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Edit: A close reading of Shramko 2012 has resolved my confusion. Thanks, everyone.
I can't shake the idea that maps should be represented classically and territories should be represented intuitionistically. I'm looking for logical but critical comments on this idea. Here's my argument:
Territories have entities that are not compared to anything else. If an entity exists in the territory, then it is what it is. Territorial entities, as long as they are consistently defined, are never wrong by definition. By comparison, maps can represent any entity. Being a map, these mapped entities are intended to be compared to the territory of which it is a map. If the territory does not have a corresponding entity, then that mapped entity is false insofar as it is intended as a map.
This means that territories are repositories of pure truth with no speck of falsehood lurking in any corner, whereas maps represent entities that can be true or false depending on the state of the territory. This corresponds to the notion that intuitionism captures the concept of truth. If you add the concept of falsehood or contradiction, then you end up with classical logic or mathematics respectively. First source I can think of: https://www.youtube.com/playlist?list=PLt7hcIEdZLAlY0oUz4VCQnF14C6VPtewG
Furthermore, the distinction between maps and territories seems to be a transcendental one in the Kantian sense of being a synthetic a priori. That is to say, it is an idea that must be universally imposed on the world by any mind that seeks to understand it. Intuitionism has been associated with Kantian philosophy since its inception. If The Map is included in The Territory in some ultimate sense, that neatly dovetails with the idea of intuitionists who argue that classical mathematics is a proper subset of intuitionistic mathematics.
In summary, my thesis states that classical logic is the logic of making a map accurate by comparing it to a territory, which is why the concept of falsehood becomes an integral part of the formal system. In contrast, intuitionistic logic is the logic of describing a territory without seeking to compare it to something else. Intuitionistic type theory turns up type errors, for example, when such a description turns out to be inconsistent in itself.
Where did I take a wrong turn?
Also possibly problematic is the dichotomy described by the summary:
seems more appropriate to contrast scientific/Bayesian reasoning, which ... (read more)