a progress in time, the continuity of which is customarily designated by the expression "flowing"  ("elapsing") (fliesende)." (A169-170/B211-212) 
"Flowing magnitudes" are those that are generated by the motion of a point. Here Kant is most likely referring to Newton.  What Newton refers to as a flowing magnitude or a fluent is a quantity generated by a continual motion.  The reason why intensive magnitudes are discussed here with regard to flowing magnitudes is precisely because they are the quantities, or functions, from which continuous lines etc. are generated and are what determine the measure such a flowing magnitude will have.
	To summarize the discussion of intensive magnitudes so far, we can say that an intensive magnitude is a quality or value and that as a form of unity it determines the value of what "flows" or is "drawn" from it.  Yet, in the Critique of Pure Reason, it still remains unclear what exactly the basis of its "measure" is.  If Kant is to claim that intensive magnitudes can be known a priori, he must provide a transcendental condition for this knowledge.  Unlike Leibniz, he cannot just dogmatically claim that intensive magnitudes exist.
	In contrast to extensive magnitudes, whose standard of measurement is whole numbers that represent the succession of units in time, in the Critique of 
Pure Reason, Kant describes the standard of measurement for intensive magnitudes as that which represents the transition from the presence to the absence of a sensation in time.  Kant writes, 
[T]here is a relation and connection between, or rather a transition from reality to negation, that makes every reality representable as a quantum, and the schema of a reality as the quantity of something insofar as it fills time, is just this continuous and uniform generation of that quantity in time as one descends in time from the sensation that has a certain degree to its disappearance or gradually ascends from negation to its magnitude. (A143/B182-183)

A schema is the expression in time of one of the pure concepts of thought.  It is a determination of time. This passage should therefore not be read as saying that the schema of reality is the degree to which a sensation can fill time.  That would make the schema a determination of sensations and would make the application of the category of reality to time something based on a subjective feeling of our own sensations.  Instead, the schema of reality should be regarded as the determination of time itself as what can be filled in degrees by sensation, and thus as what makes possible the metric of intensive magnitudes.  In this way, the standard for measuring the degrees of intensity of a sensation is derived from a moment of time considered, not as a unit that can be followed by other moments, but as something that can be filled up to a greater or lesser degree.  Still, Kant's account leaves it unclear how we are to measure this "greater or lesser," this "quantity of something" with regard to how it fills up a moment of time.
Guyer's discussion of Kant's attempt in the Anticipations of Perception to assimilate "his theory of intensive magnitude into the theory of time determination" makes clear how problematic intensive magnitudes are for Kant.  In order for Kant to be able to say that the instant in which a sensation occurs can also be a measure of the increase or decrease in intensity of the sensation, individual sensations of a given quality need to be thought of as "members of a potential series of instances of the same kind of sensation, which are undergoing an increase or decrease of intensity over time."  But, Guyer contends, the premise of Kant's argument, which is that "apprehension, merely by means of sensation fills only an instant" (A167/B209), conflicts with the idea that sensations can come in a continuous variation of intensities.  This is because what is apprehended in an instant does not necessarily bring with it any indication of another temporal determination.  A shade of blue could indicate a stage in a series of degrees of blue or it could not.  And if it is a stage of a series of degrees, then it is being measured in an extensive form of time.  As Guyer points out, it is not inconceivable that any given sort of sensation can come in only one strength.  What Kant needs is some form of intuition that could make possible the representation of the degree of a sensation that is apprehended in an instant.  
One can picture this form of intuition as being a scale vertical to the horizontal time line, so that a sensation would have two temporal coordinates; one representing the extensive time in which the sensation occurs, the other representing the second order of time it would have taken the sensation to ascend from negation to its magnitude.  Such an order would represent the complete range of the (increase or decrease of) degrees of sensation "anticipated" as possible on the basis of the present sensation.  In fact, this would be very similar to the "intension" of a living force that Kant describes in Living Forces-- the internal power pent up in a body that could increase the rate of its motion.  However, since such a form of intuition that would make an evaluation of intensity possible is not argued for in the Critique of Pure Reason, Guyer is right that the Anticipations of Perception results in confusion.  Indeed, as I will argue in the next section, this is due to the fact that the categories, including that of "reality," are only meant to be applied to what is intuited in a complete instant of homogeneous time.  Consequently, a priori judgments of intensive magnitudes are impossible within the context of the Critique of Pure Reason.  However, it is precisely such a form in which intensity can be measured that is presented in the Critique of the Power of Judgment.

2.  Time, Concepts, and the Imagination in the First Critique
Before proceeding to my analysis of the Critique of the Power of Judgment, I will show that for Kant concepts can only be applied to representations that have been apprehended and reproduced in an extensive form of time.  In the next section, I will then show that what is apprehended in an intensive form--and what consequently cannot be thought by means of a concept--is what forms the basis of a judgment of taste.
According to Kant, the role of concepts in cognition is to produce a synthesis of a manifold of representations according to a rule.  Implicit in his discussion of the synthesis produced according to a concept is the idea that what is synthesized is discreet representations each contained in one moment of time.  In the Subjective Deduction of the first edition of the Critique of Pure Reason, Kant describes the "synthesis of recognition in the concept" as follows: 
If, in counting, I forget that the units that now hover before my senses were successively added together by me, then I would not cognize the generation of the multitude through this successive addition of one to the other, and consequently I would not cognize the number; for this concept consists solely in the consciousness of this unity of the synthesis.  The word "concept" itself could already lead us to this remark.  For it is this one consciousness that unifies the manifold that has been successively intuited, and then also reproduced, into one representation. (A103)	

The synthesis of recognition in the concept serves to unify a manifold in one consciousness according to a rule.  This act of synthesis orders our representations according to a concept that makes it possible for our cognition to be of an object and not be a mere subjective association of perceptions.  A concept is required for such a unified representation, since the manifold that is to be unified consists of past representations contained in the discrete moments of their successive apprehension.  These can be unified only on the condition that there is a transcendental form of apperception, a "numerical unity" of consciousness, which grounds the conscious activity (however weak) of unifying these representations according to a concept.  
Moreover, our representations can only be unified by a concept if they are in fact the distinct and absolute unities contained in their original moments of apprehension.  Kant writes, "Every intuition contains a manifold in itself, which, however, would not be represented as such if the mind did not distinguish the time in the succession of impressions on one another: for as contained in one moment no representation can ever be anything other than absolute unity" (A99).  Recognition is only possible if what is recognized is the same as it once was.  If, in counting, the units that now hover before my senses were to merge or be reproduced as overlapping one another, then they would no longer be recognizable as the original representations they were.  The unity of the synthesis would not be a sum and thus the concept which is of the sum of these units could not be applied.
Of course, by calling a concept "something that serves as a rule" for the unification of appearances, Kant is not referring just to the rule of addition.  He is referring to the fact that all concepts are normative and organize the manifold according to an ordered procedure.  According to Kant, there are twelve fundamental rules of this sort, each of which is followed when an object is thought by means of them.  But no matter what category is used for the synthesis of the manifold, one particular form of time is required in order for it to be possible to recognize what is reproduced by the imagination.  This is time considered extensively as the basis of a series of homogeneous distinct successive moments.  And when these moments are connected, they are in fact "added" to one another.  Kant writes in the Second Edition Deduction, "the empirical consciousness that accompanies different representations is by itself dispersed and without relation to the identity of the subject.  The latter relation (that to the identity of the subject) does not come about by my accompanying each representation with consciousness, but rather by adding (hinzusetzen) one representation to the other and being conscious of their synthesis" (B133).  
But what if representations were not unitary or apprehended successively?  Would it be possible for them to be unified by a concept?  In this case, I believe, it would be difficult to find the concept that could serve as the rule for these representations.  Indeed, Kant writes, "if representations reproduced one another without distinction, just as they fell together, there would in turn be no determinate connection between unruly heaps (regelose Haufen) of them, and no cognition at all would arise" (A121). What happens in a situation where the imagination reproduces a previously apprehended representation "without distinction," so that it "falls together," overlaps, or merges with another representation?  These, I believe, can be instances in which the imagination is working with an intensive form of time that makes it possible for different representations to be compared, not with regard to their temporal order, but with regard to how long they endure with respect to each other, or the rate of speed at which a sequence of moments takes place, or how the moments overlap or merge.  Here, the image of time is not that of a one-dimensional line, but of a two dimensional plane that can contain many lines, and be “shaded in” to various degrees.
This view of time can be explained with reference to Kant's First Analogy of experience. He writes,
Our apprehension of the manifold of appearance is always successive, and is therefore always changing.  We can therefore never determine from this alone whether this manifold, as object of experience, is simultaneous or successive, if something does not ground it which always exists, i.e. something lasting and persisting, of which all change and simultaneity are nothing but so many ways (modi of time) in which that which persists exists…If one were to ascribe such a succession to time itself, one would have to think yet another time in which this succession would be possible. Only through that which persists does existence in different parts of the temporal series acquire a magnitude, which one calls duration. (A182-183/B226).  

Kant's point in the First Analogy is that the concept of substance must have objective validity if we are to be able to say that objects change.  If we were not able to determine something as persisting in time through the category of substance, we would not be able to say that anything about this substance has changed.  For all we know, it could just have become a completely different substance. Similarly, without something persisting, the measurement of the duration of time would be impossible.  
My point, however, is that in order to apprehend, not the succession or simultaneity of objects of experience, but their rate of speed, or acceleration, for example, we must indeed think "another time" in which the degree of change in speed can be measured.  Just as one clock measures the succeeding moments of time and quantifies them, another clock is needed to measure whether or not those moments on the first clock themselves are accelerating.  This "other time," which can be said to be what is used to reflect upon the first measure of time, is what I am calling an intensive form of time, since, by means of it, one can measure the degree to which what is apprehended in extensive time takes up time.  It is with regard to this form of time, for example, that we could compare the movement of the second hand on two different clocks to see whether it takes each of them the same time to hit the one-second mark.  It is this second order, or, reflective form of time that attributes a value to the first measures of time.  I believe that it is this form of time that the imagination uses in a judgment of taste, where what matters is "what I make of this representation in myself, not how I depend on the existence of the object" (5: 205).  Such a form of time makes it possible for the mind to “linger” over representations as they are apprehended.

3. Intensive Magnitudes in the Critique of the Aesthetic Power of Judgment
	According to Kant, in a judgment of taste, the faculties of imagination and understanding must be in a harmony that makes it possible for what the imagination freely presents to be in accord with the lawfulness of the understanding, although no concept of the understanding can be applied to this presentation.  This particular "harmony," or "free play," of the faculties is the mental state whose universal communicability is the ground for judgments of taste as well as the pleasure we take in an object judged to be beautiful (5: 217).  In order to understand what Kant means by the "harmony of the faculties," it is helpful to take literally Kant's term "harmony" and to understand the understanding and the imagination as if they were two strings on an instrument.  If they are stroked together in one stroke, their harmony will be rather simple.  But if one is made to vibrate at a different rate than the other, the chord will be more complex and interesting.  When the imagination does not work with the extensive form of time, which is what is required in order for what it apprehends to be subsumed under the understanding, but rather apprehends a different, intensive, form of time, the reflection of the faculty of judgment on this more complicated form of harmony can result in a feeling of pleasure. Kant writes, "all stiff regularity (whatever approaches mathematical regularity) is of itself contrary to taste: the consideration of it affords no lasting entertainment, but rather…it induces boredom" (5: 242).
Since it is the free play of the imagination that is distinctive of judgments of taste, my task here is to show that this play is due to the freedom of the imagination from the extensive form of intuition presented in the first Critique, and that this is why, in judgments of taste "it is not a matter of a determinate concept" (20: 220).  However, my argument that judgments of taste require an intensive form of intuition might seem to be weakened by the fact that Kant does not explicitly discuss intensive magnitudes with regard to judgments of taste, whereas he does discuss them in the Critique of Pure Reason with regard to judgments of cognition.  Still, it is noteworthy that, in the third Critique, when discussing the apprehension of the form of an object of intuition that is not related to the object, but to the subject, Kant refers to the imagination as itself a faculty of intuition; he calls it “the faculty of a priori intuitions” (5:190).  This seems to imply that Kant has in mind a form of intuition in the third Critique that is different from space and time in the first.  
If my view is right, why, then, does Kant not make it explicit in the third Critique that judgments of taste involve an intensive form?  I think that the answer to this question is that, since Kant’s aim in the Critique of Aesthetic Judgment is to provide a justification for judgments of taste rather than to argue for a distinctive ontology, the fact that intensive forms play a role at many levels of Kant’s argument remains implicit to his discussion.  It is in fact the same with the role of extensive forms in the Critique of Pure Reason.  Although Kant argues there that synthetic a priori judgments are limited to what can appear in the a priori forms of intuition, space and time, he never makes explicit the implication of this—that the ontology of the first Critique is of extensive magnitudes rather than intensive magnitudes (perhaps if he had done so, he would also have become more aware of the difficulties in his discussion of the categories of quality).  My argument here can thus be understood to be making explicit that the ontology that corresponds to judgments of reflection in the third Critique is intensive, and moreover that it is therefore different from the ontology of the first Critique.  It is by highlighting this distinction between the two Critiques that I hope to show that the “world” to which judgments of taste pertain is quite different from that to which cognitive judgments pertain (as well as moral judgments, for that matter).
Still, one might ask what is the relationship between the intensive magnitudes that Kant does refer to in the first Critique and those I am arguing are fundamental in the third? I believe that judgments of taste have an intensive form in common with the mere sensations that Kant refers to in the first Critique. However, this does not prevent judgments of taste from being distinctive. The subjective element of an aesthetic judgment differs from mere sensations in that only aesthetic judgments involve a feeling of pleasure or displeasure.  This is because, in the case of aesthetic judgments, what is apprehended by the imagination is referred solely to the subject and not to any concept so as to give rise to determinate cognition (5: 189).  In contrast to the intensive magnitude of a sensation which, as Kant explains in the Anticipations of Perception, is a measure of the sensation of the subject with regard to an external object of the senses, the intensive magnitude in an aesthetic judgment is the measure of the subject's feeling of her own mental state.  And, according to Kant, the way that the subject feels his or her own state is by means of a feeling of pleasure or displeasure.  
We can therefore categorize different kinds of intensive forms.  The feeling of pleasure or displeasure in a judgment of taste can be said to be a pure intensive intuition, and that of mere sense, an empirical intensive intuition. The pure form of intensive intuition makes possible the feeling of pleasure in the subject's own mental state. When applied to empirical sensibility, as in the Anticipations of Perception, an intensive form is supposed to ground objective empirical judgments of the intensity of the real object of sensation.  The difference between the intensive magnitudes in the Anticipations of Perception in the first Critique and the intensive magnitudes in the third Critique is thus based on the fact that the third Critique concerns the a priori form of such magnitudes, whereas the first Critique concerns the possibility of empirical judgments of intensive magnitudes. Thus the "confusion" that, according to Guyer, arises in the first Critique with regard to how to assimilate Kant's theory of intensive magnitudes into his theory of time determination can be resolved, once we see Kant's discussion of the Anticipations of Perception in the light of the third Critique, where the principle of reflective judgment makes possible judgments of intensive magnitudes.
If I am right that judgments of taste involve an intensive form created by the imagination, what would such a form be like? Kant's discussion of the aesthetic normal idea (Normalidee) of beauty provides an example of the imagination at work in presenting an idea free from the laws of understanding.  The form the imagination produces here is one that can have a harmonious relation to the understanding, but still not be determined by the understanding.  Kant writes,
It should be noted that the imagination does not only know how to recall for us occasionally signs of concepts, even after a long time, in a way that is entirely incomprehensible to us; it also knows how to reproduce the image and shape of an object out of an immense number of objects of different kinds, or even of one and the same kind; indeed, when the mind is set on making comparisons, it even knows how, by all accounts actually if not consciously, as it were to superimpose one image on another and by means of the congruence of several of the same kind to arrive at a mean that can serve them all as a common measure.  Someone has seen a thousand grown men.  Now if he would judge what should be estimated as their comparatively normal size, then, (in my opinion) the imagination allows a great number of images (perhaps all thousand) to be superimposed on one another, and, if I may here apply the analogy of optical presentation, in the space where the greatest number of them coincide and within the outline of the place that is illuminated by the most concentrated colors, there the average size becomes recognizable, which is in both height and breadth equidistant from the most extreme boundaries of the largest and smallest statures; and this is the stature for a beautiful man.  (One could get the same result mechanically if one measured all thousand men, added up their heights, widths (and girths) and then divided the sum by a thousand.  But the imagination does this just by means of a dynamic effect, which arises from the repeated apprehension of such figures on the organ of inner sense). (5: 233-234) 

In this passage, the work of the imagination is contrasted with the mechanical process of additive measurement.  Here, what could be obtained mechanically is obtained otherwise by means of a "dynamic effect, which arises from the repeated apprehension of such figures on the organ of inner sense."  In this case, the apprehension of the imagination is multiple, and, as the illustration from optics shows, it is not a succession, but an overlapping of representations.  Here, indeed, the imagination is apprehending representations according to an intensive form and creating a unity that can serve as the ground of the measures that can follow from it.  The normal idea of beauty is thus analogous to the point of highest intensity.  Moreover, the act of comparison described here is not that of finding what makes each of these representations the same, but of finding the average between them and what they should have in common.  For example, if, after overlapping all of these men, as in Kant's example, we found that the average was six feet tall, it is still possible that none of the men is exactly six feet tall.  In this case, the "concept that this comparison makes possible" would not be of any particular object that could fall under it. Nor would it be the same as a concept of what each of these men have in common, for example, that they are men, have two legs etc. 
Although Kant's example here is meant to explain what an archetype or ideal of the beautiful might be and not free beauty which is the object of a pure judgment of taste, the activity of the imagination that he describes in this passage is still common to both pure judgments of taste and the ideal of beauty.  The reason why an ideal of beauty does not belong to the object of an entirely pure judgment of taste is that an ideal is the representation of an individual thing that is an instance of a concept of reason.  As such, the ideal of beauty is determined by a concept and therefore cannot be the object of a pure judgment of taste.  In his discussion of the ideal of beauty, however, Kant makes the distinction between two elements that are involved in this ideal.  The first is the aesthetic normal idea, the second is the idea of reason (5: 233).  The aesthetic normal idea is a mere image, an intuition of the imagination.  The idea of reason, on the other hand, is that principle by which the ends of humanity are judged to be presented in the figure of the human being. The aesthetic normal idea itself, which I have argued is produced by the imagination when it works independently of the understanding, is not a beauty fixed by a concept of objective purposiveness, but is what is still free from this concept and hence a vague beauty.  This intuition of the imagination, as the passage quoted above explains, is not a recollected image produced by a concept, but is an intense image that is the work of the imagination alone which creates an "unruly heap" by means of superimposition from which some common measure can possibly be found.
Kant explains that the normal idea is 
not derived from the proportions taken from experience, as determinate rules; rather it is in accordance with it that rules for judging first become possible.  It is the image for the whole species, hovering among all the particular and variously diverging intuitions of individuals, which nature used as the archetype underlying her productions in the same species, but does not seem to have fully achieved in any individual.  It is by no means the entire archetype of beauty in this species, but only the form that constitutes the indispensable condition of all beauty, and so merely the correctness in the presentation of the species. (5: 235)
The aesthetic normal idea (which is an individual intuition of the imagination) constitutes the indispensable condition of all beauty since it is the image produced by the imagination at play in making comparisons between objects of many different kinds.  It is an image, or form, that hovers among various individuals.  This form is not produced under the guidance of a concept that would direct the imagination to recall a representation previously apprehended in an extensive form of time, but is the result of the play of the imagination in superimposing many images into one that can be apprehended in one moment in time.  When the imagination apprehends in this way and the understanding tries to subsume this image under its laws, the subsequent relationship between the two faculties is the basis for a judgment of taste. 
This relationship between the imagination and the understanding is the harmony that is created when the two mental powers, working in different "meters," entertain each other with the indeterminate purpose of making what the imagination apprehends subsumable under the laws of the understanding.  Kant writes of cognition that 
the regularity that leads to the concept of an object is of course the indispensable condition (conditio sine qua non) of grasping the object in a single representation and determining the manifold in its form.  This determination is an end with regard to cognition; and in relation to this it is also always connected with satisfaction (which accompanies the accomplishment of any aim, even a merely problematic one).  But then it is merely the approval of the solution, and not a free and indeterminately purposive entertainment of the mental powers with that which we call beautiful, where the understanding is in the service of the imagination and not vice versa. (5: 242)

In contrast to a cognitive judgment, a judgment of beauty is based on the activity that occurs when the imagination apprehends in an intensive form and the understanding tries to follow the activity of the imagination (is in its "service") and grasp the form the imagination creates with rules that can nevertheless only be used for what has been apprehended extensively. 
	According to Kant, the pleasure we take in a beautiful object is "the very consciousness of the merely formal purposiveness in the play of the cognitive powers of the subject in the case of a representation through which an object is given" (5: 222).  This play is precisely that between the multiple apprehension of a representation by the imagination to form an image of the highest intensity and the understanding seeking to make discursive and uniform this reinforcement of representations.  Kant writes, "we linger over the consideration of the beautiful, because this contemplation strengthens (stärkt) and reproduces itself" (5: 222).  This play promotes such a lingering contemplation, because it is none other than the reinforcing and reproducing activity of the imagination as it tries to create an intense image, and the understanding as it tries to think this as something that can be contained in one moment of time.  This activity is indeed distinctive of the mental state that is required for a judgment of beauty, since it is the state of freely coming up with a standard. In a judgment of taste, the activity of the imagination acts as an a priori intensive form that shapes the representations that are given to it in order to come up with a standard, which is the form with the highest intensity, by which representations of the same kind can be judged, and which they can meet to some degree.  A beautiful object, which is such an exemplary object (see 5:308), is thus one whose form makes us linger, not because it homogeneous, and requires extended contemplation of the same thing, but because it is intense, and therefore requires the consciousness of the accumulation of the variety of forms contained within it.  Descriptions of a beautiful object as having a richness or depth attest to the intuitive correctness of Kant's view that a beautiful object is one that enables the mind to find multiple forms condensed within one object, and thus that the form of a beautiful object is an intensive form.  These are the same properties in which we take pleasure in a judgment of taste. 

4. The Sensus Communis
 	So far I have argued that what distinguishes aesthetic judgments from cognitive judgments is the intensive form in which the imagination apprehends the manifold.  It is because of this difference in the form of intuition that aesthetic judgments are not based on concepts, since concepts can only recognize what has been apprehended in an extensive form of time.  I will now argue that the condition for the normativity of judgments of taste, what Kant calls "a common sense," or sensus communis, itself has the form of an intensive magnitude and makes possible both our consciousness (or “sensing”) of the intensive forms created by the imagination and their evaluation.  
The sensus communis is the condition of the possibility of sensing the intensive form presented by the imagination in judgments of beauty.  It is also the basis of the particular kind of universality claimed in a judgment of taste.  As is the case with all intensive forms, the sensus communis provides both the ground for the attribution of a value in general to a thing as well as the norm with respect to which the value of that thing can be evaluated.  Here, the sensus communis is the condition for the possibility that "the free play of our cognitive powers" that occurs in a judgment of taste have an effect on us that can be attributed with the value of being either pleasurable or displeasurable.  In other words, it is what makes possible the feeling of pleasure or displeasure in a judgment of taste.  The sensus communis is also what provides the norm by which this feeling (of pleasure or displeasure) can be judged to be universally valid.
For Kant, judgments of taste are normative because they are claims that the subjective feeling of pleasure or displeasure one takes in an object also be felt by everyone.  In other words, they are claims that my judgment is an example of the standard of judging that ought to be used by everyone in making judgments of taste.  They are thus claims that everyone ought to feel the same pleasure in a judgment of taste that I do.  The sensus communis is what makes it possible to claim that the feeling produced by the cognitive faculties when the imagination and the understanding are in a state of "free play" is a feeling that "ought" to be shared by everyone and is therefore normative.  On my view, we can understand how the sensus communis grounds the normativity of judgments of taste once we see that it an intensive form of sense.  What the sensus communis senses is precisely the particular relationship of the harmony of the imagination and the understanding that occurs in a judgment of taste.  By understanding the sensus communis in this way, it is possible to answer a question that is central to current discussions of Kant's third Critique, namely how the normativity of, and the pleasure taken in, judgments of taste are necessarily related; that is, why Kant thinks that the pleasure I take in a judgment of taste must be the same as the pleasure I take in the in the universal communicability of my judgment of taste.  My claim is that the ground for the distinctive pleasure taken in the harmony of the faculties is the same ground for the communicability of this pleasure.  This ground is the sensus communis, considered as an intensive form of sense.
Like space and time, the sensus communis is a form of sense. According to Kant, the sensus communis is the subjective "sense" possessed by each of us that makes communication possible.  He writes that it is a 
faculty for judging that in its reflection takes account (a priori) of everyone else's way of representing in thought…Now this happens by one holding his judgment up not so much to the actual as to the merely possible judgment of others, and putting himself into the position of everyone else, merely by abstracting from the limitations that contingently attach to our own judging. (5: 294)
The sensus communis thus makes possible the communicability of a judgment by enabling us to see what in our own private judgment would be held in common with others.  But what exactly does the sensus communis sense?  It does not sense others' mental states directly.  Instead, it is a sense for our own mental state that can determine whether this state is something that we can have in common with others. The sensus communis is thus a "common sense" in more than one way.  It is a sense we have in common for a mental state we can have in common.  In addition to this, the sensus communis is, in the Aristotelian sense, a sense for what is common among one's own cognitive faculties and thus of the relationship between the cognitive faculties, or, our mental state.  In fact, Kant describes the sensus communis as that "by which, however, we do not mean any external sense but rather the effect of the free play of our cognitive powers" (5: 238).   
	What the sensus communis senses is thus the relationship between the cognitive faculties, such as that which produces a mental state of "animation," "harmony," or "quickening," which is the mental state in a judgment of taste (5:219), or that of the proportion suitable for cognition.  Kant writes, 
if cognitions are to be able to be communicated, then the mental state, i.e. the disposition of the cognitive powers for a cognition in general, and indeed that proportion which is suitable for making cognition out of a representation (whereby an object is given to us) must also be capable of being universally communicated…But this disposition of the cognitive powers has a different proportion depending on the difference of the objects that are given.  Nevertheless, there must be one in which this inner relationship is optimal for the animation of both powers of the mind (the one through the other) with respect to cognition (of given objects) in general; and this disposition cannot be determined except through the feeling (not by concepts)." (5: 238-239)

When the cognitive powers are in a certain "optimal" relationship, the mind is disposed towards cognition.  And, when they are in a relationship with a different proportion of activity, this produces a judgment of taste.  This "more interesting" proportion, I have argued, occurs when the object given to the mind is one that is intuited by the imagination in an intensive form.  The sensus communis is the faculty that makes possible the feeling of our mental state whatever the proportion of the relationship between the faculties.    However, its capacity to make sensible this "quickened" state of mind is what explains the role of the sensus communis as the necessary condition for universal communicability of judgments of taste in particular.  
Although the sensus communis is the form that makes possible the intuition of any mental state, whatever proportion the cognitive faculties are in, its distinctive function is to serve as the basis for the normativity of the pleasurable state that occurs when the imagination is in a state of free play.  Judgments of cognition do not require the sensus communis for their normativity.  They require the categories.  Since they have a determinate objective principle, anyone making a judgment in accordance with that principle is also claiming that her judgment is unconditionally necessary (5: 237).  Judgments of taste, however, require the communicability of the judgment as a necessary condition for their normativity.  This is precisely what is distinctive about them.  This is in contrast to cognitive judgments, for which communicability is a result of their meeting the norm of objectivity, rather than their necessary ground.  This is why Kant writes that "taste can be called a sensus communis with greater justice than can the healthy understanding and that the aesthetic power of judgment rather than the intellectual can bear the name of a communal sense. (One could designate taste as the sensus communis aestheticus  (and) common human understanding as sensus communis logicus)" (5: 295/295n).
Kant describes the normativity of judgments of taste by saying that the necessary liking required of the object of a judgment of taste is a "should, i.e. the objective necessity of the flowing together (Zusammenfleißens) of the feeling of everyone with that of each" (V: 240).  His claim is that this necessary flowing together of everyone's feeling is based on the sensus communis as a sense that is common to all for what is common to all.  It is noteworthy that Kant's use of the word "flowing" here is reminiscent of his discussion of flowing magnitudes in the Anticipations of Perception.  The sensus communis here functions as the measure of intensive magnitudes in contrast to units of extensive magnitude.  But in this case, the intensive magnitude being measured is not a particular sensible representation apprehended by the imagination in its freedom, but human sensibility as such, "the flowing together of everyone's feeling."  It is in this way that the sensus communis functions as the basis of the normative feeling that is claimed in judgments of beauty.  When I claim that something is beautiful, I do not merely demand that someone else agrees with me, in the sense of adding her judgment to mine and saying she thinks so too.  It is not that I require others to line up and vote the same way as I do.  Rather, I demand that they share my feeling of pleasure in the object.  Indeed, I do not think that my judgment could count as a judgment of taste unless I believe everyone ought to agree with me.  And if I do make such a claim and others disagree with me, I do not merely feel a difference between us, but alienated from an important aspect of humanity, namely, a shared sensibility.  Because the sensus communis is intensive in form it is a shared or "communal" (5:293) sense, not merely something that each of us has in common.
 This relation of part to whole, of one sensing subject to the rest of sensing subjects, is thus not a relation of one unit to the total aggregate of units.  It is not a relation of whole numbers.  Instead it is an intensive or "flowing" quantum in which each part is measured as a degree of the whole, and which has value only with regard to the whole, just as in the example of the silver discussed above.  In other words, my feeling of pleasure in a judgment of taste only has any worth, or only "counts" as an appropriate feeling of pleasure if I can assume as a standard a unity, or coalition, of the feeling of judging subjects.  Indeed, what Kant calls the "problem of a deduction of judgments of taste," namely

How is a judgment possible which, merely from one's own feeling of pleasure in an object, independent of its concept, judges the pleasure, as attached to the representation of the same object in every other subject a priori, i.e. without having to wait for the assent of others? (5: 288)

has the same strangeness Kant ascribes to the principle of the Anticipations of Perception:

If it were supposed that there is something which can be cognized a priori in every sensation, as sensation in general (without a particular one being given), then this would deserve to be called an anticipation in an unusual sense, since it seems strange to anticipate experience precisely in what concerns it matter, which one can only draw out of it. (A167/B209)

A judgment of taste is an anticipation in the same way as the claim that every possible object of sensation has an intensive magnitude is, since a judgment of taste claims a priori of all subjects that they must experience the same pleasure in an object, prior to receiving their assent.  The basis of both anticipations is an intensive form.  With regard to the real in appearances, we can anticipate that it has a degree that can be the object of sensation.  With regard to the feeling of other subjects, we must assume that the value of each of us as evaluating subjects depends on a common sensibility that must be shared.
	I have argued that the difference between cognitive judgments and judgments of taste, with regard to both their structure and their claim to normativity, can be explained by means of one point of distinction: the former involve extensive forms whereas the latter involve intensive forms. I believe that this one distinction can solve many of the puzzles involved in trying to figure out how, for Kant, the same group of mental faculties can, in one instance, claim that its experience is of a fact, and, in another instance, claim that something has the value of beauty. It can also begin to provide an account of the particular absorption, or intensity, that pertains only to aesthetic experience.  This is because the form of an object judged to be beautiful is itself intensive.