Kant first begins his exposition of logic with a division of the definition of logic. Logic is divided into a General Logic and Special Logic. General logic is, for Kant, a discipline as certain as mathematics, whose contents were more or less established and completed by Aristotle, and whose modern iterations consist in nothing more than (sometimes illicit) embellishments. [KrV B VIII] This completeness and certainty of logic is entirely due to its limitation of its subject matter to the laws of thought alone, thus possessing a comparably narrow scope in comparison with any of the other sciences. Differences in the nature of the objects of thought produce differences in our ways of thinking about them, and this is how Special Logic arises. A special logic would consist, not in the complete articulation of the laws of thought as regards an object in general, but only those laws which are used in the thinking of a certain domain of objects. For example, there could be special logics of biology or of archaeology, which would detail the laws of thinking which pertain to life and history generally. Kant then proceeds to divide General Logic into Pure and Applied Logics. An applied logic would be a logic of the empirical conditions under which thought is exercised, and would be distinct from the laws of thinking an object in general. It would contain studies of doubt, conviction, memory, imagination, distraction and the influences of the senses on thinking, and so on.
Pure logic is distinct from applied and special logic because, unlike either of them, it is wholly universal and it is a priori. (1.) As a species of general logic, it abstracts from all differences in objects, and deals only with the form, and not the matter of thought. (2.) As a uniquely pure logic, it admits absolutely no empirical (psychological) principles, and everything contained in it must be certain a priori. Pure or formal logic, being concerned with the laws of thought common to all thinking independently of particular objects, must thus operate in ignorance of those laws governing specifically synthetic a priori thinking (judging). This is to say that pure logic is ignorant of, and incapable of addressing, the problem of the Kritik der reinen Vernunft.
Pure logic is further divided by Kant into an Elementarlehre and a Methodenlehre (a stoicheiology and a methodology). The Methodenlehre of pure logic is the practical or technical part of logic, and is an art rather than a proper science. Its topic is the distinctness, clarity, exactness and systematic arrangement of our thought; one could say it concerns the Aufbau rules for the architecture we construct in thought, while the Elementarlehre yields the materials first put to use in this architecture. The Elementarlehre, in contrast to the Methodenlehre, is the dogmatic or theoretical part of pure logic. The Elementarlehre is then divided into an Analytic and a Dialectic [Logik, Einleitung II 3]
The analytic of pure logic, straightforwardly enough, divides formal thinking into pure elements and displays these elements as the first principles put to use in the logical criticism of all knowledge. Since pure logic thinks in independence of any particular object, and since, (according to Kant) truth can only be a correspondence of thought with its object [KrV A58/B82, A58/B83; A157/B196; A191/B236; A237/B296], it follows that pure logic cannot make use of the principles it yields to carry out a criticism of the truth of our thinking, but must rather concern itself with mere formal validity of thought. Kant puts this another way by saying that pure logic supplies only the negative criterion, the sine qua non of truth. If this is the case, then logic is incapable of being used as an organon of thought (i.e., used to amplify our knowledge beyond what is given by the nature of the understanding, or the objects of alone), but must always be put to use for only the criticism of the validity of thought; i.e., as a canon used for the criticism of thought, setting the boundaries which thought may not with any right go beyond. A way of pointing out by way of example what was said above which somewhat pre-empts the following discussion, is to say that judgments which are formally self-contradictory can never be true of any object; but from this alone it does not follow that wholly coherent and systematically self-consistent judgments, on account of this self-consistency alone, could be known to apply to an object on this basis. These judgments, for all their coherence to one another, may yet have no object to which they correspond—and the criticisms of the validity of thought supplied by pure logic in its employment as the canon of all thinking in general, could never yield such an object: this must be first given in experience.
Kant then moves on to discuss the Dialectic of pure logic. Any use of logic to extend our knowledge is usage of logic as an organon; this application is always illegitimate (as was proven above) and is therefore called by Kant dialectical logic. The Dialectic of pure logic is therefore an analysis of illusion (an analysis not of Erscheinung but of mere Schein). These distinctions mirror prior, traditional distinctions, and have their origin in Aristotle’s separation of logic into analytics (Ἀναλυτικὰ) and topics (Τοπικά). It should be noted that for Aristotle the analytics separates thought into term, proposition and the figures of syllogism, and that this doctrine of analytics, while somewhat reflected in Kant’s doctrine, is still distinguished by Kant’s calling these parts concept, judgment and inference. On the other hand, Aristotle’s topics are a study of dialectical (rhetorical) syllogisms, and deal, therefore, with merely probable premises (and therefore the Topics are not properly to be entitled scientific). Kant probably got this distinction from Meier where it can be found here detailed exactly as explained above: “Die Vernunftlehre handelt entweder von einer völlig gewissen gelehrten Erkenntnis und dem Vortrage derselben, oder von der wahrscheinlichen gelehrten Erkenntnis und den Vortrage derselben (§1.). Jene ist die Vernunftlehre der ganz gewissen gelehrten Erkenntnis (analytica), und diese die Vernunftlehre der wahrscheinlichen gelehrten Erkenntnis (dialectica, logica probabilium). Wir handeln die erste Vernunftlehre ab.” [G.F. Meier, Auszug aus die Vernunftlehre, Einleitung §6]
In Kant’s analytic of the Elementarlehre of pure logic, three elements, and three corresponding faculties (sometimes subsumed under the general name of ‘the Understanding’) are elucidated. These are: Conceiving, Judgding, and Inferring, which correspond to the faculties of Understanding, Judgment, and Reason. [KrV A133n/B173n; A130-1/B169; cf. A75n/B100n] Kant believes that all the laws of pure logic are knowable completely a priori. [Logik, Einleitung I] This means not that such laws are totally independent of any experience whatsover, but only of any particular experience we might happen to have. Kant is not a Platonist when it comes to logic, and does not believe that the laws of logic are (temporally) before experience, as he makes abundantly clear about the nature of the a priori in general in the introduction to the Kritik: “Daß alle unsere Erkenntnis mit der Erfahrung anfange, daran ist gar kein Zweifel; denn wodurch sollte das Erkentnisvermögen sonst zur Ausübung erweckt werden, geschähe es nicht durch Gegenstände…” [KrV B1] We discover the laws of thought only by means of an observation of the natural usage of the understanding; it’s own acts of concept formation, judging and inferring. Logic, according to Kant, is a priori in that by abstracting from or ignoring all the particular differences which distinguish the objects of thought, its laws must thus therefore be universally applicable as well as necessary, no matter the nature or origin of the object which happens to be thought. When Kant is being cautious, he does not make the (absurd) claim that pure or formal logic thinks thought without an object; rather, he is arguing that logic ignores differences in objects. In the Aesthetic, the varying matter of sense was abstracted from, and this abstraction led to the discovery of the universal and necessary condition (form) of all sensible appearances. This condition, namely, space and time taken jointly, was taken to be necessary in a twofold sense not clearly separated by Kant in the Kritik. The condition of sensibility (space and time), was taken not only necessary as regards the very possibility of an appearing in general of a cognizable object in experience (external necessity), but also, as space and time, exhibited in themselves a kind of internal necessity such that they were understood as structurally self-coördinated in such a way as to be transparently knowable through and through; to be knowable a priori. This double necessity alone justifies their title as the forms of sensibility and not just another part of the matter or content of intuition as such. Kant believes, therefore, that by a similar act of abstracting from the alterable content of thought, another discovery is possible; this time of the universal and necessary forms of intelligibility. These forms of thought can only become transparent to us through our observation of the understanding in its natural application, but in independence from any particular (thinkable) content. Such laws as are provided by this process of observation have to be ‘necessary’ in just the same twofold way as the the forms of sensibility showed themselves to be in the Aesthetic, viz., (1) necessary in themselves, having internal necessity; and (2) necessary as conditions of all thinking, exhibiting external necessity.
We turn now to Kant’s doctrine of concepts. A concept is defined by Kant as a universal (or general) representation, rather than a singular representation (which would be an intuition). As an ‘allgemeiner Begriff‘, a concept contains what is common, ‘gemein‘, to many different objects. Conceiving always involves a unifying representation of a plurality of objects; intuiting by contrast always involves the immediate singular object of sense. Concepts have both form and matter. [Logik §5] The matter of a concept is the object(s) with which it deals in thinking, while the form of a concept is strictly its universality. Put another way, the matter of thought is what we think by means of concepts, while the form of thought is how we think. Kant’s usage in discussing the parts of thought is somewhat unfortunate, as he calls whatever is determined in thinking and conceiving the matter of the same. This is because, for Kant, thought has both a content and an object, and these must be kept entirely separate. This separation is due to the nature of truth, which is the correspondence of thought with, specifically, its object and therefore not its content. So, while Kant calls both of these the ‘matter’ of thought, they are distinct. For example the concept of a manticore surely has a determinate content, namely, ‘a creature with the head of a man, the body of a red lion, and the tail of a scorpion’, but being a completely a product of arbitrary fancy, has thus no corresponding object.
Kant defines a concept in Latin as a repraesentatio per notas communes; ‘eine Vorstellung durch gemeine Merkmale.’ [Logik §1] The content of concepts is composed of ‘Teilvorstellungen’ or ‘Partialvorstellungen’. All concepts, Kant argues, (with the obvious exception of those that are wholly simple) are made up of other concepts, ‘Teilbegriffe’. Kant wants to claim that the content of a concept is composed of ‘Partialvorstellungen’ because he believes that the content of our concepts must finally be contained in, or referred back to, individual representations (=intuitions). [Logik, Einleitung VIII; §7] Ultimately, since by their very nature concepts cannot possibly exhaust the multitude of our representations in their contents, every concept can at most be a Teilbegriff (a ‘part-concept’). [Logik §7] Likewise, all (complex) concepts are composed of ‘Merkmale’ (notas), that is to say, ‘marks’. From a certain standpoint, the matter of concepts is contained in intuitings of individual objects (Partialvorstellungen), and from another perspective this same matter is composed of Merkmale (marks, tokens, attributes) which serve as criteria such that the individual objects given in intuition are capable of being (re)cognized (erkannt). [Logik, Einleitung VIII] This division in the nature of the matter of concepts could be referred to as the internal and external usages of Merkmale. For example, our concept of the ‘yellowness’of gold is present as a partial representation in all our intuitings of the object ‘gold’ and also serves as the ‘token’ (Merkmal) whereby we re-identify ‘gold’ in experience. Understood as consisting in a unity of Partial- or Teilvorstellungen (‘partial representations’), the matter of every concept can be split into an Inhalt or an intentional content, that about which the concept as thinking is directed; and into an Umfang (Sphaera) or a denotational, extensive content, the individual things of which the concept serves as the criterion.
In sum of what has been said so far, the form of concepts is universality (generality), while the matter can be separated into the content and the object(s) of thought. The content itself is then divided into its composition from partial representaitons on the one hand, and ‘marks’ or ‘tokens’ on the other, which thus separate the content of the matter into an Inhalt (content proper) and Umfang (extent). This division of the content is Kant’s way of capturing what he thinks of as the intensive, as well as extensive referential capacities of concepts. Kant takes it that concepts are universal (according to their form) specifically because of their ability to be put to use in the (re)cognition of objects. But all this has gone beyond the exposition of a merely pure or formal logic, and shows that Kant’s theory of the form of concepts essentially depends on his account of the faculty of judgment. [KrV A69/B94]
We now continue on to the ways that various concepts are differentiated among themselves, with the note that these analyses only properly belong to the exposition of a transcendental, not pure logic. The matter of a concept may be given either a posteriori (empirical matter), that is, given to sense (e.g. the contents ‘shiny’, ‘bitter’, or ‘cold’) or, it may be given entirely a priori (pure matter) from the nature of the understanding as such; finally, the matter can be produced arbitrarily: these concepts are entitled factitious concepts. These varying types of concepts are explained by Kant as being separated by the epistemic status of their sources. In general, concepts (conceptual contents) are either given (conceptus dati) or made (conceptus factitii). Now, of given contents, these can be provided either from nature itself in experience, or from the nature of the understanding; the former of these kind of given concepts are called Erfahrungsbegriffe, concepts of experience, the latter intellectual concepts or Notionen. Factitious concepts are arbitrary products of imagination, and have their origin in a subjective combination of elements by an individual mind; e.g. the concept of a substance existing in space which yet does not occupy any space. Even in the case of some given concepts, which, upon examination empirical, there may nevertheless contain Merkmale which are given a priori. For example, the concept of ‘body’ is in the last analysis empirical; yet, this concept presupposes a priori the concept of substance. IT is to be noted that one sort of factitious concept Kant acknowledges can be completely a priori: mathematical concepts. [A729/B757; Logik §102] The intentional objects which from the content of mathematical concepts consist in arbitrarily delimited homogeneous spaces (or quanta). By containing (or entailing) absolutely no sensible matter, these concepts deal, in the strict sense, with the forms of objects in general, rather than proper objects. [Logik §§4-5; A727/B755ff] All of the above distinctions between given and factitious concepts concern only how the matter of concepts differentiates them according to their epistemic origins. We have seen how, for Kant, even in the case of an entirely factitious concept, the matter, or more properly the elements of which the matter is composed, is never made. In the most arbitrary example of a concept, what is at most present in its matter that is attributable to us is merely the special combination of those particular elements. By implication, then, in the case of given concepts, not even the combination of the elements present in their matter involves any active contribution on the part of the subject.
From this discussion of the fixed matters of given concepts, we now turn to the way concepts are distinguished according to their form. As it turns out, Kant believes that all concepts share a common form, i.e., universality, which he believes is always made and never given. [Logik §4] For a concept to be a concep, a universal (general) representation, entails its use as a criterion or discriminating characteristic of an object capable of being given in a possible intuition. When Kant connects the facticity of concepts with their discursivity (that is, with their general application to a plurality of objects and so mediateness) what he is saying amounts to the following: to be a discursive representation is to be employed in the (re)identification and so (re)cognition of objects in experience. Thus all thinking (which is to say all judging) is essentially discursive in nature. [A19/B33] But all of the above mentioned doctrine of distinguishing concepts according to their origins is something with which pure logic, by its very nature, excludes from consideration. Pure logic is not concerned with discrepancies in the multitudinous ways that concepts come to be in our understanding; it thinks only the pure laws according to which all thought as a rule must conform, and these alone.
In review, Kant’s assertion that the form of concepts as such is universality is based on the way concepts can refer (must refer) to a plurality of objects. [Logik §5] As regards the form of concepts, they are produced by the three logical acts of the understanding: comparison, reflection, and abstraction. [Logik §6] Kant gives an example of an ordinary person observing a spruce, a lime and a willow. She first compares them, and observes that they differ from one another as regards their trunk, branches and leaves. Then she reflects on those things that they possess in common, namely, a trunk, branches, and leaves. Finally, she abstracts from all those traits with which she was first occupied in comparison, and obtains the idea of a ‘tree’. In this account of what underlies or is necessarily involved in every act of conceiving, to conceive is to think abstractly of a common element discovered among the various objects of experience. For Kant, the acts of comparison, reflection and abstraction serve as the conditions of the production of any concept whatsoever, and are his explanation of what makes the referential capacities of concepts possible. This theory, it may be added, shares many features with that of Locke, who also explained the power of words to name many distinct ideas at once by a faculty of abstraction. [Essay Concerning Human Understanding. II, xi, §9; but cf. also §§4-8 on comparison and compounding]
Though Kant explains the production of universal concepts in terms of abstraction, he is quick to qualify the power of abstraction; it can at be at most the negative condition in the making of concepts: it is a negation of the commonalities and differences first brought into our awareness by means of the acts of comparison and reflection, which Kant thus identifies with the positive conditions of produciton. [Logik §6; A3] A concept is understood by Kant as the predicate of a possible judgment, just as an intuition is an object of a possible sensation. It is of extreme importance that we note diligently that pure logic does not deal with merely the analytic judgment but the overall form of concepts simpliciter. An analytic judgment performs an analysis on a concepts and shows what is already contained in them, and nothing more; the form of concepts is something else entirely. For Kant, the act of making of a concept (conceiving) is always just as much an act of judging; on the other hand, all judging is itself already an act of conceiving, a thinking in accordance with concepts. Conceiving and judging should be understood, in Kant’s doctrine, to be mutually dependent and inseparable. We see this when Kant says that all the activities of the understanding can be reduced to judgment in the Kritik: “Wir können aber alle Handlungen des Verstandes auf Urteile zurückführen, so daß der Verstand überhaupt als ein Vermögen zu urteilen vorgestellt werden kann.” [A69/B94] Pure logic is a consideration of the details of concepts from a merely subjective standpoint; it concerns itself only with how concepts can refer to multiple objects. It cannot cover them from an objective standpoint (on account of its purity), wherein alone the ability of concepts to not merely refer to, but further to determine objects through Merkmale. This further, essential or determining character of concepts falls entirely outside the view of pure logic, and could only be given explanation in a Transcendental Logic. This is because a transcendental logic would not ignore all the differences in the matter of thought, but would discriminate among concepts according to their (epistemic) origins.
These notes are deeply indebted to H.J. Paton’s wonderful commentary Kant’s Metaphysic of Experience, and at several points amount to little more than a paraphrase on some of the chapters on logic contained therein (especially the citations).