Can reality contradict itself?
No, because a contradiction asserts every world at once, and a description that permits everything rules nothing out. Picture a bank ledger saying an account holds nothing and also a hundred pounds. From the hundred pounds it follows that either the account holds a hundred pounds or the moon is a biscuit. The ledger also says the account holds nothing, which rules out the first half, so the moon is a biscuit. Put any sentence in place of the biscuit and the ledger certifies it. Gottlob Frege found this out in June 1902, when a letter from Bertrand Russell showed that his system of arithmetic proved everything. So consistency is part of the founding demand. A structure counts as existing exactly insofar as it accounts for itself with nothing left over, and a self-contradicting structure distinguishes nothing.
This answer comes from OPH, Observer Patch Holography. OPH is a rigorous, consistent and complete description of the unified, self-creating computational Universe we inhabit. Its consistency is machine-checked: the fixed point at its core is constructed explicitly, and a theory with a model contains no contradiction.
To understand OPH and check every step yourself, start with the free book Reverse Engineering Reality. It builds the theory from the ground up, and the OPH Notebook answers your questions while you read.
read the free bookask the notebookor ask sage:read chapter 2: Why Is There Anything Rather Than Nothing?watch a universe make its own particles