The popular terms "modern" and "postmodern" are grounded in Western history and culture. So, unless Japan has been thouroghly Westernized over the past five hundred years, Japan can't be labeled either "modern" or "post-modern." The label "pre-modern" is a much better fit for Japan.
There is a small percentage of Japanese who could be labeled "modern" because thier thinking has been strongly influenced by Western ideas. This type of person tends to be very well-educated and has spent time living in the West. They are far more likely than the average Japanese to make logical arguments based on reason.
One extremely interesting aspect of this discussion is that "postmodern" Westerners and "pre-modern" Japanese share a lot of similarities with each other. In other words, the West is moving East.
What does this mean for the church in Japan which has been so heavily influenced by modernism?
How do we effectively present the gospel to "pre-modern" Japanese?
Here is an excellent article on postmodernism:
TOWARD A THEOLOGICAL UNDERSTANDING OF POSTMODERNISM by Daniel J. Adams