Previous Lecture

Critique of Pure Reason

Lecture Notes: Metaphysical Deduction

G. J. Mattey

Having completed our study of Transcendental Aesthetic, the doctrine of sensibility and its intuitions, we now turn to Part II of the Doctrine of the Elements, Transcendental Logic, the doctrine of the understanding and its concepts. This part makes up the bulk of the book. In this lecture, we will examine the Introduction, “Idea of a Transcendental Logic” and Chapter I of the Analytic of Concepts, “On the Guide for the Discovery of All Pure Concepts of Understanding.” The latter chapter is known in the literature as the “Metaphysical Deduction.” This title comes from a reference Kant made in the second edition Transcendental Deduction. “In the metaphysical deduction we established the a priori origin of the categories as such through their complete concurrence with the universal logical functions of thought” (§26, B159).

General Logic

Logic was understood by Kant as the study of the rules according to which the understanding thinks. Some of these rules are derived from experience, and they would have no place in logic today. Others cannot be derived from experience and are not based on the psychological study of the way the understanding actually operates. Rather, they are to be sought in the nature of the understanding itself. Still, because in it the ultimate basis of logic is mental, Kant’s approach would be rejected by most contemporary logicians. They regard logic as the study of logical truths, certain forms of valid inference, etc., which are taken to be independent of all thought. (What is regarded as “psycholgistic” has been mostly excluded from logic since Frege.)

Kant begins his discussion of the understanding by making a number of distinctions between types of logic. The first is between general and special logic. General logic “contains the absolutely necessary rules of thought without which the understanding cannot be used at all” (A52/B76), while special logic “contains the rules for thinking correctly about a certain kind of objects” (A52/B76). Some examples of special logic taken from contemporary philosophy might be quantum logic (restricted to the peculiar realm of quantum mechanics) and deontic logic (restricted to the concepts of obligation and permission). Special logic is an “organon” of the specific “science” to which it applies, according to Kant. This means that it contains substantive principles of that science.

The next distinction is that between applied and pure general logic. Applied logic is overtly psychological. It “deals with attention; attention’s being impeded and the consequences thereof; the origin of error; the states of doubt, of having scruples, of conviction, etc.” (A54/B78-9). Pure general logic, on the other hand, presents rules for the formal employment of the understanding (it is a “canon” for the understanding). It is pure because its source is not to be found in experience, as is the source of applied general logic. “Pure general logic is demonstrated doctrine, and everything in it must be completely a priori” (A54/B78).

Transcendental Logic

The final distinction is between general logic and “transcendental logic.” Whereas general logic is not concerned with the origin of our cognitions, treating all of them alike, transcendental logic would contain rules for the use of a priori cognitions. The Aesthetic had already established that there are a priori intuitions, and this suggests that there may be a priori concepts or thoughts of objects. A logic governing such concepts could be called “transcendental” because it would deal only with a priori concepts and not with empirical concepts. Because it discriminates between the types of cognitions it treats, it is a form of special logic rather than general logic.

A second feature of transcendental logic that distinguishes it from general logic is that it “would also deal with the origin of our cognition of objects” (A55-6/B80). This seems to be a departure from Kant’s basic conception of logic, since the question of how our cognitions arise seems to be independent of the rules which govern their use. But as will be seen, Kant does not keep these two issues separate. This is one of the hallmarks of his philosophy, for better or for worse.

Kant adds here a note (which “must be remembered carefully”) about the proper use of the expression ‘transcendental’ as modifying ‘cognition.’ Only some a priori cognitions are transcendental. In effect these are meta-cognitions, cognitions whose objects are themselves cognitions. So, if we present a cognition as being a priori in origin, our presentation of this cognition is a transcendental presentation. Regarding space and its geometric determinations, “we may call transcendental only the cognition that these presentations are not at all of empirical origin, and the possibility whereby they can nonetheless refer a priori to objects of experience” (A57/B81). Thus, the use of the term ‘transcendental’ does not concern the reference of cognitions of objects, but only “the critique of cognitions” (A57/B81).

Analytic and Dialectic

Both general and transcendental logic are divided by Kant into analytic and dialectic. The more modest analytic shows how a priori concepts and the principles associated with them provide a negative criterion of truth. Truth or falsehood of cognitions is the distinction between those cognitions to which an object agrees or corresponds, and those to which one does not. For example, a principle of general logic is that of contradiction, so that any concept which is self-contradictory is thereby “false,” in the sense that it does not apply to any object whatsoever. A principle of transcendental logic is that of causality, according to which no event occurs without being the consequence of a previous state of affairs and a law of nature. So a presentation of an uncaused event is “false,” because it conflicts with transcendental analytic.

Dialectic purports to give a positive criterion of truth. General logic in its dialectical use attempts to parlay its rules into an “organon,” a doctrine stating exactly which truths hold. Kant gives no examples of such a procedure, but he declares that it produces nothing but illusion, or “idle chatter.” Transcendental logic attempts to extend the principles of the understanding beyond experience, making judgments even “about objects that are not given, or indeed about objects that perhaps cannot be given in any way at all” (A63/B88). This “hyperphysical” employment of the understanding will be criticized in the second division of Transcendental Logic, the Transcendental Dialectic.

The task of transcendental analytic is the “dissection” of the faculty of the understanding into its elements. This complicated task is divided into two parts. The first, the Analytic of Concepts, is to show which pure concepts the understanding generates and to show by what right the understanding applies them to objects. The second, the Analytic of Principles, shows how specific principles which employ the pure concepts are justified. Kant laid out four “concerns” to be met in the Analytic: to show that the concepts are pure and not empirical, that they belong to the understanding, that they are fundamental, and that the system of such concepts be complete (A64/B89).

Analytic of Concepts

Philosophers before Kant pursued their investigation of pure concepts by beginning with whatever concepts lay at hand and trying to analyze or dissect them into their components. This is not Kant’s task. Instead, what he will try to dissect is “the power of understanding itself” (A65/B90). This dissection should turn up the pure concepts which Kant expected, given that he had already unearthed pure intuitions by dissecting the receptive faculty of sensibility.

Hence we shall trace the pure concepts all the way to their first seeds and predispositions in the human understanding, where these concepts lie prepared, until finally, on the occasion of experience, they are developed and are exhibited by that same understanding in their purity, freed from the empirical conditions attaching to them. (A66/B91)
The metaphysical deduction is the attempt to carry out the first task, that of discovering the origin of pure concepts in the human understanding. The rest of the analytic of concepts concerns the second, much more difficult, task.

The method which had been used by Wolff and his followers cannot do the job. They collected concepts haphazardly and then tried to place them into a systematic arrangement. Concepts got into the system because they had some use within the system or simply were traditionally included in metaphysics. For example, the concepts “one,” “true,” “perfect” are at one point introduced arbitrarily under the concept of “being.” That these concepts got “honorable mention” was due to their long-standing presence in scholastic philosophy (or so Kant claimed in §12, B113). Kant, on the other hand, claimed to be able to show how such concepts could be derived from his own list of pure concepts.

Kant claimed that the categories, the pure concepts of the understanding, must be generated in a systematic way, from a single principle. His reason for so insisting is that the understanding itself is a unity, so the system of its concepts must be unitary. (A65/B89-90, A67/B92). But this seems to be a flat-out non-sequitur. There is no reason to think that the product of something unitary must itself be unitary.

Many of Kant’s critics (most notably Norman Kemp Smith in his A Commentary to Kant’s “Critique of Pure Reason”) maintain that this kind of arguing is mere subterfuge, covering up Kant’s personal predilection for orderliness. In many cases, Kant’s views on a subject are summarily dismissed as due to his “passion for architectonic.” In the present case, though, Kant did have good reason to complain that the Wolffians and their predecessors had never provided the proper credentials for their pure concepts.

Empiricists could reply that they take whatever concepts they can get from experience. But rationalists like Wolff thought that these concepts are the product of pure reason. Kant thought that they at least owe us an explanation as to how pure reason generates these concepts, whether by one principle or by more than one.

Functions of the Understanding

The thread that connects pure concepts of the understanding together is the claim that unlike intuitions, which depend on our being affected, concepts “rest on functions” (A68/B93). The understanding is spontaneous, which is to say that it is active in the production of its cognition. Its activity in the use of concepts is to arrange “various presentations under one common presentation” (A68/B93). Kant calls the unity of that act of arranging a “function.”

How does the understanding use concepts? Only by judging by means of them. And judging is the very way in which presentations are unified. For example, I might bring my intuition of my body under the concept of divisibility, judging that my body is divisible. I present my body indirectly in the judgment, through the concept. This is the only way the understanding could present my body to me, since it is intuition which presents it directly, and the human understanding is not intuitive.

A more general judgment states that all bodies are divisible. Here we have two concepts combined in a judgment, and the predicate concept applies to my body only through the concept of body. This kind of consideration indicates that all judgments are “functions of unity among our presentations” (A69/B94). Judgments “draw many possible cognitions together into one.” Since judging is the only activity of the understanding, “we can find all the functions of the understanding if we can exhibit completely the functions of unity in judgment” (A69/B94). If concepts are also functions of the understanding, then it may be that in our exhibition of the functions of unity in judgments we can find the seeds of the suspected pure concepts of the understanding. This is the germ of the metaphysical deduction.


The first task in carrying out the project is to exhibit the whole list of functions of unity in judgments. This boils down to finding all the ways in which cognitions can be combined in a single judgment. Kant thought that all the logicians before him had hit upon most of the functions of judgment, but he again thought that their procedure was haphazard and lacked unity.

His own proposal was first to reduce the kinds of judgments to four headings. Under each heading are placed three “forms” of judgment. In this way, Kant generated what he thought was a complete list of the functions of judgment.

Table of Judgments

TypeLogical FormExample
Universal All A is BAll men are mortal.
Particular Some A is BSome men are learned.
Singular a is BCaius is mortal.
Affirmative A is BCaius is mortal.
Negative A is not BSome men are not learned.
Infinite A is a non-BSome men are non-learned.
Categorical A is B All men are mortal.
Hypothetical If A is B, then C is D If there is a perfect justice, then the obstinately wicked are punished.
Disjunctive a is A or B or C The world exists either through blind chance, or through inner necessity,
or through an external cause.
Problematic A may be BThe soul of man may be immortal.
Assertoric A is BThe soul of man is immortal.
Apodeictic A must be BThe soul of man must be immortal.

This list is perhaps not systematic enough for Kant. Ideally, he would proceed with a single form and generate a second pair by division, reaching his list of four types of judgment by a second division. But nothing remotely like this is going on. For example, Kant admits that the modality of a judgment contributes nothing to its content, as can be readily seen by the fact that three kinds of judgments with the same subject and predicate can have different modalities. But this does not hold for the other three types of judgment-forms, so the modal forms were not reached by division from more general types.

Another peculiarity of the modal judgment-forms is that Kant treats them epistemically, rather than the way one would expect modality to be treated in a general logic. To judge that the soul of man may be mortal is to express a shortfall of evidence for the truth of that judgment: this is why it is “problematic.” The distinction between a problematic and an assertoric judgment depends on the way it is “uttered” (A75/B101). Kant says that the problematic judgment expresses “logical possibility” but he explains this in epistemic terms: “it expresses a free choosing to let such a proposition stand—a mere electing to admit it into the understanding” (A75/B101). The apodeictic judgment similarly is supposed to express “logical necessity,” but in fact it only “thinks the assertoric one as determined by these laws of the understanding themselves, and hence thinks it as maintaining [this or that] a priori” (A76/B101).


With the table of judgments, in hand, Kant introduces a new notion that will lead him from judgment-forms to pure concepts of the understanding. We have seen that for Kant, the understanding is spontaneous and that it creates unity in judgments. The activity which creates the unity is what Kant calls “synthesis.”

By synthesis, in the most general sense of the term, I mean the act of putting various presentations with one another and of comprising their manifoldness in one cognition. (A77/B103).
The presentations whose manifoldness is “comprised” in an act of synthesis may be a priori (as with space and time) or empirical (perhaps as with sensations). Whatever their source, they must be given before synthesis must take place. The result of synthesis is a cognition. “Hence, if we want to make a judgment about the first origin of our cognition, then we must first draw our attention to synthesis” (A78/B103).

Synthesis is the product of the imagination, which itself is “a blind but indispensable function of the soul” that is necessary for cognition but of which we are rarely conscious (A78/B103). The contribution of the understanding is to bring “this synthesis to concepts” (A78/B103). Kant gives as an example of “bringing a synthesis to concepts” the act of counting. We successively add one number to another “according to a common basis of unity (such as the decimal system)” (A78/B104). If the basis of unity is a priori, then we have what Kant calls “pure synthesis.”

General logic operates with already-given concepts and brings presentations under them. For example, if I know that all A are B and that x is an A, I can bring x under the concept B. Kant proposes that transcendental logic is not at all concerned with this procedure. What is brought to (not under) concepts is “not presentations but the pure synthesis of presentations” (A78/B104).

Kant describes the process of pure synthesis as having three stages. For the first stage, a manifold must be given. Space and time provide us with a pure (non-empirical) manifold. The second stage is for the imagination to synthesize this manifold. This synthesized manifold is not yet cognition (presentation of an object). The third stage is for concepts of the understanding to provide unity to the pure synthesis. (This threefold process is described in detail in the first edition Transcendental Deduction, A98-A110.)

Now we are finally in a position to discover the origin of the pure concepts of the understanding. What gives unity to the synthesis of a manifold is the concept. So the concept is a function. Kant claims that this function which unifies intuition is the same function as that which unifies presentations in a judgment. The fact that a synthesis involving pure intuition and the imagination are involved means that “transcendental content” has been introduced into the presentations, which “is something general logic cannot accomplish” (A79/B105). Given that the functions that unify pure synthesis and the functions that unify presentations in a judgment are the same, we can generate a table of pure concepts (which Kant now calls “categories,” following Aristotle) from the table of judgments.

Table of Categories

TypePrinciple Using Category
Unity All aggregates are multitudes of previously given parts.
PluralityAll appearances are intuited as aggregates.
AllnessAll appearances can be cognized only through successive synthesis of part to part in apprehension.
Reality What in empirical intuition corresponds to sensation is reality.
NegationWhat in the empirical corresponds to the lack of sensation is nothing.
LimitationThe degree of magnitude in a reality contained in appearance can always be lessened.
Inherence and SubsistenceIn all variation in appearances, substance is permanent.
Causality and Dependence All changes occur according to the law of connection of cause and effect.
Community All substances, insofar as they can be perceived in space as simultaneous, are in thoroughgoing interaction.
Possibility and Impossibility What agrees with the formal conditions of experience is possible.
Existence and Non-ExistenceWhat coheres with the material conditions of experience exists.
Necessity and ContingencyThat whose coherence with the actual is determined according to universal conditions of experience is necessary.

The table of categories is said to be generated from a single principle, namely, the principle of the identity of the function of unifying synthesis and of judging. Kant notes that one could form a more extensive list by adding to each category its more specific “predicables.” Thus the concept of causality has as predicables force and action. The enumeration of the predicables and their associated principles is a task he leaves for later. Kant also declines to define the categories, which he claimed would distract the reader from the main task.

Interestingly, Kant thought that he could show how the table is organized according to division, something that he apparently failed to do for the table of judgments. Since concepts are directed ultimately at intuitions as their objects, we begin with intuition. The division is between categories of quantity and quality, on the one hand, and categories of relation and modality on the other. The first group, the mathematical categories, concerns objects of intuition and the second, dynamical categories, concerns the existence of these objects. (Nothing is said, though, of the second division.) The third category in each group is said to be generated by a combination of the first and the second. (This device presaged the “dialectical logic” of Hegel in the nineteenth century.)

The rest of the chapter deals with two special cases, the category of community and what are traditionally called the “transcendental” concepts “one,” “true” and “good,” mentioned above. As these are side-issues, they will not be treated further here.

[ Next Lecture | Philosophy 175 Home Page | Lexicon ]