How can postmodernism be reasonable when in its own nature, it remains paradoxical?

On one hand, postmodernity makes sense through its principles of deconstructing logical principles and essentially eliminating objectivity. The paradox is that by its skepticism it indirectly deconstructs itself and using the exact logic it rejects, claims an objective statement. How is it reasonable to make a statement and claim it valid when with the same logic it entails everything else to be invalid?