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Critique of Pure Reason

Lecture Notes: Substance

G. J. Mattey

Book II of the Transcendental Analytic is entitled “Analytic of Principles,” or “Transcendental Doctrine of the Power of Judgment.” Its most important part is Chapter II, “System of All Principles of Pure Understanding.” In that chapter, Kant lays down principles for the application of the twelve categories to objects of experience. He describes the principles as “synthetic judgments that . . . emanate a priori from pure concepts of understanding and that lie a priori at the basis of all other cognitions” (A136/B175). The exposition and defense of some of these principles will be the focus of this lecture and the three following it.

Chapter I is entitled “Schematism, which will be described briefly below. Chapter III concerns the distinction between phenomena and noumena, that is, between “beings of sense” and “beings of the understanding,” and it is the subject of a later lecture. The appendix to the Transcendental Analytic is the “Amphiboly of the Concepts of Reflection,” which was covered in an earlier lecture.

Power of Judgment

Thus far, Kant has been operating with a broad distinction between sensibility and understanding. Objects are given to the passive sensibility and are thought by the spontaneous understanding. In the introductory passage of the Analytic of Principles, Kant distinguishes three “mental powers comprised under the broad sense of an understanding as such” (A131/B170). These powers, and what they govern, are the following.

General logic, i.e., logic which is purely formal and has abstracts from the nature of its content, can prescribe rules for the use of all three of the listed powers. Such use would apply to any object. But transcendental logic, a kind of “special logic,” is limited to “the content of pure a priori cognitions only” (A131/B170).

The specific a priori cognitions associated with the three powers of the understanding are as follows.

Because all of these cognitions have a specific source in the understanding (in the broad sense), it is possible that some or all of them might apply to no objects at all, or that they apply to objects in a peculiar way. And indeed, Kant’s view was that the first two kinds of cognition apply only to objects of experience, while the third kind fails to apply straightforwardly to any object. The aim of the Analytic of Principles is to show how the principles that are based on the power of judgment are subject to a “canon” for their applications to objects. “The Analytic of Principles will be a canon solely for the power of judgment, teaching it to apply to appearances the concepts of understanding, which contain the condition for a priori rules” (A132/B171).


Chapter I of the Analytic of Principles concerns the relation between sensible intuitions and a priori concepts or categories. Each stems from an entirely different source (sensibility and understanding, respectively). According to Kant, “pure concepts of understanding . . . are quite heterogenous from empirical intuitions (indeed, from sensible intuitions generally)” (A137/B176). That is, there is nothing in common between the intuition and the category. This raises the question of what it is that allows us to subsume a sensible intuition under a category, that is, to apply the category to the object.

For example, a sensible intuition might be that of a plate: a round, extended, impenetrable body existing in a part of space. This intuition can be brought under the concept circle, since the concept and the intuition share a common feature: roundness. The pure concept of substance, on the other hand, concerns only the relation of priority of a subject and a predicate. Substance is a subject that cannot itself be a predicate of a subject (B149). Unlike our being able to intuit roundness, we cannot intuit being a subject or being a predicate, much less the relation between the two.

Kant’s solution to this puzzle is to claim that there is in fact an intermediary between pure concept and sensible intuition, something that plays the role of roundness in the above example. It is what Kant calls a “transcendental schema” common to both, and thus forming a mediating link between sensible intuition and pure concept. The schema is “transcendental time determination” (A138/B177).

All sensible intuition is subject to time as its form. Time has in common with categories the fact that it is a priori in origin. Insofar as an intuition is determined in time, that is, insofar as something definite holds about its temporal characteristics, the intuition can be brought (or “subsumed”) under the category. These time-determinations are incorporated into the synthesized intuitions in the transcendental synthesis. “Such a schema is . . . only the pure synthesis conforming to a rule, expressed by the category, of unity according to concepts as such” (A142/B181). We will give two examples of schemata, one for the category of substance and the other for the category of cause.

The first determination or property of time is that it is “immutable and enduring” (A144/B183). The correlate in sensible intuition of the immutable and enduring character of time is the permanence of the real in appearance. There is, in appearances, always something that does not change while other things do. We call what is permanent and unchanging in appearance substance. Cognizing appearances as substance is what allows us to determine whether things are succeeding one another or enduring at the same time. Moreover, what is permanent is the kind of thing that can be a subject of predicates and not the predicate of any subject.

Time is also successive, and the successiveness of different times is reflected in the successiveness of appearances. But not just any successive appearances will do as a surrogate for the successiveness of time. The transition must be an orderly one, subject to a rule, in order to reflect the regularity of temporal succession. So, “The schema of the cause and of the causality of a thing as such is the real upon which, whenever it is posited, something else always follows” (A144/B183).

The Schematism is not an attempt to prove that categories are applicable to sensible intuitions in the guise of time-determinations. Rather, it is simply an enumeration of the time determinations that would fulfill the function of uniting the intuition and the concept. Kant thought he had already shown in the Transcendental Deduction that sensible intuitions must fall under the categories, and here he merely describes how this takes place. This is crucial for the rest of the Analytic of Principles, for the principles for the application of the categories must make reference to the objects of sensible intuition. It does so through the time-determinations listed in the Schematism. (For more on the Schematism, click here.)

Synthetic Judgments

Chapter II of the Analytic of Principles, “System of All Principles of Pure Understanding,” begins with a discussion of issues that were first broached in the Introduction. There, Kant had made the distinction between analytic and synthetic judgments. The principles at issue here are synthetic. A synthetic judgment requires, besides the cognitions which it connects, some third thing which brings the two cognitions together. (An analytic judgment, by contrast, requires nothing more than the content of one of the cognitions to produce the content of the other.) In an a posteriori judgment, the third thing is experience. But what is it in the case of judgments a priori (A9/B13)?

In Section II, “On the Supreme Principle of All Synthetic Judgments,” we are finally told what this third thing is. It turns out that it is the operative principle for a posteriori as well as a priori judgments.

The supreme principle of all synthetic judgments is this: Every object is subject to the conditions necessary for synthetic unity of the manifold of intuition in a possible experience. (A158/B197)
In the case of a priori judgments, these conditions involve “the formal conditions of a priori intuition, the synthesis of the imagination, and the necessary unity of this synthesis in a transcendental apperception” (A158/B197). These three conditions are what make experience possible. So any object of experience must be judged in conformity to them. Now recall that truth is the agreement of a cognition with its object. Then an a priori judgment is true because the object necessarily agrees with the cognition that made it possible in the first place.

Synthetic Principles

At this point, Kant is ready to produce his system of principles, following the table of categories. He divides the principles into two types, the mathematical and the dynamical. The first type deals with individual intuitions and their objects, describing them as quantifiable magnitudes. These principles are capable of “intuitive” certainty (A162/B201). The second type deals with the existence of appearances. This requires more than mere intuition, but “empirical thought” (A160/B200) as well. Because thought (which is always discursive, involving concepts) is an element of dynamical principles, they are capable only of “discursive” certainty, (A162/B201) and the evidence for them is not immediate.

The members of the first set of mathematical principles apply the categories of quantity—unity, plurality, and totality—to objects of experience. Kant calls these principles “Axioms of Intuition,” and they all fall under a common principle, “All intuitions are extensive magnitudes” (A162/B201). A magnitude is extensive when “the presentation of the parts makes possible (and hence necessarily precedes) the presentation of the whole” (A162/B203). The presentation of a unified intuition requires that the intuition be generated by successive addition of spaces and times. “Appearances can be apprehended only through the assembly of what is homogeneous and the consciousness of the synthetic unity of this manifold” (A162/B203).

Here we see a more detailed description of the “synthesis of apprehension” invoked in the second part of the Transcendental Deduction. In the presentation of the argument in the last module, it was asked why it is that the intellectual synthesis according to a category plays a role in synthesis of an empirical intuition. This question is answered with respect to the category of quantity. If we synthesize intuitions that are determined in space and time, we must do so by adding part to part, thus producing a quantity. So the synthesized manifold falls under the category of quantity. Moreover, “the successive synthesis of the productive imagination in the generation of shapes is the basis of the mathematics of extension (i.e., geometry) with its axioms” (A163/B204). (For more on the Axioms of Intuition, see here.)

The members of the second set of mathematical principles apply the categories of reality—negation, and limitation—to empirical objects. These principles are “Anticipations of Perception,” and their overarching principle is, “In all appearances the real that is an object of sensation has intensive magnitude, i.e., a degree” (A166/B207). Unlike with the first set of principles, the proof of these does not appeal to the way in which a manifold is unified, and it is therefore much less convincing. From the fact that there is a possible “stepwise change” in the degree of intensity of a sensation, Kant concludes that “there is likewise possible a synthesis in the production of a sensation’s magnitude, from the sensation’s beginning, i.e., from pure intuition, = 0, up to this or that magnitude of sensation” (BA166/B208).

Perhaps what Kant had in mind is this. Suppose I take a sensation of a colored point, no matter how faint. I might produce the equivalent of a less faint sensation by superimposing a second one of the same faintness as the original, and so on up to any degree of intensity. Kant gives an example in his exposition of the next set of principles. “Thus, e.g., I can assemble the degrees of sensation of sunlight from some 200,000 illuminations provided by the moon, and can determinately give that degree a priori, i.e., construct it” (A179/B221).

But even supposing that this could be done, it seems implausible as an explanation of what does happen. The magnitude of sensations seems just to be given, rather than synthesized. Kant only claimed that sensations could be “synthetic” in this way, but this is not what he needs for the necessary applicability of his principles, given that they are supposed to be based on synthesis. (For more on the Anticipations of Perception, click here.)

Analogies of Experience

The set of principles corresponding to the relational categories of substance, causality, and community, is called “Analogies of Experience.” These are dynamical principles, which apply to the existence of objects of experience. The general principle of the analogies is that, “Experience is possible only through the presentation of a necessary connection of perceptions” (A176/B218). There are three specific principles, each of which has its own proof in addition to the proof of the general principle. (In this, the Analogies differ from the Axioms and the Anticipations.)

The proof of the general principle is of central importance to Kant’s main project. It contains the germ of his response to Hume, who denied the principle on the grounds that one cannot find in experience a source of a necessary connection. Kant agrees with Hume on this point (Prolegomena, Preamble) but invokes an a priori source of the connection.

The first point to notice is that the argument of the second edition Transcendental Deduction is not relevant here. Even if the mathematical categories are required in the synthesis of a single (or perhaps unified) perception, this tells us nothing about how single (or unified) perceptions are connected with one another. Kant put it this way in a paragraph added to the Analogies in the second edition.

In experience perceptions do indeed come together only contingently, so that no necessity in their connection is, or even can be, evident from the perceptions themselves. For apprehension is only a compilation of the manifold of empirical intuition; and we find in it no presentation of the necessity of the linked existence in space and time of the appearances that it compiles. (B219).
Kant calls the general principle of the Analogies “regulative,” as opposed to the “constitutive” general principles of the Axioms and the Anticipations. “For since existence cannot be constructed, the principles will deal only with the relation of existence” (A179/B221-2). If, as it seems to some, the argument of the B Deduction was incomplete, it is completed with respect to the limited number of the categories treated in the Analogies.

The fact that the principles of the Analogies are regulative rather than constitutive explains why Kant called them “analogies.” When we present perceptions as connected necessarily, we do so using the schemata of the categories of relation, not the categories themselves. For example, we do not present objects of experience as substances, but as permanent. Nor do we present them as causes, but only as being subject to a rule which ties objects of experience together. So the necessary connection is made by something (the schema) that is like the category in a certain way, but is not the category itself. “Hence these principles will entitle us to assemble appearances only by an analogy with the logical and universal unity of concepts” (A181/B224).

The central claim of the proof of the general principle of the Analogies is that a necessary connection of perceptions is required to place them in a determinate order of time. Experience requires that perceptions be placed in a determinate time order, so a necessary connection of perceptions is required for experience. The basic argument runs as follows.

  1. If I experience an object, then my cognition of the object is determined by connecting my perceptions of it.
  2. If my cognition of the object is determined by connecting my perceptions of it, then the object is determined in time.
  3. If an object is determined in time, then it is determined either through a perception of time itself or through the linking of perceptions in time.
  4. Time cannot be perceived.
  5. So, if an object is determined in time, then it is determined through the linking of perceptions in time. [3, 4]
  6. If an object is determined through the linking of perceptions in time, then it is determined through concepts connecting them a priori.
  7. So, if I experience an object, then what that object is is determined through concepts connecting perceptions a priori. [1, 2, 3, 6]
  8. A concept connects perceptions a priori if and only if it connects concepts with necessity.
  9. So, if I experience an object, then my cognition of the object is determined through concepts connecting perceptions with necessity. [7, 8]
Obviously the key step here is 6. The claim is that so long as we cannot perceive time itself, the only way we have of placing our perceptions in a time-order is through the use of the category. No support is given for this claim in this argument, so perhaps we will have to look to the more specific claims about how an object is determined in time to see why categories are required.

There is an argument following shortly after the one just reconstructed that might be used to support the key premise in that argument. There, Kant invokes apperception. “The general principle of all three analogies rests on the necessary unity of apperception in regard to all possible empirical consciousness (i.e., perception) at every time” (A177/B220). The premise is that since the determination of the time-relations of an object is a synthetic activity, it must take place in a unified consciousness: “Now all this manifold is to be united, as regards its time relations, in original apperception” (A177/B220).

From this it is supposed to follow that “this synthetic unity in the time relation of all perceptions, a unity which is determined a priori, is this law: that all empirical time determination must be subject to rules of universal time determination” (A177-8/B220). But once again, it seems that we are confronted with a non sequitur. From the fact that necessarily the perceptions are unified in one consciousness it does not follow that their unity is based on necessary laws. Kant has not shown here, as he did not show in the Transcendental Deduction, that only such laws could allow the perceptions to be united in a single consciousness.

Substance and Accident

The category of substance in its most general sense is “the concept of something that can exist as a subject but never as a mere predicate” (B149, second edition Transcendental Deduction). The schema of substance is that of “a substratum which . . . endures while all else varies” (A144/B183, Schematism). In the First Analogy, Kant enunciates the “Principle of the Permanence of Substance. In all variation by appearances, substance is permanent, and its quantum in nature is neither increased nor decreased” (A182/B224). Thus, a substance, insofar as it is appearance, is something permanent, which does not come to be and does not pass away. An accident, by contrast, inheres in a substance and may come to be or pass away.

Kant begins his argument for the principle with a discussion of the unity of time. Time endures and does not vary, and all variation of appearances is in time, for only in time can there be any succession. “For time is that alone in which, and as determinations of which, sequentiality or simultaneity can alone be presented” (A182/B225). The next claim was already made in the argument for the general principle of the Analogies—that time cannot by itself be perceived.

So, if we are to determine objects in time, we must do so relative to something in appearances that is enduring and unchanging. This feature of appearances is what Kant calls “the substrate which presents time as such, and in which all variation or simultaneity can in apprehension be perceived through the appearances’ relation to it” (A182/B225). Such a substrate is substance, and since it is the bedrock against which all variation is measured, “its quantum in nature can also be neither increased nor decreased” (A182/B225).

We shall now reconstruct the argument.

  1. I perceive some appearance as varying.
  2. If I perceive an object as varying, then I perceive it as one way at one time and as another way at a later time.
  3. If I perceive some objects as one way at one time and as another way at another time, then there is a single time by reference to which I determine their variation.
  4. So, there is a single time by reference to which I determine the variation of some appearances. [1, 2, 3]
  5. If I determine the variation of some appearances by reference to a single time, then something I perceive presents this single time.
  6. If something I perceive presents a single time, then it is either the single time itself or a permanent appearance.
  7. I cannot perceive time itself.
  8. So, there is a permanent appearance by which I determine the variation of some objects of appearance. [4, 5, 6]
  9. A permanent appearance is permanent substance
  10. So, I determine the variation of some appearances by permanent substance [8, 9].
  11. If substance could come to be or pass out of existence, it is not be permanent.
  12. So, I determine the variation of some appearances by substance which cannot come to be or pass out of existence. [10, 11]
Step 6 is the first key move here. Given the plausible step 7, it yields step 8, which establishes the existence of something permanent. The second key move is step 11, which explains that permanence is absolute, rather than relative to a finite stretch of time.

But here one must ask whether an absolute notion of permanence is required to make step 6 true. Suppose there were an object that endured throughout my lifetime. Then there is no reason why I could not use that object as the substrate against which I could determine the variation of objects. A further problem with the argument is that at best it establishes that there is at least one substance: “something underlying in experience is there always—i.e., something enduring and permanent ” (A182/B225-6). But Kant wanted to generalize the argument to the conclusion that no substance can come to be or pass away. So much work remains to be done for the argument to persuade the critical reader.

Kant not only wanted to establish the existence of the permanent with this argument, but he also wanted to establish that “all variation and simultaneity are only so many ways (modes of time) in which the permanent exists” (A182/B226). It is not at all clear that this follows from the argument. Suppose there are appearances which come and go. All the argument establishes, if anything, is that we need to refer to a permanent in order to establish whether they are simultaneous or successive. But this does not imply that they must be determinations of the permanent.

Philosophers, as well as the general public, have taken his principle for granted without trying to prove it, in Kant’s view. He himself uses it to derive the generally held principles that matter endures, while its form alone changes, and that nothing can come from nothing. He notes that the latter principle is questioned by some on the grounds that it conflicts with the doctrine of creation of the universe by God. But he discounts this concern because his doctrine applies only to appearances, not things in themselves. “This permanence is nothing more than our way of presenting the existence of things (in appearance)” (A186/B230).

The principle also allows Kant to clear up some misconceptions in the received view of substance. First, it may be thought that substance is a category of relation because it involves a relation between what subsists (the substance itself) and what inheres in the substance (its accidents). But in fact there is only one being, the substance, and accidents are only positive ways in which the substance exists. Kant rather clumsily excuses his placing substance under the heading of relation, saying he did so “more as the condition of relations than as itself containing a relation” (A187/B230). He does not explain this any further.

Second, change must be understood only as a way of existing of the permanent followed by a different way of its existing. So only a substance changes, strictly speaking. The accidents of a substance do not change but only vary. So if a leaf turns from green to red, there is no change, but only variation, in its color. The leaf (if it is a substance) is what changes.

The discussion ends with two arguments that might be used to defend the main argument against the charges that have been leveled against it here. Kant first claims that an absolute arising or ceasing to be could not be perceived. He proposes a thought-experiment in which one supposes that something comes to be. If this were to occur, there would be a point in time in which the thing was not. The only way to determine this point is by reference to something that endures. “But if you tie this arising to things that were beforehand and that continue up to the something that arises, then this something was only a determination of what, as the permanent, was beforehand” (A188/B231).

Again, the conclusion seems not to follow from the premises. To “tie” the arising of a thing to what already existed is not the same thing as to perceive it as a determination of that existing thing. One must make reference to that thing to assign it a time of coming-to-be, but that does not make the new thing inhere in that time.

The final argument seems even worse. Kant claims that if some substance were to come to be or cease to be, the unity of time would be annulled. “Appearances would then refer to two different times wherein existence would be flowing by concurrently--which is absurd” (A188/B232). We get a reference to two times an earlier passage where Kant claimed that time itself cannot change. If it did, then it would have to be embedded in another time against which its change could be determined (A183/B226).

What Kant may have had in mind is this. Suppose that there are two substances, A and B, and that A arose and B passed away. Could they have done so in a single unitary time? I would have to pinpoint A’s arising relative to B. When B passes away, I must now make reference to A in order to determine the time of B’s passing away. Kant might have assumed that the time-series in which A exists comes into existence relative to the time-series in which B exists, and that the time-series in which B exists passes away with the demise of B. But why make this assumption? So long as at least one substance is in existence, it can be used as the basis of the determination of the time of the coming-to-be and passing away of any other substance.

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