I would have enjoyed this article if it dropped the Buddhism and kept the math.
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.
For example, it is the case that self-referential statements don't always have well-defined truth values and that allowing them to have values like {} and {false,true} is a fruitful way to think about it. But this approach can be grounded in two-valued logic (and vice versa), and it doesn't solve the problem of self-reference (consider "This statement is not {}, is not {false}, is not {true}, is not {false,true}").
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.
For example, it is the case that self-referential statements don't always have well-defined truth values and that allowing them to have values like {} and {false,true} is a fruitful way to think about it. But this approach can be grounded in two-valued logic (and vice versa), and it doesn't solve the problem of self-reference (consider "This statement is not {}, is not {false}, is not {true}, is not {false,true}").