Jehu,
What you don’t seem to understand is that the physical sciences have as their foundation, an implicit metaphysical stance or view; that is to say, the belief that at least some kinds of things (material objects) are real, and are possessed of their own constitutive and operative cause (properties).
How could the physical world not be real? You could only picture this by adopting some objective, third person view on humans vs. reality. I say it again that humans don't have any right to access that metaphysical, theoretical, abstract view. To do so (and posit any meaning to them) is to commit an error.
The problem with this view is that is has never been logically demonstrated, and though it is admittedly how the world appears to be, there are numerous logical inconsistence that arise with it.
Logic is just another human tool that developed, ultimately, from the empirical world. You only arrive at these "logical inconsistencies" after trying to take your worldly tool with you beyond the world. If "the beyond" doesn't conform to your earthly tool I'd say that perhaps you tool is flawed.