Kant’s arguments for the principles of space can be broken down into: two arguments for why space is a priori, two arguments for why it is an intuition, and one argument using geometry to show how it is both a priori and an intuition. Reducing a couple of his arguments to their logical forms, I take issue with a some of his points.
First, his argument in which he relates that, “One can never represent that there is no space, though one can very well think that there are no objects to be encountered in it” (CPR 175). Essentially, it is possible to conceptualize the absence of all objects and appearances in space, but impossible to conceptualize the absence of everything, including space. I find this to be contradictory when translated into a sufficient and necessary condition. If S represents the existence of space, and O represents the existence of objects, than Kant is saying: if S, then O; but if not O, then still S. Normally it would follow that if Space is a necessary and sufficient condition for the appearances of objects, than the absence of all appearances would mean no space, if not O, then not S. I’m not sure why it’s not possible to think of a complete non-existence of space, of absolute nothingness. At the same time, I realize that a discussion of a void of existence is more of a subjective, hypothetical argument.
Another point I have trouble with is his distinction, “if one speaks of many spaces, one understands by that only parts of one and the same unique space. And these parts cannot as it were precede the single all-encompassing space as its components, but rather only thought in it” (CPR 175). I interpreted this as a conceptualization of the whole is needed to conceptualize its parts. In addition to this, however, is the distinction that what makes something considered space is its relationship to Space, and what distinguishes different spaces from each other is only their relations to one another within Space. I originally took this to be a form of reductionism, but Kant seems to be saying that Space has properties not entirely explained by the sum of its parts. Essentially, Space gives identity to its infinitely divisible parts, but does not receive any reciprocal identities. I am in agreement, however, that an awareness of Space is necessary to distinguish between smaller spaces. I’m just puzzled why smaller pieces of space cannot be thought of as components of Space.
Kant basically uses the same argument forms when discussing Time, but I don’t really have the same problems with them as I do with Space. Basically, it’s easier for me to understand Time as an a priori intuition as opposed to Space, which I imagine more as a physical substance.
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I am not sure if I agree with your objection to Kant in regard to the relation of space to objects. I do agree that you cannot imagine objects without space. And although it would be difficult to imagine a space without objects it still remains possible. Kant’s logical proposition, I believe, remains valid. For instance if you replace the relation of space and objects with a different example say a supposed man named Frank and the human race, it seems to work out. Now, I can conceive of Frank not existing while the human race still exists. However, I cannot conceive of Frank if there were no such thing as the human race. The general idea is that objects are necessarily dependent on space, which holds the possibility for all of extension, just as Frank is necessarily dependent on the human race for existence.
I don't necessarily agree with you in your criticism of Kant's first argument. As I understand, he is not saying that it is"possible to conceptualize the absence of all all objects and appearances in space, but impossible to conceptualize the absence of everything, including space." Instead, he argues that we can only conceptualize objects in space. While we can think of space without objects, we cannot think of objects without space. In terms of your example, i would phrase it as: if S, then O within S; but if not S, then not O. As such, space stands as the groundwork for objects.
Originally I took issue with the contraposition modus tollens from Kant's argument, but phrasing in terms of objects within space makes much more sense to me. I still think Kant's argument makes more conceptual sense than logical sense, but imagining objects with no space is an example I'm more willing to agree with.
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