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Critique of Pure Reason

Lecture Notes: Causality

G. J. Mattey

The Second Analogy is one of the most intriguing sections of the Critique. Its aim is to justify a principle for applying the a priori concept of causality to objects of experience. This is something that Hume had tried and failed to do. So if Kant was successful, he has achieved a fundamental result in metaphysics—one which he considered indispensable if there is to be a science of metaphysics at all.

Hume’s Problem

In the Prolegomena, Kant assessed the significance to metaphysics of Hume’s failure to justify the application of an a priori concept of causality to objects of experience: “nothing has ever happened which could have been more decisive to its fate” (Preface, Ak 4:257). The problem begins “mainly from a single but important concept in metaphysics, namely, that of the connection of cause and effect” (Preface, Ak 4:257). It ends with the conclusion that “there is not, and cannot be, any such thing as metaphysics at all” (Preface, Ak 4:258). The basis for this claim has been discussed in an earlier lecture.

The causal connection for which Hume could not find a source in reason was that something is “so constituted that if that thing be posited, something else also must necessarily be posited; for this is the meaning of the concept of cause” (Preface, Ak 4:257). Hume noted that the concept of any given thing is compatible with the non-existence of any other given thing.

From the first appearance of an object, we can never conjecture what effect will result from it. But were the power or energy of any cause discoverable by the mind, we could forsee the effect, even without experience; and might, at first, pronounce with certainty concerning it, by the mere dint of thought and reasoning. (Enquiry concerning Human Understanding, Section 7, “The Idea of a Necessary Connection”)
Hume went on to show in detail why none of the observed qualities of matter reveal anything of power in them. He then argued that power is not to be found in anything observed in the mind. His conclusion was that, “All events seem entirely loose and separate. One event follows another, but we can never observe any tie between them. They seem conjoined, but never connected” (Enquiry concerning Human Understanding, Section 7, “The Idea of a Necessary Connection”).

As Kant put it in the Prolegomena, the key to the solution of Hume’s problem is to recognize that objects of experience are appearances, and not things in themselves. Hume assumed that the objects in which he tried to find power are things in themselves, and so he was doomed to fail to find it. All he could find was constant conjunction, which he proceeded to identify with the causal relation. But if the objects in question are appearances, we can say that the constant conjunctions can be upgraded, so to speak, by adding to it necessity and universal validity, so that it is “considered as a law,” applying to appearances “for the purposes of a possible experience which requires universal and therefore necessarily valid rules” (Second Part, §29, Ak 4:312).

Given that the category of causality is limited in its use to experience, Kant needed an argument to show why necessary rules of connection are required to make experience possible. He could not argue that these rules are necessary for the intuition of any single object of appearance. For as he had correctly recognized, the causal principle is not constitutive, but only regulative (A180/B223). As he put it in the Prolegomena, “I have no conception of such a connection of things in themselves, how they can . . . act as causes and I can just as little think such properties in appearances as such” (Prolegomena, Second Part, §28, Ak 4:311).

In this sense, Hume’s observation that one cannot find power in a single object is correct, even if the object is only an appearance. So the burden of Kant’s argument falls on his finding some feature of experience that requires that its objects conform to necessary rules connecting them with one another. Hume certainly thought that experience is possible even if objects are merely regularly conjoined but not necessarily connected.

The Category of Causality

The form of judgment from which the category of cause is supposed to be derived is the hypothetical, whose form is: if p, then q. The antecedent of the hypothetical (or conditional) judgment is said by Kant to be the “ground” and the consequent the “consequence” (A73/B98; cf. Prolegomena, Second Part, §28, Ak 4:311). “Whether these two propositions are in themselves true remains undecided here; only the implication is thought through this hypothetical judgment” (A73/B98). As the hypothetical judgment relates to judgments to each other, it is a relational form of judgment.

The category of “causality and dependence” (or “cause and effect,” A80/B106) which corresponds to the hypothetical judgment is therefore itself relational. As concepts, causality and dependence are supposed to apply to what exists, so that the category indicates that something is the ground of the existence of something else which is the consequence of, and dependent upon, that ground. The pure concept of causality and dependence makes no reference to time. “Of the concept of cause (if I omit from it the time in which something succeeds something else according to a rule) I would find, in the pure category, nothing more than that it is something from which the existence of something else can be inferred” (A243/B301, Phenomena and Noumena).

As with any category, its application to intuition is mediated by a schema, which is a determination of time. “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 also follows” (A144/B183, Schematism). At the base of the schema is temporal succession, so that the “whenever” is a time and the “following” is temporal. The schema as it is stated is consistent with Hume’s definition of a cause, as “an object, followed by another, and where all the objects, similar to the first, are followed by objects similar to the second” (Enquiry concerning Human Understanding, Section 7). There is nothing in the schema that indicates necessity, that the “something else” must follow the existence of “the real.”

This description of the schema not only refers to causality but also to the cause. We should think of causality as a relational property (“the real”) of something, which thing is called a cause when it has that property. Similarly, dependence is a relational property of something, which is called an effect when it has that property. Kant later will speak of the “causality of the cause” (A532/B560). In such cases he wants to emphasize the relational property of something that is a cause, the point there being that this very property is itself dependent and requires a cause.

The Causal Principle

The “Principle of Temporal Succession According to the Law of Causality” applies the schema of causality to every change which takes place in time. “All changes occur according to the law of the connection of cause and effect” (A189/B232). This statement is ambiguous. It could mean that there is a law according to which whenever a change occurs, there is a causality in a thing whose existence always brings about the change in a dependent thing. A stronger reading would be that whenever a change occurs, there is a causality in a thing whose existence brings about the change in the dependent thing in accordance with a law. Note that even the weaker claim could not be accepted by Hume, because Hume claims that there is no property of causality in things. But Kant’s proof of the principle shows that he adopts the stronger one.

In the second edition of the Critique, Kant gives a proof in the second paragraph of the Second Analogy, after a giving a “preliminary reminder” that refers back to the First Analogy (B233). The conclusion of the First Analogy was that the only kind change in appearances is variation in the “determinations of substance, which is itself permanent” (B232). There is no change which consists of the coming to be or passing away of a substance. Kant later refers to “states” of a substance as being what varies (A207/B253), and we will adopt this terminology in what follows. So if we speak of an appearance as a cause, we understand its causality as a sufficient condition for the coming to be or ceasing to be of a state of a substance at some later time.

Proof of the Principle

Now the proof of the principle, as given in the second edition, will be reconstructed in two phases. The first result is negative, namely, that perception cannot determine the objective order of the succession of the states of an object.

  1. I perceive that at one time a thing is in state A and later it is in state B.
  2. If I perceive that at one time a thing is in state A and later it is in state B, then I am connecting state A and state B in time.
  3. If I am connecting state A with state B in time, then I am connecting A and B by a synthetic activity of the imagination.
  4. I cannot perceive time.
  5. If I cannot perceive time, and I am connecting A and B by a synthetic activity of the imagination, then I cannot determine whether my imagination alone is responsible for the order of A and B.
  6. So, if I am connecting A and B by a synthetic activity of the imagination, then I cannot determine whether my imagination alone is responsible for the order of A and B. [4, 5]
  7. If I cannot determine whether my imagination alone is responsible for the order of A and B, then my perceiving that state A is first and state B is later does not determine that A actually precedes B.
  8. So, my perceiving state A first and state B later does not determine that A actually precedes B. [1, 2, 3, 6, 7]
Step 2 depends on Kant’s assumption that any connection is a connecting. Hume would undoubtedly object that one can perfectly well perceive one event after the other without connecting the two. Kant would respond that perceiving things as succeeding one another does require a connecting, a “determination” of the state B as being a later state.

But Hume could respond that there is a difference in vivacity between perceiving and imagining, so that the reason one perceives B as later is because B was given as later. Kant’s rejoinder is that things are not given in a time-order, but rather that they are placed in a time-order by the synthetic activity of the productive imagination. Hume’s comparison of vivacity would apply (if at all) only to the reproductive imagination. We can at least see from this fictitious exchange that Kant is relying heavily on his own peculiar account of perception in this argument.

The second part of the argument fills the gap left by perception.

  1. If A is experienced as actually preceding B, then A’s position before B in my perception is determined by some cognition.
  2. The cognition that determines A’s actual position before B in my perception is either a perception or a rule of the understanding.
  3. The cognition that determines A’s actual position before B is not a perception. [First Part of the Argument]
  4. So, if A is experienced as actually preceding B, then A’s position before B in my perception is determined by a rule of the understanding. [1,2,3]
  5. A rule of the understanding that determines the position of A before B in my perception is one according to which the order of A and B is fixed.
  6. So, if A actually precedes B, then A’s position before B in my perception is determined by a rule of the understanding according to which the order of A and B is fixed. [4,5]
  7. A rule of the understanding according to which the order of A and B in my perception is fixed is a rule which determines A as the cause and B as the effect.
  8. So, if A is experienced as actually preceding B, then A’s position before B is determined by a rule according to which A is the cause and B is the effect. [6,7]
Hume would no doubt reject the first step of this argument. He would say that the position of A and B in experience are independent of what order they might be assigned by human cognition. The response to this would have to be that experience is nothing more than connected perception, and perception is connected by some activity of the understanding, either blindly by the imagination or according to a rule of the understanding. Hume’s rebuttal would probably be as with the first part of the argument: experience as connected perception does not imply that there is a connecting which is responsible for its order. If I perceive that B follows A, it is because B did follow A in the order of things.

Hume might grant that the argument is effective in cases in which neither state A nor state B is observed directly. Then, indeed, we would have to revert to some rule which determines which is the cause and which is the effect. But in that case, the rule could be simply that As have always been followed by Bs. Kant would respond that such a rule would not really determine which is first, because it allows for the possibility of an exception. Hume could reply that in this strict sense of ‘determine,’ we cannot determine which is first: we can have recourse only to induction, which yields general rules which have never been violated but could be violated. For Kant, reliance on such rules is an admission of skepticism. “The rule’s universality and necessity would then be attributed to it only fictitiously and would have no true universal validity, because they would be based not on anything a priori, but only on induction” (A196/B241).

What Kant needs to break the impasse is to claim that the very perception of states as unfolding in a certain order requires the use of a rule of the understanding. But it does not seem so far that he is entitled to that claim, due to the fact that causality is not constitutive of objects. It seems that on Kant’s account of perception, it is the order in which the matter of sensibility, sensation, is given that determines the order of perceptual states. When we are paying attention to how sensation unfolds, we have all we need to determine the order of states, assuming that we are functioning normally.

Objective Succession

One remedy for this problem is to say that the apprehension of a subjective order of succession of perceptions is not a sufficient basis for us to determine an objective order of succession. If an event were not preceded by something that it must follow according to a rule, “all succession of perception would be determined solely in apprehension, i.e., merely subjectively; but this would not at all determine objectively which item in fact precedes in perception and which follows” (A194/B239). Kant’s reason for making this claim is not at all clear. He seems to have thought that in the absence of cause, chaos would reign. “We would in that way have only a play of presentations that would not refer to any object whatever,” since “succession in apprehending is in that case everywhere the same” (A194/B239).

To evaluate Kant’s claim, suppose that Bs have always been preceded by As, and that a B occurs without its being preceded by an A, but by a C instead. Kant is saying that we could not determine that B happened after C. We would have two apprehension, one of a B and one of a C, with no way to decide which came first. Yet it seems that where I am presently apprehending a B and remember having apprehended a C, I would be able to determine the order, purely on the basis of apprehension.

A possible rebuttal is based on the claim in step 5 of the first part of the argument from the second edition. Recall that this was the claim that the imagination could just as well present B as preceding A as following A. Kant makes the case more clearly in the original version of the Analogy (which is preserved in the second edition).

All empirical cognition involves the synthesis of the manifold by the imagination. This synthesis is always successive, i.e., in it the presentations always succeed one another. In the imagination itself, however, this sequence is not at all determined as regards order (i.e., as to what must precede and what must follow), and the series of the presentations following one another can be taken as proceeding backward just as well as forward. (A201/B246)
This claim does not seem to be of any use, though. Granted that “in the imagination itself” the sequence is not determined regarding its order: the imagination is free to mix up its presentations in any order when it is operating by itself. But in the synthesis of apprehension, the imagination is not operating by itself. Its synthetic activity presupposes a manifold of empirical intuitions, sensations. How these sensations are synthesized into a cognition of an object is restricted by the order of the sensations themselves. If A comes before B in the object, then the sensations that are ingredients in the presentation of A will come before the sensations that are in the presentation of B.

Objective Reference

A final stand can be made by arguing that causal rules are required in order to determine that B occurred in the first place. Suppose I have an apprehension purporting to be of state B. How do I determine whether the object of my apprehension really is in state B? The only recourse I have is to see whether its being in B is determined by a rule that states that it must first have been in A. Then I can check whether it had been in A. “If I posited what precedes and the event did not succeed it necessarily, then I would have to regard this event as only a subjective play of my imaginings” (A201-2/B247).

The Humean response to this argument would be that it is correct up to a point. We oftentimes find ourselves wondering whether something really happened, and the only way to check is by trying to find whether its cause occurred or whether it has brought about its effects. But why must the rule be a necessary one? If A causes B in Hume’s sense of A’s being constantly conjoined with B, we can use this as a test just as well. Kant certainly would say that this kind of test is not absolutely decisive, given that it remains possible that A occurs without B. Hume’s view would commit him to a very mild skepticism.

I think Hume would grant this and just shrug his shoulders. Our criterion for determining whether an event has occurred is theoretically imperfect, even if it has never failed us in practice. The fact that without necessary causal laws we could in principle be mistaken, though we have no reason to think we ever will be, does not prove that there are necessary causal laws.

Substance and Action

Having completed his attempted proof of the causal principle, Kant turns his attention to the concept of action, which is derivative from that of cause. He says that he will not bother trying to analyze the concept, but instead will consider its use as an empirical criterion for substances. Although the schema of substance is permanence, we can determine something as being a substance “better and more easily through action” (A204/B249), presumably because action can be detected at any given moment. On the other hand, it may be hard to identify whether something is unchanging if I “search for the subject’s permanence by perceptions that I have compared” (A205/B251).

Philosophers such as Leibniz had said that action and substance are necessarily connected, but Kant asks how it can be shown that action is characteristic of what is permanent. The problem is insoluble if one is confined only to analyzing concepts, since neither the concept of permanence nor the concept of action contains the other. Kant’s argument connecting action and substance on his own account is basically that action indicates variation, and variation is only the change in the state of a substance, so that where there is action, there is substance.


The final topic of the Second Analogy is the way in which change occurs. Kant lays down the principle that “all change is possible only through a continuous action of the causality” (A208/B254). He regards the principle as obvious but feels constrained to prove it in light of the many failed principles of change that metaphysicians have advanced. The argument begins with the previous result that appearances are synthesized in time, and that in this synthesis, there is a progression in time. Kant then claims that as perceptions are produced through the progression, they go through all degrees of magnitude. Given this unsupported claim, he can connect change, which is only change in appearance, with the continuous degrees of magnitude of perceptions, which is described in the Anticipations of Perception (beginning at A166/B207).

The Third Analogy

The Third Analogy announces and defends the principle that “All substances, insofar as they can be perceived in space as simultaneous, are in thoroughgoing interaction” (A222/B257). This interaction is called in the second edition influence, which is the relation of substances wherein the one substance contains determinations whose basis is contained in the other substance (B257-8). In both editions, this influence is described as being causal, and what is determined by the causal relation is the position of a substance in time. Now only what is the cause of something else, or of its determinations, determines for that something its position in time (A212/B259). For the action to be thoroughgoing is for the relation of interaction to hold with respect to one another for all substances perceived to be simultaneous. (Note that in the Second Analogy, Kant had allowed for simultaneous causation (A202-3/B247-8).)

Kant may have had in mind the Newtonian view that all bodies exert gravitational force on all other bodies. But neither his statement of the principle nor its proof depends on any evidence from physics. If the principle is a priori, it is surprising that until Newton, the prevailing view was “mechanistic”: that bodies act only on those bodies with which they are in immediate contact. Leibniz had even claimed that substances do not interact at all.

The argument in both editions depends on a structural fact about the perception of simultaneous objects—that the order of perception of simultaneously existing objects is reversible. If it is reversible, I may first, at time t1 , see the earth and then, at time t2, the moon, or first see, at time t1, the moon and then, at time t2 , the earth (B257). (This reversibility does not hold for successive states of objects.) So the issue is whether the perceptions are reversible. But one can only have successive perceptions and cannot go back from t2 to t1, but can only move from t2 to t3, at which time a new perception arises, and the object may not be the same. So something else is required to establish simultaneity.

The argument in the second edition appears to fill a gap in the earlier argument, which is based on successive perceptions. Suppose one perceives two objects in a single act of perception. It would seem that at least at that moment, they co-exist at the same time. But the fact of their both being perceived at the same time is said not to be sufficient to establish their simultaneous existence, for this requires that the order of their perception be reversible, a fact that cannot be established in a glance. Because time cannot be perceived, from the fact that things are placed in the same time we cannot glean that their perceptions can follow one another reciprocally (B257). Again, something more is required to establish simultaneity.

The basis of the experience of simultaneity must be found in the objects themselves, since it is not to be found in perception: the reciprocal succession of the perceptions has its basis in the object (B257). It is what determines for that something its position in time (A212/B259). Now the only thing that is capable of determining any properties of a thing (here, position in time) is influence or causality. Now only what is the cause of something else, or of its determinations, determines for that something its position in time (A212/B259). The causality of the moon then determines the position in time of the earth, and the causality of the earth influences the position in time of the moon. In general, the position in time of any one thing is determined by the causality of all the things existing simultaneously with it. Therefore every substance (since it can be a consequence only in regard to its determinations) must contain within itself the causality of certain determinations in the other substance and simultaneously contain within itself the effects of the other substance’s causality . . . (A212/B259). So for simultaneity to be cognized in any possible experience, substances must stand in a relation of dynamical community (A212-3/B259).

The Analogies

The three principles, of substance, causality, and community, are the basis for the assembly of appearances, either as permanent, as successive, or as simultaneous. The three properties of the resultant objects of experience are temporal, and hence are not to be found in the pure categories of understanding, which are ways of thinking of objects as such, independently of human forms of intuition, including time.

The categories are themselves functions which bring unity to the synthesis of presentations in an intuition (A79/B104). As such, they are neutral with respect to the forms of intuition. It is only through the schema of a category that its unity be applied to objects of human experience. The three schemata of the categories of relation are the aforementioned permanence, succession, and simultaneity.

The principles for assembling appearances as permanent, successive, and simultaneous, therefore, are not principles which would give unity to any objects of thought subject to the categories substance/inherence, causality/dependence, and community. Hence these principles will entitle us to assemble appearances only by an analogy with the logical and universal unity of concepts (A181/B224). It is only when the schemata have been joined to the category, or we put the schema alongside the category as a restricting condition of it that the principles can be generated and proved (A181/B224).

Although an example is not given, one is not hard to come by. The category causality/dependence unifies what exists in the sense that if one existence is posited, the existence of another must be posited. But this tells us nothing about succession of objects in time. It could be that what is later determines what is earlier, for example. Analogous to the broadly general unification brought about by the category is the more specific principle that if a certain state of a substance exists at a time, a determinate later state of the subject must follow.

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