A Counterexample to Theorems of Cox and Fine

Proceedings of the AAAI Conference on Artificial Intelligence, 13

Volume

Proceedings of the AAAI Conference on Artificial Intelligence, 13

Foundations

Cox’s well-known theorem justifying the use of probability is shown not to hold in finite domains. The counterexample also suggests that Cox’s assumptions are insufficient to prove the result even in infinite domains. The same counterexample is used to disprove a result of Fine on comparative conditional probability.