ABSTRACT: In the neglected 'Amphiboly of the Concepts of Reflection,' Kant introduces a new transcendental activity, Transcendental Deliberation (Kemp Smith calls it 'Transcendental Reflection'). It aims to determine to which faculty a representation belongs and does so by examining the representation's relationships to other representations. This enterprise yields some powerful ideas. (1) Some of the relationships studied have great interest, numerical identity in particular. Indeed, seeing Kant discuss it here, one wonders why he did not include it in the Table of Categories. (2) Kant gives a solid argument for the necessity of a sensible element in representations, something not found elsewhere in the Transcendental Analytic.

In the neglected Amphiboly of the Concepts of Reflection, Kant introduces a new transcendental activity, Transcendental Deliberation (Kemp Smith calls it Transcendental Reflection). It aims to determine to which faculty a representation belongs and does so by examining the representation's relationships to other representations. This enterprise yields some powerful ideas. (1) Some of the relationships studied have great interest, numerical identity in particular. Indeed, seeing Kant discuss it here, one wonders why he did not include it in the Table of Categories. (2) Kant gives a solid argument for the necessity of a sensible element in representations, something not found elsewhere in the Transcendental Analytic.The Transcendental Analytic of Kant's Critique of Pure Reason ends with a little appendix on what Kant calls the Amphiboly of the Concepts of Reflection. As an appendix, the passage is more than a little curious. The point that Kant eventually gets around to defending, that we are aware only of appearances, not things as they are in themselves, is familiar, but the argument that Kant now gives for it is entirely new and so interesting that one wonders why Kant relegated it to an appendix.

Second, the passage introduces an important new concept, namely, numerical identity. For the first time in the Critique so far, Kant treats the notion separately and gives it important work to do. The Table of Categories does not so much as mention numerical identity, even though the concept would seem to be at least as good a candidate for categorial status as, say, modality.

Third, the passage argues for the claim that knowledge requires sensible intuitions as well as concepts. Prior to the Amphiboly Kant has of course asserted this many times — but try to find an argument! Here he offers one.

1. What is an Amphiboly?

Kant tells us that both Leibniz and Locke commit an amphiboly of concepts of reflection, though in roughly opposite ways. What is an amphiboly? An amphiboly, Kant tells us, is "a confounding of an object of pure understanding with appearance" (A270=B326). This confounding can happen in two ways. One way is to take something delivered by the senses to be an object solely of the understanding. This is the route that Leibniz took. The other is to take something that we gain nonsensibly (a priori) to be delivered by the senses. This is the route that Locke took.

"In a word, Leibniz intellectualized appearances, just as Locke... sensualised all concepts of the understanding, i.e., interpreted them as nothing more than empirical or abstracted concepts ... ." [A271=B327, italics in original]

For Kant, any amphiboly is a serious mistake, but Leibniz' is more serious than Locke's. On Leibniz' view, all representation is taken to consist in conceptual judgment, acts of the understanding. Were this right, sensible experience would have no essential role to play in determining which beliefs are true and which are false; this Kant could not allow. Moreover, were Leibniz right, we would, or at least could, be aware of things as they are in themselves; the objects of which we would be aware would be objects purely of the understanding, thus internal to us, thus accessible to us. Locke's amphiboly makes out that everything in knowledge comes from the senses. This psychologizes knowledge, that is to say, makes the necessity and universality required for mathematics or physics impossible, but is a less serious error than Leibniz'. Leibniz is clearly Kant's main target. Indeed, Locke hardly appears again.

2. The work of Transcendental Deliberation

Kant begins the appendix by introducing a new form of transcendental thought, Transcendental Deliberation (hereafter TD). TD, he tells us in the very first paragraph, is "the consciousness of the relationship of representations to our different sources of knowledge" (A260=B316). The different sources of knowledge in question are sensibility and understanding, and the task for TD is to determine whether a given representation requires one or the other or both.

Kant's refutations of Leibniz and Locke fall out of this account: Leibniz mistook representations for which we require sensibility to be representations requiring only understanding. Locke, on the other hand, mistook representations requiring acts of understanding for representations derived solely from sensibility. These general claims may sound less than fascinating, but Kant's arguments for them are full of interesting ideas.

Kant says that four kinds of relationships among represented objects are relevant — identity (1) and difference, agreement and opposition, inner and outer, and matter and form. Though he never says it in so many words, these four pairs are presumably the concepts of reflection. For reasons of time, we will restrict ourselves to identity and difference and agreement and opposition (a fuller treatment of these four pairs of concepts is available on request).

3. Identity and Difference

Relations of identity and difference concern the conditions under which a plurality of representations is representing one and the same object, that is, the conditions under which there is identity of object across representations. The kind of identity in question is numerical identity, being one and the same thing (numerica identitas) (A263=B319). This concept of numerical identity is the single most important concept introduced in the Appendix.

Kant proceeds by way of an attack on Leibniz' principle of the identity of indiscernibles. Contrary to Leibniz's principle, Kant urges, the objects of two representations can be entirely indiscernible, that is to say, qualitatively indistinguishable, yet be different objects. He then introduces the famous example of the drops of rain: two drops of rain can be indiscernible — have all the same properties — yet be different drops. How so? Because they have different locations. This argument requires that location not be a property of the drops but that is something that Kant believed; we supply location when we synthesize a representation of an object. Even if Kant were wrong about this, however, he would have been right to urge that spatial location is not a property that the understanding could supply. We have to use the senses to become aware of it. If so, the drops of rain are indiscernible to the understanding but are still numerically different; and the only way to become aware of this difference is by recourse to sensible intuition. Leibniz has committed the amphiboly of confusing concepts, conceptual objects and the relationships we find among such objects with objects of the senses and the relations we find there. (The question of what exact difference between understanding and sensibility Kant is appealing to is interesting but we do not have time to go into it.Kant's remarks about numerical identity here mark the first time in the whole of the Analytic that Kant has recognized numerical identity as a concept of any importance. He has used the concept before, of course. It underlies the synthesis of recognition, for example, and he even used the word 'identity' once in that context (A115). Then there is the numerical identity of consciousness (A108 and A113 for example). He also speaks of the notion of a unit, a quantity of one, in connection with the synthesis of apprehension (B162, for example) and of the "successive apprehension of an object" (A145=B184) in the Schematism section. Likewise, he talks of persistence through change in the first Analogy and he lays out some conditions of apprehending an object in the second (A198=B243). Yet nowhere does Kant take any explicit notice that it is the concept of numerical identity that is at work in these passages. All this is more than a little peculiar — what could be more basic to representation of objects than individuation and reidentification? One would think that the concept of identity would be front and centre.

Even in the Appendix, Kant's treatment of identity is peculiar. Having demonstrated the importance of individuation and reidentification, what does he do? He drops the subject! In particular, he says nothing about how we can do the work of individuation and reidentification.

Numerical identity would seem to have been a strong candidate for inclusion in the Table of Categories. What was Kant's attitude? The question must have worried him because he suddenly turns to it in the middle of a discussion of a different point in the Note to the Appendix and flatly denies that the concepts of reflection are categories — as of course he must. Identity and difference and the other concepts of reflection, he tells us,

are distinguished from the categories by the fact that they do not present the object according to what constitutes its concept (quality, reality), but only serve to describe ... comparison of the representations, which is prior to the concepts of things. [A269=B325]

Kant seems to be suggesting that we apply the concept of identity and the other concepts of reflection prior to application of the categories, prior to the representation of objects. This is a strange claim.

Whatever may be true of the other concepts of reflection, as a claim about numerical identity what Kant says here would seem to fly directly in the face of what he said about synthesis of recognition in a concept earlier. There he urged that retaining and reidentifying earlier represented contents is part of recognizing them as an object in concepts. It is hard to see Kant's move here as much more than a stab in the dark. An unjustly neglected concept has suddenly presented itself and Kant tries to dismiss the threat.

There are a number of ways in which one might think to try and rescue Kant from the charge that he should have included identity in the Table of Categories. Unfortunately, none of them works very well.

1. 'Perhaps Kant saw the concept of identity as already built into the concept of quantity.'

That won't work; the concept of being one of something of a particular kind at and over time goes far beyond the notion of simply being a unit.

2. 'Perhaps numerical identity is supposed to fall out of the schematized extension of the concept of number.'

This proposal seems plausible initially, but then why didn't Kant actually talk about identity in the Schematism section, or somewhere in the Principles at least? As we saw, he does talk about successive apprehensions of the same object in the Schematism, of persistence through change in the first Analogy, and of recognizing an object by its spatio/temporal and causal relations in the Second Analogy — but he never mentions numerical identity, not by name.

3. 'Perhaps Kant considered the concept of numerical identity to be a collective responsibility of some combination of the classes of categories.'

On this proposal, individuation would be done by using two or more of the four classes of categories, perhaps quantity (number and quantitative magnitude), quality (degree) and relations. This suggestion is interesting — the attack on the Amphiboly is indeed based on the ways judgments of qualitative identity are compatible with difference of number — but again Kant's failure even to mention identity and individuation in his discussion of the Categories is left unexplained. In short, it is not easy to think of a way to rescue Kant from the problem that identity poses for the completeness of the Table of Categories.

4. Agreement and Opposition

Let us turn now to agreement and opposition. We will treat it more briefly. Relations of agreement and opposition are supposed to be about the ways in which two or more objects of representation can be in opposition to one another. What Kant really has in mind here, however, is two different kinds of agreement and opposition. One of them is appropriate to conceptual representation, the other to sensible representation.

What is supposed to be possible on the conceptual side is none too clear, being enmeshed in Leibniz' principle that, as Kant puts it, "realities ... never logically conflict" (A273=B329). Fortunately, this problem is not fatal because kinds of opposition are possible on the sensible side that are perfectly clear and could not possibly have any purely conceptual analogue. Indeed, there are many different forms of such opposition. As examples Kant offers the way one force can counteract another and the way feelings of pain "counterbalance" feelings of pleasure (A265=B321; see Kant 1763, pp. 180-181). In short, sensible objects can oppose one another in ways very different from any of the ways in which objects such as numbers and concepts can be in opposition. Kant's point against Leibniz is that to experience conflicts of the former kind, we need sensible input. His point against Locke is that to experience the more conceptual kind of conflicts, we need also representations from the understanding. The amphiboly they commit is to think that one or the other can do the job alone.

5. Experience requires intuitions as well as concepts

Let us now apply the observations we have made about identity and difference and agreement and opposition to Kant's deeply held belief that to represent objects, we require sensible intuitions as well as concepts. Kant's treatment of this requirement is at least as peculiar as his treatment of identity. He articulates the requirement as early as the Introduction (A15=B29, A19=B33), indeed as early as the Preface in the B-edition (Bxxiii-iv), repeats it in the very first paragraphs of the Analytic of Concepts, and then asserts it over and over and over again through the Analytic. As he says, "without sensibility no objects would be given to us, ... thoughts without content are empty" (A51=B74). The trouble is, he never argues the point — not prior to the Appendix on the Amphiboly. He mounts an argument that we need concepts, of course, indeed very specific concepts, and he mounts an argument that we need the forms of intuition, that is, space and time. But he never mounts an argument that we need sensible intuitions, what he calls the matter of knowledge (A86=B118; A166=B207; A267=B323).

Kant does argue the point in other works, the discussion of incongruent counterparts being one example. But the closest we find to an argument in the Analytic prior to the Appendix are two obscure anticipations of the Appendix in the sections immediately preceding it. (The sections are the General Note to the Principles, which was added in the B-edition [B288], and the chapter on Phenomena and Noumena [A240=B299].) One might think that the argument that to have more than analytic truths, to know anything synthetic, we need, in addition to the two linked terms, some third element connecting them is a counter-example but it is not (B15-16; A89=B121; A151=B196). It does not argue that this third element has be sensible (Interestingly, Kant repeats this argument on the very last page before the Appendix begins [A259=B315].)

Most commentators focus on the drops of water argument. As an argument for the necessity of a sensible component in empirical representation, many have thought that it is decisive. In fact, it is not. All it claims is that spatial location plays a role in some judgments of identity. But spatial location is purely formal, something derived from the forms of intuition. If so, the drops of water example is no argument that we need the particular, contingent contents of sensible intuition. Fortunately, there is something better: the argument from agreement and opposition. Without particular sensible intuitions, Kant argues here, we could not represent opposition of forces, the opposition of pain and pleasure, etc., to ourselves. These observations seem to be decisive. One only wonders why did Kant not introduce them when he first made his claims about sensible intuitions much earlier.

To summarize, in this short paper we have attempted to lay out the structure of Kant's argument that Leibniz and Locke both commit an amphiboly of concepts of reflection, and we have tried to bring out some of the very great interest that argument has (even if Kant himself was not aware of it). In particular, Kant's attack on the amphiboly explicitly discusses the concept of numerical identity for the first time in the whole Analytic of the Critique of Pure Reason and it contains the first real arguments to be found in the Critique for Kant's claim that to represent objects we require sensible intuitions as well as concepts.


(1) There is a translation question here. Kant's word is 'Einerleiheit'. Kemp Smith translates it 'identity', Pluhar 'sameness'. Strictly speaking, Pluhar probably made the better choice. Since, however, Kant clearly has numerical identity in mind-four lines down he actually speaks of numerica identitas (A263=B319)-we will follow Kemp Smith.

(2) We owe the observation about how directly the concept of numerical identity is at work in the first Analogy to William Harper.

Some may want to suggest that the gap we identify is filled by the Schematism, in which the categorial concepts are interpreted temporally, and in particular by the concept of substance. About this we have two comments. First, we have just cited all the references, direct or by inference, to numerical identity in the Analytic of Principles. The only one from the Schematism is the one about "successive apprehension". Second, the concept of substance is more like what we would now call a stuff concept than a sortal concept. On this topic and others, we have benefited from discussions with Dr. Hilmar Lorenz.

(3) We owe the question of how much Kant's argument for sensible intuition actually proves to Lorne Falkenstein.


Brook, A. 1994. Kant and the Mind. New York: Cambridge University Press.

Kant, I. 1763. 'Attempt to Introduce the Concept of Negative Magnitudes into Philosophy'. In Walford, D. ed. Immanuel Kant: Theoretical Philosophy, 1755-1770. Cambridge: Cambridge University Press, pp. 203-241.

Kant, I. 1781/87. Critique of Pure Reason. Trans. Norman Kemp Smith as Immanuel Kant's Critique of Pure Reason. London: Macmillan Co. Ltd., 1963.