http://plus.maths.org/content/not-carrot
SNIP: "Paraconsistent mathematics is a type of mathematics in which contradictions may be true. In such a system it is perfectly possible for a statement A and its negation not A to both be true. How can this be, and be coherent? What does it all mean? And why should we think mathematics might actually be paraconsistent? We'll look at the last question first starting with a quick trip into mathematical history...."
SNIP: "Paraconsistent mathematics is a type of mathematics in which contradictions may be true. In such a system it is perfectly possible for a statement A and its negation not A to both be true. How can this be, and be coherent? What does it all mean? And why should we think mathematics might actually be paraconsistent? We'll look at the last question first starting with a quick trip into mathematical history...."