Aesthetics
In the context of Kant's philosophy, aesthetics has nothing to do with arts. Rather, Kant used the word aesthetics in a sense which it has now lost. Aesthetics, in this context, refers to sensation and sensitive perception. Therefore Kant thought it would be an appropriate name for the part of the Critique of Pure Reason which deals with sensibility and perception.
Analytic judgement
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 what is meant by the subject) already entails the predicate. These judgements are true by definition. 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 can not 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”.
A priori
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. For example, 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.
Kant gives two criteria which should allow to recognize 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.
A posteriori
A posteriori knowledge, as opposed to a priori knowledge, is knowledge that relies on experience. This knowledge is learnt through experience and observation. It comes from seeing, hearing, touching, tasting or smelling. For example, “this pen is blue” is an a posteriori judgement. This judgement is founded on the experience I have of my pen.
Experience can not offer necessity. “Experience teaches us, to be sure, that something is constituted thus and so, but not that it could not be otherwise.” 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, because it is impossible to experience all objects of the same kind. I can never experience all pens, past, present and future.
Concept
A concept is a general representation that allows us to think about many objects together. A concept represents what is common between a plurality of phenomena to which the concept applies. There are empirical concepts that are derived from experience and pure concepts that are independent of experience. Concepts are applied to intuition by our understanding; by doing so, we think the intuitions and make them intelligible. For example, I have the concept “dog”, which represents “having 4 paws” as something that is common between dogs.
Intuition
According to Kant: “In whatsoever mode, or by whatsoever means, our knowledge may relate to objects, it is at least quite clear that the only manner in which it immediately relates to them is by means of an intuition.” Intuition is an immediate relation between knowledge and an object. If we take the example of seein a red apple, the actual seeing of the red apple is an intuition. I have a visual intuition of a red apple. However, this intuition is pre-conceptual. I have not yet applied any concepts (“red”, “apple”, “round”) to what I see.
Judgement
A judgement is a mental act that combines different representations in a person's consciousness. Judgements are used to think something about something, to affirm or deny something. Judgements either pose the relation between two conceptions or the relation between two or more judgements. The basic units of knowledge consist of judgements of the form “subject is predicate”. The subject is something about which we are talking. The predicate is what is said about the subject. For example: “This dog is black.” In this judgement “dog” is the subject and “black” is the predicate.
Phenomenon
“The undetermined object of an empirical intuition is called phenomenon.” This means that when we see a red apple, the apple is the phenomenon. But as it is given in intuition. this apple is not yet understood as an apple because intuitions are not yet conceptual.
Schematism
Schemas in Kant’s philosophy are meant to solve a very particular problem: how can pure concepts of understanding be applied to intuitions? After all, there is a fundamental difference in nature between a concept and an experience. How can we apply our concepts at all? For this we need a schema. A schema is a mediating representation between a concept and an intuition. It is neither concept nor image, but it allows the application of concepts to intuition. The schema is a sort of bridge. For example: “The schema of substance is the permanence of the real in time.” This allows for the application of the concept of substance to the intuition of something permanent and real in time.
Sensibility
According to Kant: “The capacity for receiving representations (receptivity) through the mode in which we are affected by objects, objects, is called sensibility.” Sensibility is the passive faculty that receives data from the world. It let’s thing appear to us. For example, if we see an red apple, our eyes see a color. The eyes passively receive a representation.
Synthetic judgements
Synthetic judgements are opposed to analytic judgements. These are judgements in which the predicate “lies entirely outside the concept [the subject]”. These judgements are not true by definition. 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.
Transcendental
Kant's goal was to establish a transcendental philosophy. Such a philosophy relies on knowledge that is not empirical nor is it rationalist speculation. Transcendental knowledge is concerned with the necessary conditions for the possibility of experience. Therefore, transcendental philosophy is concerned with the possibility of a priori knowledge. For example, Kant will establish in the transcendental aesthetics that space and time are conditions for the possibility of experience and that they are necessary in order to have mathematics and physics. Transcendental philosophy should put limits on human knowledge. This should ensure that we will not try to understand more than is possible.
Understanding
According to Kant, understanding is the faculty that organizes and makes sense experience and intuition. This is done by applying concepts and rules to experience. By applying concepts, understanding organises our intuitions. For example, by seeing a red apple we have an immediate relation (intuition) to this object. However, if the apple is only given in intuition, then the apple is not yet understood as an apple. It is understanding that makes sense of this experience by applying different concepts to it. When presented with a red apple, understanding will apply the concepts “red”, “apple”, “round”, etc.
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