Unlike many philosophers, Kant believed that synthetic judgments could either be a posteriori or a priori, stating that however, analytic judgments are always a priori which holds the principle of contradiction. Kant uses the example, “all bodies are extended.” On the other hand, “all bodies have weight” would be counted as a synthetic judgment. To say all bodies do not have weight is not necessarily contradictory, although, it may be false.

Descartes and Kant are very similar. Descartes' cogito (think therefore I am) relates to Kant, in that we think with our minds, therefore we must exist. If we did not exist, there would be no way we could think, breath, or live with our minds. Kant also has a similar opinion. For example, we clearly know that 2+2=4 and willl always equal four no matter how you look at it. Mathematics and our minds would both appear to be existent, innate objects that we have.

Kant made a bold statement in believing that both rationalists and empiricists are mistaken, which would include our old buddies Hume, Descartes, and Locke . We already know that Kant believes in synthetic a priori knowledge, which ironically would be most likely challenged by the likes of Hume, Descartes, and Locke. Kant goes on to argue that geometry, science, arithmetic, and metaphysics are all synthetic a priori. He example 7 + 5 = 12 to demonstrate why arithmetic is synthetic a priori (there are no properties of 12 in 7 or 5). The empiricists on the other hand, which include Locke and Hume, would argue that the basis of all knowledge is a posteriori, but would agree that the basis of all knowledge is also synthetic, hence they believe knowledge is only obtained by observation and that the idea that synthetic knowledge is innate or a priori. Now, the rationalists, whom Descartes happens to be, would concur that the basis of all knowledge is a priori, but would dispute that synthetic knowledge is priori.

As cazy as it sounds, Kant believes the basis of all knowledge is synthetic a priori. Aren’t we taught all academic knowledge in school and all other knowledge by observation? Kant seems to think that teachers almost serve as guides and that they help bring out the knowledge that you already have. Kant also argues that natural sciences, namely physics, are synthetic a priori. However, I must bring up how Hume points out the pool ball example, which contradicts this statement. Hume claims we do not know a priorily which angle the ball will move at until we observe the action, thus deeming this knowledge to be synthetic a posteriori.

Kant believes that arithmetic and numbers hold no meaning. He points out that numbers can be replaced by any other sign or symbols, to which as long as there is a set, known pattern, one can calculate an answer. The action of addition is the succession of items. Kant argues that a similar operation occurs when one talks about time. Time is the succession of items as well, hence knowing what occurred chronologically. Kant goes on to argue that geometry is the relation of items, such as the concept of space. Time and space are not a posteriori but rather are a priori. If time relates to arithmetic and space relates to geometry, would that then mean geometry and arithmetic are also be a priori knowledge? Knowledge of time and space is clearly not analytic but instead is synthetic.

Kant claims that there are 2 different styles of judgements, which happen to be polarities. There are judgments caused by one's perception and judgments caused by one's experience. Judgments from perception are simple impressions usually brought on by the senses and are synthetic a posteriori. Hume feels these certain judgments act as the centerpiece of one's knowledge as they do not do any further investigative research. This would mean that a perceptive judgment is noncontroversial to the empiricist while judgments brought on through experience are controversial. Kant states that judgments through experience is the separation of sensory information into categories, which also is synthetic a priori.