What do you make of quantum entanglement experiements, where it can be demonstrated that two entangled quanta can affect each other instantaneously over any distance?
Typically the experiment involves two photons, but it can be done with fermions (matter particles) as well. If you are not familiar with the specifics, wikipedia has a fairly cogent explanation, but the only feasible conclusions from these experiments are that either superluminal speeds of infinite energy are possible (which contradicts relativity and thermodynamics) or that space does not exist as humans perceive it (which contradicts locality). It is likely the latter because the former not only requires infinites, but it requires the creation of those energies from nothing, which also destroys notions of causality.
But if it is the latter answer, and man's notion of space is mistaken, then the Law of Identities is also a mistake, and we cannot properly assign a specific identity to anything because nothing is truly discrete; everything is but a facet of one whole existence and cannot be accurately described as parts with specific qualia. This has the further complication of putting a stop to the progress of epistemology, the sure footing of which only goes as far as "existence exists" and "I exist because I am thinking, and thinking requires existence." Beyond that, no maxims would be self-proving and the rest of human "knowledge" is actually opinion; belief.
If the results of quantum entanglement are what scientists think they are, then a square, a circle and a triangle are all really the same thing, yet something about our perception only shows us parts of them at a time, so that we peceive one shape where there are many. How's that for confusing?