All right, allow me to settle this debate once and for all.
There is our shared consensus of how the world should be. Fighters should stab things effectively, wizards should harness the powers of magic, evil rotty magic doesn't work well against undead and shiny divine magic does, and so forth. We each have a set of these perceptions, and most of them are pretty well aligned.
Now, there are also the set of numbers used to describe the world. And most of these numbers line up with the majority of our perceptions.
Now, let us take the view that the numbers are fundamentally important, and the only thing that matters is our perceptions. In this view, the numbers exist so we can play with dice; if numbers come up that disagree with our perceptions, we throw them out and make up new ones. In this view, looking at the numbers distracts us from the simple expression of shared consensus.
However, another view is that numbers and shared consensus are both important, and that when they are misaligned, one or the other should be shifted around. If we perceive a hit from a longsword and a hit from a longbow as being pretty much equivalent in terms of human squishing potential, but one does 2d6 and the other does 1d4, we will see our expectation of the world violated in actual play. We need to either adjust our perception, or adjust the numbers, and in order to know which to do, it helps to have a lot of data in one place.