One of the origins of scientific method was with trying to find a philosophical validation for god. That doesn't mean that science is religion.
Mathematics, and logic, are entirely abstract entities. ENTIRELY. Whatever issues you may have with their application, they are not based in measurement, but on axiom. Mathematics is correct for its set of axioms. If you disagree with one of the axioms, then you're just making a different mathematics.
Oh, and re- apple =! apple... what if the only property you are measuring is that it can be referred to as an apple? Surely then any given apple = any other, or indeed the same, given apple, since the only properties you can compare are that they are, in fact, apples?
Space and time are not absolutes. This has been empirically proved over and over and over again.
Daymare, you're arguing with invalid technical and philosophical arguments.