In a world plagued by conflict, one might expect that the exact sciences of logic and mathematics would provide a safe harbor. In fact, these disciplines are rife with internal divisions between different, often incompatible systems. This original work explores apparently intractable disagreements in logic and the foundations of mathematics and sets out conflict resolution strategies that evade these stalemates. The book is a significant contribution to such areas of philosophy as logic, philosophy of language and argumentation theory. It is also of interest to mathematicians and computer scientists.