You are not using the same definition of logic EY does. For him logic is everything that is not physics in his physics+logic (or territory+maps, in the previously popular terms) picture of the world. Mathematical logic is a tiny sliver of what he calls "logic". For comparison, in an instrumentalist description there are experiences+models, and EY's logic is roughly equivalent to "models" (maps, in the map-territory dualism), of which mathematics is but one.