Until now, we have more or less been considering space and time as a single concept, without greatly distinguishing between them: both are pure, a priori intuitions that ground all experience and make sensation possible. But in writing about the transcendental aesthetic, Kant begins to make distinctions that separate space and time. In particular, space is “the form of all appearances of outer sense…under which alone outer intuition is possible for us” (CPR 159), while time is “the form of inner sense, i.e., of the intuition of our self and inner state” (163).
Whatever the differences between space and time, another commonality that Kant asserts to exist between them is their transcendental ideality, such that they do not exist outside of perceiving subjects. Kant holds that not only are space and time a priori intuitions, but that they definitely do not objectively exist as things-in-themselves. He does not hold a more modest, agnostic view on this question of their objective existence, but is certain that they have no such existence.
He sets out to prove it so: if one thinks that space and time have an “absolute reality” (166), then one must see them as either subsisting or inhering. If one holds the former view, then one “must assume two eternal and infinite self-subsisting non-entities (space and time), which exist (yet without there being anything real) only in order to comprehend everything real within themselves (166-167). Why this “must” be the case, I do not understand. It seems to me that one could think of space and time as finite and having been caused by something, as in the Big Bang theory.
If one holds the latter view, then one “must dispute the validity or at least the apodictic certainty of a priori mathematical doctrines in regard to real things (e.g., in space),” because our understanding of space would be through experience and thus not produce apodictic certainty. For Kant, this outcome is unacceptable: mathematics, he is sure, is certain and thus a priori.
But is the concept of space and time as objectively existent mutually exclusive with the concept of space and time as a priori intuitions? That is, can space and time be a priori intuitions (and therefore give mathematics an apodictic certainty) and nonetheless have an absolute reality? Kant’s argument seems to assume that the two are mutually exclusive: if they objectively exist, then they are not a priori intuitions. Whether or not Kant is too hasty in assuming this will have ramifications for his position that space and time cannot have an objective existence.
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I'm not sure if I can accept the concept of Space and/or Time being finite (please excuse my basic understanding of physics, but I'm not sure if even the catalystic Big Bang actually created Space or Time, so much as it did expand them or alter their properties...but I could be horribly wrong.
Even so, I do think that if one were to consider Space and/or Time "eternal and self-subsisting non-entities", it would be necessary to consider them infinite...
...maybe.
I agree with Xusana that the concepts of Space and Time can't really be considered finite. If we assign Space and Time fixed values, then they seem to lose their legitimacy of universal applicability. Thus, it's necessary to think of Space and Time as infinite if we want to refer to them as intuitions that ground all experience. At the same time, I also have a problem with Kant's assertion that they cannot objectively exist. I would of thought that the way in which Space and Time relate to appearances would have pointed otherwise.
I agree as well. The Big Bang, as taught, was an alteration of matter that led to a series of evolutions resulting in the primordial soup of the Earth as we know it today. My issue with this is Kant's approach to mathematics as a priori, and I shall turn to physics as an example. Many calculations made by NASA and other space programs are of the highest form--that is to say the calculations to know the exact distance of a lunar landing requires more than the knowledge of "1+1=2"(which can be proven through a priori understanding). Some of these calculations depend on fractions of fractions of fractions to be correct. Does this render mathematical knowledge as being a prosteriori? It appears that the mathematics used are so precise that this may exceed our human capacity to experience. Hopefully.
Relative to me and my knowledge of physics, you are a gaggle of Stephen Hawkings, so I'll stop with the unfounded scientific claims (it will be hard).
Comment 1. Xusana, I agree that if we consider time and/or space to be "eternal and self-subsisting non-entities," then it seems they would have to be infinite. My question is: why must they be "eternal and self-subsisting non-entities?" Kant seems certain on this point, but I am not.
2. Even if space and time ground our experience, is it "necessary to think of Space and Time as infinite..."? Perhaps our ability to experience is limited and finite.
3. That's an interesting point. I wonder, if "1+1=2" can be proven a priori, then can those detailed equations be thought of as derivatives of--grounded in--those simpler a priori equations?
To be quite honest, I was shocked when I learned more about Kant's view on space and time. I used to think that what he considered to be a priori intuition was that which was absolute, not merely the cognitive faculties of our minds. Simply put, I just do not see how he can go from saying that space and time are only real in our minds (CPR 159, 165), as the grounding of the possibility of experience, to eventually making assertions as bold as the categorical imperative. I empathize with his plight, namely the attempt to determine the bounds of knowledge, but I just do not see how knowledge is at all possible if elements as fundamental as space and time are restricted to the human psyche. He even says that space and time would disappear without us (168). I would venture to say that our experience is within space and time, as a direct result of our minds being created in space and time. This seems much more obvious and coherent to me. Ultimately, I think Kant's Copernican turn, or his almost exclusive focus on the subject, is dangerous in that it turns reality into ideality, and knowledge into manmade fiction, which seems to be contrary to what he is trying to achieve, i.e. knowledge.
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