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Critique of Pure Reason

Lecture Notes: Possibility, Existence, Necessity

G. J. Mattey

The final set of principles of pure understanding applies to experience the modal categories, possibility/impossibility, existence/non-existence, necessity/contingency. Kant calls these principles “The Postulates of Empirical Thought As Such.” The treatment of the Postulates differs from that of the other three sets of principles, in that no proof is given for them. Instead, there is an “elucidation.” In the middle of the elucidation of the postulate of actuality, there is interposed in the B edition a section entitled “Refutation of Idealism.” This section interrupts the flow of the elucidations and will be treated separately in the next lecture.

In the concluding paragraphs of the elucidation, Kant explains his use of the term “postulates” to describe his principles of modality. He uses it, he tells us, in accordance with the practice of mathematicians. A postulate in Euclidean geometry is an assumption about what kinds of geometrical objects can be constructed. It does not, however, make any substantive claim about the nature of those objects. Similarly, the postulates of empirical thought say nothing about the nature of the objects of appearances, but only “indicate the way in which the concept is connected with the cognitive power as such” (A234-5/B287).

Although modality had been a topic in metaphysics since the time of Aristotle, it gained new prominence at the hands of Leibniz, who made modality the centerpiece of his metaphysical system. It was no less important in the subsequent metaphysical system of Christian Wolff. As will be seen, Kant undertook in the Postulates to re-fashion the prevailing treatment of modality.

The Modes of Modality

Although Kant classified “existence/non-existence” (Dasein/Nichtsein) as modal categories, today only possibility/impossibility and necessity/contingency are called “modal.” Existence and non-existence are now taken to be non-modal. (However, some current logics of modality recognize actuality in a sense similar to that of Kant’s existence. This must not be confused with the category of reality.) Kant’s account of modality was non-standard in his time. There were three different accounts of the other pairs of modalities in German metaphysics before Kant. Modalities were taken as ways in which:

Propositions were classified as being necessarily true, possibly true, contingently true, or necessarily false (in which case their truth is impossible). For example, Leibniz states that “the truths of reasoning are necessary and their opposite is impossible” (Monadology §33). He distinguishes truths of reasoning from truths of fact, which are contingent truths (Monadology §36.) Contemporary propositional modal logic provides a formal way of representing propositional modalities. For example, if ‘p’ represents a proposition, ‘◊p’ represents the possible truth of p.

In the literature of early modern philosophy, it was common to claim that one object, namely God, exists necessarily, while everything that can exist does so either contingently or merely possibly. God, the being said to exist necessarily, is described through some property, such as being perfect (Descartes) or most real (Kant). For example, in the Replies to the First Objections to the Meditations, Descartes wrote, “It must be noted that possible existence is contained in the concept or idea of everything that we clearly and distinctly understand; but in no case is necessary existence so contained, except in the case of the idea of God” (Adam and Tannery, VII, 116). And Leibniz maintained that, “God alone, (or the necessary being) has this privilege, that he must exist if he is possible” (Monadology §45). We nowadays represent the existence of an object x with an existential quantifier ‘(∃x).’ Where φ is a description of a kind of object, the existence of a φ-object can be represented as: ‘(∃x)φx.’ That a φ-object possibly exists is represented as ‘◊(∃x)φx’ and that it necessarily exists as ‘□(∃x)φx.’

The question of the way in which an object has its properties was most strongly tied to the issue of free will, both of humans and of God. Leibniz called it “the question of the possibility of things that do not happen” (Theodicy, §169). If a human being acts in a certain way, and the “not-happening” of this action is impossible, then it would seem that the act (or the agent) is not free with respect to this action. Similarly, if it is impossible that God not act as God does (for example, for the reason that the act brings about the best consequences), perhaps God is not free either. The possibility of a different state of an object from the state φ that the object is actually in can be represented in modern notation as (with ‘∧’ for ‘and’ and ‘∼’ for ‘not,’): ‘(∃x)(φx∧◊∼φx).’

Kant’s treatment of modality in the Postulates concerns the application of the modal categories to objects. Thus, his discussion is limited to the second and third kinds of modality. One of his main innovations was to claim that while possibility/impossibility applies to kinds of objects, necessity applies only to the properties (or more properly, states) of objects. This way of treating modality will be described in what follows. But before we turn to Kant’s own views about modality, the stage will be set through a brief examination of the views of modality put forward by Leibniz and Wolff.

Modality in Leibniz

Much of Leibniz’s work on modality was not published and therefore was unknown to Kant. (But he could have had access to the “Mondadology” and the Theodicy, so quotations from Leibniz will be limited to those works.) According to Leibniz, possibility regarding the existence of object of kind φ depends on the concept of the object as being φ. The fundamental principle governing the possibility of objects of kind φ is the principle of contradiction. An object of kind φ is impossible if the concept of its being φ is self-contradictory, and an object of kind φ is possible if the concept of its being φ is self-consistent. Thus, in Kant’s terminology, all judgments of the possibility of an object of a given kind φ should be analytic, being based purely on the explication of the concept of its being φ.

A problem with the application of this view of possibility is that it can be difficult to detect whether a given concept refers to a possible object. This difficulty is especially urgent with respect to the concept of God, which involves infinity and therefore might conceal some inconsistency that cannot be detected by a finite mind. On the other hand, there is no difficulty in confirming the possibility of an object if it is known to be actual, since nothing actual is impossible (or, equivalently, whatever is actual is possible: in the language of the scholastics, ab esse ad posse).

Leibniz distinguished between two sorts of possibility. Absolute possibility is distinct from another kind of possibility, which is relative or hypothetical. An absolute possibility is one whose concept contains no contradiction. For example, there may be no contradiction in the concept of myself as a being which sprouts wings and flies, and so, this state is absolutely possible. On the other hand, this state is not possible on the hypothesis that the laws of nature are what they are. Although there is no contradiction in the concept of my sprouting wings and flying, there is a contradiction in the larger concept of the world of which I am a part if added to it is a state of myself soaring through the air on wings.

Leibniz recognized that possibility is the “dual” of necessity. A necessary object would be one whose non-existence is impossible. And a possible object is one whose non-existence is not necessary. Since possibility is understood purely conceptually, necessity must be so understood as well. Leibniz also accepted the principle that necessity implies possibility. So, he held that a necessary object is a possible object, the thought of whose non-existence is contradictory. He claimed that God is such an object. (Though, as we have just seen, it is not trivial to prove that a being with the properties of God is possible, since such a being would be infinite.)

The distinction between absolute and hypothetical possibility carries over to necessity. God is the only absolutely necessary object, since there is a contradiction in the concept of a non-existing God. Other objects are hypothetically necessary. This means that their non-existence is inconsistent with a given condition. The condition invoked by Leibniz was that God has decreed the existence of a world containing a given object. Under that condition, the non-existence of an object is impossible.

Although the definitions of possibility and necessity of existence dictate under what conditions an object conforming to a concept is possible and under what conditions it is necessary, they are silent about contingent existence, that is, existence that is possible but not necessary. Contingent existence cannot be determined through concepts alone.

A further principle is needed to determine which objects exist contingently. This is the principle of sufficient reason (or of sufficient “basis,” as Pluhar translates the German Grund). What exists contingently does so because something else exists which is sufficient for the existence of the contingent object. To avoid an infinite regress of bases for existence, Leibniz claimed, there has to be an absolutely necessary object, which for him is God (Monadology, §§37-38). So God is the basis for the existence of all contingent objects.

Leibniz tries to explain how the existence of contingent objects has its basis in God. As a perfect knower and a perfectly benevolent being, God creates a world that is the best among all those that are possible. This possible world, and the objects populating it, have a kind of reality in God’s mind as mere possibilities antecedently to their creation, but they attain existence upon being created.

As far as the necessity of the states of objects is concerned, Leibniz gave the same account. States of created beings are contingent on God’s decrees to create the beings themselves, but they are necessary given that God has made the decree.

It may be said in a certain sense that it is necessary that the blessed should not sin; that the devils and the damned should sin; that God himself should choose the best; that man should follow the course which after all attracts him most. But this necessity is not opposed to contingency; it is not of the kind called logical, geometrical or metaphysical, whose opposite implies a contradiction. (Theodicy §282)
Thus, the necessity of both the existence of things of a certain kind, and the states that kind of thing has, are not absolutely necessary but are only hypothetically necessary. The claim that they are not absolutely necessary allows Leibniz to conclude both that God is free not create the objects God did create, and that human beings are able to act freely, in the sense that there is no contradiction in the concept of them as not acting as they actually do act.

Modality in Wolff

For the most part, Wolff and his follower Baumgarten stuck with the Leibnizian conceptual account of possible and necessary existence. But Wolff added a new wrinkle by trying to give further content to the concept of existence. He referred to existence as the “complement” or “fulfillment” of possibility. (The Latin word Wolff and Baumgarten use is ‘complementum’ (Wolff, Ontologia, §174, Baumgarten, Metaphysica, §55). The corresponding German word is ‘Erfüllung’ (Wolff’s “Deutsche Metaphysik,” §14, Baumgarten’s German Metaphysik, §41). Thus, there is some further ingredient (some affections, or internal determinations) that the concept of a merely possible being lacks, and whose addition would transform possible existence into real existence. For Leibniz, the concept of a possible object is complete: it contains all the affections of the object. There is no difference between essential affections and contingent affections for Leibniz. This view presented a number of problems for him which do not arise for Wolff. (See Leibniz’s correspondence with Arnauld for some of these problems.)

As with Leibniz, the principle of sufficient basis is the principle of existence. What distinguishes Wolff from Leibniz is that the basis adds something that is not found in the concept of the object as a mere possibility. (This intrinsic possibility was called by Baumgarten the “non ens privitivum,” Metaphysica, §41, Metaphysica, §54.) The merely possible object lacks a number of contingent affections; (or what the medieval philosophers called “accidents”) which are acquired only when it is connected with existing objects.

Wolff’s idea is that each possibly existing thing is not fully determined with respect to its properties. It has a set of internal properties which make it the kind of thing it is, but this set of properties is not complete. It becomes complete only when it is connected with other objects and hence takes on what we now call relational properties. Wolff’s example is the existence of a tree. The tree exists only when what is in its seed is “completed” through the relation of the seed with other things (Ontologia, §175). When the essence (the suite of intrinsic properties) gets “filled up,” so to speak, the merely possible object becomes actual.

Modality in Kant

The modal categories possibility/impossibility, existence/non-existence, necessity/contingency, are derived from the problematic, assertoric, and apodeictic forms of judgment, respectively. These forms add nothing to the content of the judgment, but rather generate what we would now call “propositional attitudes” toward the judgment’s content. They represent degrees of certainty in the “holding-to-be-true” (fürwahrhalten) of the proposition the judgment expresses. In the problematic judgment, the truth of the proposition is not asserted but merely taken as possible. In the assertoric judgment it is asserted, and in the apodeictic judgment, it is asserted as being necessarily the case (A74-6/B100-1).

While the content of a modal judgment is a proposition that may be taken as true in various ways, the content of a modal concept is the objects to which the proposition refers. So while the judgment-forms indicate “logical” possibility, truth (or “actuality”), and necessity, the modal categories would indicate the possibility, reality, and necessity of objects. The schemata of the modal categories are ways in which a thing can exist in time. The schema of possibility is “the harmony of the synthesis of different presentations with the conditions of time as such” (A144/B184). An example of such a harmony is the assignment of opposite properties of a thing to different times. Kant then describes the schema as “the determination of the presentation of a thing to some time” (A144/B184, deviating from the Pluhar translation). The schema of actuality is “existence within a determinate time,” and the schema of necessity is “the existence of an object at all time” (A145-6/B184).

The notions of existence at some time and existence at all times are fairly clear, but they seem to leave no alternative except existence at no time. Yet this cannot be the schema of possibility unless we are to admit that nothing possible is actual. The schema which Kant invokes relates not existence, but the presentation of a thing, to some time. In the case of actuality, an actual thing exists at a specific or determinate time. But in the case of possibility, it seems, the presentation is related to some time or other, without reference to a single determinate time.

Kant’s schemata are a version of the “Diodorian” interpretation of modality, which was first presented by the ancient logician Diodorus Cronos. In the modern period, it was advocated explicitly by Thomas Hobbes in his book Of Body. Diodorian modality is most appropriate for deterministic metaphysical systems. In such systems, whatever is possible will be at one time or another. Kant’s Second Analogy implies determinism for objects of experience, as he freely admitted in the Third Antinomy. (See, for example, A536/B564.)

This can be seen by noting that when the modal categories are applied to appearances, possibility is merely hypothetical. At issue is which objects are possible given the laws of nature that govern all appearances. The answer must be that the only objects that can exist under such a condition are those do exist at some time or other.

When Kant begins the elucidation of the principles of the modal categories, he implicitly rejects the Wollfian approach. Just as the modal judgment-forms add nothing to the content of the judgment to which they are attached, the modal concepts add nothing to the concepts to which they apply. “Through these categories no further determinations are thought in the object itself; rather, the question is only how the object (along with all its determinations) relates to understanding and its empirical use” (A219/B266). So the category of actuality cannot be the completion of possibility, since possibility is already complete.

Now as we have seen, Leibniz did not regard actuality as “filling up” the concept of a possible object, since the complete concept contains already everything about the object. But this point of agreement with Leibniz does not make Kant’s account Leibnzian. Kant will claim that actuality is ascribed to objects only insofar as they are given sensibly as appearances. Leibnzian modal categories, on the other hand, are supposed to apply to things in themselves and are not primarily about the relation of the objects to the human powers of cognition.


The principle of possibility is that, “What agrees (in terms of intuitions and concepts) with the formal conditions of experience is possible” (A218/B265). Kant’s elucidation makes it clear that the principle is concerned with the possibility of various kinds of objects, and not directly with the possibility of specific objects. His examples are such as “a figure enclosed by two straight lines,” which is impossible because it cannot be synthesized in space (A220-1/B268), and “a triangle,” which is possible because it does admit of a synthesis in space (A223-4/B271). The possibility here is hypothetical, insofar as it depends on the condition that space is the form of outer intuition.

Moreover, the principle is only of real use in determining the possibility of kinds of objects described using pure concepts. If the concepts are empirical, then the possibility of their objects can be established from the existence of the thing. “I leave aside everything whose possibility can be gleaned only from [the things’] actuality in experience, and here examine only the possibility of things through a priori concepts” (A223/B270-1). The possibilities Kant has in mind here are those of the kinds of spatio/temporal objects that would fall under the relational categories of substance, cause and community. For example the category of substance (applied to objects in time) holds of objects that are permanent. The principle of possibility postulates that permanent objects are possible.

On the other hand, the principle rules out the possibility of “a substance that would be present permanently in space but not occupying it (like that intermediate something between matter and thinking beings which some have wanted to introduce)” (A222/B270). Yet we can from the principle of possibility alone establish the possibility of “a thing that is permanent, so that whatever varies in it belongs merely to the thing’s state” (A221/B268). Although the concept of a thing that is not a substance is not self-contradictory, it is in conflict with the formal conditions of experience and thus is not possible in the sense of possibility that applies to objects of experience. “A concept comprising a synthesis is to be considered empty, and refers to no object, if this synthesis does not pertain to experience” (A220/B267).

The treatment of the principle of possibility fits more or less well with the description of the schema of possibility in terms of the harmony of the presentation of a thing to the conditions of time as such. The principle more broadly states that the possible is what agrees with “the formal conditions of experience,” which includes space and the categories. But all spatial presentations are in time, and categories apply to objects of experience only insofar as they are presented temporally.

The principle should also relate to the schema described as the determination of a presentation of a thing to some (apparently indeterminate) time. In the case of the triangle, it seems plausible that due to the imprecision of human perception, no real triangle has even be or ever will be synthesized by a human being, so it will exist at no time. Hume made a very strong case for this claim in Book II of the Treatise of Human Nature. Kant presumably would answer that even if a triangle exists at no determinate time, it can be presented as existing at some time or another, which is enough to make it possible.

A further question is raised by the example of a permanent being. According to the First Analogy, because our apprehension of appearances is always successive, we cannot determine from it alone whether states of objects of experience are simultaneous instead of being successive. The only way this can be determined is if something underlying in experience is there always—i.e., as something enduring and permanent of which all variation and simultaneity are only so many ways (modes of time) in which the permanent exists (A182/B225). Thus the permanent is necessary in the Diodorian sense. So agreeing with the category of substance is what makes permanent beings possible, actual, and indeed necessary. Perhaps what Kant had in mind was to be able to meet Leibniz’s demand that in order to prove the existence of something necessary, one must first establish that it is possible.

The apparent mismatch between the Postulates and and the second formulation of the schema of possibility seems to lie in the demands of the structure of the schematism, according to which the application of any category to appearances requires a time-determination. To meet this demand, Kant refers presentation to some time, which apparently is an ambiguously described time. If the way in which an object is conceptualized is consistent with the rules according to which an object can be synthesized, then the presentation refers to an indeterminate time or possible time. (Of course, one might wish to describe it as a possible time, but here one must take pains to avoid a circular account of possibility.)


The principle for the category of existence (Dasein) is stated in terms of actuality. So we shall assume that here the two notions are used equivalently (and are not equivalent to the qualitative category of reality or with the notion of existence used to define the schema of actuality). The principle is, “What coheres with the material conditions of experience (with sensation) is actual” (A218/B266). Kant elucidates this principle as follows: “The postulate for cognizing the actuality of things requires perception, and hence sensation of which we are conscious” (A225/B272). So an object which is perceived is actual, as is an unperceived object which is connected with a perceived object through causal laws. In a somewhat strained attempt to relate this principle to a priori cognition, Kant notes that this indirect confirmation of actuality is “comparatively a priori” (A225/B273; see Introduction, B2 for the difference with what is absolutely a priori).

The example Kant gives of an object falling under the category of existence is “a magnetic matter,” which is inferred from the behavior of iron filings. Although the human senses are too coarse ever to detect it, this matter would be perceived “if our senses were more delicate” (A225/B273). This claim appears to be going too far. There are many other possible explanations of the behavior of iron filings in the presence of a magnet (as modern science shows). The explanation in terms of a magnetic matter may show that such a thing is possible, but it falls short of showing that it is actual.


The principle of necessity is, “That whose coherence with the actual is determined according to universal conditions of experience is necessary” (A218/B266). This is in contrast to the pure (unschematized) category of necessity as that whose non-existence cannot be thought. Since this principle refers to the category of actuality or existence, it has application only to objects that are, or at least could be, perceived. Moreover, whatever is necessary can be determined to be so only in relation to given objects of perception.

Now it would seem, given the schema for necessity and the First Analogy, that the existence of substance is necessary, since, as an object of experience, substance is permanent, existing at all times. But Kant claims that “The existence whose necessity we can alone cognize is . . . not that of things (substances), but only of their state” (A227/B279). The reason is that only the relation of cause and effect is determined by applying universal conditions of experience to perceived objects. Necessity “does not hold for the existence of things as substances, because substances can never be regarded as empirical effects, or [i.e.] as something that occurs and arises” (A227/B280). This is indeed correct, given the Second and Third Analogies. So what we find is that the principle of necessity serves a purpose different from the motivation for the schema of necessity, which is that of existence at all time.

Derivative Principles

Kant cites four “transcendental” principles that can be derived from the principles for the various categories (A228-30/B280-2).

The first principle rules out the alleged possibility raised by Hume that events could arise in some random way without there being any determinate cause. The second principle rules out the unintelligibility of the occurrence of any event. The third principle states that all change is gradual, so that, for example, an object becomes warm by passing through a continuous series of ever-warmer states. The last rules out a void or vacuum, as it would have to be at least potentially (as with magnetic matter) the object of perception. But a void can never be perceived. The last two principles appear to be inconsistent with the results of modern science, which leads us to doubt Kant’s assumption that what is connected with perception must itself be at least in principle perceivable.

The Realm of Possibility

Kant applies his principles of modality to a question central to the metaphysics of Leibniz and Wolff. Is the realm of possible objects greater than the realm of actual objects, or in other words, are there non-existent possible objects? Leibniz and Wolff both thought there must be such objects in order to allow for human and divine freedom by making the existence of actual things contingent on God’s choice. The question of whether the possible outstrips the actual cannot, Kant maintained, be answered by appeal to the principles of possibility and actuality.

As Kant understood the question, it asks whether there are series of appearances other than appearances for human beings. For example, are there appearances for beings with “different forms of intuition (from space and time) and likewise different forms of understanding (from the discursive form of thought or of cognition through concepts)” (A230/B283)? Whether such a series of appearances is possible cannot be decided by appeal to the postulate of possibility, which is restricted to the series of appearances for humans. One would need a principle which tells us whether such an object is possible “in every respect,” and we have no such principles at our disposal (A232/B284). An object would be possible in every respect just in case it is possible given any condition. But the only conditions for possibility we have are the forms of intuition and judgment. (For further discussion, see the Transcendental Dialectic, A324-5/B380-2.)

General Comment on the System of Principles

Chapter II of the Analytic of Principles ends with two observations, added in the second edition, about the system of principles which has now been concluded. The first is the familiar claim that none of the principles could be generated through mere concepts, but intuitions must always be taken into account.

The second comment is that not only must intuition be taken into account, but specifically that the relevant intuition is spatial. (Compare these two comments with the structure of the B deduction, where the argument of §20 concerns objects of intuition in general, and the argument of §26 concerns objects as given to human intuition.) Here Kant elevates space to a higher status than he gave it in the first edition. Only time is the form of all intuition, inner and outer. But space is required for the applicability of the dynamical principles of understanding. We need an intuition of space to present substance as permanent. Moreover, an intuition of space is needed to comprehend causality, since we can never present one event as occurring before another without reference to a permanent. And we cannot understand how substances can stand in a connected community unless we present them as simultaneous, which can only be done through the intuition of space.

One consequence of this view is that we cannot properly comprehend ourselves as objects in time alone without reference to space. A second is that it helps confirm the Refutation of Idealism (B293). We have delayed our discussion of that piece of the postulate of actuality added in the second edition. In the next lecture, we shall consider it in detail.

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