"Critique of Pure Reason" and the discussion of issues related to

Occasionally read Kant (Immanuel Kant) of <Critique of Pure Reason>, with most recently in answer undergraduates <logic and computing> curricula ZFC set theory, when the next review some basic questions, again feel that knowledge is interconnected and of. Although this feeling when my college taking shape, but until the students had only piqued my interest, so will always think of things down (I installed twitter ). Of course, some ideas may lack of consideration, but not as a formal academic articles published, and discussing their own or with no problem.

Sad to say that Kant had read the book, plus unfortunately do not understand German, not directly Duyuan Zhu, only read the English translation (it is the turn of the general) ... but Kant's masterpieces of this is too shocked, read a little bit of thinking which I think can be a long time, and therefore do not care about the level of how to translate a. just check the dictionary of philosophy, only to find Kant's first critique (be the first book by philosophers criticism, while the second criticism is the "Critique of Practical Reason", the third criticism is the "Critique of Judgement") is recognized in the history of one of the most obscure books, so I read it seems it is normal for the struggling ...

The first Chinese translation of the title: Why is called "Critique of Pure Reason" rather than "pure reasoning criticism" (Critique of Pure Reason) and the like oh?

Second, is the most interesting so-called "second law of paradoxical" (antinomy): I really do not know why the original Chinese translator in the translation of a translation of the term .... This is my jump chapters, very interesting, actually did not read before !

Priori knowledge about the system and two law paradoxical:

First be noted that the premise of this discussion: the main schools of philosophy before Kant, Descartes and Leibniz is a rationalist school, etc. (the typical mathematician), as well as Locke, Hume and Berkeley and other great philosopher of empiricism, We are sure that all school and maintain their own ideas, so see those non-stop, Kant itself should read a lot of Hume's empiricism to make, but he tried to find a comprehensive line of two schools, it is a purely rational routes so-called pure reason, is a priori (a priori) reason: Can come from experience and reasoning of its derivatives, the so-called a priori knowledge.

On a priori knowledge, the concept is very complex: first the knowledge must be "given", that metaphysics must be pre-existing in the human mind. is continuous development of human reason, but also because it is itself development to the needs of only some of the knowledge of experience can not be used to explain the problem and therefore should be in the human mind in some metaphysical reason. Kant's transcendental philosophy used to refer to such a system: it has all the a priori knowledge, these knowledge beyond the nature and substance, experience, and so the scope of the same time, is also very important: the system must be complete, that all a priori knowledge of the system inside.

Here is my doubts: this system is so powerful, it contains the root of all human knowledge, its expression must be expressed in Peano's mathematical ability of the system over countless times, while it is a complete, Well, according to Godel's incompleteness theorem, the system must contain contradictions, then the system can of course introduce a proposition P, P can also infer the inverse proposition, so paradoxical, of course all of the second law can get out of. have Based on this reasoning that the system is not reliable.

Further thought: Suppose human knowledge is derived from a similar system, then human knowledge if it is complete, then our human reason is unreliable! Of course, also possible that human knowledge is not complete (it is obviously a lot of knowledge of human will never understand), then this system is that Kant does not exist: it is impossible to complete a collection of the best source of all human a priori knowledge.

Further assume that: I the above analysis is based on Gödel's theory, but also the people to know Gödel ah ... all his knowledge was originally derived from a priori knowledge and experience is knowledge, then Gödel obtained based on incomplete knowledge theorem, then Theorem itself is not correct and reliable it is difficult to say, from now on, I assume that Gödel's theorem is correct the same time, I follow Kant's theory, by default there is a very powerful and complete human priori knowledge of the system [too contradictory ... speechless].

Then the second law is the so-called paradoxical, the fact that two mutually inverse proposition can be justified. In fact, this is a normal phenomenon of ancient philosophy, philosophy master Socrates. Zeno and so not all sophistry genius? whether it is anti, they can say piles of reasons, so the second law of paradoxical is easy for them, however, Kant presented here is about the secret of humankind's most want to know, is the recent numerous scientists for centuries fought, those most basic human problems, such as: universe begin?
The following translation of the second law of paradoxical intention I had to copy from Baidu and make changes, because the word too much, too lazy to play with the original ... not the same as found on Wikipedia ... unfortunately ... still have not found yourself typing ...

The first group antinomy.

(1) <time has a beginning, and space is limited>

This is the anti-thesis (2) <the universe has no starting point, the space is infinite>

Kant is the reductio ad absurdum to prove the general proposition (1): Suppose the universe is infinite in time, there is no beginning, then at each point in time (such as now), there is eternal or infinite time series has ended, that the universe has an infinite sequence of actions and state has gone up. infinite can not be achieved with a combination of continuous (My questions: So for example, set theory in mathematics, we believe that unlimited can be combined with the sequence, right? Of course, this sequence is the starting point, then the infinity of time must be reflected no beginning and no end in it? Can a beginning but no end? such as the Axiom of Choice, composed of infinite way depends on the formation of this sequence, need to be further explored), because there can be an infinite sequence of time has passed such a fact, so the universe must have a starting point. [Time has a beginning]

Assuming the universe is infinite, the universe can not measure the marginal, it is not even imagine it, then need to think about the universe, only to fill method, the basic unit from the beginning to the universe itself in order to achieve its own ( My questions: Particle physicists have yet to reach an agreement is not infinitely divisible, the basic unit in the end there is still a big problem or not ....) If we have an infinite universe, then a continuous overlay process would certainly have done, that this process an infinite universe of things are enumerated in the light of (Kant's implication is: otherwise how could the universe exist? my question: According to Hawking, etc. to say, the universe In the expansion, is not it can be considered as a superposition of the process is always going on, that is, the universe is not marginal, it did not reach infinity?), then the completion of such a process is bound to make unlimited unlimited period of time has passed But just now we have proven time and can not be without starting point, so to contradictions. [space is limited]