Say, I would like to minimize ((X-2)*(X-2)+3)^^^3, where X is the number I'm going to observe on the screen. This is a pretty self-contained specification, and yet it refers to the world. The "logical" side of this can be regarded as a recipe, a symbolic representation of your goals. It also talks about a number that is too big to fit into the physical world.

Okay, sure. We agree about this, then.