Good philosophers provide new solutions to problems. Great philosophers provide new problems that demand solutions. Kant indubitably falls into the second category. The leading question of the Critique of Pure Reason: how are synthetic a priori judgements possible? It is up to the introduction to pose this question and to properly explain the difference between synthetic and analytical judgements and the difference between a priori and a posteriori judgements. A good understanding of these two distinctions is essential to understanding the first critique.
Let us first understand what is meant by a judgement. All judgements have the same form: “subject is predicate”. The subject is what we talk about; the predicate is what is said about the subject. Take, for example, the judgement “this dog is black”. In this judgement “this dog” is the subject; we are talking about this dog. “Black” is the predicate of this judgement; we add the property of being black to the dog. Kant distinguishes different types of judgements, but they all correspond to this formula.
A priori and a posteriori
All judgement and knowledge is either a priori or a posteriori. This means that they are either independent from experience or they rely on it. Kant defines a priori knowledge as “independent of all experience and even of all impressions of the senses”. This kind of knowledge is grasped by reason, not by experience. A priori knowledge is opposed to a posteriori knowledge, which is known through experience. Let’s go over two examples! The judgement “all bachelors are unmarried” is a priori knowledge. This judgement does not require any experience; I do not need to ask all bachelors in the world whether they are married or unmarried to know this judgement to be true. Rather, it follows from the definition of a bachelor to be unmarried. On the other hand, “this pen is blue” is an a posteriori judgement. This judgement is founded on the experience I have of my pen.
Kant gives two criteria which should allow one to recognise a priori judgements: necessity and universality. A proposition is necessary if it could not be otherwise—it is true in all possible circumstances. A proposition is universal if it applies in all cases, to all things of a kind, and without exception. The idea behind these criteria is that “experience teaches us, to be sure, that something is constituted thus and so, but not that it could not be otherwise.” This means that experience does not offer necessity. For example, experience does tell me that my pen is blue; however, it does not tell me that it could not be red. My pen is not red, but it is not logically impossible to have a red pen. Experience is also incapable of giving strict universality. Take, for example, the judgement “all ravens are black”. This knowledge cannot come from experience since it is impossible to see all ravens, past, present and future. What experience can provide is relative universality of the type “no one has ever seen a raven that is not black”. These two kinds of universality are fundamentally different.
Synthetic and analytic judgements
Kant makes a second distinction between synthetic and analytic judgements. Kant defines analytic judgements as judgements in which “the predicate B belongs to the subject A as something that is (covertly) contained in this concept A”. This means that the concept of the subject, that which is meant by the subject, already entails the predicate. Take, for example, the judgement “dogs are animals”. This is an analytic judgement. The subject “dogs” contains the predicate “animals”. Put simply, when I think of a dog, I am also always thinking of an animal. I cannot separate what it is to be a dog from what it is to be an animal. These judgements are also called judgements of clarification. While “dogs are animals” does clarify what it is to be a dog, it does not provide us with any new information that is not contained by the concept “dog”.
Analytic judgements are opposed to synthetic judgements. These are judgements in which the predicate “lies entirely outside the concept [the subject]”. For example: “This dog is black.” This is a synthetic judgement. The concept of a dog does not contain blackness because dogs can have all sorts of colours. Synthetic judgements are judgements of amplification. They amplify the knowledge I have and add something new.
Kant becomes hard to follow once we start mixing a priori and a posteriori judgements with synthetic and analytic judgements. I have given examples above of analytic a priori judgements and synthetic a posteriori judgements. “Dogs are animals” is an analytic a priori judgement. The predicate “animal” is contained within the concept of a dog. Furthermore, the judgement is universal because it talks about all dogs. All dogs cannot be found in experience; therefore, this judgement cannot be a posteriori. “This dog is black” is an example of a synthetic a posteriori judgement. It is synthetic because the concept of a dog does not contain blackness. It is a posteriori because this blackness can only come from experience.
There are two more types of judgement that we can consider: analytic a posteriori judgements and synthetic a priori judgements. Analytic a posteriori judgements are simply not possible. Analytic judgements do not need experience; they solely require us to look at the concept of the subject. But what about synthetic a priori judgements? Such a judgement has three conditions:
It is not true by definition (not analytic).
It doesn't rely on empirical evidence (not a posteriori).
It expresses necessary and universal knowledge.
The case of mathematics
Kant proves that there are synthetic a priori judgements by giving us examples taken from mathematics. Kant’s most famous example is that 7 + 5 = 12. It should be obvious that this judgement does not rely on empirical evidence and that it expresses necessary and universal knowledge. This is an a priori judgement. But what makes it a synthetic judgement? Kant only gives a negative proof of the syntheticity of this judgement. We can decompose this judgement into several concepts: the concept of 7, of 5, of 12 and the concept of addition. According to Kant, we can analyse the concept of 7, of 5 and, in addition, all we want; we will never come to the concept of 12. In order to get to the concept of 12, “one must go beyond these concepts”. Because this judgement cannot be analytic, it has to be synthetic. So, this judgement is a synthetic a priori judgement.
Kant gives more examples like “the shortest distance between two points is a straight line” and “every event has a cause”. These judgements are a priori because they are necessary and universal. They are synthetic because the idea of “shortest distance” adds something new to the concept of a “straight line” and because the concept of “event” doesn’t logically contain “cause”.
The case of metaphysics
According to my last post on the preface of the Critique of Pure Reason, this book examines how metaphysics can become a science. But what do synthetic a priori judgements have to do with metaphysics? Kant’s claim is that metaphysical knowledge should be synthetic and a priori. Metaphysical knowledge cannot be a posteriori because its topics go beyond the sensible and therefore beyond experience. But why does metaphysical knowledge have to be synthetic? This is because synthetic knowledge is the most relevant kind of knowledge. Analytical knowledge merely clarifies a concept, but it is from synthetic knowledge that we actually learn something. An analytical metaphysics would be severely limited and uninteresting according to Kant.
So what is the problem? Why is metaphysics not a science? This is because synthetic judgements always need something to support and justify this judgement. In the case of synthetic a posteriori judgements, this is easy; the experience justifies the judgement. The experience of the blackness of a dog justifies me judging that this dog is black. Mathematical synthetic a priori judgements do not depend on experience but can get verified by experience. I do not need experience to judge that “the shortest distance between two points is a straight line”. However, I can justify this claim with experience. Whenever I draw two points on a piece of paper, the shortest distance between these two points is always a straight line.
Metaphysics has the problem of not being able to verify their synthetic a priori judgements in experience. This means that they can not justify their knowledge. Kant hopes that the answer to the question “How are synthetic a priori judgements possible?” can also provide a foundation for metaphysics. The rest of his first critique is dedicated to this question.
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