Kant’s Critique of Pure Reason Analytic of Concepts: Chapter II: The deduction of the pure concepts of the understanding Section 1: The Principles of Any Transcendental Deduction Summary: Once again, Kant is addressing the problem of universals that arises from empiricism. As he puts it, universal concepts (such as the necessity of a cause/effect) “must either be grounded completely a priori in the understanding, or must be entirely given up as a mere phantom of the brain.” Given this problem, Kant proposes that one must find the ground of these concepts so that one may use them. He begins by asserting that transcendental deduction is necessary to find the grounding of a priori concepts. A transcendental deduction differs from an empirical deduction because it is concerned with the conditions of knowledge itself and can therefore not rely on empirical evidence, which presupposes and is made known by those conditions of knowledge. Next, he points out that there are two kinds of a priori concepts: those based on a priori intuitions and those that make up the categories. The latter are the objects of interest in this section, because Kant has already found the grounding for the former in the transcendental deduction of sensibility. A transcendental deduction of the categories is also necessary because even the concepts of space and time are contingent on these prior categories. In fact, these categories are universal and are prior to all conditions of sensibility (everything one can imagine or think is subject to them, otherwise it is unintelligible and contradictory.) In performing this transcendental deduction, he finds that representations must a priori determine the object, for it is only possible to know anything as an object if a representation is given. The first condition for this is the presence of a priori intuitions and the second condition is the presence of a priori concepts. Concepts are the a priori conditions of the possibilities of experience. At the end, Kant addresses the errors of Locke, brought to light by Hume (inability to explain verifiable a priori knowledge, like math). His goal is to find the determinate limits of reason, so as to keep open the whole field of her appropriate activities”. Detailed Outline of Section B117 In law, one distinguishes between the question of right and the question of fact. How one goes about proving each of these differs. The former requires a deduction, while the latter requires an appeal to experience, which we trust without a deduction. There are also some concepts, which are so universally recognized that we do not often ask for their grounding, and when the question does arise, we are perplexed. Among these concepts are the a priori concepts, which seem to be independent of all experience. Though we often take them for granted, their ‘right to be employed’ really requires a transcendental deduction. Because we understand them to be universal and necessary, an empirical deduction will not be of use, but will only show the instances in which we can see them at work. B118 There are two kinds of a priori concepts that relate to objects: those arising from the a priori intuitions of space and time, and those arising from the understanding. The former are the forms of sensibility and the latter are the forms (or categories) of the understanding. It is worthless to seek an empirical deduction of these, because they claim universal validity. In experience, we can find occasions of their production, yet we do not find their grounding as universally valid. B120 While one may think that this kind of deduction is not necessary because we have trace the concepts of space and time to their sources to show their a priori objective validity before doing so, this is erroneous. These concepts have been validated because we have shown their grounding in a priori intuitions. We have not yet found such a grounding for the categories. Categories relate to objects universally and are not grounded in a priori intuitions; they do not result from the intuitions of space and time. B122 In the field of the understanding, the question of how the subjective conditions of thought can have objective validity must be answered. That is, how can these categories set the conditions for the possibility of all knowledge of objects? Let us take the example of cause. While the objects of sensible intuitions must conform to the formal conditions of the sensibility to be objects for us, they must also conform to the conditions of the understanding if they are to become objects to us. The fact that appearance presents cases where the rule of cause and effect are illustrated does not mean that the rule can be deduced from our intuitions; rather, it means that our intuitions are formed into a unity by the understanding and are understood according to these universal and necessary rules. The concept of cause must be grounded completely a priori in the understanding, or it is a fiction that only appears to have objective validity. B125 Transition to the Transcendental Deduction of the Categories There are two ways in which synthetic representations and their objects can be related to each other. Either the object must make the representation possible or the representation must make the object possible. If the object makes the representation possible, the representation can never be a priori. Now, while the representation does not make the object exist, it is through the representation that it is possible to know anything as an object. Knowledge of an object requires an intuition, where the object is given as an appearance, and a concept, through which the object that corresponds to the intuition is thought. Given this order, one can say that all appearances agree with the formal condition of sensibility and all objects agree with the antecedent conditions of the a priori concepts. In other words, the concepts of objects underlie all empirical knowledge as its a priori conditions and through them alone does experience become possible. A94 A priori concepts are the a priori conditions of the possibilities of experience. One can point to experience for their illustration, but one cannot deduce them from experience. B127 Locke, however, did attempt to deduce them from experience, and Hume recognized that this was impossible. Because he could not explain how these concepts could be universal and necessary, he deemed them illusions that passed beyond the limits of experience. This meant that he could not account for pure mathematics and the science of nature. Kant’s solution, which places these a priori concepts within the understanding means that they are only useful when they are applied to objects that come to us through intuitions, but they are still known priori to these intuitions, rather than being deduced from them. PP 276-296 The Amphiboly of Concepts of Reflection: Arising from the Confusion of the Empirical with the Transcendental Employment of Understanding. Summary: Reflection is a state of mind where we discover the subjective conditions under which we are able to arrive at concepts. That is, it is the awareness of how we think and of the various sources of our knowledge. We begin this reflection by asking how our representations are connected. The point of this examination of judgment is to give ourselves the grounding necessary to know that our judgments are true. As it is concerned with the process of knowing, it can be called transcendental reflection. There are four relations that rise in this reflection: those of identity and difference, agreement and opposition, the inner and the outer, and the determinable and the determination. These are the conceptions of comparison, which we use not only to compare different representations, which we treat as being, but also to perform the activity of transcendental reflection. They are different from the categories because they serve to compare the manifoldness of =the representation to the concept of an object. Now, an amphiboly is the “confounding of an object of pure understanding with an experience”. This can occur in two ways, the first represented by the error of Leibniz and the second represented by the error of Locke. According to Kant, Leibniz mistook representations for which we require sensibility to be representations requiring only understanding and Locke took representations requiring acts of the understanding to be representations derived solely from sensibility. Here, Kant is more concerned with the error of Leibniz than of Locke and uses the concepts of comparison to demonstrate why it is erroneous and to argue that sensible intuitions are necessary for knowledge. Detailed Summary: B316 Reflection is the process that asks, “Under what conditions are we able to arrive at concepts?” It is the consideration of the process of knowing that asks about the relation of given representations to the different sources from which they come. We often accept the validity of our judgments without examining their grounds, but all judgments require reflection, and the act by which I determine whether a representation belongs to pure understanding or sensible intuition is transcendental reflection. The right determining of the relationship between the representation and the faculty to which it belongs depends upon the use of the comparative concepts of identity and difference, agreement and opposition, the inner and the outer, and the determinable and the determination. B318 Given that the question of transcendental reflection concerns the content of the concepts and their relation to our faculty of knowledge, one can use the abovementioned concepts to distinguish how the representations relate to the faculties of sensibility and understanding, respectively. While logical reflection is a “mere act of comparison” of different things and presupposes the objectivity of those things, transcendental reflection focuses on objects themselves and provides the ground for the possibility of comparing objects with one another by establishing how we know each of them. Transcendental reflection is a duty and no one can claim to make a priori about things without having done so. B320 Identity and Difference When one object is presented to us on many occasions with the same qualities, the understanding takes it to be one and the same. Even so, there are many of the same kinds of things, and we are able to distinguish between them because of their position in space. That is, because the sensibility plays a part in how we know. It is because of the faculty of sensibility that we can justify two drops of water to be numerically different: if one falls into the bucket before the other then they are intuited simultaneously in different positions. Plurality and numerical difference are given by space as the condition of outer appearances. B321 Agreement and Opposition If reality were given only by the understanding, we could not know oppositions that cancel each other out (3-3=0). This is because realities cannot logically conflict given the principle of non-contradiction. Sensible objects can oppose each other in a different way than this; a feeling of pleasure can counter a feeling of pain, for example. B322 The Inner and the Outer We can have no concept of the outer without an experience of it. For this reason Leibniz saw substances as monads, without outer relations. Object of pure understanding have inner determinations, as do the monads (simple subjects with powers of representation), as far as I can tell. B323 Matter and Form Matter signifies the determinable and form signifies the determination. In any judgment, the concepts are the matter and their relation is the form (Bongo is a golden retriever). Also, unlimited reality was viewed as the matter of possibility and its limitation was the form. Further, in order for the understanding to determine anything something must first be given; it is matter to be formed. Consequently, Leibniz first assumed things to be monads with a power of representation that founded their outer relations upon this basis. Kant finds this problematic and says that the form precedes the things and determines their possibility because it is a subjective condition and a formal intuition. B325 The place where we assign a concept, either to sensibility or pure understanding is its transcendental location. The decision as to its location is made according to the rules denoted by the transcendental topic. This topic, which allows one to distinguish the cognitive faculty to which each concept belongs, acts as a safeguard against error. It contains the four aforementioned distinctions. These concepts are not categories because they are not concerned with what constitutes the concept, but rather, how to distinguish between the manifoldness of the representation prior to and the concept of the object. This requires a determination of where the things that are being compared belong- either to the pure understanding or sensibility. This process is important because without this reflection, one risks mistaking an object of pure understanding with an appearance. B327 The error of Leibniz is exactly this. He has erected “an intellectual system of the world” on which he believed he could obtain knowledge of the inner nature of things by comparing objects only with the understanding, and the formal concepts therein. The table of the concepts of the reflections, however, point out his error. 1. We can see that Leibniz saw the conditions of sensible intuition as a confused mode of representation rather than a separate source of representations. Leibniz compared objects of the senses with each other merely in regard to understanding. That is, he could not think of their position in intuition and has no explanation of how any drop of water is different from any other. 2. It is a true proposition that concepts can never logically conflict but it is not true that reality cannot conflict. Leibniz’ system does not account for this. 3. For Leibniz’ monads, substances have a simple internal nature and are free from outer relations. There seems to be a problem of communication of intelligibility here. 4. Leibniz’ doctrine of time and space: the intelligible form of the connection of things in themselves. For him, the senses only confused and distorted representations. B333 Essentially, Kant says that the demand that we should be able to know things without senses demands a faculty of knowledge that is very different from the human. Further, even if the whole of nature were revealed to us, we would still be unable to answer those “transcendental questions which go beyond nature.” We can never know the relationship of sensibility to an object and the transcendental grounds of this unity. If we can only know ourselves through our inner sense and as appearance, then our sensibility cannot be treated as a tool for discovering anything except other appearances. Thus, while appearances are not things-in-themselves within the objects of pure understanding, they are the only objects that our knowledge can possess. B337 While it is true that whatever universally agrees or contradicts a concept also agrees with or contradicts every particular under it, this is not to say that whatever is not included in the universal concept cannot be included in the particular. Concepts are particular because they include in themselves more than is in the universal. Leibniz confuses these, saying that if a distinction is not found in the concept of a thing in general, it is not to be found in things themselves. The mere concept abstracts from the many necessary conditions of its intuition. One example is the distinction of location through which one can differentiate between two similar objects. Similarly, just because conflict is not found within the concepts of reality is to say that reality is all in agreement with itself. B339 Kant shows how Leibniz’ contentions would be justified if one only had access to mere concepts and again affirms that something is contained in intuition that could never be known through mere concepts: space and time. B343 Merely intelligible objects are impossible because the employment of concepts of the understanding require intuition; if we abstract from intuition, the concepts have no relation to any object. The categories do not extend beyond the conditions of the sensibility- they do not lead to knowledge of things in themselves. If we speak of noumena, the categories are not valid; the noumenon is not an object. The noumenon is “a problem unavoidable bound up with the limitation of our sensibility.” We do not know whether it would cease to exist without sensibility or whether it would remain; it is an empty concept that is of no service except to mark the limits of sensible knowledge and to open a space that we can fill neither through possible experience nor thought pure understanding”. When we determine an object by thought alone, we are giving a logical form without content, and this is empty. Goodbye metaphysics. A290 Without having decided whether the noumenon is something or nothing, we can draw table that divides up the concept of nothing. 1. An empty concept without an object (opposite of all, many, and one) 2. An empty object of a concept (absence of an object- shadow, cold) 3. An empty intuition without an object (pure space, pure time) 4. An empty object without a concept (this contradicts itself- a two sided rectilinear figure). We can do it!! 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