The first question for Kant is "how is pure mathematics possible?" If math is based on synthetic a priori cognitions, we should, in theory, be able to draw connections between different concepts by pure intuition. Intuition would connect two things that are connected in synthetic judgments. There are two different types of intuitions for Kant, namely, empirical intuitions and pure intuitions. The first are what we normally call perception. Since math basically consists of the former, meaning synthetic, a priori judgments, there should be a form of pure intuition that is innate in us and allows us to connect different concepts without any reference to the experience of our senses. The reply that Kant gives is that space and time are not things in themselves, but they are the form and sensibility. These are innate intuitions that shape how we perceive the world. Thus, before any concept the things we experience as a result of our senses, we would still have some concept of space and time. Space and time are not things in and of themselves, rather they are empty forms that determine how things appear to us. This is true for all the objects that we perceive within space and time. They do not exist alone, but the objects that we perceive are appearances of things.
Kant was lead, as a result, to three final remarks:
1. That we can have a priori certainty of geometry only because we have pure intuition of space. This certainty is due to the fact that we are only examining our own mental framework, and not things as they are in the world.
2. The says that he is not engaged in idealism. According to the view of idealists there are no real objects in the world. The only things that really exist are minds. Though he believes that we can not perceive things them self, Kant does not deny the existence of the object or any other reality in the world besides minds.
3. Appearance can be deceptive. We can misinterpret what we see and be deceived by such. If space and time exist as realities, then they can be misinterpreted by us, but since they are not realities, but just appearances, they are a priori certain.
Kant was lead, as a result, to three final remarks:
1. That we can have a priori certainty of geometry only because we have pure intuition of space. This certainty is due to the fact that we are only examining our own mental framework, and not things as they are in the world.
2. The says that he is not engaged in idealism. According to the view of idealists there are no real objects in the world. The only things that really exist are minds. Though he believes that we can not perceive things them self, Kant does not deny the existence of the object or any other reality in the world besides minds.
3. Appearance can be deceptive. We can misinterpret what we see and be deceived by such. If space and time exist as realities, then they can be misinterpreted by us, but since they are not realities, but just appearances, they are a priori certain.
2 comments:
On point three, i would say the problem is not our interpretation but, the lack of and inability to aqcuire data.
exactly how does Kant derive the two different kinds of intuition? This seems like a good question to me. Before he can go on, he himself would have to prove that there are such things and that they are not just some way of categorization created by him.
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