Perhaps adding a “semantic” understanding is like another bridge between informal and formal reasoning. These bridges are only partly formal—they’re also partly informal, the concepts and gesturing around the equations and proofs.
Nice. This seems like a surprisingly well-motivated way of reducing everything to physics: there’s just “syntactic” machinery made out of physics, and any semantics that might be attributed to parts of this machinery is merely a partially informal device (i.e. a collection of cognitive skills) that human mathematicians might use as an aid for reasoning about the machinery. Even when the machinery itself might in some sense be said to be semantically reasoning about something or other, this description of the machinery can be traced back to human mathematicians who use it as a partially informal device for understanding the machinery, and so it won’t strictly speaking be a property of the machinery itself.
In other words, in this view semantics is an informal art primarily concerned with advancement of human understanding, and it’s not fundamental to the operation of intelligence in general, it’s not needed for properly designing things, responding to observations or making decisions, any more than curiosity or visual thinking.
Nice. This seems like a surprisingly well-motivated way of reducing everything to physics: there’s just “syntactic” machinery made out of physics, and any semantics that might be attributed to parts of this machinery is merely a partially informal device (i.e. a collection of cognitive skills) that human mathematicians might use as an aid for reasoning about the machinery. Even when the machinery itself might in some sense be said to be semantically reasoning about something or other, this description of the machinery can be traced back to human mathematicians who use it as a partially informal device for understanding the machinery, and so it won’t strictly speaking be a property of the machinery itself.
In other words, in this view semantics is an informal art primarily concerned with advancement of human understanding, and it’s not fundamental to the operation of intelligence in general, it’s not needed for properly designing things, responding to observations or making decisions, any more than curiosity or visual thinking.