One of the things I was thinking about recently was our perception of symmetries. For example, formal logics tend to have a symmetry between true/false, and/or, etc. Formally true and false aren't particularly distinguished, but they certainly have different meanings to us! This is one of those things that makes me suspicious of using formal logic as an underpinning of AI.
Are there similar isometries for natural languages? Could you switch other important concepts around, and a document remain just as consistent and useful? I don't think there is much of this. Why? Natural language is glued to the real world in a way formal languages aren't. When it comes down to it, language is bolted onto us as animals - there can't be the same symmetries amongst concepts that control life and death. In other words, perhaps a good way of creating an AI is to, say, base it around a program that wants to be happy! :p
Anyway, there are some symmetries in the real world, not just in language, but in our perception of the world itself. For example, I may perceive the colour red to look like what you think of the colour blue, and vice versa. As long as we're used to the colour schemes of the world, and have a consistent naming convention, we'll never know. Moreover, if my left-right perception of the real world were reversed, I'd have no way to tell. This one seems more odd to me, as there is (arguably!) an orientation to the real world, but I can never know if I'm seeing it correctly.
Despite these mappings of the real world to our perceptions being arbitrary, they're so taken for granted that people hardly notice they're there. What is the symmetry-breaking mechanism here? Is it really arbitrary? Are these different mappings truely isomorphic, or do the variations change our perception of the world? I have no idea!