T he T ension beTween Two K anTian D efiniTions of The n oTion of C onCepT . T he a bsTraCTive r epresenTaTion anD The f unCTion

allgemeiner Begriff Verhältnissen der Dinge überhaupt, eine reine Anschauung. erstlich kann man sich nur einen einigen Raum vorstellen, und wenn man von vielen Räumen redet, so versteht man darunter nur Teile eines und desselben alleinigen Raumes. Diese Teile können auch nicht vor dem einigen allbefassenden Raume gleichsam als dessen Bestandteile (daraus seine Zusammensetzung möglich sei) vorhergehen, sondern nur in ihm gedacht werden. Er ist wesentlich einig, das Mannigfaltige in ihm, mithin auch der allgemeine Begriff von Räumen überhaupt, beruht lediglich auf Einschränkungen. Abstract: the Transcendental Aesthetics, Kant introduces the distinction between intuitions and concepts. Intuitions are immediate and singular representations. Concepts are mediate and universal representations. In the Transcendental Logic, Kant defines the concept as a function or rule. The concept is a rule of unity of the multiplicity of intuition. This investigation aims to show that there is a tension between the definition of concept in the Aesthetics and the Dialectic with the notion of concept as function, according to its presentation in the Transcendental Logic. Our hypothesis is that the definition of concept as a function that is introduced in the Transcendental Logic is grounded on a sui generis notion of concept that comes into tension with the definition of concept as a representation by common marks.


Laura PELEGRIN (Universidad Diego Portales-University of Leiden) 1 inTroDuCTion
In the Transcendental Aesthetics, Kant introduces the distinction between intuitions and concepts. Intuitions are immediate and singular representations. Concepts are mediate and universal representations. Concepts refer to the object through their common marks. Understanding produces concepts, sensibility provides intuitions. Concepts have their origin in the understanding. They are mediate and universal representations. On the contrary, intuitions have their origin in sensibility. Intuitions are immediate and singular representations while concepts are mediated representations of the object. Concepts refer to the objects of experience by their marks. In conceptual representations, the parts precede the whole. The conceptual representation is constituted from the parts of the intuitive representation. The concept is a representation that contains the marks of the object that operate as characteristics common to many things. Concepts refer to the object of experience by their marks. They are predicates of multiple objects. Therefore, "... every concept must be thought of as a representation that is contained in an infinity of different possible representations (as their common marks), and therefore contains them under itself." 2 For this reason, the concept is a universal representation. In the process of concept formation, the parts precede the whole. In Transcendental Aesthetics, Kant uses this feature of concepts to argue that space and time are intuitions. Kant maintains that in the representation of time and space, the parts cannot precede the whole; therefore, they are intuitive and not conceptual representations; since the conceptual representations are precisely those in which the whole is formed from the parts. These definitions that Kant https://doi.org/10.36311/2318-0501.2022.v10n1.p199 PELEGRIN, L. introduces in the Aesthetics are developed in the Dialectic. Kant explains that genus is the representation. Perception is a sensation with consciousness. The concept is the form of perception that is obtained through common marks of the object. Concepts refer to the object of experience by the common marks of many objects 3 . The concept is a representation by common marks. Concepts refer to the object of experience by their marks. This definition of the concept as a representation by common marks is in line with the definition used by Kant in his lectures on logic. In short, in the Aesthetics and the Dialectics, and in his logic lessons, Kant defines the notion of concept as an abstractive representation.
However, on the other hand, in the Transcendental Logic, Kant defines the concept as a function or rule. Kant argues that the understanding is the source of concepts. Understanding is the source of concepts, and those concepts are rules of unification. The concept is the function of the understanding to give unity to the multiplicity. The concept is a rule of unity of the multiplicity of intuition. It is an act of synthesis. This synthesis is produced by the pure understanding itself 4 . The understanding produces different forms of synthesis, and these forms of synthesis are the different concepts. In this sense, the concept is a rule. This rule is the function that determines the specific way in which the multiplicity is unified. Since the understanding is the faculty of concepts, it is also "the law of the synthetic unity of all phenomena" 5 . Understanding is a source of concepts. The concept must be understood as a rule, as a function. Likewise, Kant maintains in the Transcendental Logic that "the concepts, without intuitions, are empty". The concept does not have a content by itself. The content of the concept is provided by intuition.
The question that we pose is how the Kantian definition of concept as abstractive representation (according to its presentation in the Aesthetics and Dialectic) is related to the definition of concept as function (definition introduced in the Transcendental Logic). If the concept is a representation abstracted from the common marks of objects, how can concepts be functions that have their origin in the pure understanding? What is the relation between the definition of concept as a common representation and the definition of concept as a function or rule? If the concept is an abstractive representation, how can pure concepts be essentially empty?
In this context of the problem, this investigation aims to show that there is a tension between the definition of concept in the Aesthetics and the Dialectic with the notion of concept as function, according to its presentation in the Transcendental Logic. Our hypothesis is that the Kantian definition of concept considered in the Aesthetics and in the Dialectic responds to the way in which empirical concepts are formed. The definition of concept as a function that is introduced in the Transcendental Logic responds to a sui generis notion of concept that comes into tension with the definition of concept as a representation by common marks. We will argue that there is a tension between these two definitions because while the definition of concept as function is a novelty of the Kantian system, the definition of concept as universal representation is borrowed from tradition.
To argue in this direction, we will proceed in three stages. In the first place, we will analyze the definition of concept according to the presentation in the Aesthetics and in the Dialectic. In this section, we will conclude that both in the Aesthetics and in the Dialectic, Kant uses the definition of concept as a representation by common marks. As we shall exhibit, this means that the concept is an abstractive representation. Second, we will study the definition of concept as a function. We will analyze the empty nature of the concept. Finally, we will exhibit the tension between the two definitions of the notion of concept. We will state that in Aesthetics and Dialectics, Kant uses the notion of concept that responds to how empirical concepts are generated but that is insufficient to characterize pure concepts; more specifically, this notion of concept does not allow us to understand pure concepts as functions. We will argue that the definition of concept as an abstractive representation is inherited from tradition and that the definition of concept as function is that of the critical system.

parT i. ConCepTs as absTraCTive represenTaTions
In Transcendental Aesthetics, Kant introduces one of the central distinctions of critical idealism. Intuitions are singular and immediate representations, and concepts are general and mediated representations. Intuitions have their origin in sensibility while concepts are products of the understanding. Kant explains: Auf welche Art und durch welche Mittel sich auch immer eine Erkenntniß auf Gegenstände beziehen mag, so ist doch diejenige, wodurch sie sich auf dieselbe unmittelbar bezieht, und worauf alles Denken als Mittel abzweckt, die Anschauung. Diese findet aber nur statt, sofern uns der Gegenstand gegeben wird; dieses aber ist wiederum uns Menschen° wenigstens nur dadurch möglich, daß er das Gemüth auf gewisse Weise afficire. Die Fähigkeit (Receptivität), Vorstellungen durch die Art, wie wir von Gegenständen afficirt werden, zu bekommen, heißt Sinnlichkeit. Vermittelst der Sinnlichkeit also werden uns Gegenstände gegeben, und sie allein liefert uns Anschauungen; durch den Verstand aber werden sie gedacht, und von ihm entspringen Begriffe. Alles Denken aber muß sich, es sei geradezu (directe), oder im Umschweife (indirecte), vermittelst gewisser Merkmale zuletzt auf Anschauungen, mithin bei uns auf Sinnlichkeit beziehen, weil uns auf andere Weise kein Gegenstand gegeben werden kann. 6 This dichotomy between intuition and concept works as a foundation upon which is built not only the Aesthetics but all the Kantian critical system. There is a general agreement that the peculiar critical conception of the distinction between intuitions and concepts is "the pillar of Kant's theoretical philosophy." 7 However, unfortunately, there is a second general agreement among the Kantian studies. Scholars agree that in the first passages of the Aesthetics, Kant is providing a series of definitions 8 . Commentators consider that these Kantian statements at the beginning of the Aesthetics are not conclusions of any previous argument provided by Kant 9 . Kant introduces the distinction as if it were completely evident, and it did not require any further explanation 10 . For this reason, as Daniel Kolb notes, the distinction between intuitions and concepts has been considered one of the weakest points of the Kantian system 11 . Mario Caimi highlights: "it is generally assumed that Kant begins by setting forth some definitions, to immediately committing himself to the study of what is considered to be the central subject of the Aesthetic, namely space and time, in §2." 12 Most of the studies of this section go in the same direction 13 .
Moreover, Kant not only assumes the definition of these concepts but the exhaustiveness of the distinction. The arguments of the Aesthetic require us to assume that all our representations are divided into intuitions and concepts. The distinction between intuitions and concepts is presented as an exhaustive one. 14 Precisely for this reason, in the arguments of Transcendental Aesthetics, it is enough to show that space and time are not concepts, to legitimately conclude that they are intuitions.
In the Transcendental Aesthetic, Kant presents the distinction between intuition and concept. Intuitions and concepts are two ways in which thinking can refer to objects. Intuition is a form of representation in which the object is given immediately. Intuitions have their origin in sensibility and concepts in the understanding. Man is not capable of intellectual intuition, since humans only know through concepts. Human beings know the object through its marks. Concepts are mediated representations of objects. The human intellect can only know the object through its common marks. The understanding refers to the object indirectly, by means of the common marks of the object. Concepts are representations that have their origin in the understanding. Since they refer to the object by their marks, the concepts are mediated representations of the object. In conceptual representations, the parts always precede the whole. The entire representation is constituted from the synthesis of the parts. The concept is a representation that contains the marks of the object that operate as characteristics common to many things. The marks of the objects are predicable of multiple objects. For this reason, "… every concept must be thought of as a representation which is contained in an infinite number of different possible representations (as their common marks), and that therefore contains them under itself. 15 " In the process of the concept formation, the parts precede the whole. This is the premise that Kant uses to argue in the Transcendental Aesthetic that space and time are intuitions. In the Transcendental Aesthetic, Kant claims: Der Raum ist kein diskursiver oder, wie man allgemeiner Begriff von Verhältnissen der Dinge überhaupt, sondern eine reine Anschauung. Denn erstlich kann man sich nur einen einigen Raum vorstellen, und wenn man von vielen Räumen redet, so versteht man darunter nur Teile eines und desselben alleinigen Raumes. Diese Teile können auch nicht vor dem einigen allbefassenden Raume gleichsam als dessen Bestandteile (daraus seine Zusammensetzung möglich sei) vorhergehen, sondern nur in ihm gedacht werden. Er ist wesentlich einig, das Mannigfaltige in ihm, mithin auch der allgemeine Begriff von Räumen überhaupt, beruht lediglich auf Einschränkungen. 16 Kant argues that the representation of space is not conceptual but intuitive. We make a representation of space as a whole. The parts of this whole cannot precede it. The parts of the space can only be conceived as limitations of the space as a whole. Kant argues that in the representation of time and space, the parts cannot precede the whole; therefore, they are intuitive and not conceptual representations; since conceptual representations are precisely those in which the whole is formed from the parts 17 . Kant uses the definition of the concept as a representation by common marks to argue that space is not a conceptual representation but an intuitive one. The argument is introduced as a disjunctive syllogism. Our representations The Tension between two Kantian Definitions of the Notion of Concept.
Artigos / Articles are either intuitive or conceptual. In intuitive representations, the whole precedes the part, in conceptual representations the part precedes the whole. In our representations of space and time, the whole precedes the part. Therefore, the representations of space and time are intuitive and not conceptual. Kant's argument is based on a disjunctive syllogism that assumes as valid the definition of intuitive and conceptual representations. In this argument, Kant presupposes the aforementioned definition of concepts. In the concept, the parts precede the whole. For this reason, the representations of space and time are conceptual representations. The argument that Kant employs in the Transcendental Aesthetic, requires that we accept this distinction. Conceptual representations are those that are obtained in a mediate way, by reference to intuition. The representation is obtained from common marks of the objects given to the intuition. In the Transcendental Aesthetic, Kant is employing the definition of concept as an abstractive representation. The analogous presentation of the Inaugural Dissertation of 1770 exhibits this point. According to Kant: "The concept of space is a singular representation comprehending all things in itself, not an abstract and common notion containing them under itself. What are called several spaces are only parts of the same immense space mutually related by certain positions…." 18 . In the Dissertation, the concept of singular representation is contrasted to the notion of abstractive representation. The representation of space is not obtained from the marks of spatial singular representations. The argument is that that space is a singular representation as it is not abstractive. Certainly, the critical Kantian notion of concept was not developed by then. Indeed, they are two different arguments 19 . However, the notion of singular representation is contrasted to the abstract universal representation both in the Dissertation and in the Transcendental Aesthetics. This is the definition of concept that Kant has in mind in the Transcendental Aesthetic. The concept is an abstractive representation of what many objects have in common.
These definitions that Kant introduces at the beginning of the Transcendental Aesthetic are clarified in the Dialectic. Kant explains that the genus is representation. Objective perception is a sensation with consciousness. The concept is the form of perception that is obtained by means of common marks of the objects. Kant presents the classification this way: Bewußtsein (perceptio). Eine Perception, die sich lediglich auf das Subject als die Modification seines Zustandes bezieht, ist Empfindung (sensatio), eine objective Perception ist Erkenntniß (cognitio). Diese ist entweder Anschauung oder Begriff (intuitus vel conceptus). Jene bezieht sich unmittelbar auf den Gegenstand und ist einzeln, dieser mittelbar, vermittelst eines Merkmals, was mehreren Dingen gemein sein kann 20 .
The concept is a representation by common marks. This definition of the concept as representation by common marks follows that definition that Kant used in his lectures on logic. In the Jäsche Logik, we find a definition very similar to the one that Kant provides in the Introduction to Aesthetics and in the Dialectic: Alle Erkenntnisse, das heißt: alle mit Bewusstsein auf ein Objekt bezogene Vorstellungen sind entweder Anschauungen oder Begriffe.-die Anschauung ist die einzellne Vorstellung (repraesentatio singularis), der Begriff eine allgemeine (repraesentatio discursiva) Oder reflektierte Vorstellung" 21 PELEGRIN, L.
Discursive or conceptual representation is a representation by common marks. As it is a representation by common marks, this representation is universal. The universal representation contains multiple parts, whose multiplicity is prior to the unity that contains it. For this reason, the concept contains a multiplicity under it. The multiple elements contained in the concept are different from each other. Thus, for example, the predicate red can correspond to multiple objects that differ from each other. The concept contains a multiplicity of possible representations, insofar as those possible multiple representations that the concept includes differ from each other 22 . Thus, in the conceptual representation, the parts precede the whole. The whole is the unity formed from the parts. That totality is always an indeterminate universal that can always contain multiple representations under it. The concept is a universal representation because it is a representation that is generated from what is common to all the objects that fall under it. More precisely, in the process of concept formation we compare many objects and make abstraction of their differences. Thus, concepts are always undetermined. Kant holds: Da nur einzelne Dinge oder Individuen durchgängig bestimmt sind, so kann es auch nur durchgängig bestimmte Erkenntnisse als Anschauungen, nicht aber als Begriffe, geben; in Ansehung der Letzteren kann die logische Bestimmung nie als vollendet angesehen werden. 23 If a certain representation is not a common representation, it is not a concept. Therefore, the complete knowledge of the object can only be given by the singular object, because "only singular things or individuals are completely determined". The possibility of complete determination is only possible as an intuitive representation; that is, "there can only be fully determined knowledge as intuitions (not as concepts)." Thus, with regard to intuitions, the logical determination can be complete, but "regarding concepts, the logical determination can never be considered as achieved. "24 The conceptual determination can never be achieved by concepts because concepts are essentially undetermined. The concepts contain common marks of many objects. These common marks, as we shall see, are obtained making abstraction of those properties in which the objects differ.
Thus, Kant defines the concept as a form of representation by common marks that are abstracted from other given representations. However, as we shall see, this definition is insufficient. Kant defines a priori concepts as rules, functions. The definition of the concept that Kant uses is insufficient to characterize the function of the concepts of the understanding. Kant uses the definition of concepts as abstractive representations to characterize concepts in general, but this definition does not work to express the function of pure concepts.

parT ii. pure ConCepTs anD empiriCal ConCepTs
The concepts are pure or empirical. Pure concepts have their origin in the understanding without reference to anything sensible 25 . Empirical concepts are obtained from the data provided by intuition. The definition of concepts aforementioned completely suits the definition of empirical concepts. All concepts are formed in a threefold process that involves The Tension between two Kantian Definitions of the Notion of Concept.
Artigos / Articles a) comparison, b) reflection, c) abstraction 26 . As Béatrice Longuenesse explains, pure concepts (and also mathematical ones) follow the model of the generic concept 27 . In the case of empirical concepts, the point of departure is the comparison of the singular objects given in intuition.
The origin of the empirical concept is in the senses. The first element is the presentation of the objects in intuition. I have the representation of certain singular objects. From these singular representations, I notice that there are certain marks that belong to one object but do not belong to another. However, I also obtain by abstraction the marks that are common to all the objects considered. From these common marks, I generate a universal representation, a representation by common marks. Kant explains this point with an example 28 . I see three types of trees, a spruce, a willow, and a linden. Indeed, they are represented as three different singular objects. The first step is the presentation of the object as a singular representation, i.e., in intuition. To form the concept, we compare the objects, and we notice that they differ in many aspects. In the case of the tree, they have different sizes, colors, etc. Secondly, we attend to the common marks of the object, they have trees, a trunk, etc. Finally, we abstract the marks of the objects and form the universal representation, for example, of the tree. The abstraction is a pure negative process. We do not "abstrahere aliquid" but "abstrahere ab aliquo". The act of abstraction is only not considering certain marks. It is a pure negative process. In the process of abstraction, we disregard the differences between the objects, and we take into consideration the remaining properties, those marks that the object has in common with the other objects. In these three steps, we obtain from the singular representation the universal representation. This process is perfectly in line with the definition of concept that Kant gave in the Dialectic. The definition of concepts as abstractive representations presented in the Dialect to characterize concepts in general agrees with this process of empirical concept formation. However, as we shall exhibit, this definition does not work to express the function of pure concepts.
Kant maintains that understanding is a source of concepts. The understanding produces concepts. As it is well known, this is one the main results of Transcendental Logic. Understanding is the source of concepts, and those concepts are rules of unification of the multiple of intuition. The concept is the function of the understanding to provide unity to the multiplicity. The concept is this gathering form of the multiplicity of intuition. This form of reunion is produced by the understanding itself. The concepts "spring, pure and unmixed, out of the understanding, which is an absolute unity, and therefore must be connected with each other according to a concept or idea." 29 The concept is a function of the unity of the representations. The concept is a function of pure thinking to give unity to the various representations. In this sense, the concept is a rule. This rule is the function that determines the specific way in which multiplicity is unified. Since the understanding is the faculty of concepts, it is therefore also "the law of the synthetic unity of all phenomena" 30 . Understanding is a source of concepts. For this reason, Kant affirmed at the beginning of Transcendental Aesthetic that concepts arise from the understanding, while intuitions rest on affections. While intuitions are grounded on affections, concepts are grounded in functions 31 . The concept must be understood as a rule, as a function. These functions or rules determine the specific way in which the content given in intuition is organized. The main function of the understanding is synthesis. The concepts are the synthetic functions of the understanding. The function is the act of ordering many PELEGRIN, L. representations in relation to a unity. The act of the function is the most proper act of the understanding. The understanding unifies the multiplicity according to certain forms of unity. These forms of unity, namely: the concepts, are productive. They produce the peculiar forms of reunion of the multiplicity given in intuition. Indeed, the concept is empty. It has no content besides the content provided by intuition. However, the peculiar forms of the reunion are a priori determined. The unity of the pure concept of the understanding does not contain a partial representation of the object, as it was the case, for example, of empirical concepts. The form of the unity is logical prior to the parts. Certainly, the concept requires the multiplicity to have content, but the multiplicity is not logically prior to the unity of the concept.
In conclusion, the general notion of concept involves comparison, reflection and abstraction. The comparison requires considering the content of different representations. After that, we disregard the differences. The abstraction "is a pure negative concept". It does not produce anything. The pure concept is productive. It is not made spontaneously by the understanding. The pure concept is synthetically generated and not by comparison, reflection and abstraction.
The Kantian definition of the concept as an abstraction of common marks does not seem to be a plausible expression of this function of the concept. Kant claimed that the concept is a representation obtained from the common marks of the objects. This universal representation is generated by comparing different representations and then making an abstraction of their differences. This corresponds to the way in which empirical concepts are formed but it is not a plausible definition to explain the operation of pure concepts of the understanding. The pure concept is productive, but the abstraction does not produce anything. 32 Therefore, abstraction is a negative concept 33 . It only leaves out the differences of the objects. Kant seems to use the empirical concept formation model to explain concept formation theory in general. The problem is that, as Kant himself marks "the use of the pure concepts of the understanding would be completely altered, if one tried to treat them only as empirical products." 34 . Then, another notion of concept is required that explains the function of the concept as a function. The problem with the notion of concept is the narrowness of the definition, which only applies to empirical concepts 35 .
One of the consequences of this problem is that, as Kemp Smith shows, in the Transcendental Aesthetic, Kant does not prove that space and time are not concepts but that they are not abstractive concepts. The only conclusion that can be drawn from this argument is that space and time are not generic class concepts. It is not shown that space and time belong to receptivity and not to spontaneity. Space and time have not been proven to be different from the categories 36 . George Schrader considers that "there is nothing in common between α priori concepts and empirical concepts save the name" 37 . Lorne Falkenstein is certainly correct to observe that Kant's notion of concept as an abstractive representation is not accurate to define the notion of concept required by the Critique 38 .
It is perfectly understandable that these two conceptions of the notion of concept differ if we take into consideration that the notion of pure concept is a novelty of the Kantian system. It is reasonable that the traditional notion of concept formation does not explain the function The Tension between two Kantian Definitions of the Notion of Concept.
Artigos / Articles of the pure concept of the understanding. Certainly, Kant differs on several points from Meier's reading and, even more so, with empiricist logic. However, the conception of it follows the line of concepts as abstractive representations. The notion of pure concept is a novelty of the system. More specifically, Kant introduces the possibility of empty concepts.
As it has been exhibited 39 , the Leibnizian rationalism, disregards the possibility of empty concepts. Leibniz holds that we have primitive ideas that can be decomposed into simple parts. Ideas can be analyzed into simple elements. These simple ideas are clear and distinct. Nature is made up of these simple elements which are "the true atoms of nature; in a word, the elements of things" 40 . Everything we can find in nature is a composition of these first elements: the monads. Perception is the temporal unity generated among multiplicity 41 . It is a temporary state in which we do not necessarily attend to the unities that belong to this higher unity. This state is temporary because it is possible to attend to the unities that compound the higher unity. Intuition is the apprehension of the simple elements that compound the multiplicity which we temporarily perceive as a unity. Clarity and distinction are the marks of intuitive cognition. Cognition is clear when the idea is present to the mind, and the mind is capable of distinguishing it from any other idea. In a clear cognition, we can separate the representation from another representation. Leibniz specifies this definition of the clarity criterion establishing a relation with the principle of non-contradiction: clear representations can always be defined with a non-contradictory definition. It is always possible to give a non-contradictory definition of a clear representation. This possibility of demarcation defines the clarity criterion. However, in clear cognition, I cannot tell apart the determinations that make this idea different from the other. Even when I can claim that they are both different, I cannot say what this difference consists of. While I can state that these ideas are different, I cannot establish how they differ. In this case, my cognition is clear but not distinct. A clear idea can be distinct or confused 42 . An idea is distinct when the mind can identify the determinations that belong to the representation. In a distinct cognition, the mind is able to discern the elements that truly belong to the thing. Intuition is the apprehension of these first simple elements that correspond to the thing, and this kind of access guarantees that we have true knowledge of the thing and not a mere notion.
The idea is distinct when I can get to these differential marks. In fact, we truly have an idea of the thing-and not a mere confused notion-when we have an intuition of the determinations that belong to the concept 43 . A cognition is adequate when it is clear and distinct, and I can guarantee that the analysis of the idea has been carried out up to the end. Adequate cognitions are very rare for us, human beings. The limitation of knowledge consists, precisely, in this incapacity to represent distinctly every part of the universe. The level of determination is a question of degree 44 . Sense perception is just this degree of confusion where I cannot clearly identify the elements that compound my perception. Once I have analysed the components of the substances and distinguished the parts that belong to them, I have intellectual cognition. The difference between intuitive cognition and intellectual cognition is a question of degree. The representations of the sensibility and understanding have the same root or, more precisely, concepts and intuitions do not come from different origins, but they have the same source. The difference between these two types of perception is the degree they achieve in the determination of the object. The intellect finds the distinctive marks that belong to the thing and turns this confused perception into a distinct one. Leibniz identifies sensibility with obscure and confused cognition and the understanding with distinct cognitions. These two faculties differ in the degree of clarity they can achieve. Actually, they are different degrees of the same function.
In his article of 2005, Gedanken ohne Inhalt sind leer, Mario Caimi showed that one of the innovations of the Kantian proposals was the introduction of the possibility of empty concepts. For Leibnizian rationalism, concepts have a content per se. On the contrary, according to Kant, pure concepts are empty. Mario Caimi exhibits that this is a novelty of the Kantian system: the possibility of empty concepts. For this reason, this innovation of the Kantian system requires a new definition of the notion of concepts. The explanation of a concept that has its origin in the pure understanding and that has no content of its own is not satisfied with the traditional definition of a concept.
In the first part of this investigation, we showed that Kant understands the notion of concept as abstractive representation in both the Aesthetics and the Dialectic. We exhibited that this definition is present in his logic lessons too. We studied how Kant used this definition to argue that space and time are intuitions and not concepts. In the second part, we studied the general definition of the notion of concept. We showed that this definition clearly explains the formation of empirical concepts but that it is insufficient to characterize the pure concept of understanding. The pure concepts of the understanding cannot be obtained, as Kant claims, by comparing reflection and abstraction. Finally, we exhibited that, the notion of the pure concept of the understanding is not satisfied with this definition because the introduction of empty concepts is a novelty of the Kantian system.