A very crucial step in Kant’s Prolegomena to Any Future Metaphysics is recognizing that there exist synthetic propositions a priori arising from pure reason. Since metaphysics, at least according to Kant, already implies this notion, it must be investigated to what extent it is possible. The intuitions of space and time are the faculties of pure reason within human life that allow this to occur, in mathematics specifically.
These pure intuitions act as forms of sensibility and appearance, in the sense that they precede empirical intuition, as well as defines it. In the past, forms have not been known in themselves, but known in being a template and a model for all other individual things. Essentially, space and time embody this idea. All of the concepts sought out in experience must reflect space and time through sensory representations. Space and time are not equipped with the concepts of things, but can be used to generate them. Perhaps this is exactly the reason Kant believes the intuitions of space and time to be innate entities. We know and understand them as they are, giving experience therafter all of its meaning. At this point, it should be rather obvious that doubting this would make it almost impossible to have synthetic judgements a priori. Consequently, pure mathematics would be looked upon as insufficient and unreliable because what then would constitute all of its concepts?
Pure mathematics illustrates the pure intuitions of space and time. If metaphysics shall be based on this principle (in its own sense of course), then it must follow that subjects of pure reason can withstand and reflect it as well. It also must be understood how it is done so that if metaphysics is to continue, the basis of it will be as solid as mathematics has proved to be. Synthetic judgements allow for the combination of distinct concepts without any assistance from the senses which is precisely how the concepts of mathematics come about. In mathematics, there is emphasis on the certainty it must hold, namely universality and necessity. Hence the reason why mathematics can never be based on experience; it lacks these things. Everything in mathematics is subject to the intuitions of space and time. There is no further way to dissect space or time because they are merely intuitions, or just the way things come to be connected in a “synthetic” manner. The knowledge we obtain from it is just enough to help make valid conclusions and synthetic propositions within this subject.
Kant discusses pure intuitions and empirical intuitions in a distinctive way, while implying that one could not be sufficient without the other; they go hand in hand. Kant distingusihes them in terms of experience in order to bring forth the underlying basis of empirical intuitions. In this case “experience” or “empirical” is referring to things within the senses. Mathematical concepts depict the form of sensibility (space and time ) to then represent them through the senses, which leads to a conclusion that pure mathematics is dominated by a priori cognitions, but facilitated by such experiences.
Hi!
ReplyDeleteI'm not sure I understand, exactly, your point in the last paragraph. Kant certainly makes the distinction early on between empirical and a priori intuitions, but it doesn't seem that he characterized their interactions quite in the way you described (i.e. going hand in hand).
From what I could gather, he (in some senses) asserts a priori congnitions and intuitions as establishing a basis for all our possible experience (which is necessarily limited to appearances) - our a priori cognitions in geometry encapsulate the entire field of our possible experience of the 'appearance' of things, our a priori intuitions and the outer appearances of things must be completely congruent, etc.
However, it doesn't seem to go the other way around - I don't see how a priori cognitions or intuitions are described in the text as being facilitated by empirical sensibilities (outside of space and time, which don't seem to really be 'empirical' in that sense). The idea actually seems pretty counter-intuitive.
Apologies if I misunderstood/misread what you're trying to say, or if my comments are not clear.
I agree that Kant dose not describe the interactions between a priori cognitions and empirical cognitions as going hand in hand. As you said, a priori intuitions act as the foundation for possible experience. The relationship betwen them then (a priori and empirical intuitions) is merely sequential. A priori cognitions precede empirical ones, as well as allows for its possibility. However, I described them as going hand in hand because both a priori and empirical intuitions are crucial to the entire scheme. Pure intuitions are representaions that make possible appearances, while empirical intuitioins are tools that use these pure intuitions to make actual the appearances. Kant was able to derive the existence of a priori cognitions from the already existing empirical ones. This takes me to where I said that a priori cognitions are facilitated by empirical cognitions. I simply meant that empirical intuitions allow for an easier, more concrete way of representation which is based off of and built upon the pure intuitions of space and time. Perhaps Kant does not imply any of what I am saying at all and I could be completely missing the point, but hope that I cleared up somewhat what you misunderstood.
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteBefore we can say that something precedes the other, we have to say that there must be time and space for this possibility to occur. This very statement - a priori precedes a posteriori - doesn't make sense from the point of view of metaphysics. This proposition can only be made in a world of experiences, it is not given, it is not a necessity.
ReplyDeleteAnimals are physical bodies that appear in physical world, that appears in the intuitions of space and time, which according to Kant are "innate". Innate to the reality, I think that's what he meant. They certainly can't "have knowledge" of space and time, for its not clear who are "animals" and what does it mean "to have knowledge" from metaphysical point of view. Because any proposition a posteriori is related to experience, and in metaphysics we can only have faith in a priori judgments, separate from experience.