This is innate knowledge. Second and third ones are independent of experience and experience is irrelevant to a priori concepts or knowledge. An example of these is that you know that it cant rain and not rain at the same time. The last one is that experience cant justify a priori knowledge claims. This means that for a priori knowledge, you need more than experience. This leads to reasoning and understanding. We can get a priori knowledge in three different ways. The first one is that the knowledge already could be in our minds at the minds inception, for instance the Forms, which is Descartes idea of God.
This goes back to the first way of a priori: Prior to experience. The second one is intuition, which is the term we use when something is just obvious and we cant explain how we know. Here we can use the same example as on second and third way of a priori: It cant rain and not rain at the same time. The last way we can get a priori knowledge is through reasoning. You know that all humans are mortal and that you are a human. Therefore, through reasoning, you know that you are mortal.
In rationalism, reasoning and understanding is more important than the senses to the establishment of knowledge. Sense experience is an incoming visual, aural, touch, taste and smell data. Empiricists believe that sense experience is the source of all knowledge or is most important for us to gain knowledge. Where knowledge is gained independently of experience in rationalism, knowledge is in empiricism a posteriori, dependent on experience. Example of a posteriori knowledge can be that humans are mortal because you have experienced people dying.
Empiricists claim that all a priori knowledge is analytic, that you understand independently of experience that The sun will set today at sunset, because you understand the meaning of the words: A sunset is when the sun sets. They also claim that only a posteriori knowledge (dependent on experience) is synthetic, which gives information about how the world is. An example of this can be The sun will set today behind a veil of cloud. This is, as Hume called it, a matter of fact, because you have experienced the sun going behind a veil of cloud.
While empiricists claim that synthetic a priori knowledge is impossible, rationalists claim that it is possible. You can know that for instance most tables are made of wood because you understand it. We can have factual or substantive knowledge of how the world is, which in this case is what most tables are made of, through reason or understanding alone. The Rationalist says that if knowledge understood by reason does not come through the senses, but independently of sense experience, where then does it come from? According to rationalism, we are born with such innate knowledge.
The Rationalist claims that a priori knowledge is the truth of logic and mathematics. We understand that 3 + 4 = 7 because it is obvious to us. Although we use our eyes when learning to count things, we still understand that three books and four books put together is the same as seven books. Descartes Wax example is a good example of how our a priori knowledge depends on reason. You know about wax, that it is yellow, doesnt have any smell, hard, solid, tasteless and scratchable etc. and that it gets squashy and lighter when warmed up.
These sense experiences alone cannot account for our understanding because it is just a stream of incoming data. This proves that the mind must have innate abilities to form understanding when sense data is fed into it. It is the same with another example of Descartes about people in the street seen from above. His claims are that our sense experience tells us that there are hats and coats moving below. Our reasoning and understanding tells us they are people. In my opinion Rationalists are not always right to claim that knowledge is a priori and depends primarily on reason.
In my opinion, you need to experience certain things before you can reason and understand it. For instance, if you havent been to the Isle of Wight Festival, but you know what kind of music the bands are playing and you know what people are going, it doesnt make you know what the festival is like. This makes me closer to empiricism. On the other hand, though empiricism says that you know that 3 + 4 = 7 because you were taught this, I believe you have this is a priori knowledge primarily because of reason.
I believe the truths of mathematics and logic are not there to experience, but to understand. This view makes me closer to rationalism. I have difficulties imagining synthetic a priori knowledge, because it is logical that we need to experience that the sun goes behind a veil a cloud, to be able to reason and understand that this is how the world works. You cannot have the knowledge that the sun will set today behind a veil a cloud before you have even experienced it it is just obvious that you need the experience.
It is the same with the statement that It cant rain and not rain at the same time. You can reason this fact because only you have experienced both rain and not rain. It is not independent on experience because you need to experience rain and not rain to understand that there is nothing in between. This view makes me closer empiricism. I believe that I understand the concept of sunset because I know the concept of sun and the concept of set. You can make two statements: I know that the word sun is that big shiny circle in the sky and I know that the word set means something that goes down.
Therefore, through my reasoning, I know that the shiny circle in the sky will go down at sunset. This makes me closer to rationalism. According to these examples, it looks like I will place myself in the middle of this line. But the fact that I claim that synthetic I priori knowledge is impossible and that I cant get to understand how synthetic a priori knowledge is possible, and that this view in my opinion is decisive to where you stand on this line, I will place myself closer to empiricism.