beautiful work. To anyone who is interested in really understanding relativity deeply without intimidating math, I recommend Tim Maudlin's book: "Philosophy of Physics: Space and Time".
While having nothing against the book or its author, I must point out that ultimately it is "math in which we trust" (even experimental science leaves room for interpretation); philosophy, on the other hand, gives us no choice but to trust the philosopher!
Not exactly sure what you mean. The foundation of philosophy is logic. Also the idea that "math in which we trust" is kind of bizzare, as mathematics is an axiomatic system. So really, it's the axioms in which we trust. But that also opens a whole can of worms, because some axioms are kind of weird and controversial (like the Axioms of Choice, Replacement, Regularity).
Not to mention that any for any system (> Peano Arithmetic) you can't have your cake and eat it, too; sound, complete, consistent: pick two.
I think the point was simply that there is no understanding of physics without the math, as the math is the only accurate description of the physics involved. Admittedly, "trusting math" was a poor phrasing.
We can trust math because it is trivially verifiable. Its relation to physics is somewhat complicated (e.g. verifying physics is not as trivial), and yes - you can understand a lot about physics without math - by combining direct observation with trusting the "philosopher".
I think you have made the arrogant mistake that this is a fluffy pop-sci book. You are incorrect. Maudlin takes real physics very seriously. The book actually gives sufficient math. The point is that high level math normally associated with SR, GR (Riemannian geometry) is unnecessary for understanding the interesting philosophical consequences of relativity.
