Also possibly problematic is the dichotomy described by the summary:
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.
seems more appropriate to contrast scientific/Bayesian reasoning, which strives to confirm or refute a model based on how well it conforms to observed reality vs deductive (a priori) reasoning, which looks only at what follows from a set of axioms. However, one can reason deductively using classical or intuitionistic logic, so it is not clear that intuitionistic logic is better suited than classical logic for “describing a territory without seeking to compare it to something else”.
I don’t see how distinguishing between deductive and inductive reasoning is mutually exclusive with the map/description distinction. That is to say, you could have each of the following combinations: deductive map, deductive description, inductive map, and inductive description.
Edit: On second thought, I see what you were saying. Thanks, I will think about it.
Also possibly problematic is the dichotomy described by the summary:
seems more appropriate to contrast scientific/Bayesian reasoning, which strives to confirm or refute a model based on how well it conforms to observed reality vs deductive (a priori) reasoning, which looks only at what follows from a set of axioms. However, one can reason deductively using classical or intuitionistic logic, so it is not clear that intuitionistic logic is better suited than classical logic for “describing a territory without seeking to compare it to something else”.
I don’t see how distinguishing between deductive and inductive reasoning is mutually exclusive with the map/description distinction. That is to say, you could have each of the following combinations: deductive map, deductive description, inductive map, and inductive description.
Edit: On second thought, I see what you were saying. Thanks, I will think about it.