Critique of Pure Reason August 10, 2021 These notes are an attempt to summarise some important ideas in Immanuel Kant’s Critique of Pure Reason in a readable way. These are nowhere near exhaustive. Contents 1 Introduction 2 2 The Transcendental Aesthetic 2 3 The Transcendental Logic 3 4 The Transcendental Analytic 4 4.1 Judgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4.2 Categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4.3.1 Judgements and Categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4.3.2 Principles of the Pure Understanding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4.4 Cause and Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4.5 Refutation of Idealism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 4.6 Phenomena and Noumena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 5 The Transcendental Dialectic 7 5.1 Antinomies of Pure Reason . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.1.1 Antinomy 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.1.2 Antinomy 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5.1.3 Antinomy 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5.1.4 Antinomy 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5.1.5 Comments on Antinomies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5.2 Arguments for God and Refutations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5.2.1 The Ontological Argument . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5.2.2 The Cosmological Argument . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 5.2.3 The Physico-Theological Argument . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 5.3 The Concept of a Necessary Being . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 6 The Transcendental Doctrine of Method 11 6.1 Mathematics vs Philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 6.2 Moral Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1 1 Introduction In the Critique of Pure Reason , Kant is trying to establish a foundation for metaphysical understanding where everything is grounded in necessary, a priori propositions. This is motivated because experience cannot be truly necessary or universal, so a priori foundations must be needed. Kant makes a distinction between analytic and synthetic propositions. Analytic propositions are those propositions where the predicate is contained in the subject. An example: “All bachelors are unmarried”. Synthetic propositions are those propositions where the predicate lies outside of the subject. An example: “All bachelors are unhappy”. You can arrive at the conclusion of an analytic proposition simply by thinking about the subject itself. The property of “unmarried-ness” is contained in the concept of a bachelor; indeed, it is part of the definition. However, the property of unhappiness is not inherently contained in the concept of a bachelor, and as such it is a synthetic proposition. Propositions can also be a priori (prior to experience) or a posteriori (derived from experience). In par- ticular, Kant wants to ground metaphysics on synthetic a priori propositions. The synthetic property is required to derive new things from the original statements (to avoid being confined to tautologies), and the a priori property is needed so that reasoning is grounded on necessary truths. Mathematical judgements are examples of synthetic a priori propositions. Kant uses two examples in the introduction. • The statement 7 + 5 = 12 is synthetic a priori. When we consider the concepts of 7, 5 and taking the sum, we understand from this the unification of 7 and 5, but cannot get the concept of 12. • “The shortest path between two points is a straight line” is also synthetic a priori. No concept of length is contained in the concept of straightness. 2 The Transcendental Aesthetic In this section, Kant outlines his concept of space and time. We will need a few terms: A representation is a general term for an object considered in the way it is determined by a subject. Intuition is a singular, immediate representation, and concepts are general representations. Appearances are described by Kant as the “undetermined object of an empirical intuition”. What happens when we consider the representation of a body, and abstract from it all its qualities except for its extension and form? Well, we are left with considering the two pure forms of sensible intuition: space and time Kant does not consider space and time to be things in themselves, but purely as necessary conditions. Space is the necessary, a priori condition for the possibility of appearances. All external intuition is grounded in space, and space does not depend on these intuitions. Time must also be presupposed in order for any appearances to be possible - it is necessary to perceive simultaneity and succession. Time determines the relation between representations in our inner state. It is a 2 subjective condition of our intuition. The transcendental aesthetic contains only space and time, which are the pure forms of all sensible intuition that are given entirely a priori and not empirically. All other concepts, such as motion, presuppose the existence of something empirical. Indeed, space and time are merely subjective conditions of our intuition, and all objects in relation to space and time are only appearances, not things-in-themselves. 3 The Transcendental Logic Kant states that pure logic must be entirely abstracted from things that are empirical. He attempts to do this via formulating the transcendental logic , where transcendental here means not reliant on experience. In particular, there is a cognition that things like space are not of empirical origin, but can nevertheless be related, a priori, to objects of experience. Logic can be divided into analytic and dialectic Analytic analyses all the elements of reason and understanding formally. Dialectic makes use of logic as a tool for making objective assertions. 3 4 The Transcendental Analytic 4.1 Judgements The concepts of pure understanding can never be related immediately to an object, but rather a judgement must mediate the relation. An example of this is the judgement that “all bodies are divisible”. This connects the concept of the divisible to the appearances associated with bodies that we see. 4.2 Categories Categories are the pure concepts of the understanding. Kant similarly formulates a table of categories. We define synthesis as putting together different representations and unifying them into one cognition. For example, counting is a synthesis in concepts, under the common ground of unity. When we count, we syn- thesise the repeated concept of one together over and over until a certain number is reached. Transcendental logic consists in bringing pure synthesis under concepts. 4 Notice in particular that the third member of each category is some sort of combination of the former two, but cannot merely be derived from the former two. So how are the categories possible, and what are they used for? Well, pure concepts of the understanding are possible a priori, because our cognition relates only to appearances. The possibility and connection between appearances lies only in ourselves, so they precede experience. The categories ground the possibility of all experience - this is a necessary relation. We cannot think of any object except through the categories. 4.3 Applications 4.3.1 Judgements and Categories The transcendental schema is a representation that mediates between a category and the appearance to which it applies. For instance, images are not sufficient to relate objects to concepts. No image of a triangle can be general enough to embody the concept of all triangles. We need something more. Here are two examples: • Number is the pure schema of magnitude. This relates an appearance to the concept of magnitude. • The existence of an object at all times is the schema of necessity. The categories merely subject appearances to general rules of synthesis, through necessary, a priori unity. Synthetic judgements arise from the combination of (1) inner sense and time, (2) imagination, and (3) ap- perception. Inner sense is the only totality in which all representations are contained. Finally, how do we know that our cognitions have any a priori objective reality? Well, they can only have a priori objective reality if they are grounded in the possibility of experience 4.3.2 Principles of the Pure Understanding Here, Kant outlines some additional principles. 1. All intuitions are extensive magnitudes . This means that representations of the parts of the intuition make possible the representation of the whole (e.g. a line segment represents an infinite line). 2. In all appearances, the sensation has an intensive magnitude, i.e. a degree 3. Experience is possible only through the representation of a necessary connection of perceptions. This is an important concept that leads into Kant’s understanding of cause and effect. Kant states that substance persists in all change of appearances, and persistence is a necessary condition which is required to determine what the appearances are. If you assume that something began to exist, then there must have been some time in which it did not exist. But this time must have been attached to something that did exist (recall that time is a condition for appearances, and not a thing-in-itself). As such, creation and annihilation are not alterations. 4.4 Cause and Effect To establish necessity in the relation between events, we need the idea of cause and effect. To begin with, it may be useful to refer back to David Hume’s understanding of causation, which Kant in a way responds to. In A Treatise of Human Nature and An Enquiry Concerning Human Understanding , Hume argues that we cannot rationally justify our belief in causality. All that we perceive is a constant 5 connection between types of events, and we acquire the idea that one causes the other through repetition and experience only. Kant agrees that it is not possible to establish absolute necessity through experience alone; we must instead try to ground it a priori. Here is an outline of the argument. • We cannot perceive something to happen unless it is a change, or alteration, from a previous state. Therefore, in order for something to happen, we need there to be a previous event. • The order in which we perceive these occurrences cannot generally be switched. It must follow some kind of necessary rule. • Therefore, the first occurrence most contain some inherent propensity to follow a rule. This rule must be entirely necessary, otherwise the order of occurrence would be merely subjective and could not be the grounds for proper cognition. • The necessity of following such rules is hence what cause and effect is grounded in. We can take this further and assert that the principle of cause and effect is what grounds the possibility of experience , because in order to have experience we must perceive some succession of events. We note also that this does not have to consist in a series of events that are actually separated in time. The cause and effect can be simultaneous, e.g. a ball placed on a pillow causes a dent in the pillow’s surface. The time separation between cause and effect may be vanishing, but the necessary relation still holds. Kant also argues for the infinite divisibility of time using cause and effect. He claims that causes do not produce effects instantaneously, but rather do so continuously between the two instants. Therefore, time must be infinitely divisible and there is no “quantum” of time; if there were one, then the aforementioned time separation could not be vanishing. 4.5 Refutation of Idealism In A Treatise Concerning the Principles of Human Knowledge , George Berkeley argues against the existence of mind-independent objects, claiming that it is impossible to conceive of them without perceiving them in the mind. Kant refutes this idealism by trying to demonstrate that the consciousness of one’s own existence proves the existence of external objects in space. The argument goes as follows: • We are conscious of our own existence in time. This presupposes the existence of something persistent in perception. • This persistent thing cannot lie in ourselves, because one’s own existence in time can be determined only through something that is really persistent. • Therefore there must exist some persistent, external thing. Kant states that idealism assumes the only immediate experience is inner experience. But outer experience can also be immediate. Indeed, alteration is possible only through a cause. All alteration presupposes something persistent in intuition, that is not found in inner sense/time. 4.6 Phenomena and Noumena We distinguish between phenomena , which are mere appearances, and noumena , which are things in them- selves. The pure concepts of the understanding (i.e. categories) are of only empirical use, not transcendental use. 6 We cannot know anything about noumena (things-in-themselves). These are objects of the understanding, not objects of sense. They are abstractions from all sensible intuition. Notably, a noumenon is defined only in a negative sense. The concept of a noumenon simply gives sensibility a limit. Understanding and sensibility can determine an object only when used in combination. 5 The Transcendental Dialectic The transcendental dialectic concerns the application of logic. Kant outlines a number of principles that relate to this. Some miscellaneous principles are summarised here. • Error arises from the unnoticed influence of sensibility on the understanding. • Syllogisms deal with concepts and judgements, and can be categorical, hypothetical or disjunctive. These are the three types of judgements that come under relation. • Our approaches must be grounded in pure idealistic concepts. A hypothetical constitution that provides for the greatest possible human freedom may not be something practicable, but it ought to be the ground of any laws we make. • Reason is the faculty of inferring via a judgement that is a universal rule. • Descartes’ cogito ergo sum is tautological, as it immediately asserts the reality, assuming the existence of “I” in the statement. • The soul is (1) substance, (2) simple in quality, (3) unity (numerically identical over time) and (4) relates to possible objects in space. • We do not really perceive external things, but only infer their existence from inner perception. 5.1 Antinomies of Pure Reason Kant outlines four antinomies , which are apparent contradictions that follow from pure reason. These are stated in thesis/antithesis form, and both “proofs” appear to be valid. 5.1.1 Antinomy 1 Thesis. The world has a beginning in time, and is bounded in space. Proof. Suppose there is no beginning. Then up to every given time, an eternity has elapsed. So an infinite series of states has occurred, requiring an infinite synthesis. (Note here that infinity means “greater than any number”, not “a maximum”, so infinity consists in the impossibility of successive synthesis). So this is impossible. Suppose unboundedness in space. Then there is an infinite given whole of simultaneous things, so an infinite, successive synthesis of its parts is required. This is also impossible. Antithesis. The world has no beginning in time, and is unbounded in space. Proof. Suppose there is a beginning. Then there must have been a preceding time with no world, which would be empty. But empty time is homogeneous so nothing could arise from it. Suppose boundedness in space. Then the world exists in an empty space, so has a relation to (“is bounded by”) an empty space i.e. a non-object. This is impossible as a non-object cannot bear any relations. Also, appearances cannot be bounded by emptiness outside themselves, as space is a condition. 7 Remark. To resolve this, we must settle whether the chain of causes is a regress to infinity (which implies an absolute, infinite magnitude), or an indefinite regress (whose magnitude is simply indeterminate). When we consider a regress of causes, we see it simply does not have a given magnitude, so such a regress of causes is simply indeterminate in magnitude. The problem that the thesis outlines is “that an infinite synthesis is impossible”, but an indefinite regress is not infinite , so does not run into the same problem of impossibility. We have that the regress is indeterminate, so the world cannot have a beginning in time or space. 5.1.2 Antinomy 2 Thesis. Every composite substance consists of simple parts, which constitute everything in composition. (That is, substances are not infinitely divisible). Proof. Suppose not. Then if we remove all composition in thought, then no composite parts are left. But by assumption there are no simple parts left, so there is nothing left at all, which is absurd. (Note: space and time do not consist of simple parts). Antithesis. No composite thing consists of simple parts. (That is, substances are infinitely divisible). Proof. Suppose not. Then every simple part must occupy a space, so it is composite - a contradiction. Finding the intuition of the simple in order to get intuition of the composite is impossible. Remark. This is something that can only be settled by experience. Whether the thesis or antithesis is correct depends if it is a continuous or discrete substance. 5.1.3 Antinomy 3 Thesis. Appearances are derived not only from causality in accordance with laws of nature, but also from causality in accordance with freedom. (Essentially - a free cause is possible). Proof. If we take it that everything needs a cause in nature, then this leads to an infinite regress. So we must need an absolute cause that arises from itself Antithesis. There is no free cause; only the laws of nature are followed in causality. Proof. A first beginning presupposes a state where there is no causal connection, which is a contradiction. Remark. If appearances are things in themselves, then there can be no freedom; time is a condition of appearances, but not of things in themselves. It is also possible that freedom and natural necessity may not be contradictory. 5.1.4 Antinomy 4 Thesis. There exists an absolutely necessary being (either part of the world, or its cause). Proof. Every alteration requires absolutely necessary conditions to have preceded it, so there must exist something absolutely necessary if an alteration is to be its consequence. This necessary being must also be in the world, because only things in time can affect things in time. In particular, something outside of a series of events cannot precede something in the series. Antithesis. There is no absolutely necessary being. 8 Proof. Suppose there were an absolutely necessary being. Then if there is a necessary beginning, then the law of causality/determination breaks. If there is no necessary beginning, we get a contradiction, because the existence of a multiplicity cannot be necessary if no part of it has necessary existence. Remark. Notice that we must be careful when we infer necessity or contingency from alterations in some series. We might think that the fact than an object is in motion is contingent, because it is possible for it to either be in motion or be at rest. But motion at one time and rest at another time are not contradictory opposites. Only motion at one time, and rest at the same time, are contradictory. So seeing the object in a different state at different times does not prove that its state is contingent. This antinomy may be resolved by showing that the members of an empirical series can all be contingent There may be a necessary being outside the series that makes it possible. 5.1.5 Comments on Antinomies How do we properly resolve these apparent contradictions? We consider practicality for a moment. The thesis seems to support morality and religion practically, whereas the antithesis does not. It seems like moral principles lose all their validity under the antithesis, but empiricism does have the advantage of grounding the understanding on its own grounds and prevents us from having to reason about things we are unfamiliar with. In these antinomies we are also trying to reason about the concept of an absolute whole . But this is some- thing impossible to perceive, so the solution cannot lie in experience. So they cannot be resolved dogmatically (meaning by considering the truth of the statements themselves), but they can be solved critically by exam- ining the cognitions on which they are founded. In particular, they can be resolved by showing that the apparent contradiction arises from applying the idea of absolute totality (a condition of things in themselves) to mere representations. 5.2 Arguments for God and Refutations Here, Kant states that there are only three possible a priori proofs for the existence of God, which are the ontological argument, the cosmological argument and the physico-theological argument. He refutes all three of these. 5.2.1 The Ontological Argument This is an argument for the existence of God that goes approximately as follows: • God is the greatest possible being that can be conceived. • A greatest possible being must necessarily exist. If God existed only in the mind, then he would not be the greatest possible being, for we can conceive of a greater being that does exist. • Therefore, it is impossible that God does not exist. Now for the refutation. We note first that the ontological argument rests on the principle that if you remove a necessary predicate from a subject, then you get a contradiction. The statement “A greatest possible being must necessarily exist” really means “A greatest possible being must have the property of existence”. But existence is not a predicate since existence does not add anything to the conception of a being. So “removing a necessary predicate” is meaningless here. Furthermore, even if existence were a predicate, if you remove existence then you remove both the predicate and the subject, and there is no contradiction here. 9 There is yet another, even more fundamental, problem. Having three angles is a necessary predicate for a triangle, but this does not say that “three angles are necessary”. It says that “if a triangle exists, then it must have three angles”. The corresponding statement in this situation is “if a greatest possible being exists, then it has the property of existence”. This is of course a mere tautology. 5.2.2 The Cosmological Argument This argument simply says that if something exists, then an absolutely necessary being must exist. I exist, so an absolutely necessary being must exist. Kant refutes this by stating that this argument presupposes that a being of highest reality is completely sufficient for the concept of an absolute necessity in existence. 5.2.3 The Physico-Theological Argument This is a type of proof of the existence of God which is grounded on determinate experience. But the idea of a necessary, all-sufficient being is so great that no experience is enough to prove such a concept. If we appeal to the order and harmony of the world, we can at most establish a proportionally great architect, but not necessarily an all-great being. In fact, this proof is grounded on the cosmological argument, which is grounded on the ontological argument. 5.3 The Concept of a Necessary Being The concept of a necessary being transcends the boundaries of experience, and can thus never be proved nor disproved using speculative reason alone. Identifying apparent teleological ends in nature and appealing to “highest wisdom” as their cause, rather than seeking universal laws in matter, would be a mistake. In order to make such an appeal, it would need to be grounded on the end of nature as a universal whole . If we cannot find this in experience, then how can we infer from this a highest being? Kant nevertheless argues that there must exist something different from the world that grounds the order of the world, because the world is a sum of appearances that must have transcendental ground. Kant says that we must assume a unique, wise author as the ground of the world’s unity, out of necessity. But this author cannot extend beyond possible experience because we only give it the properties necessary to ground the unity we experience in nature. Another additional thing is mentioned near the end of the transcendental dialectic that is worth mentioning. We have considered a highest being, but reason also dictates that no species ought to be regarded as the lowest being either. This is because each species contains only a common concept that cannot be thoroughly determined. So it must contain other concepts under itself and not be the lowest. This is essentially Kant’s counter-razor to Occam’s razor, which states that “entities ought not to be multiplied unnecessarily”. Kant’s counter-razor asserts that “the varieties of entities are not to be diminished rashly”. 10 6 The Transcendental Doctrine of Method 6.1 Mathematics vs Philosophy Philosophical cognition is rational cognition from concepts. Mathematical cognition is rational cognition from the construction of concepts, i.e. an a priori examination. The intuition for reality can come only from experience. Empirical concepts cannot be defined , but only explicated: concepts such as substance, cause, right and equity cannot be defined a priori. Therefore, while mathematics is grounded on definitions, axioms and demonstrations, philosophy cannot be. We do not begin with definitions when doing philosophy. 6.2 Moral Laws The final aims of transcendental speculative reason are to prove or disprove (1) freedom of the will, (2) immortality of the soul, and (3) the existence of God. All interest of reason is united in the following three questions: 1. What can I know? (Speculative) 2. What should I do? (Practical) 3. What may I hope? (Practical and theoretical) We observe that all human beings seem to be endowed with moral judgements, and therefore we can suppose the existence of pure moral laws . Pure reason contains moral principles that have objective reality. In par- ticular, Kant is known for stating the principle that “ought implies can”, which implies that no moral law can hold that is not possible for its subject to do. We can answer the second question by “do that through which you will become worthy to be happy”. Kant says that we can only hope to have a system of self-rewarding morality that is founded on freedom if it is grounded on a highest reason . In order for happiness to be distributed in accordance with morality, a wise author is necessary and hence the laws are regarded as commands Kant emphasises that without a God, the moral ideas would not be able to fulfil the ends of rational beings. To be clear, however, we regard laws as divine command because we are internally obligated to follow them. This is not the same as getting the laws from the divine being, for in such a case the laws would be merely contingent and subject to the will of some being. 11