> Alternate logics are interesting, but you tend to be able to reduce them into each other in the same way that universal turing machines can simulate each othe

> Alternate logics are interesting, but you tend to be able to reduce them into each other in the same way that universal turing machines can simulate each other. They don't add new functionality, they add succinctness. So it's really strange to me to frame them as totally different philosophies. When it comes to classical logic versus intuitionistic logic, I frame the difference in terms of totally different philosophies, for precisely this reason. Sufficiently expressive versions of either logic encode the other, but no-one runs the encoding. And in many cases, both groups want to express the same proposition using exactly the same symbols, but will disagree as to whether or not the proposition is a theorem (see the least upper bound property, for example). There's a deeper disagreement going on when neither side acknowledges a possibility of translation. However, I suspect this disagreement is unique to classical versus intuitionistic logic. I doubt that trivial four or five-valued propositional logics, or Priest's paraconsistent logic, are pointing to any fundamental disagreement about how to get something done.