What does it mean for a map to be “accurate” at an abstract level, and what properties should my map-making process have in order to produce accurate abstracted maps/beliefs?
The notion of a homomorphism in universal algebra and category theory is relevant here. Homomorphisms map from one structure (e.g. a group) to another, and must preserve structure. They can delete information (by mapping multiple different elements to the same element), but the structures that are represented in the structure-being-mapped-to must also exist in the structure-being-mapped-from.
Analogously: when drawing a topographical map, no claim is made that the topographical map represents all structure in the territory. Rather, the claim being made is that the topographical map (approximately) represents the topographic structure in the territory. The topographic map-making process deletes almost all information, but the topographic structure is preserved: for every topographic relation (e.g. some point being higher than some other point) represented in the topographic map, a corresponding topographic relation exists in the territory.
The notion of a homomorphism in universal algebra and category theory is relevant here. Homomorphisms map from one structure (e.g. a group) to another, and must preserve structure. They can delete information (by mapping multiple different elements to the same element), but the structures that are represented in the structure-being-mapped-to must also exist in the structure-being-mapped-from.
Analogously: when drawing a topographical map, no claim is made that the topographical map represents all structure in the territory. Rather, the claim being made is that the topographical map (approximately) represents the topographic structure in the territory. The topographic map-making process deletes almost all information, but the topographic structure is preserved: for every topographic relation (e.g. some point being higher than some other point) represented in the topographic map, a corresponding topographic relation exists in the territory.