On the other hand, there is a truth of the matter, which may someday be discovered, about whether Mallory and Irvine reached the summit in 1924. Consider two theories of mountain climbing, T 1 and T 2. Besides these theories, there is T 3 based on plate tectonics that tells us that Everest is still getting higher. In the simpler theory T 1, there is a list of names of mountains paired with lists of climbing expeditions or names of climbers. T 2 contains routes up the mountain of the various parties.
Routes are approximate entities.
T 1 is an approximation to T 2, but T 1, may be regarded as not approximate at all. In particular, it can be complete, e.g. it decides any sentence in its limited language. One approximate theory may be less approximate than another. We want to discuss relations between sentences in a theory and sentences in a less approximate theory. It makes the ideas neater if we imagine that there are true and complete theories of the world even if they're not finitely expressible and none of the language of any of them is known.