What consequences do modern physics and cognitive science have on Kant's philosophy?

Answer 1

The American Philosopher Charles S. Peirce had a lot to say about this.

The short answer is, quite a lot.

Peirce's Pragmatism was influenced greatly by Kant, and Peirce had the goal to answer the very questions you're asking.

I would suggest getting started here:

http://www.peirce.org/