A synthesis: the resulting tension from a thesis and its antithesis. In formal mathematics, proofs are constructed over a bedrock of previously constructed axioms. In a way, arriving at a truth in math could be dialectical in nature. You have a statement A, its consequences. Then, you have a negation of A, and its consequences. The relation of A and its negation tells us whether the statement is correct, but it does not arrive at a new statement or a synthesis. So what could be done? Is this the end of dialectics and its relation to math?
Dialectics and Math: A Synthesis
A synthesis: the resulting tension from a thesis and its antithesis. In formal mathematics, proofs are constructed over a bedrock of previously constructed axioms. In a way, arriving at a truth in math could be dialectical in nature. You have a statement A, its consequences. Then, you have a negation of A, and its consequences. The relation of A and its negation tells us whether the statement is correct, but it does not arrive at a new statement or a synthesis. So what could be done? Is this the end of dialectics and its relation to math?