Like Objectivist philosophers such as Leonard Peikoff, I think of the principles of noncontradiction and excluded middle as not themselves fundamental laws of reality, but fundamental laws of correct thinking. The familiar proviso at the same time and in the same respect that we state in the principles of noncontradiction and excluded middle arises from the fact that time and respect are constituents of identity, that is, they are in reality.
Relativistic time is the time of reality.
Temporal relations pertain to particular identity. The time proviso in the principles of noncontradiction and excluded middle reflects the constraint of particular identity in reality. It seems then that our understanding of the principles of noncontradiction and excluded middle are refined by what we have learned of simultaneity from special relativity, but though our concept of time stood to be corrected by special relativity, our principles of noncontradiction and excluded middle did not. References Armstrong, D. M. 1989. A Combinatorial Theory of Possibility .