1. Is the dialectic of logic identical with the misuse of logic (wherein one asserts an objective fact using only logic)? Or is the dialectic simply the part of logic in which one would commit this error, IF one were to commit this error?
2. I'm afraid I know very little geometry, though Kant uses his notion of the subject as evidence in several sections. Can geometry somehow be a human 'construct,' such that it is apodictic because that is how we 'make' it? As an a priori certainty, Kant seems to take it to be more sacrosanct than that.
3. Some commentators talk about Kant's dependence on Euclidean geometry for his ideas about geometry. How, if at all, does non-Euclidean geometry affect his ideas?
4. Was anyone else surprised to find out that Konigsberg was that far east, in what is now Kaliningrad? Always thought it was in present-day Germany.
5. To paraphrase Kant (hopefully correctly), he talks of experience triggering a priori concepts. What is the relationship between these latent faculties and the experience that activates them?
Thursday, March 4, 2010
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3. First of all James you have to keep in mind that, according to Wikipedia, non-Euclidiean geometries were not "widely accepted until the 19th century." http://en.wikipedia.org/wiki/Non-Euclidean_geometry#History
So, it's pretty fair that he's dependent on this business.
Secondly, I think you should clarify what you mean about "his ideas about geometry." Discussing this with my dad the math major, the major differences between Euclidean and non-Euclidean geometry concerns the nature of parallel lines, and it still seems to me that Kant's conceptions of space and the a priori synthetic nature of mathematics would apply here. Past that, please clarify.
Jenna, I think I can clarify where James I going with this question. There is a debate between non- Euclidean and Euclidean and their role in Kant’s philosophy that seems to be extensive. You’re right in saying that difference between these to types of geometry lies mainly in parallel lines, but it has many more implications than that. Non- Euclidean geometry relies on curved, such as hyperbolic and elliptic line lines to formulate a geometrical system that counterpoints that of Euclidean geometry. I guess one could say that goes against the synthetic a priori qualities of geometrical judgments, but I think the opposition to Kant lies farther than here. No, I am in no way an expert in non- Euclidean geometry, but I do know that Einstein took this concept and applied it in revolutionary ways to physics, transforming, and even shattering, many of the assumptions we once held about time and space. Non- Euclidean geometrics, as Riemann introduced them, make no objection to Kant, or at least so it seems to me, but I can see why they would the way they are used in Einsteinian physics. From the little understanding I have of it, non- Euclidean geometry stands as one of the basis for the theory of general relativity. Using this type of geometry, Einstein brought forth the idea that space curves the closer it gets to energy. This, in short, for example, accounts for the Earth’s rotation around the Sun and gravitational pull. Again, I can’t go into detail of all the implications of Einstein’s theory because I myself do not know them exhaustively. I do know it led to the development of some interesting ideas that might be relevant. The curvature of spacetime accounts for things such a time dilation and shifts in light. Moreover, this led to the discovery of black holes, or at least the determination for the possibility of them. As you may know, black holes refer to a region of space in time in which the energy and radiation levels are so high that space and time are distorted in such ways that nothing can escape. Interestingly enough, it is believed that if a person were falling into a black hole and could survive the strong gravitational pull (which he or she couldn’t, but let’s ignore that for now) the time it would take for that person to reach the black hole would be infinite for an observer. Many other implications revolve around he curvature of spacetime. Wormholes and the possibility of time traveling all rely on this concept, even things such Einstein’s claim that a fourth dimension, unreachable to man, exists can be related to this idea. This certainly brings up a different concept of space and time. One could even say that space and time, as derived from non- Euclidean, are very different from the time and space Kant is talking about. We may even go as far as say these are just as legitimate concepts of space and time, and they stand as the ground for completely different experience (or, in the case of black holes, no experience at all (?)). If that were to be case, time and space would not be the pure a priori intuitions Kant makes them out to be. Of course, there is a lot more to the argument, and my understanding of it is very limited as this is some of the most complex stuff out there, so I could never make such claim. Yet, it is definitely a question worth entertaining.
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