K ant and the objective , logical and transcendental meaning of the categories

intuition to a pure sensible intuition, which likewise takes place a priori . Thus in the above proposition a beginning is made of a deduction of the pure concepts of understanding; and in this deduction, since the categories have their source in the understanding alone, independently of sensibility , I must abstract from the mode in which the manifold for an empirical intuition is given, and must direct attention solely to the unity which, in terms of the category, and by means of the understanding, enters into the intuition. In what follows (cf. §26) it will be shown, from the mode in which the empirical intuition is given in sensibility, that its unity is no other than that which the category (according to §20) prescribes to the manifold of a given intuition in general. (KrV, B144-145) If by ‘noumenon’ we mean a thing so far as it is not an object of our sensible intuition , and so abstract from our mode of intuiting it, this is a noumenon in the negative sense of the term. But if we understand by it an object of a non-sensible intuition , we thereby presuppose a special mode of intuition, namely, the intellectual, which is not that which we possess, and of which we cannot comprehend even the possibility. This would be ‘noumenon’ in the positive sense of the term. Abstract: The “Transcendental Analytic” of the Critique of Pure Reason contains a complex theory of the meaning ( Bedeutung ) of the categories. The main purpose of this article is to identify and reconstruct three levels of meaning in that part of the first Critique . In particular, I argue that: (1) the categories receive an objective meaning insofar as they are applied to sensible intuitions given to our spatial and temporal sensibility; (2) the categories retain a logical meaning after elimination of the forms of our sensibility, but not of the sensible character of intuition; (3) the categories have a transcendental meaning insofar as all sensible intuition is suppressed; (4) logical and transcendental meanings are the result of different kinds of abstractions made on the basis of objective meaning.


the semantic function of transcendental schemata
Schematism 4 fulfils a semantic function, whereby the categories obtain objective meaning: The schemata of the pure concepts of understanding are thus the true and sole conditions under which these concepts obtain relation to objects and so possess significance [Bedeutung]. In the end, therefore, the categories have no other possible employment than the empirical (KrV, A 145-6/B185).
The reference to objects gives meaning to the categories. Therefore, schematism enables the objective meaning of the categories, since without the schemata the reference of the categories to objects would not be possible. 5 This leads us to the notion of object that is at stake in the Schematism chapter. In different passages of the KrV Kant uses different conceptions of object. Of particular relevance is the distinction between an object in general, in which the spatial and temporal forms of our sensibility are suppressed, and an object which is given according to the forms of our sensibility. The notion of objective meaning considers the object in the latter sense. Hereafter I will use the term "X-OBJECT" to allude to the object in general in which a sensible manifold is synthesised, but making abstraction of the forms of our sensibility. And by the expression "ST-OBJECT" I will refer to every possible object of cognition (spatially and temporally given). 6 Since schemata are transcendental determinations of time, it could be objected that the intervention of space is unnecessary. However, in this paper I assume that the objects that are subsumed under the categories are spatial and temporal. In the B edition of the KrV, Kant explicitly states that: " [...] in order to understand the possibility of things in conformity with the categories, and so to demonstrate the objective reality of the latter, we need, not merely intuitions, but intuitions that are in all cases outer intuitions" (KrV,B291). In this context, to exhibit the objective reality of the categories amounts to applying the latter to sensible intuition, which as we already know presupposes schematism. 7 It is beyond the limits of this paper to provide a solution to the conflict between the strictly temporal formulation of the schemata and those passages of the B edition of the KrV that stress the necessity of spatial intuitions to grant objective reality to the categories. One possible solution is to point out that although schemata are formulated in temporal terms, they implicitly contain a reference to external intuition. Another alternative would be to affirm that schemata express necessary but not sufficient conditions for the subsumption of intuitions under the categories. 8 Regardless of the correct way to solve this problem, I assume here that categories can only be applied to spatial and temporal intuitions. Otherwise, it would not be possible to apply, for example, the category of substance, since the latter requires something permanent in intuition, which can only be found in space (Cf. KrV, B291).
Categories have an objective meaning when they are referred, by means of schemata, to ST-OBJECTS. And since schematism constitutes a mediation between pure concepts of the understanding and intuitions given to our sensibility, the only legitimate use of the categories is possible when they refer to ST-OBJECTS. This does not imply, however, that all the meaning Kant and the objective, logical and transcendental meaning of the categories.
Artigos / Articles of the categories is exhausted in such a reference: "[…] there certainly does remain in the pure concepts of understanding, even after elimination of every sensible condition a meaning; but it is purely logical, signifying only the bare unity of the representations" (KrV, A 147/B 186). In the following section, I will argue that logical meaning does not imply an elimination of all sensible intuition in general, but only an abstraction of spatial and temporal intuitions. At this point of our exposition, it is enough to claim that logical meaning is insufficient to apply categories to ET-OBJECTS. For instance, the unschematised (or pure) category of substance possesses a logical meaning insofar as it synthesises a sensible intuition in general according to the logical function contained in the judgement of the form "A is B". The variable A is understood as the ultimate subject of predication. And this logical meaning does not make explicit what sensible features A must possess in order to be an ultimate subject of predication. Therefore, the unschematised category of substance is insufficient to decide which sensible intuitions must take the place of A and which are appropriate to take the place of B. Nor are there any indications coming from the manifold given to our sensibility, which merely receives a sensible datum according to the forms of time and space. 9 In contrast, the schematised category of substance implies that the logical function "A is B" must be interpreted according to the temporal condition of permanence. Schemata play the role of interpreters that allow us to connect heterogeneous representations: the categories and the ET-OBJECTS. Two processes converge in this process of interpretation: (1) the category ceases to be a mere logical function and acquires sensible characters; (2) our sensible intuition receives a logical structure (e.g. thanks to the schema of permanence, the temporal manifold is synthesised in such a way that it is possible to distinguish in time a permanent substratum as opposed to an incessant flow of representations). 10 These two processes converging in the schema allow us to speak of a sensibilisation of the categories and a conceptualisation of the sensible intuition.
In short, we can identify the following levels: (1) unschematised categories have logical meaning. As we shall see below, at this level categories refer to X-OBJECTS; (2) schemata offer interpretations of categories in terms of our sensibility; (3) categories receive objective meaning when they are applied to ST-OBJECTS. This application is made possible by the schemata.

the logical meaning as a suppression of space and time
In this section, I will show that the logical meaning of the categories is what survives when space and time, as the sensible conditions implied in the objective meaning of the categories, are eliminated. First, I will emphasize that the logical meaning of the categories may be found in the first step of the second edition of the "Transcendental Deduction of the Categories" (hereafter B TD). Then, I will analyse the relation between the first and second step of the B TD to show that the logical meaning is the result of a suppression of space and time.
In the first step of the B TD ( § § [15][16][17][18][19][20], Kant shows the reference of the categories to a sensible intuition in general. In that first step, the forms of our sensibility are suppressed. As a result of this elimination, it remains a sensible intuition in general and the unschematised categories make it possible to think of an X-OBJECT. Due to this abstraction of space and time, it is not possible to apply the categories to ST-OBJECTS. In this part of the B TD there occurs a peculiar kind of combination named intellectual synthesis. By means of the latter, the categories retain a logical meaning, and they combine the manifold of sensible intuition in general in the unity of an X-OBJECT. 11 With such a logical meaning we cannot determine any ST-OBJECT, since for the latter we must have at our disposal empirical intuitions, given according to the forms of our sensibility. The pure categories are mere forms of thought containing logical functions expressed in the forms of judgement, which express the synthetic unity of transcendental apperception. 12 Without the input of our empirical intuition, the categories are empty concepts. 13 Let us now start with the analysis of the relation between the two steps of the B TD. The second major step of the B TD ( § §21-27) arises thanks to the consideration of our sensibility. At this point, we are no longer faced with a merely intellectual synthesis, but with a figurative synthesis that considers the spatial and temporal form of the manifold to be synthesised. By means of this figurative synthesis, the objective meaning of the categories, which now refer to ST-OBJECTS, is made possible.
I consider that X-OBJECTS give logical meaning to categories, while ST-OBJECTS give them an objective meaning. This contrast between two notions of object is to be found in the following passage: The pure concepts of understanding relate, through the mere understanding, to objects of intuition in general, whether that intuition be our own or any other, provided only it be sensible. The concepts are, however, for this very reason, mere forms of thought, through which alone no determinate object is known [erkannt]. (KrV,B150) An X-OBJECT is the result of an intellectual synthesis which refers to an intuition in general (cf. KrV, B151). And the intellectual synthesis is the result of a suppression, performed on the basis of the figurative synthesis. This interpretation finds textual support in § § 20 and 21 of the B TD. In §20, Kant argues that "all sensible intuitions are subject to the categories, as conditions under which alone their manifold can come together in one consciousness" (KrV, B143). At this point in the B TD he emphasises that the manifold of a sensible intuition is necessarily subject to the synthetic unity of apperception, as it is only through apperception that the unity of intuition is possible. The logical functions of judgments, contained in the categories, makes it possible to bring the manifold of intuition under the unity of apperception (cf. KrV, B143).
In §21 we can find an explanation of the relationship between the two main parts of the B TD: A manifold, contained in an intuition which I call mine, is represented, by means of the synthesis of the understanding, as belonging to the necessary unity of self-consciousness; and this is effected by means of the category. This [requirement of a] category therefore shows that the consciousness of a given manifold in a single intuition is subject to a pure self-consciousness a priori, just as is empirical Kant and the objective, logical and transcendental meaning of the categories.
Artigos / Articles intuition to a pure sensible intuition, which likewise takes place a priori. Thus in the above proposition a beginning is made of a deduction of the pure concepts of understanding; and in this deduction, since the categories have their source in the understanding alone, independently of sensibility, I must abstract from the mode in which the manifold for an empirical intuition is given, and must direct attention solely to the unity which, in terms of the category, and by means of the understanding, enters into the intuition. In what follows (cf. §26) it will be shown, from the mode in which the empirical intuition is given in sensibility, that its unity is no other than that which the category (according to §20) prescribes to the manifold of a given intuition in general. (KrV, I will explain this paragraph in a detailed way. Doing so will help us to see that intellectual synthesis presupposes a process of abstraction by which the forms of our sensibility are set aside. In the first sentence of this passage, Kant argues that the manifold of an intuition which I call mine is represented as belonging to the unity of transcendental apperception. This presupposes the categorial activity, since the unity of intuition (through which an object is given) always includes a categorial synthesis. Only in this way can sensible manifold be referred to the unity of apperception.
In the second sentence of the passage quoted above, Kant draws a parallel between empirical intuition and empirical consciousness: whereas the former is subject to pure intuition, the latter is subject to pure a priori self-consciousness. The main result of the first part of the B TD is thus presented: "all sensible intuitions are under the categories, as conditions only under which the manifold of them can come together in one consciousness" (KrV, B143).
In the third sentence Kant points out that all sensible intuitions (regardless of whether they are spatial or temporal) are subsumed under the categories, for otherwise such intuitions could not be mine. In this first step of the B TD it is emphasised that the categories arise from the understanding, independently of the sensibility. Therefore, in this first step we have to abstract from the way in which the manifold is given in our empirical intuition. We can thus confirm that the intellectual synthesis arises as the result of an abstraction that must be carried out on the basis of the figurative synthesis that takes into account the forms of our sensibility.
My reading seems to threaten the purely intellectual origin of the categories. Against this objection, it should be emphasised that the question of the meaning of the categories should not be identified with the inquiry into their nature. The intellectual nature of the categories is guaranteed by their foundation in the spontaneity of thinking. 14 Besides, the problem of the meaning of the categories takes into account that these conceptual representations have an intellectual origin. For this very reason, the categories are empty concepts if they are not referred to ST-OBJECTS.
In sum, I have advanced the following claims in this section: (1) the intellectual synthesis is the result of a suppression or abstraction effected on the basis of the figurative synthesis; (2) the intellectual synthesis makes it possible for the categories to have a logical meaning; (3) the figurative synthesis makes it possible for the categories to have an objective meaning; (4) the logical meaning of categories is the result of an abstraction which suppresses the forms of our sensibility, but not the sensible character of the intuition; (5) logical meaning as the result of an abstraction is compatible with the purely intellectual origin of the categories.

the transcendental meaning of categories
In the chapter of the KrV on Phenomena and Noumena Kant holds that the categories cannot be applied outside the realm of phenomenal experience. In this context, the categories possess a transcendental meaning by means of which it is possible to think of (though not to cognise) that which exceeds the limits of our sensible intuition.
The notion of phenomena implies the concept of a noumenon. Objects are phenomenal and therefore they appear according to the forms of our sensibility. The noumenon is the inevitable counterpart of the phenomenon, for the thesis according to which something appears conditioned by the forms of our sensibility implies that this thing can be thought of independently of the conditions imposed by sensibility. That which can be thought of independently of sensibility is the noumenon.
In the following paragraphs, I will analyse in what sense categories possess meaning in relation to this noumenal instance. Kant distinguishes between the transcendental and the empirical use of concepts. By means of the empirical use categories refer to objects which are given according to the forms of our sensibility. And the alleged transcendental use of concepts would entail a reference to things in themselves, i.e., to non-sensible objects. Nevertheless, as a result of the "Transcendental Aesthetics" and the "Transcendental Deduction of the Categories", the objects of our experience are phenomena (i.e., they are not things-in-themselves) and the categories can be used legitimately only when they refer to empirical objects. Thus, it is not possible to make a transcendental use of categories, but only an empirical use.
Although the categories cannot be applied to the noumenon, they possess a transcendental meaning by means of which it is possible to think about (though not to cognise) that which lies outside the limits of sensibility: The pure categories, apart from formal conditions of sensibility, have only transcendental meaning; nevertheless they may not be employed transcendentally, such employment being in itself impossible, inasmuch as all conditions of any employment in judgments are lacking to them, namely, the formal conditions of the subsumption of any ostensible object under these concepts. (KrV, A248/B305) In this passage we find two relevant claims: (1) the transcendental use of pure categories is impossible; (2) the categories possess a transcendental meaning. I will argue that the key to justifying the first of these theses is the notion of subsumption. There is use of a concept if and only if an object is subsumed under such a concept. As previously discussed, in the case of empirical use, the subsumed objects are phenomenal, whereas in the case of transcendental use, the alleged subsumed objects would be things-in-themselves. In addition, transcendental schemata not only allow phenomenal objects to be subsumed under the categories, but at the same time restrict the legitimate field within which the categories can be applied: "[...] although the schemata of sensibility first realise the categories, they at the same time restrict them, that is, limit them to conditions which lie outside the understanding, and are due to sensibility" (KrV, A146/B185-186). Thus, the impossibility of the transcendental use of the categories is Kant and the objective, logical and transcendental meaning of the categories.
Artigos / Articles an immediate consequence of the doctrine of schematism, which restricts the legitimate use of categories to the conditions of sensibility.
With these results in mind, we can turn to the second thesis mentioned above, according to which the categories possess a transcendental meaning. First, this level of signification should not be identified with a categorial determination of the noumenal realm, for as we have already seen the transcendental use of the categories is impossible. The categories have a transcendental meaning, by means of which it is possible to think about, for example, the pure form "If S, then P" (underlying the category of causality), without this pure form combining any intuition. 15 Second, the transcendental meaning of the categories cannot arise without their empirical use. 16 This is because the noumenon can only be thought of as the counterpart of the phenomenon. Namely, the phenomenon, as something that appears in a sensible way, implicitly contains the contrast with something that is not sensibly conditioned and can only be thought about. A consequence of this reading is that the empirical use of the categories implies not only an objective meaning, but also a transcendental meaning. Through the latter it is possible to think an indeterminate instance that indicates the limitation of our sensibility. That which can be thought outside the limits of our sensibility is the noumenon or the thingin-itself: Understanding accordingly limits sensibility, but does not thereby extend its own sphere. In the process of warning the latter that it must not presume to claim applicability to things-in-themselves but only to appearances, it does indeed think for itself an object in itself, but only as transcendental object, which is the cause of appearance and therefore not itself appearance, and which can be thought neither as quantity nor as reality nor as substance, etc. (because these concepts always require sensible forms in which they determine an object). We are completely ignorant whether it is to be met with in us or outside us, whether it would be at once removed with the cessation of sensibility, or whether in the absence of sensibility it would still remain. If we are pleased to name this object noumenon for the reason that its representation is not sensible, we are free to do so. But since we can apply to it none of the concepts of our understanding, the representation remains for us empty, and is of no service except to mark the limits of our sensible knowledge and to leave open a space which we can fill neither through possible experience nor through pure understanding. (KrV, From this passage, we can formulate the following theses: (1) understanding, through its capacity to think about the thing-in-itself, establishes the limits of sensibility; (2) categories cannot be applied to the thing-in-itself; (3) categories can only be applied to objects that are given according to the forms of sensibility. 17 Moreover, it is clear that at least in this context, Kant uses the concepts of noumenon 18 and thing-in-itself interchangeably.
The empirical use of categories implies an objective meaning, which contains a transcendental meaning of the categories. This is because the phenomena that give objective meaning to the categories are the inevitable counterpart of the noumenon. Transcendental meaning emerges as a result of an abstraction that is made on the basis of objective meaning. This interpretation of transcendental meaning as an abstraction is consistent with the Kantian characterisation of the noumenon in the negative sense: If by 'noumenon' we mean a thing so far as it is not an object of our sensible intuition, and so abstract from our mode of intuiting it, this is a noumenon in the negative sense of the term. But if we understand by it an object of a non-sensible intuition, we thereby presuppose a special mode of intuition, namely, the intellectual, which is not that which we possess, and of which we cannot comprehend even the possibility. This would be 'noumenon' in the positive sense of the term. (KrV,B307) The noumenon in the negative sense is the result of an abstraction of our mode of intuition, which is characterised by the fact that it is sensible. Kant rejects the noumenon in its positive meaning, for a positive categorical determination of that which is outside the limits of our sensibility is not possible. That is, categories can only determine objects that are sensibly given. An object given in a non-sensible way would require an intellectual intuition. Since we lack the latter, the noumenon in its positive meaning must be rejected. As sensibility has limits, we must accept the noumenon in its negative meaning (i.e. as something that can be thought independently of sensibility).
Insofar as they allow us to think of objects in general (abstracting from sensibility), the categories extend further than sensible intuition, but they do not thereby determine a wider sphere of objects. Since we are not allowed to suppose an intuition different from our own, nor can we deny it, objects in general, understood as negative noumena, can only be thought about. These negative noumena are a consequence of the very notion of the phenomenon, which contains as its counterpart a merely thinkable object.
These results allow us to formulate the main characteristics of the noumenon in the negative sense. First, the noumenon is a problematic concept, since it is a non-contradictory concept but lacks objective reality. In order to grant objective reality to the concept of the noumenon it would be necessary to have a non-sensible intuition. Secondly, the noumenon is a concept that indicates the limits of possible experience, which indicates at the same time the limits of sensibility and of the empirical use of the categories. Finally, it is a necessary concept, for if we could not think of the noumenon, the very notion of phenomenon would be meaningless.
Since the noumenon in the negative sense is that which gives transcendental meaning to the categories, we can characterise this level of meaning by means of the features of the noumenon in the negative sense. Therefore, the transcendental meaning of the categories possesses the following features: (1) it is problematic; (2) it fulfils the function of a limit and (3) it is necessary. It is a problematic meaning because it allows us to think about something that is non-contradictory but without objective reality, for here no intuition is given in correspondence with the thought. It is a meaning that fulfils the function of a limit, since it indicates in a negative way the scope of the empirical use of the categories. Finally, it is a necessary meaning, since it is contained in the objective meaning of categories.
In short, the categories cannot be applied to the noumenon in their negative sense, but they possess a transcendental significance insofar as the application of the categories to phenomena necessarily implies the concept of something which negatively establishes the limits of possible experience.
Kant and the objective, logical and transcendental meaning of the categories.

the distinction between logical and transcendental meaning
In this section I will argue that despite the similarities between logical and transcendental meaning, these notions must be differentiated. 19 I argue that the basis of this distinction is to be found in the different senses of abstraction at work in each of these notions of meaning.
Certainly, there are remarkable similarities between the logical meaning and the transcendental meaning of the categories. Both logical and transcendental meaning are revealed as insufficient to determine the object of our experience. Logical meaning is insufficient to apply categories to the noumenon, for there is no non-sensible intuition for the noumenon to be given. Transcendental meaning, on the other hand, lacks objective reference, for it merely points out that in applying categories to phenomena, we must at least think about the noumenal counterpart of the phenomena. Thus, logical and transcendental meanings lack reference to objects and presuppose an abstraction that is made on the basis of objective meaning.
Despite these similarities, there is an important difference between logical and transcendental meaning. Whereas the former allows us to think about the objects of a sensible intuition in general, the latter only enables us to think of a non-sensible instance, since the negative noumenon can only be thought about (which requires us to abstract even from sensibility in general). In other words, the X-OBJECT of the first part of the B TD can be thought about and intuited. In contrast, the negative noumenon can only be thought about. One advantage of this reading is that it avoids the overlap between the notions of the logical and transcendental meaning of categories. 20 I would like to emphasise here that the difference between the logical and transcendental meaning of categories comes down to the question of the kind of abstraction that at work at each of these levels. We have seen that logical meaning implies a suppression of the spatial and temporal character of the sensible manifold, but presupposes a sensible intuition in general. By comparison, the abstraction that gives rise to the noumenon in the negative sense involves suppressing not only the forms of our sensibility, but also the sensible character of our mode of intuition. If only spatiality and temporality were suppressed, the noumenon in the negative sense could contain an intuition in general. But the latter is incompatible with the idea according to which the negative noumenon is a merely thinkable object.
This conception of the noumenon in the negative sense as something that is abstracted from all sensible intuition and can only be thought is textually supported the following passages: There thus results the concept of a noumenon. It is not indeed in any way positive, and is not a determinate knowledge [Erkenntnis] of anything, but signifies only the thought of something in general, in which I abstract from everything that belongs to the form of sensible intuition. (KrV, A252) The categories accordingly extend further than sensible intuition, since they think objects in general, without regard to the special mode (the sensibility) in which they may be given. But they do not thereby determine a greater sphere of objects. For we cannot assume that such objects can be given, without presupposing the possibility of another kind of intuition than the sensible [...]. (KrV, A254/ B309) On the one hand, in the first of these passages it is emphasised that the noumenon in the negative sense is only the thought of something in general, in which we abstract from all forms of sensible intuition. On the other hand, the second passage shows that the categories allow us to think about objects in general, without taking into account the sensible way in which these objects can be given.
To sum up, the transcendental meaning of the categories enables us to think of the noumenon in a negative sense. By means of mere thinking, the categories are not applied to or made to refer to any object, for here we abstract from all sensible intuition in general. This allows us to distinguish the logical from the transcendental meaning of categories. In the former we abstract from spatial and temporal form, but there is still a sensible intuition to be synthesised. In the latter we abstract from every kind of sensible intuition. This distinction between logical and transcendental meaning implies that the categories retain meaning not only when the forms of our sensibility are suppressed, but also when all sensible intuition in general is left aside. This absolute lack of intuition shows that the noumenon in the negative sense can only be thought about in a negative and indeterminate way. In other words, pure categories are useless to characterising the noumenon in a negative sense. The latter is just an indeterminate instance that marks the limits of sensibility.

conclusions
Three notions of the meaning of the categories in the "Transcendental Analytic" of the KrV have been identified. First, objective meaning arises as a consequence of the application of the categories to our sensible intuition. Second, logical meaning is the outcome of applying the categories to sensible intuition in general, making an abstraction of the forms of our sensibility. Third, transcendental meaning is the result of pure thought which takes place after the elimination of all sensible intuition in general. The distinction between logical and transcendental meaning is the correlate of two kinds of abstraction that are performed on the same basis of objective meaning.

Abstract:
The "Transcendental Analytic" of the Critique of Pure Reason contains a complex theory of the meaning (Bedeutung) of the categories. The main purpose of this article is to identify and reconstruct three levels of meaning in that part of the first Critique. In particular, I argue that: (1) the categories receive an objective meaning insofar as they are applied to sensible intuitions given to our spatial and temporal sensibility; (2) the categories retain a logical meaning after elimination of the forms of our sensibility, but not of the sensible character of intuition; (3) the categories have a transcendental meaning insofar as all sensible intuition is suppressed; (4) logical and transcendental meanings are the result of different kinds of abstractions made on the basis of objective meaning.