One consolation of the dull job I'm doing at the moment is that it's within easy walking distance of my favourite London bookshop. Last week I managed to escape there at lunchtime, and spent a happy half-hour browsing the shelves. Glancing through a (very good) book on paradoxes, I was startled by a section towards the end describing an account of truth on which contradictions can be true , called dialetheism. It's a shame that the supposedly definitive book on the subject is so prohibitively priced, especially when it's the only book which Amazon classify as both Logic and Occult.
There's even a Logical Pluralism weblog! Anyway, dialetheism (in various forms) has a long history:
"In ancient Indian logic/metaphysics, there were standardly four possibilities to be considered on any statement at issue: that it is true (only), false (only), neither true nor false, or both. Early Buddhist logic added a fifth possibility: none of these."